Cosmographia, or, A view of the terrestrial and cœlestial globes in a brief explanation of the principles of plain and solid geometry applied to surveying and gauging of cask : the doctrine of primum mobile : with an account of the Juilan & Gregorian calendars, and the computation of the places of the sun, moon, and fixed stars ... : to which is added an introduction unto geography / by John Newton ...
         Newton, John, 1622-1678.
      
       
         
           1679
        
      
       Approx. 1185 KB of XML-encoded text transcribed from 286 1-bit group-IV TIFF page images.
       
         Text Creation Partnership,
         Ann Arbor, MI ; Oxford (UK) :
         2004-11 (EEBO-TCP Phase 1).
         A52257
         Wing N1055
         ESTC R17177
         12546927
         ocm 12546927
         63077
         
           
            This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of
             Creative Commons 0 1.0 Universal
            . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission.
          
        
      
       
         Early English books online.
      
       
         (EEBO-TCP ; phase 1, no. A52257)
         Transcribed from: (Early English Books Online ; image set 63077)
         Images scanned from microfilm: (Early English books, 1641-1700 ; 326:7)
      
       
         
           
             Cosmographia, or, A view of the terrestrial and cœlestial globes in a brief explanation of the principles of plain and solid geometry applied to surveying and gauging of cask : the doctrine of primum mobile : with an account of the Juilan & Gregorian calendars, and the computation of the places of the sun, moon, and fixed stars ... : to which is added an introduction unto geography / by John Newton ...
             Newton, John, 1622-1678.
          
           [15], 510, [16] p., [12] leaves of folded plates : ill.
           
             Printed for Thomas Passinger ...,
             London :
             1679.
          
           
             "Tables for the measuring of timber" and "Astronomy, the second part, or, An account of the civil year" have special title pages.
             Advertisement: p. [13]-[16] at end.
             Reproduction of original in Yale University Library.
          
        
      
    
     
       
         Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford.
         Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors.
      
       
         EEBO-TCP is a partnership between the Universities of Michigan and Oxford and the publisher ProQuest to create accurately transcribed and encoded texts based on the image sets published by ProQuest via their Early English Books Online (EEBO) database (http://eebo.chadwyck.com). The general aim of EEBO-TCP is to encode one copy (usually the first edition) of every monographic English-language title published between 1473 and 1700 available in EEBO.
         EEBO-TCP aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the Text Encoding Initiative (http://www.tei-c.org).
         The EEBO-TCP project was divided into two phases. The 25,363 texts created during Phase 1 of the project have been released into the public domain as of 1 January 2015. Anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source.
         Users should be aware of the process of creating the TCP texts, and therefore of any assumptions that can be made about the data.
         Text selection was based on the New Cambridge Bibliography of English Literature (NCBEL). If an author (or for an anonymous work, the title) appears in NCBEL, then their works are eligible for inclusion. Selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. In general, first editions of a works in English were prioritized, although there are a number of works in other languages, notably Latin and Welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so.
         Image sets were sent to external keying companies for transcription and basic encoding. Quality assurance was then carried out by editorial teams in Oxford and Michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet QA standards were returned to the keyers to be redone. After proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. Any remaining illegibles were encoded as <gap>s. Understanding these processes should make clear that, while the overall quality of TCP data is very good, some errors will remain and some readable characters will be marked as illegible. Users should bear in mind that in all likelihood such instances will never have been looked at by a TCP editor.
         The texts were encoded and linked to page images in accordance with level 4 of the TEI in Libraries guidelines.
         Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements).
         
          Keying and markup guidelines are available at the
           Text Creation Partnership web site
          .
        
      
       
         
         
      
    
     
       
         eng
      
       
         
           Geometry -- Early works to 1800.
           Calendar -- Early works to 1800.
           Geography -- Early works to 1800.
           Astronomy -- Early works to 1800.
        
      
    
     
        2004-04 TCP
        Assigned for keying and markup
      
        2004-05 Aptara
        Keyed and coded from ProQuest page images
      
        2004-08 John Latta
        Sampled and proofread
      
        2004-08 John Latta
        Text and markup reviewed and edited
      
        2004-10 pfs
        Batch review (QC) and XML conversion
      
    
  
   
     
       
         
           
             
             
               Imprimatur
               ;
            
             
               
                 
                   Guil.
                   Iane
                
                 R.
                 P.
                 D.
                 Hen.
                 Episc.
                 Lond.
                 à
                 Sacris
                 Dom.
                 
              
            
          
           
             
             
               COSMOGRAPHIA
               ,
               OR
               A
               VIEW
               OF
               THE
               Terrestrial
               and
               Coelestial
               GLOBES
               ,
               IN
               A
               Brief
               Explanation
               OF
               THE
               PRINCIPLES
               Of
               plain
               and
               solid
               GEOMETRY
               ,
               Applied
               to
               Surveying
               and
               Gauging
               of
               CASK
               .
            
             
               The
               Doctrine
               of
               the
               Primum
               Mobile
               .
            
             
               With
               an
               Account
               of
               the
               Juilan
               &
               Gregorian
               Calendars
               ,
               and
               the
               Computation
               of
               the
               Places
               of
               of
               the
               Sun
               ,
               Moon
               ,
               and
               Fixed
               Stars
               ,
               from
               such
               Decimal
               Tables
               of
               their
               Middle
               Motion
               ,
               as
               supposeth
               the
               whole
               Circle
               to
               be
               divided
               into
               an
               hundred
               Degrees
               or
               Parts
               .
            
             
               To
               which
               is
               added
               an
               Introduction
               unto
               GEOGRAPHY
               .
            
             
               By
               John
               Newton
               ,
               
                 D.
                 D.
              
               
            
             
               London
               ,
               Printed
               for
               Thomas
               Passinger
               ,
               at
               the
               Three
               Bibles
               on
               London-Bridge
               1679.
               
            
          
           
             
             
             
               TO
               THE
               Most
               Honourable
               HENRY
               SOMERSET
               ,
               Lord
               Herbert
               ,
               Baron
               of
               Chepstow
               ,
               Raglan
               ,
               and
               Gower
               ,
               Earl
               and
               Marquess
               of
               Worcester
               ,
               Lord
               President
               and
               Lord
               Lieutenant
               of
               Wales
               and
               the
               Marches
               ,
               Lord
               Lieutenant
               of
               Gloucester
               ,
               Hereford
               and
               Monmouth
               ,
               and
               of
               the
               City
               and
               County
               of
               Bristol
               ,
               Knight
               of
               the
               Most
               Noble
               Order
               of
               the
               Garter
               ,
               and
               one
               of
               His
               Majestie
               's
               Most
               Honourable
               Privy
               Council
               .
            
             
               HE
               that
               adventures
               upon
               any
               thing
               contrary
               to
               the
               General
               received
               practice
               ,
               what
               ever
               his
               own
               courage
               and
               resolutions
               are
               ,
               had
               need
               to
               be
               supported
               ,
               not
               only
               by
               the
               most
               Wise
               and
               Honourable
               ,
               but
               also
               
               the
               most
               Powerful
               Persons
               that
               are
               in
               a
               Nation
               or
               Kingdom
               ;
               For
               let
               the
               Proposals
               be
               never
               so
               advantagious
               to
               the
               Publick
               ,
               they
               shall
               not
               only
               be
               decried
               and
               neglected
               ,
               but
               it
               is
               well
               ,
               if
               the
               Promoter
               be
               not
               both
               abused
               and
               ruined
               :
               Yet
               I
               ,
               notwithstanding
               all
               these
               discouragements
               ,
               have
               not
               been
               silent
               ,
               but
               in
               order
               to
               Childrens
               better
               Education
               ,
               have
               long
               since
               published
               my
               thoughts
               ,
               
                 and
                 have
                 and
                 do
                 declare
                 ,
                 that
                 the
                 multitude
                 of
                 Schools
                 for
                 the
                 learning
                 of
                 the
                 Latine
                 and
                 Greek
                 Tongues
                 ,
                 are
                 destructive
                 both
                 to
                 our
                 youth
                 and
                 the
                 Commonwealth
              
               ;
               and
               if
               the
               Opinion
               of
               Sir
               
                 Francis
                 Bacon
              
               in
               his
               Advice
               to
               King
               Iames
               concerning
               
               Sutton's
               Hospital
               ,
               be
               not
               sufficient
               to
               warrant
               my
               Assertion
               ,
               I
               could
               heartily
               wish
               that
               no
               such
               Evidence
               could
               have
               been
               produced
               ,
               as
               the
               late
               unhappy
               Wars
               ,
               in
               the
               Bowels
               of
               this
               Kingdom
               hath
               afforded
               us
               ;
               for
               what
               he
               saith
               there
               by
               way
               of
               Advice
               ,
               we
               by
               woful
               Experience
               have
               found
               too
               true
               ;
               that
               by
               reason
               of
               the
               multitude
               of
               Grammar
               Schools
               ,
               more
               Scholars
               are
               dayly
               brought
               up
               ,
               than
               all
               the
               Preferments
               in
               this
               Nation
               can
               provide
               for
               ,
               and
               so
               they
               become
               uncapable
               of
               other
               Professions
               ,
               and
               unprofitable
               in
               their
               own
               ,
               and
               at
               last
               become
               ,
               
                 materia
                 rerum
                 novarum
              
               ;
               whether
               this
               be
               an
               essential
               or
               an
               accidental
               Effect
               ,
               
               I
               will
               not
               here
               dispute
               ;
               the
               truth
               of
               it
               ,
               I
               am
               sure
               ,
               cannot
               be
               denied
               :
               but
               that
               is
               not
               all
               ;
               by
               this
               means
               it
               comes
               to
               pass
               ,
               that
               four
               of
               the
               seven
               Liberal
               Arts
               ,
               are
               almost
               wholly
               neglected
               ,
               as
               well
               in
               both
               Universities
               ,
               as
               in
               all
               Inferiour
               Schools
               ;
               and
               setting
               aside
               the
               City
               of
               London
               ,
               there
               are
               but
               few
               Places
               in
               this
               Nation
               ,
               where
               a
               man
               can
               put
               his
               Son
               ,
               to
               be
               well
               instructed
               in
               
                 Arithmetick
                 ,
                 Geometry
                 ,
                 Musick
              
               and
               Astronomy
               ;
               and
               even
               that
               Famous
               City
               was
               without
               a
               Publick
               School
               for
               Mathematical
               Learning
               ,
               till
               His
               present
               Majesty
               was
               pleased
               to
               lay
               the
               Foundation
               ;
               nay
               so
               averse
               are
               men
               in
               the
               general
               to
               these
               Arts
               (
               which
               are
               the
               support
               of
               all
               Trade
               )
               that
               without
               a
               high
               hand
               ,
               it
               will
               be
               almost
               impossible
               ,
               to
               make
               this
               People
               wise
               for
               their
               own
               good
               :
               I
               come
               therefore
               to
               your
               Honour
               ,
               humbly
               to
               beg
               your
               Countenance
               and
               Assistance
               ,
               that
               the
               Stream
               of
               Learning
               may
               be
               a
               little
               diverted
               ,
               in
               those
               Schools
               that
               are
               already
               erected
               ,
               and
               to
               be
               instrumental
               for
               the
               erecting
               more
               ,
               when
               they
               shall
               be
               wanting
               ;
               that
               we
               may
               not
               be
               permitted
               still
               to
               begin
               at
               the
               wrong
               end
               ;
               but
               that
               according
               to
               the
               practice
               of
               the
               Ancient
               Philosophers
               ,
               Children
               may
               be
               instructed
               in
               
                 Arithmetick
                 ,
                 Geometry
                 ,
                 Musick
              
               and
               Astronomy
               ;
               before
               the
               Latine
               and
               Greek
               
               Grammars
               are
               thought
               on
               ,
               these
               Arts
               in
               themselves
               ,
               are
               much
               more
               easie
               to
               be
               learned
               ,
               tend
               more
               to
               a
               general
               good
               ,
               and
               will
               in
               a
               great
               measure
               facilitate
               the
               Learning
               of
               the
               Tongues
               ,
               to
               as
               many
               as
               shall
               after
               this
               Foundation
               laid
               ,
               be
               continued
               at
               School
               ,
               and
               provided
               for
               in
               either
               Universities
               .
               Your
               Honour
               was
               instrumental
               to
               enlarge
               the
               Maintenance
               for
               God's
               Minister
               in
               the
               Place
               where
               I
               live
               ,
               and
               perhaps
               it
               may
               please
               God
               to
               make
               you
               so
               ,
               not
               only
               in
               making
               this
               Place
               in
               particular
               ,
               but
               many
               other
               Places
               in
               this
               Land
               happy
               ,
               by
               procuring
               Schools
               for
               these
               Sciences
               ,
               and
               not
               only
               so
               ,
               but
               by
               your
               Loyal
               and
               Prudent
               managing
               the
               several
               Trusts
               committed
               to
               you
               ,
               you
               may
               do
               much
               for
               God's
               Glory
               ,
               your
               Countries
               Good
               ,
               and
               the
               continuance
               of
               your
               own
               Honour
               to
               all
               Future
               Generations
               ,
               which
               is
               ,
               and
               shall
               be
               the
               Prayer
               of
               ,
            
             
               
                 Your
                 Honour
                 's
                 Obliged
                 and
                 Devoted
                 Servant
                 ,
                 
                   JOHN
                   NEWTON
                
                 .
              
            
          
           
             
             
               TO
               THE
               READER
               .
            
             
               MY
               Design
               in
               publishing
               these
               Introductions
               to
               Geometry
               and
               Astronomy
               ,
               is
               so
               well
               known
               by
               all
               the
               Epistles
               ,
               to
               my
               other
               Treatises
               of
               
                 Grammar
                 ,
                 Arithmetick
                 ,
                 Rhetorick
              
               ,
               and
               Logick
               ,
               that
               I
               think
               it
               needless
               to
               tell
               thee
               here
               ,
               that
               it
               is
               my
               Opinion
               ,
               that
               all
               the
               Arts
               should
               be
               taught
               our
               Children
               in
               the
               English
               Tongue
               ,
               before
               they
               begin
               to
               learn
               the
               Greek
               or
               Latin
               Grammar
               ,
               by
               which
               means
               many
               thousands
               of
               Children
               would
               be
               fitted
               for
               all
               Trades
               ,
               enabled
               to
               earn
               their
               own
               Livings
               ,
               and
               made
               useful
               in
               the
               Commonwealth
               ;
               and
               that
               before
               they
               attain
               to
               twelve
               years
               of
               age
               ;
               and
               by
               consequence
               the
               swarming
               of
               Bees
               would
               be
               prevented
               ,
               who
               being
               compelled
               to
               leave
               their
               Hives
               ,
               for
               want
               of
               room
               ,
               do
               spread
               themselves
               abroad
               ,
               and
               instead
               of
               gathering
               of
               Honey
               ,
               do●
               sting
               all
               that
               come
               in
               their
               way
               .
               We
               should
               not
               have
               such
               innumerable
               company
               of
               Gown-men
               to
               the
               loss
               and
               prejudice
               of
               themselves
               and
               the
               Common-wealth
               ;
               and
               those
               we
               had
               would
               probably
               be
               more
               learned
               ,
               and
               better
               regarded
               .
            
             
             
               His
               Majesty
               being
               pleased
               to
               begin
               this
               Work
               ,
               by
               His
               Bounty
               towards
               a
               Mathematical
               School
               in
               
               Christ's
               Church
               London
               ;
               I
               am
               not
               now
               without
               hopes
               ,
               to
               see
               the
               same
               effected
               in
               many
               other
               Places
               in
               this
               Kingdom
               ;
               and
               to
               this
               purpose
               I
               have
               to
               my
               Introductions
               to
               the
               other
               Arts
               ,
               added
               these
               also
               to
               Geometry
               and
               Astronomy
               ;
               which
               I
               call
               by
               the
               name
               of
               Cosmographia
               ;
               and
               this
               I
               have
               divided
               into
               four
               Parts
               ;
               in
               the
               first
               I
               have
               briefly
               laid
               down
               the
               first
               Principles
               belonging
               to
               the
               three
               kinds
               of
               Magnitude
               or
               continued
               Quantity
               ,
               Lines
               ,
               Planes
               and
               Solids
               ;
               which
               ought
               in
               some
               measure
               to
               be
               known
               ,
               before
               we
               enter
               upon
               Astronomy
               ,
               and
               this
               part
               I
               call
               an
               Introduction
               unto
               Geometry
               :
            
             
               The
               second
               and
               third
               Parts
               treat
               of
               Astronomy
               ;
               the
               first
               of
               which
               sheweth
               the
               Doctrine
               of
               the
               
                 Primum
                 Mobile
              
               ,
               that
               is
               ,
               the
               Declination
               ,
               Right
               Ascension
               ,
               and
               Oblique
               Ascensions
               of
               the
               Sun
               and
               Stars
               ,
               and
               such
               other
               Problems
               ,
               as
               do
               depend
               upon
               the
               Doctrine
               of
               Spherical
               Triangles
               .
            
             
               The
               second
               Part
               of
               Astronomy
               ,
               treateth
               of
               the
               motion
               of
               the
               Sun
               ,
               Moon
               and
               Fixed
               Stars
               ;
               in
               order
               whereunto
               ,
               I
               have
               first
               given
               thee
               a
               brief
               account
               of
               the
               Civil
               Year
               ,
               with
               the
               cause
               of
               the
               difference
               between
               our
               Julian
               and
               
                 Gregorian
                 Calendar
              
               ,
               and
               of
               both
               from
               the
               true
               ;
               for
               it
               must
               be
               acknowledged
               
               that
               both
               are
               erroneous
               ,
               though
               ours
               be
               the
               worse
               of
               the
               two
               ;
               yet
               not
               so
               bad
               ,
               but
               that
               our
               Dissenting
               Brethren
               have
               I
               hope
               some
               better
               Arguments
               to
               justifie
               their
               Non-conformity
               ▪
               than
               what
               I
               see
               published
               in
               a
               little
               Book
               without
               any
               name
               to
               it
               ,
               concerning
               two
               Easters
               in
               one
               Year
               ;
               by
               the
               General
               Table
               ,
               saith
               this
               learned
               man
               ,
               who
               owneth
               the
               Feast
               of
               Easter
               was
               to
               be
               observed
               Anno
               1674.
               upon
               the
               19
               day
               of
               April
               ,
               so
               the
               Almanacks
               for
               that
               Year
               ,
               as
               well
               as
               the
               General
               Table
               set
               before
               the
               Book
               of
               Common
               Prayer
               ;
               but
               by
               the
               Rule
               in
               the
               said
               Book
               of
               Common
               Prayer
               given
               ,
               the
               Feast
               of
               Easter
               should
               have
               been
               upon
               the
               twelfth
               of
               
                 April
                 ,
                 for
                 Easter-Day
                 must
                 always
                 be
                 the
                 first
                 Sunday
                 after
                 the
                 first
                 Full
                 Moon
                 ,
                 which
                 happeneth
                 next
                 after
                 the
                 one
                 and
                 twentieth
                 day
                 of
              
               March
               ,
               
                 and
                 if
                 the
                 Full
                 Moon
                 happen
                 upon
                 a
                 Sunday
                 ,
                 Easter-Day
                 is
                 the
                 Sunday
                 after
              
               ;
               Now
               in
               the
               Year
               1674.
               the
               19
               of
               April
               being
               Friday
               was
               Full
               Moon
               ,
               therefore
               by
               this
               Rule
               ,
               Easter-Day
               should
               be
               the
               twelfth
               ,
               and
               by
               the
               Table
               and
               the
               Common
               Almanacks
               April
               the
               tenth
               ;
               but
               this
               learned
               man
               must
               know
               ,
               that
               the
               mistake
               is
               in
               himself
               ,
               and
               not
               in
               the
               Rule
               or
               Table
               set
               down
               in
               the
               Book
               of
               Common
               Prayer
               ;
               for
               if
               he
               please
               to
               look
               into
               the
               Calendar
               ,
               he
               will
               find
               that
               the
               Golden
               Number
               Three
               ,
               (
               which
               was
               the
               Golden
               Number
               for
               that
               Year
               )
               is
               
               placed
               against
               the
               last
               day
               of
               March
               ,
               and
               therefore
               according
               to
               the
               supposed
               motion
               of
               the
               Moon
               ,
               that
               Day
               was
               New
               Moon
               ;
               and
               then
               the
               Full
               Moon
               will
               fall
               upon
               the
               fourteenth
               day
               of
               April
               ,
               and
               not
               upon
               the
               tenth
               ,
               and
               so
               by
               consequence
               the
               Sunday
               following
               the
               first
               Full
               Moon
               after
               the
               21
               day
               of
               March
               was
               the
               nineteenth
               of
               April
               and
               not
               the
               twelfth
               .
               And
               thus
               the
               Rule
               and
               the
               Table
               in
               the
               Book
               of
               Common
               Prayer
               for
               finding
               the
               Feast
               of
               Easter
               are
               reconciled
               ;
               and
               when
               Authority
               shall
               think
               sit
               ,
               the
               Calendar
               may
               be
               corrected
               and
               all
               the
               moveable
               Feasts
               be
               observed
               upon
               the
               days
               and
               times
               at
               first
               appointed
               ;
               but
               till
               that
               be
               ,
               a
               greater
               difference
               than
               one
               Week
               will
               be
               found
               in
               the
               Feast
               of
               Easter
               between
               the
               Observation
               thereof
               according
               to
               the
               Moons
               true
               motion
               ,
               and
               that
               upon
               which
               the
               Tables
               are
               grounded
               ;
               for
               by
               the
               Fathers
               of
               the
               Nicene
               Council
               it
               was
               appointed
               ,
               that
               the
               Feast
               of
               Easter
               should
               be
               observed
               upon
               the
               Sunday
               following
               the
               first
               Full
               Moon
               after
               the
               Vernal
               Equinox
               ,
               which
               then
               indeed
               was
               the
               21
               of
               March
               ;
               but
               now
               the
               tenth
               ,
               and
               in
               the
               Year
               1674.
               
               Wednesday
               the
               11
               of
               March
               was
               Full
               Moon
               ,
               and
               therefore
               by
               this
               Rule
               ,
               Easter-Day
               should
               have
               been
               upon
               March
               the
               fifteenth
               ,
               whereas
               according
               to
               the
               Rules
               we
               go
               by
               ,
               it
               was
               not
               till
               April
               the
               nineteenth
               .
            
             
             
               The
               Tables
               of
               the
               Sun
               and
               Moons
               middle
               motions
               are
               neither
               made
               according
               to
               the
               usual
               Sexagenary
               Forms
               ,
               nor
               according
               to
               the
               usual
               Degrees
               of
               a
               Circle
               and
               Decimal
               Parts
               ,
               but
               according
               to
               a
               Circle
               divided
               into
               100
               Degrees
               and
               Parts
               ,
               and
               this
               I
               thought
               good
               to
               do
               ,
               to
               give
               the
               World
               a
               taste
               of
               the
               excellency
               of
               Decimal
               Numbers
               ,
               which
               if
               a
               Canon
               of
               Sines
               and
               Tangents
               were
               fitted
               to
               it
               ,
               would
               be
               found
               much
               better
               ,
               as
               to
               the
               computing
               the
               Places
               of
               the
               Planets
               ;
               but
               as
               to
               the
               
                 Primum
                 Mobile
              
               ,
               by
               reason
               of
               the
               general
               dividing
               a
               Circle
               into
               360
               Degrees
               ,
               I
               should
               think
               such
               a
               Canon
               with
               the
               Decimal
               Parts
               most
               convenient
               ,
               and
               in
               some
               cases
               the
               common
               Sexagenary
               Canon
               may
               be
               very
               useful
               ,
               and
               indeed
               should
               wish
               and
               shall
               endeavour
               to
               have
               all
               printed
               together
               ,
               one
               Table
               of
               Logarithms
               will
               serve
               them
               all
               ,
               and
               two
               such
               Canons
               ,
               one
               for
               the
               Study
               and
               another
               for
               the
               Pocket
               ,
               would
               be
               sufficient
               for
               all
               Mathematical
               Books
               in
               that
               kind
               ;
               and
               then
               men
               may
               use
               them
               all
               or
               either
               of
               them
               as
               they
               shall
               have
               occasion
               ,
               or
               as
               every
               one
               is
               perswaded
               in
               his
               own
               mind
               .
            
             
               What
               I
               have
               done
               in
               this
               particular
               ,
               as
               it
               was
               for
               mine
               own
               satisfaction
               ,
               so
               I
               am
               apt
               to
               believe
               ,
               that
               it
               will
               be
               pleasing
               to
               many
               others
               ;
               and
               although
               I
               shall
               leave
               every
               one
               to
               abound
               in
               his
               own
               sense
               ,
               yet
               I
               cannot
               think
               
               that
               Custom
               should
               be
               such
               a
               Tyrant
               ,
               as
               to
               force
               us
               always
               to
               use
               the
               Sexagenary
               form
               ,
               if
               so
               ,
               I
               wonder
               that
               men
               did
               not
               always
               use
               the
               natural
               Canon
               ;
               if
               no
               alteration
               may
               be
               admitted
               ,
               what
               reason
               can
               be
               given
               for
               the
               use
               of
               Logarithms
               ;
               and
               if
               that
               be
               found
               more
               ready
               than
               the
               natural
               ,
               in
               things
               of
               this
               kind
               ,
               where
               none
               but
               particular
               Students
               are
               concerned
               ,
               I
               should
               think
               it
               reasonable
               ,
               to
               reduce
               all
               things
               hereafter
               ,
               into
               that
               form
               ,
               which
               shall
               be
               found
               most
               ready
               and
               exact
               ;
               now
               the
               Part
               Proportional
               in
               the
               Artificial
               Sines
               and
               Tangents
               in
               the
               three
               first
               Degrees
               cannot
               be
               well
               taken
               by
               the
               common
               difference
               ,
               and
               the
               way
               of
               finding
               them
               otherwise
               will
               not
               be
               so
               easie
               in
               the
               Sexagenary
               Canon
               ,
               as
               in
               either
               of
               the
               other
               ,
               and
               this
               me
               thinks
               ,
               should
               render
               that
               Canon
               which
               divides
               each
               Degree
               into
               100
               Parts
               more
               acceptable
               ;
               but
               thus
               to
               retain
               the
               use
               of
               Sines
               ,
               Degrees
               ,
               and
               Decimal
               Parts
               ,
               doth
               not
               to
               me
               seem
               convenient
               ,
               and
               to
               reckon
               up
               ,
               a
               Planets
               middle
               motion
               ,
               by
               whole
               Circles
               will
               sometimes
               cause
               a
               Division
               of
               Degrees
               by
               60
               ,
               which
               hath
               some
               trouble
               in
               it
               also
               ,
               but
               if
               a
               Circle
               be
               divided
               into
               100
               Degrees
               ,
               this
               inconvenience
               is
               avoided
               ,
               and
               were
               there
               no
               other
               reason
               to
               be
               given
               ,
               this
               me
               thinks
               should
               make
               such
               a
               Canon
               to
               be
               desirable
               ;
               but
               till
               I
               can
               find
               an
               opportunity
               of
               publishing
               such
               an
               one
               ,
               I
               shall
               forbear
               to
               
               shew
               any
               further
               uses
               of
               it
               ,
               and
               for
               what
               is
               wanting
               here
               in
               this
               subject
               ,
               I
               therefore
               refer
               thee
               to
               Mr.
               
               Street's
               
                 Astronomia
                 Carolina
              
               ,
               and
               the
               several
               Books
               written
               in
               English
               by
               Mr.
               Wing
               .
            
             
               The
               fourth
               Part
               of
               this
               Treatise
               is
               an
               Introduction
               unto
               Geography
               ,
               in
               which
               I
               have
               given
               general
               Directions
               ,
               for
               the
               understanding
               how
               the
               habitable
               part
               of
               the
               World
               is
               divided
               in
               respect
               of
               Longitude
               and
               Latitude
               in
               respect
               of
               Climes
               and
               Parallels
               with
               such
               other
               Particulars
               as
               will
               be
               found
               useful
               unto
               such
               as
               shall
               be
               willing
               to
               understand
               History
               ;
               in
               which
               three
               things
               are
               required
               ;
               The
               time
               when
               ,
               and
               this
               depends
               upon
               Astronomy
               ;
               the
               place
               where
               ,
               and
               this
               depends
               upon
               Geography
               ;
               and
               the
               Person
               by
               whom
               any
               memorable
               Act
               was
               done
               ,
               and
               this
               must
               be
               had
               from
               the
               Historical
               narration
               thereof
               ;
               and
               he
               that
               reads
               History
               without
               some
               knowledge
               in
               Astronomy
               and
               Geography
               will
               find
               himself
               at
               a
               loss
               ,
               and
               be
               able
               to
               give
               but
               a
               lame
               account
               of
               what
               he
               reads
               ;
               but
               after
               the
               learning
               of
               these
               Arts
               of
               Grammar
               ,
               (
               I
               mean
               so
               much
               thereof
               ,
               as
               tends
               to
               the
               understanding
               of
               every
               ones
               Native
               Language
               )
               
                 Arithmetick
                 ,
                 Geometry
              
               and
               Astronomy
               ;
               a
               Child
               may
               proceed
               profitably
               to
               Rhetorick
               and
               Logick
               ,
               the
               reading
               of
               History
               ,
               and
               the
               learning
               of
               the
               Tongues
               ;
               and
               sure
               there
               is
               
               no
               studious
               and
               ingenious
               man
               ,
               but
               will
               stand
               in
               need
               of
               some
               Recreation
               ,
               and
               therefore
               if
               Musick
               in
               the
               Worship
               and
               Service
               of
               God
               be
               not
               Argument
               enough
               to
               allow
               that
               a
               place
               among
               the
               Arts
               ,
               let
               that
               poor
               end
               of
               Delight
               and
               Pleasure
               be
               her
               Advocate
               ;
               and
               although
               that
               all
               men
               have
               not
               Voyces
               ,
               yet
               I
               can
               hardly
               believe
               ,
               that
               he
               expects
               any
               Melodious
               Harmony
               in
               Heaven
               ,
               that
               will
               not
               allow
               Instrumental
               Musick
               a
               place
               on
               Earth
               ;
               and
               as
               for
               those
               that
               have
               Voyces
               ,
               surely
               the
               time
               of
               learning
               Vocal
               Musick
               ,
               must
               be
               in
               Youth
               ,
               and
               I
               am
               perswaded
               that
               the
               Arts
               and
               Sciences
               to
               some
               good
               degree
               may
               be
               learned
               by
               Children
               before
               they
               be
               full
               twelve
               years
               old
               ,
               and
               would
               our
               Grammer
               Masters
               leave
               off
               their
               horrible
               severity
               ,
               and
               apply
               themselves
               to
               such
               ways
               of
               teaching
               Youth
               ,
               as
               the
               World
               is
               not
               now
               unacquainted
               with
               ,
               I
               am
               perswaded
               that
               it
               is
               no
               difficult
               matter
               ,
               in
               four
               years
               time
               more
               to
               fit
               Children
               in
               some
               good
               measure
               for
               the
               University
               .
            
             
               The
               great
               Obstruction
               in
               this
               Work
               ,
               is
               the
               general
               Ignorance
               of
               Teachers
               ,
               who
               being
               unacquainted
               with
               this
               Learning
               ,
               cannot
               teach
               others
               what
               they
               know
               not
               themselves
               .
               I
               could
               propound
               a
               remedy
               for
               this
               ,
               
                 Sed
                 Cynthius
                 aurem
                 vellit
              
               ;
               Therefore
               I
               will
               forbear
               and
               leave
               what
               I
               have
               written
               ,
               to
               be
               perused
               and
               censured
               as
               thou
               shall
               think
               fit
               .
            
             
               
                 John
                 Newton
                 .
              
            
          
        
         
           
             
             
               Practical
               Geometry
               ;
               OR
               ,
               THE
               ART
               of
               SURVEYING
               .
            
             
               
                 CHAP.
                 I.
                 
              
               
                 
                   Of
                   the
                   Definition
                   and
                   Division
                   of
                   Geometry
                   .
                
              
               
                 GEometry
                 is
                 a
                 Science
                 explaining
                 the
                 kinds
                 and
                 properties
                 of
                 continued
                 quantity
                 or
                 magnitude
                 .
              
               
                 2.
                 
                 There
                 are
                 three
                 Kinds
                 or
                 Species
                 of
                 Magnitude
                 or
                 continued
                 Quantity
                 ,
                 Lines
                 ,
                 Superficies
                 and
                 Solids
                 .
              
               
                 3.
                 
                 A
                 Line
                 is
                 a
                 Magnitude
                 consisting
                 only
                 of
                 length
                 without
                 either
                 breadth
                 or
                 thickness
                 .
              
               
                 4.
                 
                 In
                 a
                 Line
                 two
                 things
                 are
                 to
                 be
                 considered
                 ,
                 the
                 Terms
                 or
                 Limits
                 ,
                 and
                 the
                 several
                 Kinds
                 .
              
               
                 5.
                 
                 The
                 term
                 or
                 limit
                 of
                 a
                 Line
                 is
                 a
                 Point
                 .
              
               
                 6.
                 
                 A
                 Point
                 is
                 an
                 indivisible
                 Sign
                 in
                 Magnitude
                 which
                 cannot
                 be
                 comprehended
                 by
                 sense
                 ,
                 but
                 must
                 be
                 conceived
                 by
                 the
                 Mind
                 .
              
               
                 7.
                 
                 The
                 kinds
                 of
                 Lines
                 are
                 two
                 ,
                 Right
                 and
                 Oblique
                 .
              
               
               
                 8.
                 
                 A
                 Right
                 Line
                 is
                 that
                 which
                 lieth
                 between
                 his
                 Points
                 ,
                 without
                 any
                 going
                 up
                 or
                 going
                 down
                 on
                 either
                 side
                 .
                 As
                 the
                 Line
                 AB
                 lieth
                 streight
                 and
                 equally
                 between
                 the
                 Points
                 A
                 and
                 
                   B.
                   Fig.
                
                 1.
                 
              
               
                 9.
                 
                 An
                 Oblique
                 Line
                 is
                 that
                 which
                 doth
                 not
                 lie
                 equally
                 between
                 its
                 Points
                 ,
                 but
                 goeth
                 up
                 and
                 down
                 sometimes
                 on
                 the
                 one
                 side
                 and
                 sometimes
                 on
                 the
                 other
                 .
                 And
                 this
                 is
                 either
                 simple
                 or
                 various
                 .
              
               
                 10.
                 
                 A
                 simple
                 Oblique
                 Line
                 ,
                 is
                 that
                 which
                 is
                 exactly
                 Oblique
                 ,
                 as
                 the
                 Arch
                 of
                 a
                 Circle
                 ;
                 of
                 Various
                 Oblique
                 Lines
                 there
                 is
                 but
                 little
                 use
                 in
                 Geometry
                 .
              
               
                 11.
                 
                 Thus
                 are
                 Lines
                 to
                 be
                 considered
                 in
                 themselves
                 ,
                 they
                 may
                 be
                 also
                 considered
                 as
                 compared
                 to
                 one
                 another
                 ,
                 and
                 that
                 either
                 in
                 respect
                 of
                 their
                 distances
                 ,
                 or
                 in
                 respect
                 of
                 their
                 meetings
                 .
              
               
                 12.
                 
                 In
                 respect
                 of
                 their
                 distances
                 ,
                 they
                 may
                 be
                 either
                 equally
                 distant
                 ,
                 or
                 unequally
                 .
              
               
                 13.
                 
                 Lines
                 equally
                 distant
                 are
                 two
                 or
                 more
                 ,
                 which
                 by
                 an
                 equal
                 space
                 are
                 distant
                 from
                 one
                 another
                 ,
                 and
                 these
                 are
                 called
                 Parallels
                 ;
                 and
                 these
                 though
                 infinitely
                 extended
                 will
                 never
                 concur
                 .
              
               
                 14.
                 
                 Lines
                 unequally
                 distant
                 ,
                 are
                 such
                 as
                 do
                 more
                 or
                 less
                 incline
                 to
                 one
                 another
                 ,
                 and
                 these
                 being
                 extended
                 will
                 at
                 last
                 concur
                 .
              
               
                 15.
                 
                 Concurring
                 Lines
                 are
                 either
                 perpendicular
                 or
                 not
                 perpendicular
                 .
              
               
                 16.
                 
                 A
                 Perpendicular
                 Line
                 ,
                 is
                 a
                 Right
                 Line
                 falling
                 directly
                 upon
                 another
                 Right
                 Line
                 ,
                 not
                 declining
                 or
                 inclining
                 to
                 one
                 side
                 more
                 than
                 another
                 ;
                 as
                 the
                 Line
                 AB
                 in
                 Fig.
                 1.
                 
              
               
                 17.
                 
                 A
                 Perpendicular
                 Line
                 is
                 twofold
                 ,
                 to
                 wit
                 ,
                 either
                 falling
                 exactly
                 in
                 the
                 middle
                 of
                 another
                 Line
                 ,
                 or
                 upon
                 some
                 other
                 Point
                 which
                 is
                 not
                 the
                 middle
                 .
              
               
                 18.
                 
                 A
                 line
                 exactly
                 Perpendicular
                 ,
                 may
                 be
                 drawn
                 in
                 the
                 same
                 manner
                 ,
                 as
                 any
                 Right
                 Line
                 
                 may
                 be
                 divided
                 into
                 two
                 equal
                 Parts
                 ;
                 the
                 which
                 may
                 thus
                 be
                 done
                 .
                 If
                 from
                 the
                 two
                 Terms
                 or
                 Points
                 of
                 the
                 Right
                 Line
                 given
                 ,
                 there
                 shall
                 be
                 described
                 two
                 Arches
                 crossing
                 one
                 another
                 above
                 and
                 below
                 ,
                 a
                 Line
                 drawn
                 through
                 the
                 Intersections
                 of
                 those
                 Arches
                 ,
                 shall
                 be
                 exactly
                 Perpendicular
                 ,
                 and
                 also
                 divide
                 the
                 Right
                 Line
                 given
                 into
                 her
                 equal
                 Parts
                 .
                 Fig.
                 1.
                 
              
               
                 For
                 Example
                 ;
                 Let
                 CD
                 be
                 the
                 Right
                 Line
                 given
                 ,
                 and
                 let
                 it
                 be
                 required
                 ,
                 to
                 bisect
                 this
                 Line
                 ,
                 and
                 to
                 erect
                 a
                 Perpendicular
                 in
                 the
                 middle
                 thereof
                 .
                 1.
                 
                 Then
                 setting
                 one
                 of
                 your
                 Compasses
                 in
                 the
                 Points
                 C
                 ,
                 draw
                 the
                 Arches
                 E
                 and
                 F.
                 2.
                 
                 Setting
                 one
                 Foot
                 of
                 your
                 Compasses
                 in
                 D
                 ,
                 draw
                 the
                 Arches
                 G
                 and
                 H
                 ,
                 and
                 from
                 the
                 Intersections
                 of
                 these
                 Arches
                 draw
                 the
                 Right
                 Line
                 KL
                 ,
                 so
                 shall
                 the
                 Right
                 Line
                 KL
                 be
                 Perpendicular
                 to
                 the
                 Right-Line
                 CD
                 ,
                 and
                 the
                 Right
                 Line
                 CD
                 also
                 divided
                 into
                 two
                 equal
                 Parts
                 ,
                 in
                 the
                 Point
                 A.
                 
              
               
                 19.
                 
                 A
                 Line
                 Perpendicular
                 to
                 any
                 other
                 Point
                 than
                 the
                 middle
                 is
                 twofold
                 :
                 for
                 it
                 is
                 either
                 drawn
                 from
                 some
                 Point
                 given
                 in
                 the
                 Line
                 ;
                 or
                 from
                 some
                 Point
                 given
                 without
                 the
                 Line
                 .
              
               
                 20.
                 
                 
                   From
                   a
                   Point
                   given
                   in
                   the
                   Line
                   ,
                   at
                   Perpendicular
                   may
                   thus
                   be
                   drawn
                   .
                
                 In
                 Fig.
                 2.
                 
                 Let
                 the
                 given
                 Line
                 be
                 CD
                 ,
                 and
                 let
                 it
                 be
                 required
                 to
                 draw
                 a
                 Perpendicular
                 Line
                 to
                 the
                 Point
                 C
                 ,
                 your
                 Compasses
                 being
                 opened
                 to
                 any
                 reasonable
                 distance
                 ,
                 set
                 one
                 Foot
                 in
                 the
                 Point
                 C
                 ,
                 and
                 the
                 other
                 in
                 any
                 place
                 on
                 either
                 side
                 the
                 Line
                 CD
                 ,
                 suppose
                 at
                 A
                 ,
                 then
                 describe
                 the
                 Arch
                 ECF
                 ,
                 this
                 done
                 draw
                 the
                 Line
                 EA
                 ,
                 and
                 where
                 that
                 Line
                 being
                 extended
                 shall
                 cut
                 the
                 Arch
                 ECF
                 ,
                 a
                 Right
                 Line
                 drawn
                 from
                 C
                 to
                 that
                 Intersection
                 shall
                 be
                 Perpendicular
                 to
                 the
                 Point
                 C
                 in
                 the
                 Line
                 CD
                 ,
                 as
                 was
                 required
                 .
              
               
                 21.
                 
                 
                   From
                   a
                   Point
                   given
                   without
                   the
                   Line
                   ,
                   a
                   Perpendicular
                   may
                   be
                   drawn
                   in
                   this
                   manner
                   .
                
                 
                 In
                 Fig.
                 2.
                 
                 Let
                 the
                 given
                 Line
                 be
                 CD
                 ,
                 and
                 let
                 it
                 be
                 required
                 to
                 draw
                 another
                 Line
                 Perpendicular
                 thereunto
                 ,
                 from
                 the
                 Point
                 F
                 without
                 the
                 Line
                 .
                 From
                 the
                 Point
                 F
                 draw
                 a
                 streight
                 Line
                 to
                 some
                 part
                 of
                 the
                 Line
                 CD
                 at
                 pleasure
                 ,
                 as
                 FE
                 ,
                 which
                 being
                 bisected
                 ,
                 the
                 Point
                 of
                 Bisection
                 will
                 be
                 A
                 ,
                 if
                 therefore
                 at
                 the
                 distance
                 of
                 AF
                 ,
                 you
                 draw
                 the
                 Arch
                 ECF
                 ,
                 the
                 Right
                 Line
                 CF
                 shall
                 be
                 Perpendicular
                 to
                 the
                 Line
                 CD
                 ,
                 as
                 was
                 required
                 .
              
               
                 22.
                 
                 Hitherto
                 concerning
                 a
                 Perpendicular
                 Line
                 .
                 A
                 Right
                 Line
                 not
                 Perpendicular
                 ,
                 is
                 a
                 Right
                 Line
                 falling
                 indirectly
                 upon
                 another
                 Right
                 Line
                 ,
                 inclining
                 thereto
                 on
                 the
                 one
                 side
                 more
                 ,
                 and
                 on
                 the
                 other
                 less
                 .
              
               
                 23.
                 
                 Lines
                 unequally
                 distant
                 ,
                 and
                 at
                 last
                 concurring
                 ,
                 do
                 by
                 their
                 meeting
                 make
                 an
                 Angle
                 .
              
               
                 24.
                 
                 An
                 Angle
                 therefore
                 is
                 nothing
                 else
                 ,
                 then
                 the
                 place
                 ,
                 where
                 two
                 Lines
                 do
                 meet
                 or
                 touch
                 one
                 another
                 ,
                 and
                 the
                 two
                 Lines
                 which
                 constitute
                 the
                 Angle
                 ,
                 are
                 in
                 Geometry
                 called
                 the
                 sides
                 of
                 the
                 Angle
                 .
              
               
                 25.
                 
                 Every
                 Angle
                 is
                 either
                 Heterogeneous
                 ,
                 or
                 Homogeneous
                 :
                 that
                 is
                 called
                 an
                 Hetorogeneous
                 Angle
                 ,
                 which
                 is
                 made
                 by
                 the
                 meeting
                 of
                 one
                 Right
                 Line
                 ,
                 and
                 another
                 that
                 is
                 Oblique
                 and
                 Crooked
                 ;
                 and
                 that
                 is
                 called
                 an
                 Homogeneous
                 Angle
                 ,
                 which
                 is
                 made
                 by
                 the
                 meeting
                 of
                 two
                 Lines
                 of
                 the
                 same
                 kind
                 ,
                 that
                 is
                 ,
                 of
                 two
                 Right
                 Lines
                 ,
                 or
                 of
                 two
                 curved
                 or
                 Circular
                 Lines
                 .
              
               
                 26.
                 
                 An
                 Homogeneous
                 Angle
                 made
                 of
                 two
                 curved
                 or
                 Circular
                 Lines
                 ,
                 is
                 to
                 be
                 considered
                 in
                 Geometry
                 as
                 in
                 Spherical
                 Triangles
                 ,
                 but
                 the
                 other
                 which
                 is
                 made
                 of
                 Right
                 Lines
                 ,
                 is
                 in
                 all
                 the
                 Parts
                 of
                 Geometry
                 of
                 more
                 frequent
                 use
                 .
              
               
                 27.
                 
                 Right
                 lined
                 Angles
                 are
                 either
                 Right
                 or
                 Oblique
                 .
              
               
               
                 28.
                 
                 A
                 Right
                 Angle
                 is
                 that
                 whose
                 legs
                 or
                 sides
                 are
                 Perpendicular
                 to
                 one
                 another
                 ,
                 making
                 the
                 comprehended
                 space
                 on
                 both
                 sides
                 equal
                 .
                 
                   Thus
                   in
                   Fig.
                   1.
                   the
                   Line
                
                 AK
                 
                   is
                   Perpendicular
                   to
                   the
                   Line
                
                 CD
                 ,
                 
                   and
                   the
                   Angles
                
                 KAC
                 and
                 KAD
                 ,
                 
                   are
                   right
                   and
                   equal
                   to
                   one
                   another
                   .
                
              
               
                 29.
                 
                 An
                 Oblique
                 Angle
                 is
                 that
                 ,
                 whose
                 sides
                 are
                 not
                 Perpendicular
                 to
                 one
                 another
                 .
              
               
                 30.
                 
                 An
                 Oblique
                 Angle
                 is
                 either
                 acute
                 or
                 obtuse
                 .
              
               
                 31.
                 
                 An
                 Acute
                 Angle
                 is
                 that
                 which
                 is
                 less
                 than
                 a
                 Right
                 .
              
               
                 32.
                 
                 
                   An
                   Obtuse
                   Angle
                   ,
                   is
                   that
                   which
                   is
                   greater
                   than
                   a
                   Right
                   .
                
                 Thus
                 in
                 Fig.
                 1.
                 
                 The
                 Angle
                 BAC
                 is
                 an
                 Acute
                 Angle
                 because
                 less
                 than
                 the
                 Right
                 Angle
                 CAK
                 .
                 And
                 the
                 Angle
                 BAD
                 is
                 an
                 Obtuse
                 Angle
                 being
                 greater
                 than
                 the
                 Right
                 Angle
                 DAK
                 .
              
               
                 The
                 Geometrical
                 Propositions
                 concerning
                 Lines
                 and
                 Angles
                 are
                 very
                 many
                 ,
                 but
                 these
                 following
                 we
                 think
                 sufficient
                 for
                 our
                 present
                 purpose
                 .
              
               
                 
                   Proposition
                   I.
                   
                
                 
                   
                     To
                     divide
                     a
                     Right
                     Line
                     given
                     into
                     any
                     Number
                     of
                     equal
                     Parts
                     .
                  
                
                 
                   Let
                   it
                   be
                   required
                   to
                   divide
                   the
                   Right
                   Line
                   AB
                   into
                   five
                   equal
                   Parts
                   .
                   From
                   the
                   extream
                   Points
                   of
                   the
                   given
                   Line
                   A
                   and
                   B
                   ,
                   let
                   there
                   be
                   drawn
                   two
                   Parallel
                   Lines
                   ,
                   then
                   from
                   the
                   Point
                   A
                   at
                   any
                   distance
                   of
                   the
                   Compasses
                   ,
                   set
                   off
                   as
                   many
                   equal
                   Parts
                   wanting
                   one
                   ,
                   as
                   the
                   given
                   Line
                   is
                   to
                   be
                   divided
                   into
                   ,
                   which
                   in
                   our
                   Example
                   is
                   four
                   ,
                   and
                   are
                   noted
                   thus
                   ,
                   1.
                   2.
                   3.
                   4.
                   and
                   from
                   the
                   Point
                   B
                   set
                   off
                   the
                   like
                   Parts
                   in
                   the
                   Line
                   BC
                   ,
                   and
                   let
                   them
                   be
                   
                   noted
                   likewise
                   thus
                   ,
                   1.
                   2.
                   3.
                   4.
                   then
                   shall
                   the
                   Parallel
                   Lines
                   ,
                   14.
                   23.
                   32
                   ,
                   and
                   41.
                   divide
                   the
                   Right
                   Line
                   AB
                   into
                   5
                   equal
                   Parts
                   ,
                   as
                   was
                   required
                   .
                
              
               
                 
                   Proposition
                   II.
                   
                
                 
                   
                     Two
                     Right
                     Lines
                     being
                     given
                     ,
                     to
                     find
                     a
                     Mean
                     propertional
                     between
                     them
                     .
                  
                
                 
                   Let
                   the
                   two
                   Right
                   Lines
                   given
                   be
                   DB
                   and
                   CB
                   ,
                   which
                   let
                   be
                   made
                   into
                   one
                   Line
                   as
                   CD
                   ,
                   which
                   being
                   besected
                   the
                   Point
                   of
                   bisection
                   is
                   A
                   ,
                   from
                   which
                   as
                   from
                   a
                   Centre
                   describe
                   the
                   Arch
                   CED
                   ,
                   and
                   from
                   the
                   Point
                   B
                   erect
                   the
                   Perpendicular
                   BE
                   ,
                   so
                   shall
                   BE
                   ,
                   be
                   the
                   Mean
                   proportional
                   required
                   ;
                   for
                   ,
                   
                     BC.
                     BE
                     ∷
                     BE.
                     BD.
                  
                   
                
              
               
                 
                   Proposition
                   III.
                   
                
                 
                   
                     Three
                     Right
                     Lines
                     being
                     given
                     ,
                     to
                     find
                     a
                     fourth
                     proportional
                     .
                  
                
                 
                   Let
                   the
                   three
                   given
                   Lines
                   be
                   
                     AB
                     .
                     BC.
                  
                   and
                   
                     AD.
                     Fig.
                  
                   5.
                   to
                   which
                   a
                   fourth
                   proportional
                   is
                   required
                   :
                   draw
                   AE
                   at
                   any
                   Acute
                   Angle
                   ,
                   to
                   the
                   Line
                   AD
                   in
                   the
                   Point
                   A
                   ;
                   and
                   make
                   DE
                   parallel
                   to
                   BC
                   ,
                   so
                   shall
                   AE
                   be
                   the
                   fourth
                   proportional
                   required
                   ;
                   for
                   ,
                   
                     AB
                     .
                     BC
                     ∷
                     AD.
                     AE
                     .
                  
                
              
               
                 
                   Proposition
                   IV.
                   
                
                 
                   
                     Vpon
                     a
                     Right
                     Line
                     given
                     ,
                     to
                     make
                     a
                     right-lined
                     .
                     Angle
                     ,
                     equal
                     to
                     an
                     Angle
                     given
                     .
                  
                
                 
                   Let
                   it
                   be
                   required
                   upon
                   the
                   Line
                   CD
                   in
                   Fig.
                   6.
                   
                   to
                   make
                   an
                   Angle
                   ,
                   equal
                   to
                   the
                   Angle
                   DAE
                   in
                   Fig.
                   5.
                   
                   From
                   the
                   Point
                   A
                   as
                   a
                   Center
                   ,
                   at
                   any
                   extent
                   of
                   the
                   Compasses
                   describe
                   the
                   Arch
                   BG
                   ,
                   between
                   the
                   sides
                   of
                   the
                   Angle
                   given
                   ,
                   and
                   with
                   the
                   same
                   extent
                   describe
                   the
                   Arch
                   HL
                   from
                   the
                   Point
                   D
                   ,
                   and
                   then
                   make
                   HL
                   equal
                   to
                   BG
                   ,
                   then
                   draw
                   the
                   Line
                   DL
                   ,
                   so
                   shall
                   the
                   Angle
                   CDL
                   be
                   equal
                   to
                   the
                   Angle
                   DAE
                   given
                   ,
                   as
                   was
                   required
                   .
                
              
            
             
               
                 CHAP.
                 II.
                 
              
               
                 
                   Of
                   Figures
                   in
                   the
                   general
                   ,
                   more
                   particularly
                   of
                   a
                   Circle
                   and
                   the
                   affections
                   thereof
                   .
                
              
               
                 HItherto
                 we
                 have
                 spoken
                 of
                 the
                 first
                 kind
                 of
                 Magnitude
                 ,
                 that
                 is
                 ,
                 of
                 Lines
                 ,
                 as
                 they
                 are
                 considered
                 of
                 themselves
                 ,
                 or
                 amongst
                 themselves
                 .
              
               
                 2.
                 
                 The
                 second
                 kind
                 of
                 Magnitude
                 is
                 that
                 which
                 is
                 made
                 of
                 Lines
                 ,
                 that
                 is
                 ,
                 a
                 Figure
                 consisting
                 of
                 breadth
                 as
                 well
                 as
                 length
                 ,
                 and
                 this
                 is
                 otherwise
                 called
                 a
                 Superficies
                 .
              
               
                 3.
                 
                 And
                 in
                 a
                 Superficies
                 there
                 are
                 three
                 things
                 to
                 be
                 considered
                 .
                 1.
                 
                 The
                 Term
                 or
                 Limit
                 .
                 2.
                 
                 The
                 middle
                 of
                 the
                 Term.
                 3.
                 
                 The
                 Thing
                 or
                 Figure
                 made
                 by
                 the
                 Term
                 or
                 Limit
                 .
              
               
                 4.
                 
                 The
                 Term
                 or
                 Limit
                 is
                 that
                 which
                 comprehendeth
                 and
                 boundeth
                 the
                 Figure
                 ,
                 it
                 is
                 commonly
                 called
                 the
                 Perimeter
                 or
                 Circumference
                 .
              
               
                 5.
                 
                 The
                 Term
                 of
                 a
                 Figure
                 is
                 either
                 Simple
                 or
                 various
                 .
              
               
                 6.
                 
                 A
                 Simple
                 Term
                 is
                 that
                 which
                 doth
                 consist
                 of
                 a
                 Simple
                 Line
                 ,
                 and
                 is
                 properly
                 called
                 a
                 Circumference
                 
                 or
                 Periphery
                 :
                 A
                 Periphery
                 therefore
                 is
                 the
                 Term
                 of
                 a
                 Circle
                 or
                 most
                 Simple
                 Figure
                 .
              
               
                 7.
                 
                 A
                 various
                 Term
                 is
                 that
                 which
                 hath
                 bending
                 or
                 crooked
                 Lines
                 ,
                 making
                 Angles
                 ,
                 and
                 may
                 therefore
                 be
                 called
                 Angular
                 .
              
               
                 8.
                 
                 The
                 middle
                 of
                 Term
                 is
                 that
                 which
                 is
                 the
                 Center
                 of
                 the
                 Figure
                 ;
                 for
                 every
                 Figure
                 ,
                 whether
                 Triangular
                 ,
                 Quadrangular
                 ,
                 or
                 Multangular
                 ,
                 hath
                 a
                 Center
                 as
                 well
                 as
                 the
                 Circular
                 ,
                 differing
                 in
                 in
                 this
                 ,
                 that
                 the
                 Lines
                 in
                 a
                 Circle
                 drawn
                 from
                 the
                 Center
                 to
                 the
                 Circumference
                 are
                 all
                 equal
                 ,
                 but
                 in
                 other
                 Figures
                 they
                 are
                 not
                 equal
                 .
              
               
                 9.
                 
                 
                   The
                   Thing
                   or
                   Figure
                   made
                   by
                   the
                   Term
                   or
                   Limit
                   ,
                   is
                   all
                   that
                
                 Area
                 
                   or
                   space
                   which
                   is
                   included
                   by
                   the
                   Term
                   or
                   Terms
                   .
                
                 And
                 here
                 it
                 is
                 to
                 be
                 observed
                 ,
                 that
                 the
                 Term
                 of
                 a
                 Figure
                 is
                 one
                 thing
                 ,
                 and
                 the
                 Figure
                 it self
                 another
                 ;
                 for
                 Example
                 ,
                 A
                 Periphery
                 is
                 the
                 Term
                 of
                 a
                 Circle
                 ,
                 but
                 the
                 Circle
                 it self
                 is
                 not
                 properly
                 the
                 Periphery
                 ,
                 but
                 all
                 that
                 Area
                 or
                 space
                 which
                 is
                 included
                 by
                 the
                 Periphery
                 ,
                 for
                 a
                 Periphery
                 is
                 nothing
                 but
                 a
                 Line
                 ,
                 but
                 the
                 Circle
                 is
                 that
                 which
                 is
                 included
                 by
                 that
                 Line
                 .
              
               
                 10.
                 
                 As
                 the
                 Term
                 of
                 a
                 Figure
                 is
                 either
                 Simple
                 or
                 Various
                 ;
                 so
                 the
                 Figure
                 it self
                 is
                 either
                 Simple
                 and
                 Round
                 ,
                 or
                 Various
                 and
                 Angular
                 .
              
               
                 11.
                 
                 A
                 Simple
                 Figure
                 is
                 that
                 which
                 is
                 contained
                 by
                 a
                 Simple
                 or
                 Round
                 Line
                 ,
                 and
                 is
                 either
                 a
                 Circle
                 or
                 an
                 Ellipsis
                 .
              
               
                 12.
                 
                 A
                 Circle
                 therefore
                 is
                 such
                 a
                 Figure
                 which
                 is
                 made
                 by
                 a
                 Line
                 so
                 drawn
                 into
                 it self
                 ,
                 as
                 that
                 it
                 is
                 every
                 where
                 equally
                 distant
                 from
                 the
                 middle
                 or
                 Center
                 .
              
               
                 13.
                 
                 An
                 Ellipsis
                 is
                 an
                 oblong
                 Circle
                 .
              
               
                 14.
                 
                 In
                 a
                 Circle
                 we
                 are
                 to
                 consider
                 the
                 affections
                 which
                 are
                 as
                 it
                 were
                 the
                 Parts
                 or
                 Sections
                 
                 thereof
                 ,
                 as
                 they
                 are
                 made
                 by
                 the
                 various
                 applications
                 of
                 Right
                 Lines
                 .
              
               
                 15.
                 
                 And
                 Right
                 Lines
                 may
                 be
                 applied
                 unto
                 a
                 Circle
                 ,
                 either
                 by
                 drawing
                 them
                 within
                 ,
                 or
                 without
                 the
                 Circle
                 .
              
               
                 16.
                 
                 Right
                 Lines
                 inscribed
                 within
                 a
                 Circle
                 ,
                 are
                 either
                 such
                 as
                 do
                 cut
                 the
                 Circle
                 into
                 two
                 equal
                 or
                 unequal
                 Parts
                 ,
                 as
                 the
                 Diameter
                 and
                 lesser
                 Chords
                 ,
                 or
                 such
                 as
                 do
                 cut
                 the
                 Diameter
                 and
                 lesser
                 Chords
                 into
                 two
                 equal
                 or
                 unequal
                 Parts
                 ,
                 as
                 the
                 Right
                 and
                 versed
                 Sines
                 .
              
               
                 17.
                 
                 
                   A
                   Diameter
                   is
                   a
                   Right
                   Line
                   drawn
                   through
                   the
                   Center
                   from
                   one
                   side
                   of
                   the
                   Circumference
                   to
                   the
                   other
                   ,
                   and
                   divideth
                   the
                   Circle
                   into
                   two
                   equal
                   Parts
                   ,
                
                 As
                 in
                 Fig.
                 7.
                 
                 The
                 Right
                 Line
                 GD
                 drawn
                 through
                 the
                 Center
                 B
                 is
                 the
                 Diameter
                 of
                 the
                 Circle
                 GEDL
                 dividing
                 the
                 same
                 into
                 the
                 two
                 equal
                 Parts
                 GED
                 ,
                 and
                 GLD
                 :
                 and
                 this
                 is
                 also
                 called
                 the
                 greatest
                 Chord
                 or
                 Subtense
                 .
              
               
                 18.
                 
                 
                   A
                   Chord
                   or
                   Subtense
                   is
                   a
                   Right
                   Line
                   inscribed
                   in
                   a
                   Circle
                   ,
                   dividing
                   the
                   same
                   into
                   two
                   equal
                   or
                   unequal
                   Parts
                   ;
                   if
                   it
                   divide
                   the
                   Circle
                   into
                   two
                   equal
                   Parts
                   ,
                   it
                   is
                   the
                   same
                   with
                   the
                   Diameter
                   ,
                   but
                   if
                   it
                   divide
                   the
                   Circle
                   into
                   two
                   unequal
                   Parts
                   it
                   is
                   less
                   than
                   the
                   Diameter
                   ,
                   and
                   is
                   the
                   Chord
                   or
                   Subtense
                   of
                   an
                   Arch
                   less
                   than
                   a
                   Semi-circle
                   ,
                   and
                   also
                   of
                   an
                   Arch
                   greater
                   than
                   a
                   Semi-circle
                   .
                
                 As
                 in
                 the
                 former
                 Figure
                 ,
                 the
                 Right
                 Line
                 CAK
                 divideth
                 the
                 Circle
                 into
                 two
                 unequal
                 Parts
                 ,
                 and
                 is
                 the
                 Chord
                 or
                 Subtense
                 of
                 the
                 Arch
                 CDK
                 ,
                 less
                 than
                 a
                 Semi-circle
                 ,
                 and
                 of
                 the
                 Arch
                 CGK
                 greater
                 than
                 a
                 Semi-circle
                 :
                 and
                 these
                 are
                 the
                 Lines
                 which
                 divide
                 the
                 Circle
                 into
                 two
                 equal
                 or
                 unequal
                 Parts
                 .
                 And
                 as
                 they
                 divide
                 the
                 Circle
                 into
                 two
                 equal
                 Parts
                 ,
                 so
                 do
                 they
                 also
                 divide
                 one
                 another
                 ;
                 The
                 lesser
                 Chords
                 when
                 they
                 are
                 divided
                 by
                 
                 the
                 Diameter
                 into
                 two
                 equal
                 Parts
                 ,
                 those
                 Parts
                 are
                 called
                 Right
                 Sines
                 ,
                 and
                 the
                 two
                 Parts
                 of
                 the
                 Diameter
                 made
                 by
                 the
                 intersection
                 of
                 the
                 Chords
                 are
                 called
                 versed
                 Sines
                 .
              
               
                 19.
                 
                 Sines
                 are
                 right
                 or
                 versed
                 .
              
               
                 20.
                 
                 Right
                 Sines
                 are
                 made
                 by
                 being
                 besected
                 ,
                 by
                 the
                 Diameter
                 ,
                 and
                 are
                 twofold
                 ,
                 
                   Sinus
                   totus
                
                 ,
                 the
                 whole
                 Sine
                 or
                 Radius
                 ,
                 and
                 this
                 is
                 the
                 one
                 half
                 of
                 the
                 Diameter
                 ,
                 
                   as
                   the
                   Lines
                
                 BE
                 or
                 BD
                 ,
                 
                   and
                   all
                   Lines
                   drawn
                   from
                   the
                   Center
                   to
                   the
                   Circumference
                   .
                
              
               
                 21.
                 
                 Sinus
                 simpliter
                 ,
                 
                   or
                   the
                   lesser
                   Sines
                   ,
                   are
                   the
                   one
                   half
                   of
                   any
                   Chord
                   less
                   than
                   the
                   Diameter
                   ,
                
                 as
                 in
                 the
                 former
                 Figure
                 CA
                 or
                 AK
                 ,
                 which
                 are
                 the
                 equal
                 Parts
                 of
                 the
                 Chord
                 CAK
                 ,
                 are
                 the
                 Sines
                 of
                 the
                 Arches
                 CD
                 .
                 and
                 DK
                 less
                 than
                 a
                 Quadrant
                 ,
                 and
                 also
                 the
                 Sines
                 of
                 CEG
                 and
                 KLG
                 greater
                 than
                 a
                 Quadrant
                 .
              
               
                 22.
                 
                 Versed
                 Sines
                 are
                 the
                 Segments
                 of
                 the
                 Diameter
                 ,
                 made
                 by
                 the
                 Chords
                 intersecting
                 it
                 ,
                 at
                 Right
                 Angles
                 ,
                 as
                 AD
                 
                   is
                   the
                   versed
                   Sine
                   of
                
                 CD
                 or
                 DG
                 
                   and
                   the
                   other
                   Segment
                
                 AG
                 
                   is
                   the
                   versed
                   Sine
                   of
                   the
                   Arch
                
                 CEG
                 or
                 KLG
                 .
              
               
                 23.
                 
                 The
                 Right
                 Lines
                 drawn
                 without
                 the
                 Circle
                 are
                 two
                 ,
                 the
                 one
                 touching
                 the
                 Circle
                 ,
                 and
                 is
                 called
                 a
                 Tangent
                 ,
                 and
                 the
                 other
                 cutting
                 the
                 Circle
                 ,
                 and
                 is
                 called
                 a
                 Secant
                 .
              
               
                 24.
                 
                 A
                 Tangent
                 is
                 a
                 Right
                 Line
                 touching
                 the
                 Circle
                 ,
                 and
                 drawn
                 perpendicular
                 to
                 the
                 Diameter
                 ,
                 and
                 extended
                 to
                 the
                 Secant
                 .
              
               
                 25.
                 
                 A
                 Secant
                 is
                 a
                 Right
                 Line
                 drawn
                 from
                 the
                 Center
                 through
                 the
                 Circumference
                 ,
                 and
                 extended
                 to
                 the
                 Tangent
                 .
                 As
                 in
                 the
                 former
                 Figure
                 ,
                 the
                 Right
                 Line
                 DF
                 is
                 the
                 Tangent
                 of
                 the
                 Arch
                 CD
                 ,
                 and
                 the
                 Right
                 Line
                 BF
                 is
                 the
                 Secant
                 of
                 the
                 same
                 Arch
                 CD
                 .
              
               
                 
                 
                   Proposition
                   I.
                   
                
                 
                   
                     The
                     Arch
                     of
                     a
                     Circle
                     being
                     given
                     to
                     describe
                     the
                     whole
                     Periphery
                     .
                  
                
                 
                   Let
                   ABC
                   be
                   an
                   Arch
                   given
                   ,
                   and
                   let
                   the
                   Circumference
                   of
                   that
                   Circle
                   be
                   required
                   .
                   Let
                   there
                   be
                   three
                   Points
                   taken
                   in
                   the
                   given
                   Arch
                   at
                   pleasure
                   ,
                   as
                   
                     A
                     ,
                     B
                     ,
                     C
                  
                   ;
                   open
                   your
                   Compasses
                   to
                   more
                   than
                   half
                   the
                   distance
                   of
                   
                     A
                     ,
                     B
                  
                   ,
                   and
                   setting
                   one
                   Foot
                   in
                   A
                   describe
                   the
                   Arch
                   of
                   a
                   Circle
                   ,
                   and
                   the
                   Compasses
                   remaining
                   at
                   the
                   same
                   distance
                   ,
                   setting
                   one
                   Foot
                   in
                   B
                   ,
                   describe
                   another
                   Arch
                   so
                   as
                   it
                   may
                   cut
                   the
                   former
                   in
                   two
                   Points
                   ,
                   suppose
                   G
                   ,
                   and
                   H
                   ,
                   and
                   draw
                   the
                   Line
                   HG
                   towards
                   that
                   Part
                   on
                   which
                   you
                   suppose
                   the
                   Center
                   of
                   the
                   Center
                   of
                   the
                   Circle
                   will
                   fall
                   .
                
                 
                   In
                   like
                   manner
                   ,
                   opening
                   your
                   Compasses
                   to
                   more
                   than
                   half
                   your
                   distance
                   of
                   
                     B
                     ,
                     C
                  
                   ,
                   describe
                   two
                   other
                   Arches
                   from
                   the
                   Points
                   E
                   and
                   C
                   ,
                   cutting
                   each
                   other
                   in
                   E
                   and
                   F
                   ,
                   then
                   draw
                   the
                   Line
                   EF
                   till
                   it
                   intersect
                   the
                   former
                   Line
                   HG
                   ,
                   so
                   shall
                   the
                   Point
                   of
                   Intersection
                   be
                   the
                   Center
                   of
                   the
                   Circumference
                   or
                   Circle
                   required
                   ,
                   as
                   in
                   Fig.
                   may
                   be
                   seen
                   .
                
              
               
                 
                   Proposition
                   II.
                   
                
                 
                   
                     The
                     Conjugate
                     Diameters
                     of
                     an
                     Ellipsis
                     being
                     given
                     ,
                     to
                     draw
                     the
                     Ellipsis
                     .
                  
                
                 
                   Let
                   the
                   given
                   Diameter
                   in
                   Fig.
                   24.
                   be
                   LB
                   and
                   ED
                   ,
                   the
                   greatest
                   Diameter
                   .
                   LB
                   being
                   bisected
                   in
                   the
                   Point
                   of
                   Bisection
                   ,
                   erect
                   the
                   Perpendicular
                   
                   AD.
                   which
                   let
                   be
                   half
                   of
                   the
                   lesser
                   Diameter
                   ED
                   ,
                   then
                   open
                   your
                   Compasses
                   to
                   the
                   extent
                   of
                   AB
                   ,
                   and
                   setting
                   one
                   Foot
                   in
                   D
                   ,
                   with
                   the
                   other
                   make
                   a
                   mark
                   at
                   M
                   and
                   N
                   in
                   the
                   Diameter
                   BL
                   ,
                   then
                   cutting
                   a
                   thred
                   to
                   the
                   length
                   of
                   BL
                   ,
                   fasten
                   the
                   thred
                   with
                   your
                   Compasses
                   in
                   the
                   Points
                   NM
                   ,
                   and
                   with
                   your
                   Pen
                   in
                   the
                   inside
                   of
                   the
                   thred
                   describe
                   the
                   Arch
                   BFKL
                   ,
                   so
                   shall
                   you
                   describe
                   the
                   one
                   half
                   of
                   the
                   Ellipsis
                   required
                   ,
                   and
                   turning
                   the
                   Thred
                   on
                   the
                   other
                   side
                   of
                   the
                   Compasses
                   ,
                   you
                   may
                   with
                   your
                   Pen
                   in
                   the
                   like
                   manner
                   describe
                   the
                   other
                   half
                   of
                   the
                   Ellipsis
                   GBHL
                   .
                
              
            
             
               
                 CHAP.
                 III.
                 
              
               
                 
                   Of
                   Triangles
                   .
                
              
               
                 HItherto
                 we
                 have
                 spoken
                 of
                 the
                 most
                 Simple
                 Figure
                 ,
                 a
                 Circle
                 .
                 Come
                 we
                 now
                 to
                 those
                 Figures
                 that
                 are
                 Various
                 or
                 Angular
                 .
              
               
                 2.
                 
                 And
                 an
                 Angular
                 Figure
                 is
                 that
                 which
                 doth
                 consist
                 of
                 three
                 or
                 more
                 Angles
                 .
              
               
                 3.
                 
                 An
                 angular
                 Figure
                 consisting
                 of
                 three
                 Angles
                 ,
                 otherwise
                 called
                 a
                 Triangle
                 ,
                 is
                 a
                 Superficies
                 or
                 Figure
                 comprehended
                 by
                 three
                 Right
                 Lines
                 including
                 three
                 Angles
                 .
              
               
                 4.
                 
                 A
                 Triangle
                 may
                 be
                 considered
                 either
                 in
                 respect
                 of
                 its
                 Sides
                 ,
                 or
                 of
                 its
                 Angles
                 .
              
               
                 5.
                 
                 A
                 Triangle
                 in
                 respect
                 of
                 its
                 Sides
                 ,
                 is
                 either
                 
                   Isopleuron
                   ,
                   Isosceles
                
                 ,
                 or
                 Scalenum
                 .
              
               
                 6.
                 
                 An
                 Isopleuron
                 Triangle
                 ,
                 is
                 that
                 which
                 hath
                 three
                 equal
                 sides
                 .
                 An
                 Isoscecles
                 hath
                 two
                 equal
                 Sides
                 .
                 And
                 a
                 Scalenum
                 hath
                 all
                 the
                 three
                 Sides
                 unequal
                 .
              
               
                 7.
                 
                 A
                 Triangle
                 in
                 respect
                 of
                 its
                 Angles
                 is
                 Right
                 or
                 Oblique
                 .
              
               
               
                 8.
                 
                 A
                 Right
                 angled
                 Triangle
                 is
                 that
                 which
                 hath
                 one
                 Right
                 Angle
                 and
                 two
                 Acute
                 .
              
               
                 9.
                 
                 An
                 Oblique
                 angled
                 Triangle
                 ,
                 is
                 either
                 Acute
                 or
                 Obtuse
                 .
              
               
                 10.
                 
                 An
                 Oblique
                 acute
                 angled
                 Triangle
                 ,
                 is
                 that
                 which
                 hath
                 all
                 the
                 three
                 Angles
                 Acute
                 .
              
               
                 11.
                 
                 An
                 Oblique
                 obtuse
                 angled
                 Triangle
                 ,
                 is
                 that
                 which
                 hath
                 one
                 Angle
                 Obtuse
                 ,
                 and
                 the
                 other
                 two
                 Acute
                 .
              
               
                 
                   Proposition
                   I.
                   
                
                 
                   
                     Vpon
                     a
                     Right
                     Line
                     given
                     to
                     make
                     an
                     Isopleuron
                     or
                     an
                     Equilateral
                     Triangle
                     .
                  
                
                 
                   In
                   Fig.
                   8.
                   let
                   it
                   be
                   required
                   to
                   make
                   an
                   Equilateral
                   Triangle
                   upon
                   the
                   Right
                   Line
                   AB
                   .
                   Open
                   your
                   Compasses
                   to
                   the
                   extent
                   of
                   the
                   Line
                   given
                   ,
                   and
                   setting
                   one
                   Foot
                   of
                   your
                   Compasses
                   in
                   A
                   ,
                   make
                   an
                   Arch
                   of
                   a
                   Circle
                   above
                   or
                   beneath
                   the
                   Line
                   given
                   ,
                   then
                   setting
                   one
                   Foot
                   of
                   your
                   Compasses
                   in
                   B
                   ,
                   they
                   being
                   full
                   opened
                   to
                   the
                   same
                   extent
                   ,
                   with
                   the
                   other
                   foot
                   draw
                   another
                   Arch
                   of
                   a
                   Circle
                   crossing
                   the
                   former
                   ,
                   and
                   from
                   the
                   Intersection
                   of
                   those
                   Arches
                   draw
                   the
                   Lines
                   AC
                   and
                   AB
                   ,
                   so
                   shall
                   the
                   Triangle
                   ACB
                   be
                   Equilateral
                   as
                   was
                   desired
                   .
                
              
               
                 
                   Proposition
                   II.
                   
                
                 
                   
                     Vpon
                     a
                     Right
                     Line
                     given
                     to
                     make
                     an
                     Isosceles
                     Triangle
                     ,
                     or
                     a
                     Triangle
                     having
                     two
                     Sides
                     equal
                     .
                  
                
                 
                   In
                   Fig.
                   8.
                   let
                   AB
                   be
                   the
                   Right
                   Line
                   given
                   ,
                   from
                   the
                   Points
                   A
                   and
                   B
                   as
                   from
                   two
                   Centers
                   ,
                   but
                   at
                   a
                   lesser
                   extent
                   of
                   the
                   Compasses
                   than
                   AB
                   ;
                   
                   if
                   you
                   would
                   have
                   AB
                   the
                   greatest
                   Side
                   ,
                   at
                   a
                   greater
                   extent
                   ;
                   if
                   you
                   would
                   have
                   it
                   to
                   be
                   the
                   least
                   Side
                   ,
                   describe
                   two
                   Arches
                   cutting
                   one
                   another
                   ,
                   as
                   at
                   F
                   ,
                   and
                   from
                   the
                   Intersection
                   draw
                   the
                   Lines
                   AF
                   ,
                   and
                   FB
                   ,
                   so
                   shall
                   the
                   Triangle
                   AFB
                   have
                   two
                   equal
                   Sides
                   ,
                   as
                   was
                   required
                   .
                
              
               
                 
                   Proposition
                   3.
                   
                
                 
                   
                     To
                     make
                     a
                     Scalenum
                     Triangle
                     ,
                     or
                     a
                     Triangle
                     ,
                     whose
                     three
                     Sides
                     are
                     unequal
                     .
                  
                
                 
                   In
                   Fig.
                   9.
                   let
                   the
                   three
                   unequal
                   Sides
                   be
                   EFG
                   make
                   AB
                   equal
                   to
                   one
                   of
                   the
                   given
                   Lines
                   ,
                   suppose
                   G
                   ,
                   and
                   from
                   A
                   as
                   a
                   Center
                   ,
                   at
                   the
                   extent
                   of
                   E
                   describe
                   the
                   Arch
                   of
                   a
                   Circle
                   ;
                   in
                   like
                   manner
                   from
                   B
                   at
                   the
                   extent
                   of
                   F
                   describe
                   another
                   Arch
                   intersecting
                   the
                   former
                   ,
                   then
                   shall
                   the
                   Right
                   Lines
                   
                     AC
                     .
                     CB
                  
                   and
                   BA
                   comprehend
                   a
                   Triangle
                   ,
                   whose
                   three
                   sides
                   shall
                   be
                   unequal
                   ,
                   as
                   was
                   required
                   .
                
              
            
             
               
                 CHAP.
                 IV.
                 
              
               
                 
                   Of
                   Quadrangular
                   and
                   Multangular
                   Figures
                   .
                
              
               
                 WE
                 have
                 spoken
                 of
                 Triangles
                 or
                 Figures
                 consisting
                 of
                 three
                 Angles
                 ,
                 come
                 we
                 now
                 to
                 those
                 that
                 have
                 more
                 Angles
                 than
                 three
                 ,
                 as
                 the
                 
                   Quadrangle
                   ,
                   Quinquangle
                   ,
                   Sexangle
                   ,
                   &c.
                   
                
              
               
                 2.
                 
                 A
                 Quadrangle
                 is
                 a
                 Figure
                 or
                 Superficies
                 ,
                 which
                 is
                 bounded
                 with
                 four
                 Right
                 Lines
                 .
              
               
                 3.
                 
                 A
                 Quadrangle
                 is
                 either
                 a
                 Parallelogram
                 or
                 a
                 Trapezium
                 .
              
               
                 4.
                 
                 A
                 Parallelogram
                 is
                 a
                 Quadrangle
                 whose
                 opposite
                 
                 Sides
                 are
                 parallel
                 having
                 equal
                 distances
                 from
                 one
                 another
                 in
                 all
                 Places
                 .
              
               
                 5.
                 
                 A
                 Parallelogram
                 is
                 either
                 Right
                 angled
                 or
                 Oblique
                 .
              
               
                 6.
                 
                 A
                 Right
                 angled
                 Parallelogram
                 ,
                 is
                 a
                 Quadrangle
                 whose
                 four
                 Angles
                 are
                 all
                 Right
                 ,
                 and
                 is
                 either
                 Square
                 or
                 Oblong
                 .
              
               
                 7.
                 
                 A
                 Square
                 Parallelogram
                 doth
                 consist
                 of
                 four
                 equal
                 Lines
                 .
                 The
                 Parts
                 of
                 a
                 Square
                 are
                 ,
                 the
                 Sides
                 of
                 which
                 the
                 Square
                 is
                 made
                 ,
                 and
                 the
                 Diagonal
                 or
                 Line
                 drawn
                 from
                 one
                 opposite
                 Angle
                 to
                 another
                 through
                 the
                 middle
                 of
                 the
                 Square
                 .
              
               
                 8.
                 
                 An
                 Oblong
                 is
                 a
                 Right
                 angled
                 Parallelogram
                 ,
                 having
                 two
                 longer
                 and
                 two
                 shorter
                 Sides
                 .
              
               
                 9.
                 
                 An
                 Oblique
                 angled
                 Parallelogram
                 ,
                 is
                 that
                 whose
                 Angles
                 are
                 all
                 Oblique
                 ,
                 and
                 is
                 either
                 a
                 Rhombus
                 or
                 a
                 Rhomboides
                 .
              
               
                 10.
                 
                 A
                 Rhombus
                 is
                 an
                 Oblique
                 angled
                 and
                 equilateral
                 Parallelogram
                 .
              
               
                 11.
                 
                 A
                 Rhomboides
                 is
                 an
                 Oblique
                 angled
                 and
                 inequilateral
                 Parallelogram
                 .
              
               
                 12.
                 
                 A
                 Trapezium
                 is
                 a
                 Quadrangular
                 Figure
                 whose
                 Sides
                 are
                 not
                 all
                 parallel
                 ;
                 it
                 is
                 either
                 Right
                 angled
                 or
                 Oblique
                 .
              
               
                 13.
                 
                 A
                 Right
                 angled
                 Trapezium
                 hath
                 two
                 opposite
                 Sides
                 parallel
                 ,
                 but
                 unequal
                 ,
                 and
                 the
                 Side
                 between
                 them
                 perpendicular
                 .
              
               
                 14.
                 
                 An
                 Oblique
                 angled
                 Trapezium
                 is
                 a
                 Quadrangle
                 ,
                 but
                 not
                 a
                 Parallelogram
                 ,
                 having
                 at
                 least
                 two
                 Angles
                 Oblique
                 ,
                 and
                 none
                 of
                 the
                 Sides
                 parallel
                 .
              
               
                 15.
                 
                 Thus
                 much
                 concerning
                 Quadrangles
                 or
                 four
                 sided
                 Figures
                 .
                 Figures
                 consisting
                 of
                 more
                 than
                 four
                 Angles
                 are
                 almost
                 infinite
                 ,
                 but
                 are
                 reducible
                 unto
                 two
                 sorts
                 ,
                 Ordinate
                 and
                 Regular
                 ,
                 or
                 Inordinate
                 and
                 Irregular
                 .
              
               
               
                 16.
                 
                 Ordinate
                 and
                 Regular
                 Polygons
                 are
                 such
                 ,
                 as
                 are
                 contained
                 by
                 equal
                 Sides
                 and
                 Angles
                 ,
                 as
                 the
                 
                   Pentagon
                   ,
                   Hexagon
                
                 ,
                 and
                 such
                 like
                 .
              
               
                 17.
                 
                 Inordinate
                 or
                 irregular
                 Polygons
                 ,
                 are
                 such
                 as
                 are
                 contained
                 by
                 unequal
                 Sides
                 and
                 Angles
                 .
                 The
                 construction
                 of
                 these
                 Quadrangular
                 and
                 Multangular
                 Figures
                 is
                 explained
                 in
                 the
                 Propositions
                 following
                 .
              
               
                 
                   Proposition
                   .
                   I.
                   
                
                 
                   
                     Vpon
                     a
                     Right
                     Line
                     given
                     to
                     describe
                     a
                     Right
                     angled
                     Parallelogram
                     ,
                     whether
                     Square
                     or
                     Oblong
                     .
                  
                
                 
                   In
                   Fig.
                   10.
                   let
                   the
                   given
                   Line
                   be
                   AB
                   ,
                   upon
                   the
                   Point
                   A
                   erect
                   the
                   Perpendic●lar
                   AD
                   equal
                   to
                   AB
                   if
                   you
                   intend
                   to
                   make
                   a
                   Square
                   ,
                   but
                   longer
                   or
                   shorter
                   ,
                   if
                   you
                   intend
                   an
                   oblong
                   ,
                   and
                   upon
                   the
                   Points
                   D
                   and
                   B
                   at
                   the
                   distance
                   of
                   AB
                   and
                   AD
                   describe
                   two
                   Arches
                   intersecting
                   one
                   another
                   ,
                   and
                   from
                   the
                   Intersection
                   draw
                   the
                   Lines
                   ED
                   and
                   EB
                   ,
                   so
                   shall
                   the
                   Right
                   angled
                   Figure
                   AE
                   be
                   a
                   Square
                   ,
                   if
                   AB
                   and
                   AD
                   be
                   equal
                   ,
                   otherwise
                   an
                   Oblong
                   ,
                   as
                   was
                   desired
                   .
                
              
               
                 
                   Proposition
                   II.
                   
                
                 
                   
                     To
                     describe
                     a
                     Rhombus
                     or
                     Rhomboides
                     .
                  
                
                 
                   In
                   Fig.
                   11.
                   
                   To
                   the
                   Right
                   Line
                   AB
                   draw
                   the
                   Line
                   AD
                   at
                   any
                   Acute
                   Angle
                   at
                   pleasure
                   ,
                   equal
                   to
                   AB
                   if
                   you
                   intend
                   a
                   Rhombus
                   ,
                   longer
                   or
                   shorter
                   if
                   you
                   intend
                   a
                   Rhomboides
                   ,
                   then
                   upon
                   your
                   Compasses
                   to
                   the
                   extent
                   of
                   AD
                   and
                   upon
                   B
                   as
                   a
                   Center
                   describe
                   an
                   Arch
                   ;
                   in
                   like
                   manner
                   ,
                   at
                   the
                   extent
                   of
                   AB
                   upon
                   D
                   as
                   a
                   Center
                   describe
                   another
                   
                   Arch
                   intersecting
                   the
                   former
                   ,
                   then
                   draw
                   the
                   Lines
                   ED
                   and
                   EB
                   ,
                   so
                   shall
                   AE
                   be
                   the
                   Rhombus
                   or
                   Rhomboides
                   ,
                   as
                   was
                   required
                   .
                
              
               
                 
                   Proposition
                   III.
                   
                
                 
                   
                     Vpon
                     a
                     Right
                     Line
                     given
                     to
                     make
                     a
                     Regular
                     Pentagon
                     ,
                     or
                     five
                     sided
                     Figure
                     .
                  
                
                 
                   In
                   Fig.
                   12.
                   
                   Let
                   the
                   given
                   Line
                   be
                   AB
                   ,
                   upon
                   A
                   and
                   B
                   as
                   two
                   Centers
                   describe
                   the
                   Circles
                   EBGH
                   and
                   CAGK
                   ,
                   then
                   open
                   your
                   Compasses
                   to
                   the
                   extent
                   of
                   BC
                   ,
                   and
                   making
                   G
                   the
                   Center
                   ,
                   describe
                   the
                   Arch
                   HAFK
                   ,
                   then
                   draw
                   the
                   Lines
                   KFE
                   and
                   HFC
                   :
                   so
                   shall
                   AE
                   and
                   BC
                   be
                   two
                   sides
                   of
                   the
                   Pentagon
                   desired
                   ,
                   and
                   opening
                   your
                   Compasses
                   to
                   the
                   extent
                   of
                   AB
                   ,
                   upon
                   E
                   and
                   C
                   as
                   two
                   Centers
                   describe
                   two
                   Arches
                   intersecting
                   one
                   another
                   ,
                   and
                   from
                   the
                   Point
                   of
                   Intersection
                   draw
                   the
                   Lines
                   ED
                   and
                   DC
                   ,
                   so
                   shall
                   the
                   Figure
                   AB
                   and
                   DE
                   be
                   the
                   Pentagon
                   required
                   .
                
              
               
                 
                   Proposition
                   IV.
                   
                
                 
                   
                     To
                     make
                     a
                     Regular
                     Pentagon
                     and
                     Decagon
                     in
                     a
                     given
                     Circle
                     .
                  
                
                 
                   In
                   Fig.
                   13.
                   upon
                   the
                   Diameter
                   CAB
                   describe
                   the
                   Circle
                   CDBL
                   ,
                   from
                   the
                   Center
                   AErect
                   the
                   Perpendicular
                   AD
                   ,
                   and
                   let
                   the
                   Semidiameter
                   AC
                   be
                   bisected
                   ,
                   the
                   Point
                   of
                   Bisection
                   is
                   E
                   ,
                   set
                   the
                   distance
                   ED
                   from
                   E
                   to
                   G
                   ,
                   and
                   draw
                   the
                   Line
                   GD
                   ,
                   which
                   is
                   the
                   side
                   of
                   a
                   Pentagon
                   ,
                   and
                   AG
                   the
                   side
                   of
                   a
                   Decagon
                   inscribed
                   in
                   the
                   same
                   Circle
                   .
                
              
               
                 
                 
                   Proposition
                   V.
                   
                
                 
                   
                     In
                     a
                     Circle
                     given
                     to
                     describe
                     a
                     Regular
                     Hexagon
                     .
                  
                
                 
                   The
                   side
                   of
                   a
                   Hexagon
                   is
                   equal
                   to
                   the
                   Radius
                   of
                   a
                   Circle
                   ,
                   the
                   Radius
                   of
                   a
                   Circle
                   therefore
                   being
                   six
                   times
                   applied
                   to
                   the
                   Circumference
                   ,
                   will
                   give
                   you
                   six
                   Points
                   ,
                   to
                   which
                   Lines
                   being
                   drawn
                   from
                   Point
                   to
                   Point
                   ,
                   will
                   constitute
                   a
                   Regular
                   Hexagon
                   ,
                   as
                   was
                   desired
                   .
                
              
               
                 
                   Proposition
                   VI.
                   
                
                 
                   
                     In
                     a
                     Circle
                     given
                     to
                     describe
                     a
                     Regular
                     Heptagon
                     or
                     Figure
                     consisting
                     of
                     seven
                     equal
                     sides
                     .
                  
                
                 
                   The
                   side
                   of
                   a
                   Heptagon
                   is
                   equal
                   to
                   half
                   the
                   side
                   of
                   a
                   Triangle
                   inscribed
                   in
                   a
                   Circle
                   ,
                   having
                   therefore
                   drawn
                   an
                   Hexagon
                   in
                   a
                   Circle
                   ,
                   the
                   Chord
                   Line
                   subtending
                   two
                   sides
                   of
                   the
                   Hexagon
                   lying
                   together
                   ,
                   is
                   the
                   side
                   of
                   a
                   Triangle
                   inscribed
                   in
                   that
                   Circle
                   ,
                   and
                   half
                   that
                   Chord
                   applied
                   seven
                   times
                   to
                   the
                   Circumference
                   ,
                   will
                   give
                   seven
                   Points
                   ,
                   to
                   which
                   Lines
                   being
                   drawn
                   from
                   that
                   Point
                   ,
                   will
                   constitute
                   a
                   Regular
                   Heptagon
                   ,
                   as
                   in
                   Fig.
                   14.
                   is
                   plainly
                   shewed
                   .
                
              
            
             
               
               
                 CHAP.
                 V.
                 
              
               
                 
                   Of
                   Solid
                   Bodies
                   .
                
              
               
                 HAving
                 spoken
                 of
                 the
                 two
                 first
                 kinds
                 of
                 Magnitude
                 ,
                 Lines
                 and
                 Superficies
                 ,
                 come
                 we
                 now
                 to
                 the
                 third
                 ,
                 a
                 Body
                 or
                 Solid
                 .
              
               
                 2.
                 
                 A
                 Body
                 or
                 Solid
                 is
                 a
                 Magnitude
                 consisting
                 of
                 length
                 ,
                 breadth
                 and
                 thickness
                 .
              
               
                 3.
                 
                 A
                 Solid
                 is
                 either
                 regular
                 or
                 irregular
                 .
              
               
                 4.
                 
                 That
                 is
                 called
                 a
                 regular
                 Solid
                 ,
                 whose
                 Bases
                 ,
                 Sides
                 and
                 Angles
                 are
                 equal
                 and
                 like
                 .
              
               
                 5.
                 
                 And
                 this
                 either
                 Simple
                 or
                 Compound
                 .
              
               
                 6.
                 
                 A
                 simple
                 regular
                 Solid
                 ,
                 is
                 that
                 whith
                 doth
                 consist
                 of
                 one
                 only
                 kind
                 of
                 Superficies
                 .
              
               
                 7.
                 
                 And
                 this
                 is
                 either
                 a
                 Sphere
                 or
                 Globe
                 ,
                 or
                 a
                 plain
                 Body
                 .
              
               
                 8.
                 
                 A
                 Globe
                 is
                 a
                 Solid
                 included
                 by
                 one
                 round
                 and
                 convex
                 Superficies
                 ,
                 in
                 the
                 middle
                 whereof
                 there
                 is
                 a
                 Point
                 ,
                 from
                 whence
                 all
                 Lines
                 drawn
                 to
                 the
                 Circumference
                 are
                 equal
                 .
              
               
                 9.
                 
                 A
                 simple
                 plain
                 Solid
                 ,
                 is
                 that
                 which
                 doth
                 consist
                 of
                 plain
                 Superficies
                 .
              
               
                 10.
                 
                 A
                 plain
                 Solid
                 is
                 either
                 a
                 Pyramid
                 ,
                 a
                 Prism
                 ,
                 or
                 a
                 mixt
                 Solid
                 .
              
               
                 11.
                 
                 A
                 Pyramid
                 is
                 a
                 Solid
                 ,
                 Figure
                 or
                 Body
                 ,
                 contained
                 by
                 several
                 Plains
                 set
                 upon
                 one
                 right
                 lin'd
                 Base
                 ,
                 and
                 meeting
                 in
                 one
                 Point
                 .
              
               
                 12.
                 
                 Of
                 all
                 the
                 several
                 sorts
                 of
                 Pyramids
                 ,
                 there
                 is
                 but
                 one
                 that
                 is
                 Regular
                 ,
                 to
                 wit
                 a
                 Tetrahedron
                 ,
                 or
                 a
                 Pyramid
                 consisting
                 of
                 four
                 regular
                 or
                 equilateral
                 Triangles
                 ;
                 the
                 form
                 whereof
                 (
                 as
                 it
                 may
                 be
                 cut
                 in
                 Pastboard
                 )
                 may
                 be
                 conceived
                 by
                 Figure
                 15.
                 
              
               
               
                 13.
                 
                 A
                 Prism
                 is
                 a
                 Solid
                 contained
                 by
                 several
                 Plains
                 ,
                 of
                 which
                 those
                 two
                 which
                 are
                 opposite
                 ,
                 are
                 equal
                 ,
                 like
                 and
                 parallel
                 ,
                 and
                 all
                 others
                 are
                 Paralellogram
                 .
              
               
                 14.
                 
                 A
                 Prism
                 is
                 either
                 a
                 Pentahedron
                 ,
                 a
                 Hexahedron
                 ,
                 or
                 a
                 Polyhedron
                 .
              
               
                 15.
                 
                 A
                 Pentahedron
                 Prism
                 ,
                 is
                 a
                 Solid
                 comprehended
                 of
                 five
                 Sides
                 ,
                 and
                 the
                 Base
                 a
                 Triangle
                 ,
                 as
                 Fig.
                 16.
                 
              
               
                 16.
                 
                 An
                 Hexahedron
                 Prism
                 ,
                 is
                 a
                 Solid
                 comprehended
                 of
                 six
                 Sides
                 ,
                 and
                 the
                 Base
                 a
                 Quadrangle
                 ,
                 as
                 Fig.
                 17.
                 
              
               
                 17.
                 
                 An
                 Hexahedron
                 Prism
                 ,
                 is
                 distinguished
                 into
                 a
                 Parallelipipedon
                 and
                 a
                 Trapezium
                 .
              
               
                 18.
                 
                 An
                 Hexahedron
                 Prism
                 called
                 a
                 Trapezium
                 is
                 a
                 Solid
                 ,
                 whose
                 opposites
                 Plains
                 or
                 Sides
                 ,
                 are
                 neither
                 opposite
                 nor
                 equal
                 .
              
               
                 19.
                 
                 A
                 Parallelipipedon
                 is
                 either
                 right
                 angled
                 or
                 oblique
                 .
              
               
                 20.
                 
                 A
                 right
                 angled
                 Parallelipipedon
                 is
                 an
                 Hexahedron
                 Prism
                 ,
                 comprehended
                 of
                 right
                 angled
                 Plains
                 or
                 Sides
                 ;
                 and
                 it
                 is
                 either
                 a
                 Cube
                 or
                 an
                 Oblong
                 .
              
               
                 21.
                 
                 A
                 Cube
                 is
                 a
                 right
                 angled
                 Parallelipipedon
                 comprehended
                 of
                 six
                 equal
                 Plains
                 or
                 Sides
                 .
              
               
                 22.
                 
                 An
                 Oblong
                 Parallelipipedon
                 ,
                 is
                 an
                 Hexahedron
                 Prism
                 ,
                 comprehended
                 by
                 unequal
                 Plains
                 or
                 Sides
                 .
              
               
                 23.
                 
                 An
                 Oblique
                 angled
                 Parallelipipedon
                 ,
                 is
                 an
                 Hexahedron
                 Prism
                 ,
                 comprehended
                 of
                 Oblique
                 Sides
                 .
              
               
                 24.
                 
                 A
                 Polyhedron
                 Prism
                 ,
                 is
                 a
                 Solid
                 comprehended
                 by
                 more
                 than
                 six
                 Sides
                 ,
                 and
                 hath
                 a
                 multangled
                 Base
                 ,
                 as
                 a
                 
                   Quincangle
                   ,
                   Sexangle
                   ,
                   &c.
                
                 
              
               
                 25.
                 
                 A
                 regular
                 compound
                 or
                 mixt
                 Solid
                 ,
                 is
                 such
                 
                 a
                 Solid
                 as
                 hath
                 its
                 Vertex
                 in
                 the
                 Center
                 ,
                 and
                 the
                 several
                 Sides
                 exposed
                 to
                 view
                 ,
                 and
                 of
                 this
                 sort
                 there
                 are
                 only
                 three
                 ;
                 the
                 Octohedron
                 ,
                 the
                 Icosahedron
                 ,
                 of
                 both
                 which
                 the
                 Base
                 is
                 a
                 Triangle
                 ;
                 and
                 the
                 Dodecahedron
                 ,
                 whose
                 Base
                 is
                 a
                 Quincangle
                 .
              
               
                 26.
                 
                 An
                 Octohedron
                 is
                 a
                 Solid
                 Figure
                 which
                 is
                 contained
                 by
                 eight
                 equal
                 and
                 equilateral
                 Triangles
                 ,
                 as
                 in
                 Fig.
                 18.
                 
              
               
                 27.
                 
                 An
                 Icosahedron
                 is
                 a
                 Solid
                 ,
                 which
                 is
                 contained
                 by
                 twenty
                 equal
                 and
                 equilateral
                 Triangles
                 ,
                 as
                 Fig.
                 19.
                 
              
               
                 28.
                 
                 A
                 Dodecahedron
                 is
                 a
                 Solid
                 ,
                 which
                 is
                 contained
                 by
                 twelve
                 equal
                 Pentagons
                 ,
                 equilateral
                 and
                 equiangled
                 ,
                 as
                 in
                 Fig.
                 20.
                 
              
               
                 29.
                 
                 A
                 regular
                 compound
                 Solid
                 ,
                 is
                 such
                 a
                 Solid
                 as
                 is
                 Comprehended
                 both
                 by
                 plain
                 and
                 circular
                 Superficies
                 ,
                 and
                 this
                 is
                 either
                 a
                 Cone
                 or
                 a
                 Cylinder
                 .
              
               
                 30.
                 
                 A
                 Cone
                 is
                 a
                 Pyramidical
                 Body
                 ,
                 whose
                 Base
                 is
                 a
                 Circle
                 ,
                 or
                 it
                 may
                 be
                 called
                 a
                 round
                 Pyramis
                 ,
                 as
                 Fig.
                 21.
                 
              
               
                 31.
                 
                 A
                 Cylinder
                 is
                 a
                 round
                 Column
                 every
                 where
                 comprehended
                 by
                 equal
                 Circles
                 ,
                 as
                 
                   Fig.
                   22.
                
                 
              
               
                 32.
                 
                 Irregular
                 Solids
                 are
                 such
                 ,
                 which
                 come
                 not
                 within
                 these
                 defined
                 varieties
                 ,
                 as
                 Ovals
                 ,
                 Frustums
                 of
                 Cones
                 ,
                 Pyramids
                 ,
                 and
                 such
                 like
                 .
              
               
                 And
                 thus
                 much
                 concerning
                 the
                 description
                 of
                 the
                 several
                 sorts
                 of
                 continued
                 Quantity
                 ,
                 Lines
                 ,
                 Plains
                 and
                 Solids
                 ;
                 we
                 will
                 in
                 the
                 next
                 place
                 consider
                 the
                 wayes
                 and
                 means
                 by
                 which
                 the
                 Dimentions
                 of
                 them
                 may
                 be
                 taken
                 and
                 determined
                 ,
                 and
                 first
                 we
                 will
                 shew
                 the
                 measuring
                 of
                 Lines
                 .
              
            
             
               
               
                 CHAP.
                 VI.
                 
              
               
                 
                   Of
                   the
                   Measuring
                   of
                   Lines
                   both
                   Right
                   and
                   Circular
                   .
                
              
               
                 EVery
                 Magnitude
                 must
                 be
                 measured
                 by
                 some
                 known
                 kind
                 of
                 Measure
                 ;
                 as
                 Lines
                 by
                 Lines
                 ,
                 Superficies
                 by
                 Superficies
                 ,
                 and
                 Solids
                 by
                 Solids
                 ,
                 as
                 if
                 I
                 were
                 to
                 measure
                 the
                 breadth
                 of
                 a
                 River
                 ,
                 or
                 height
                 of
                 a
                 Turret
                 ,
                 this
                 must
                 be
                 done
                 by
                 a
                 Right
                 Line
                 ,
                 which
                 being
                 applied
                 to
                 the
                 breadth
                 or
                 height
                 desired
                 to
                 be
                 measured
                 ,
                 shall
                 shew
                 the
                 Perches
                 ,
                 Feet
                 or
                 Inches
                 ,
                 or
                 by
                 some
                 other
                 known
                 measure
                 the
                 breadth
                 or
                 height
                 desired
                 :
                 but
                 if
                 the
                 quantity
                 of
                 some
                 Field
                 or
                 Meadow
                 ,
                 or
                 any
                 other
                 Plain
                 be
                 desired
                 ,
                 the
                 number
                 of
                 square
                 Perches
                 must
                 be
                 enquired
                 ;
                 and
                 lastly
                 ,
                 in
                 measuring
                 of
                 Solids
                 ,
                 we
                 must
                 use
                 the
                 Cube
                 of
                 the
                 measure
                 used
                 ,
                 that
                 we
                 discover
                 the
                 number
                 of
                 those
                 Cubes
                 that
                 are
                 contained
                 in
                 the
                 Body
                 or
                 Solid
                 to
                 be
                 measured
                 .
                 First
                 ,
                 therefore
                 we
                 will
                 speak
                 of
                 the
                 several
                 kinds
                 of
                 measure
                 ,
                 and
                 the
                 making
                 of
                 such
                 Instruments
                 ,
                 by
                 which
                 the
                 quantity
                 of
                 any
                 Magnitude
                 may
                 be
                 known
                 .
              
               
                 2.
                 
                 Now
                 for
                 the
                 measuring
                 of
                 Lines
                 and
                 Superficies
                 ,
                 the
                 Measures
                 in
                 use
                 with
                 us
                 ,
                 are
                 Inches
                 ,
                 Feet
                 ,
                 Yards
                 ,
                 Ells
                 and
                 Perches
                 .
              
               
                 3.
                 
                 An
                 Inch
                 is
                 three
                 Barley
                 Corns
                 in
                 length
                 ,
                 and
                 is
                 either
                 divided
                 into
                 halves
                 and
                 quarters
                 ,
                 which
                 is
                 amongst
                 Artificers
                 most
                 usual
                 ,
                 or
                 into
                 ten
                 equal
                 Parts
                 ,
                 which
                 is
                 in
                 measuring
                 the
                 most
                 useful
                 way
                 of
                 Division
                 .
              
               
                 4.
                 
                 A
                 Foot
                 containeth
                 twelve
                 Inches
                 in
                 length
                 ,
                 and
                 is
                 commonly
                 so
                 divided
                 ;
                 but
                 as
                 for
                 such
                 things
                 as
                 are
                 to
                 be
                 measured
                 by
                 the
                 Foot
                 ,
                 it
                 is
                 far
                 
                 better
                 for
                 use
                 ,
                 when
                 divided
                 into
                 ten
                 equal
                 Parts
                 ,
                 and
                 each
                 tenth
                 into
                 ten
                 more
                 .
              
               
                 5.
                 
                 A
                 Yard
                 containeth
                 three
                 Foot
                 ,
                 and
                 is
                 commonly
                 divided
                 into
                 halves
                 and
                 quarters
                 ,
                 the
                 which
                 for
                 the
                 measuring
                 of
                 such
                 things
                 as
                 are
                 usually
                 sold
                 in
                 Shops
                 doth
                 well
                 enough
                 ,
                 but
                 in
                 the
                 measuring
                 of
                 any
                 Superficies
                 ,
                 it
                 were
                 much
                 better
                 to
                 be
                 divided
                 into
                 10
                 or
                 100
                 equal
                 Parts
                 .
              
               
                 6.
                 
                 An
                 Ell
                 containeth
                 three
                 Foot
                 nine
                 Inches
                 ,
                 aud
                 is
                 usually
                 divided
                 into
                 halves
                 and
                 quarters
                 ,
                 and
                 needs
                 not
                 be
                 otherwise
                 divided
                 ,
                 because
                 we
                 have
                 no
                 use
                 for
                 this
                 Measure
                 ,
                 but
                 in
                 Shop
                 Commodities
                 .
              
               
                 7.
                 
                 A
                 Pole
                 or
                 Perch
                 cotaineth
                 five
                 Yards
                 and
                 an
                 half
                 ,
                 and
                 hath
                 been
                 commonly
                 divided
                 into
                 Feet
                 and
                 half
                 Feet
                 .
                 Forty
                 Poles
                 in
                 length
                 do
                 make
                 one
                 Furlong
                 ,
                 and
                 eight
                 Furlongs
                 in
                 length
                 do
                 make
                 an
                 English
                 Mile
                 ,
                 and
                 for
                 these
                 kinds
                 of
                 of
                 lengths
                 ,
                 a
                 Chain
                 containing
                 four
                 Pole
                 ,
                 divided
                 by
                 Links
                 of
                 a
                 Foot
                 long
                 ,
                 or
                 a
                 Chain
                 of
                 fifty
                 Foot
                 ,
                 or
                 what
                 other
                 length
                 you
                 please
                 ,
                 is
                 well
                 enough
                 ,
                 but
                 in
                 the
                 measuring
                 of
                 Land
                 ,
                 in
                 which
                 the
                 number
                 of
                 square
                 Perches
                 is
                 required
                 ;
                 the
                 Chain
                 called
                 Mr.
                 Gunters
                 ,
                 being
                 four
                 Pole
                 in
                 length
                 divided
                 into
                 100
                 Links
                 ,
                 is
                 not
                 without
                 just
                 reason
                 reputed
                 the
                 most
                 useful
                 .
              
               
                 8.
                 
                 The
                 making
                 of
                 these
                 several
                 Measures
                 is
                 not
                 difficult
                 ,
                 a
                 Foot
                 may
                 be
                 made
                 ,
                 by
                 repeating
                 an
                 Inch
                 upon
                 a
                 Ruler
                 twelve
                 times
                 ,
                 a
                 Yard
                 is
                 eight
                 Foot
                 ,
                 and
                 so
                 of
                 the
                 rest
                 ;
                 the
                 Subdivision
                 of
                 a
                 Foot
                 or
                 Inch
                 into
                 halves
                 and
                 quarters
                 ,
                 may
                 be
                 performed
                 by
                 the
                 seventeenth
                 of
                 the
                 first
                 ,
                 and
                 into
                 ten
                 or
                 any
                 other
                 Parts
                 by
                 the
                 first
                 Proposition
                 of
                 the
                 first
                 Chapter
                 ,
                 and
                 all
                 Scales
                 of
                 equal
                 Parts
                 ,
                 of
                 what
                 scantling
                 you
                 do
                 desire
                 .
                 And
                 this
                 I
                 
                 think
                 is
                 as
                 much
                 as
                 needs
                 to
                 be
                 said
                 concerning
                 the
                 dividing
                 of
                 such
                 Instruments
                 as
                 are
                 useful
                 in
                 the
                 measuring
                 Right
                 Lines
                 .
              
               
                 9.
                 
                 The
                 next
                 thing
                 to
                 be
                 considered
                 is
                 the
                 measuring
                 of
                 Circular
                 Lines
                 ,
                 or
                 Perfect
                 Circles
                 .
              
               
                 10.
                 
                 And
                 every
                 Circle
                 is
                 supposed
                 to
                 be
                 divided
                 into
                 360
                 Parts
                 called
                 Degrees
                 ,
                 every
                 Degree
                 into
                 60
                 Minutes
                 ,
                 every
                 Minute
                 into
                 60
                 Seconds
                 ,
                 and
                 so
                 forward
                 this
                 division
                 of
                 the
                 Circle
                 into
                 360
                 Parts
                 is
                 generally
                 retained
                 ,
                 but
                 the
                 Subdivision
                 of
                 those
                 Parts
                 ,
                 some
                 would
                 have
                 be
                 thus
                 and
                 100
                 ,
                 but
                 as
                 to
                 our
                 present
                 purpose
                 either
                 may
                 be
                 used
                 ,
                 most
                 Instruments
                 not
                 exceeding
                 the
                 fourth
                 part
                 of
                 a
                 Degree
                 .
              
               
                 11.
                 
                 Now
                 then
                 a
                 Circle
                 may
                 be
                 divided
                 into
                 360
                 Parts
                 in
                 this
                 manner
                 ,
                 Having
                 drawn
                 a
                 Diameter
                 through
                 the
                 Center
                 of
                 the
                 Circle
                 dividing
                 the
                 Circle
                 into
                 two
                 equal
                 Parts
                 ,
                 cross
                 that
                 Diameter
                 with
                 another
                 at
                 Right
                 Angles
                 through
                 the
                 Center
                 of
                 the
                 Circle
                 also
                 ,
                 so
                 shall
                 the
                 Circle
                 be
                 divided
                 into
                 four
                 equal
                 Parts
                 or
                 Quadrants
                 ,
                 each
                 Quadrant
                 containing
                 90
                 Degrees
                 ,
                 as
                 in
                 
                   Fig.
                   7.
                   
                   GE.
                   ED.
                   DL
                
                 and
                 LG
                 ,
                 are
                 each
                 of
                 them
                 90
                 Degrees
                 ;
                 and
                 the
                 Radius
                 of
                 a
                 Circle
                 being
                 equal
                 to
                 the
                 Chord
                 of
                 the
                 sixth
                 Part
                 thereof
                 ,
                 that
                 is
                 to
                 the
                 Chord
                 of
                 60
                 Degrees
                 ,
                 as
                 in
                 Fig.
                 14.
                 if
                 you
                 set
                 the
                 
                   Radius
                   GB
                
                 from
                 L
                 towards
                 G
                 ,
                 and
                 also
                 from
                 G
                 towards
                 L
                 ,
                 the
                 Quadrant
                 GL
                 will
                 be
                 subdivided
                 into
                 three
                 equal
                 Parts
                 ,
                 each
                 Part
                 containing
                 30
                 Degrees
                 ,
                 
                   GM
                   .
                   30.
                   
                   MH
                
                 30
                 and
                 
                   HL
                   30
                
                 ,
                 the
                 like
                 may
                 be
                 done
                 in
                 the
                 other
                 Quadrants
                 also
                 ;
                 so
                 will
                 the
                 whole
                 Circle
                 be
                 divided
                 into
                 twelve
                 Parts
                 ,
                 each
                 Part
                 containing
                 30
                 Degrees
                 .
              
               
                 And
                 because
                 the
                 side
                 of
                 a
                 Pentagon
                 inscribed
                 in
                 a
                 Circle
                 is
                 equal
                 to
                 the
                 Chord
                 of
                 72
                 Degrees
                 ,
                 or
                 
                 the
                 first
                 Part
                 of
                 360
                 ,
                 as
                 in
                 Fig.
                 13.
                 therefore
                 if
                 you
                 set
                 the
                 Chord
                 of
                 the
                 first
                 Part
                 of
                 the
                 Circle
                 given
                 from
                 G
                 to
                 L
                 or
                 L
                 to
                 G
                 ,
                 in
                 Fig.
                 7.
                 you
                 will
                 have
                 the
                 Chord
                 of
                 72
                 Degrees
                 ,
                 and
                 the
                 difference
                 between
                 GP
                 72
                 and
                 GH
                 60
                 is
                 HP
                 12
                 ,
                 which
                 being
                 bisected
                 ,
                 will
                 give
                 the
                 Arch
                 of
                 6
                 Degrees
                 ,
                 and
                 the
                 half
                 of
                 six
                 will
                 give
                 three
                 ,
                 and
                 so
                 the
                 Circle
                 will
                 be
                 divided
                 into
                 120
                 Parts
                 ,
                 each
                 Part
                 containing
                 three
                 Degrees
                 ,
                 to
                 which
                 the
                 Chord
                 Line
                 being
                 divided
                 into
                 three
                 Parts
                 ,
                 the
                 Arch
                 by
                 those
                 equal
                 Divisions
                 may
                 be
                 also
                 divided
                 ,
                 and
                 so
                 the
                 whole
                 Circle
                 will
                 be
                 divided
                 into
                 360
                 ,
                 as
                 was
                 desired
                 .
              
               
                 12.
                 
                 A
                 Circle
                 being
                 thus
                 divided
                 into
                 360
                 Parts
                 ,
                 the
                 Lines
                 of
                 Chords
                 ,
                 Sines
                 ,
                 Tangents
                 and
                 Secants
                 ,
                 are
                 so
                 easily
                 made
                 (
                 if
                 what
                 hath
                 been
                 said
                 of
                 them
                 in
                 the
                 Second
                 Chapter
                 be
                 but
                 considered
                 )
                 that
                 I
                 think
                 it
                 needless
                 to
                 say
                 any
                 more
                 concerning
                 their
                 Construction
                 ,
                 but
                 shall
                 rather
                 proceed
                 unto
                 their
                 Use.
                 
              
               
                 13.
                 
                 And
                 the
                 use
                 of
                 these
                 Lines
                 and
                 other
                 Lines
                 of
                 equal
                 Parts
                 we
                 will
                 now
                 shew
                 in
                 circular
                 and
                 right
                 lined
                 Figures
                 ;
                 and
                 first
                 in
                 the
                 measuring
                 of
                 a
                 Circle
                 and
                 Circular
                 Figures
                 .
              
            
             
               
               
                 CHAP.
                 VII
                 .
              
               
                 
                   Of
                   the
                   Measuring
                   of
                   a
                   Circle
                   .
                
              
               
                 THe
                 squaring
                 of
                 a
                 Circle
                 ,
                 or
                 the
                 finding
                 of
                 a
                 Square
                 exactly
                 equal
                 to
                 a
                 Circle
                 given
                 ,
                 is
                 that
                 which
                 many
                 have
                 endeavoured
                 ,
                 but
                 none
                 as
                 yet
                 have
                 attained
                 :
                 Yet
                 Archimedes
                 that
                 Famous
                 Mathematician
                 hath
                 sufficiently
                 proved
                 ,
                 That
                 the
                 Area
                 of
                 a
                 Circle
                 is
                 equal
                 to
                 a
                 Rectangle
                 made
                 of
                 the
                 Rodius
                 and
                 half
                 the
                 Circumference
                 :
                 Or
                 thus
                 ,
                 The
                 Area
                 of
                 a
                 Circle
                 is
                 equal
                 to
                 a
                 Rectangle
                 made
                 of
                 the
                 Diameter
                 and
                 the
                 fourth
                 part
                 of
                 the
                 Circumference
                 .
                 For
                 Example
                 ,
                 let
                 the
                 Diameter
                 of
                 a
                 Circle
                 be
                 14
                 and
                 the
                 Circumference
                 44
                 ;
                 if
                 you
                 multiply
                 half
                 the
                 Circumference
                 22
                 by
                 7
                 half
                 the
                 Diameter
                 ,
                 the
                 Product
                 is
                 154
                 ;
                 or
                 if
                 you
                 multiply
                 11
                 the
                 fourth
                 part
                 of
                 the
                 Circumference
                 ,
                 by
                 14
                 the
                 whole
                 Diameter
                 ,
                 the
                 Product
                 will
                 still
                 be
                 154.
                 
                 And
                 hence
                 the
                 Superficies
                 of
                 any
                 Circle
                 may
                 be
                 found
                 though
                 not
                 exactly
                 ,
                 yet
                 near
                 enough
                 for
                 any
                 use
                 .
              
               
                 2.
                 
                 But
                 
                   Ludolphus
                   Van
                   Culen
                
                 finds
                 the
                 Circumference
                 of
                 a
                 Circle
                 whose
                 Diameter
                 is
                 1.00
                 to
                 be
                 3.14159
                 the
                 half
                 whereof
                 1.57095
                 being
                 multiplied
                 by
                 half
                 the
                 Diameter
                 50
                 ,
                 &c.
                 the
                 Product
                 is
                 7.85395
                 which
                 is
                 the
                 Area
                 of
                 that
                 Circle
                 ,
                 and
                 from
                 these
                 given
                 Numbers
                 ,
                 the
                 Area
                 ,
                 Circumference
                 and
                 Diameter
                 of
                 any
                 other
                 Circle
                 may
                 be
                 found
                 by
                 the
                 Proportions
                 in
                 the
                 Propositions
                 following
                 .
              
               
                 
                 
                   Proposition
                   I.
                   
                
                 
                   
                     The
                     Diameter
                     of
                     a
                     Circle
                     being
                     given
                     to
                     find
                     the
                     Circumference
                     .
                  
                
                 
                   As
                   1.
                   to
                   3.14159
                   :
                   so
                   is
                   the
                   Diameter
                   to
                   the
                   Circumference
                   .
                   Example
                   .
                   In
                   Fig.
                   13.
                   
                   Let
                   the
                   Diameter
                   IB
                   be
                   13.
                   25.
                   
                   I
                   say
                   as
                   1.
                   to
                   3.
                   14159.
                   so
                   IB
                   .
                   13.25
                   to
                   41.626
                   the
                   Circumference
                   of
                   that
                   Circle
                   .
                
              
               
                 
                   Proposition
                   II.
                   
                
                 
                   
                     The
                     Diameter
                     of
                     a
                     Circle
                     being
                     given
                     to
                     find
                     the
                     Superficial
                     Content
                     .
                  
                
                 
                   As
                   1.
                   to
                   78539
                   ;
                   so
                   is
                   the
                   Square
                   of
                   the
                   Diameter
                   given
                   ,
                   to
                   the
                   Superficial
                   Content
                   required
                   .
                   Example
                   ,
                   Let
                   the
                   Diameter
                   given
                   be
                   as
                   before
                   
                     IB
                     13.25
                  
                   the
                   Square
                   thereof
                   is
                   175.5625
                   therefore
                   .
                
                 
                   As
                   1.
                   to
                   78539
                   :
                   so
                   175.5625
                   to
                   137.88
                   the
                   Superficial
                   Content
                   of
                   that
                   Circle
                   .
                
              
               
                 
                   Proposition
                   III.
                   
                
                 
                   
                     The
                     Circumference
                     of
                     a
                     Circle
                     being
                     given
                     ,
                     to
                     find
                     the
                     Diameter
                     .
                  
                
                 
                   This
                   is
                   but
                   the
                   Converse
                   of
                   the
                   first
                   Proposition
                   :
                   Therefore
                   as
                   3.14159
                   is
                   to
                   1
                   :
                   so
                   is
                   the
                   Circumference
                   to
                   the
                   Diameter
                   ;
                   and
                   making
                   the
                   Circumference
                   an
                   Unite
                   ,
                   it
                   is
                   .
                   3.
                   14159.
                   1
                   
                   ∷
                   1.
                   318308
                   ,
                   and
                   so
                   an
                   Unite
                   may
                   be
                   brought
                   into
                   the
                   first
                   place
                   .
                   Example
                   ,
                   Let
                   the
                   given
                   Circumference
                   
                   be
                   41.
                   626.
                   
                   I
                   say
                   ,
                
                 
                   As
                   1.
                   to
                   318308
                   :
                   so
                   41.626
                   to
                   13.
                   25.
                   the
                   Diameter
                   required
                   .
                
              
               
                 
                   Proposition
                   IV.
                   
                
                 
                   
                     The
                     Circumference
                     of
                     a
                     Circle
                     being
                     given
                     to
                     find
                     the
                     Superficial
                     Content
                     .
                  
                
                 
                   As
                   the
                   Square
                   of
                   the
                   Circumference
                   of
                   a
                   Circle
                   given
                   is
                   to
                   the
                   Superficial
                   Content
                   of
                   that
                   Circle
                   :
                   so
                   is
                   the
                   Square
                   of
                   the
                   Circumference
                   of
                   another
                   Circle
                   given
                   to
                   the
                   Superficial
                   Content
                   required
                   .
                   Example
                   ,
                   As
                   the
                   Square
                   of
                   3.14159
                   is
                   to
                   7853938
                   :
                   so
                   is
                   1.
                   the
                   Square
                   of
                   another
                   Circle
                   to
                   079578
                   the
                   Superficial
                   Content
                   required
                   ,
                   and
                   so
                   an
                   Unite
                   for
                   the
                   most
                   easie
                   working
                   may
                   be
                   brought
                   into
                   the
                   first
                   place
                   :
                   Thus
                   the
                   given
                   Circumference
                   being
                   41.
                   626.
                   
                   I
                   say
                   ,
                
                 
                   As
                   1.
                   to
                   0.79578
                   :
                   so
                   is
                   the
                   Square
                   of
                   41.626
                   to
                   137.88
                   the
                   Superficial
                   Content
                   required
                   .
                
              
               
                 
                   Proposition
                   V.
                   
                
                 
                   
                     The
                     Superficial
                     Content
                     of
                     a
                     Circle
                     being
                     given
                     ,
                     to
                     find
                     the
                     Diameter
                     .
                  
                
                 
                   This
                   is
                   the
                   Converse
                   of
                   the
                   second
                   Proposition
                   ,
                   therefore
                   as
                   78539
                   is
                   to
                   1.
                   so
                   is
                   the
                   Superficial
                   Content
                   given
                   ,
                   to
                   the
                   Square
                   of
                   the
                   Diameter
                   required
                   .
                   And
                   to
                   bring
                   an
                   Unite
                   in
                   the
                   first
                   place
                   :
                   I
                   say
                   .
                
                 
                   As
                   7853978.
                   1
                   
                   ∷
                   1.
                   1.
                   27324
                   ,
                   and
                   therefore
                   if
                   the
                   Superficial
                   Content
                   given
                   be
                   137.88
                   ,
                   to
                   find
                   the
                   Diameter
                   :
                   I
                   say
                   ,
                
                 
                 
                   As
                   1.
                   to
                   1.27324
                   :
                   so
                   137.88
                   to
                   175.5625
                   whose
                   Square
                   Root
                   is
                   13.25
                   ,
                   the
                   Diameter
                   sought
                   .
                
              
               
                 
                   Proposition
                   VI.
                   
                
                 
                   
                     The
                     Superficial
                     Content
                     of
                     a
                     Circle
                     being
                     given
                     ,
                     to
                     find
                     the
                     Circumference
                     .
                  
                
                 
                   This
                   is
                   the
                   Converse
                   of
                   the
                   Fourth
                   Proposition
                   ,
                   and
                   therefore
                   as
                   079578
                   is
                   to
                   1
                   :
                   so
                   is
                   the
                   Superficial
                   Content
                   given
                   ,
                   to
                   the
                   Square
                   of
                   the
                   Circumference
                   required
                   ,
                   and
                   to
                   bring
                   an
                   Unite
                   in
                   the
                   first
                   place
                   :
                   I
                   say
                   ,
                
                 
                   As
                   079578.
                   1
                   
                   :
                   :
                   1.
                   12.5664
                   ,
                   and
                   therefore
                   if
                   the
                   Superficial
                   Content
                   given
                   be
                   137.88
                   ,
                   to
                   find
                   that
                   Circumference
                   :
                   I
                   say
                   ,
                
                 
                   As
                   1.
                   to
                   12.5664
                   :
                   so
                   is
                   the
                   137.88
                   to
                   1732.7
                   whose
                   Square
                   Root
                   is
                   626
                   the
                   Circumference
                   .
                
              
               
                 
                   Proposition
                   VII
                   .
                
                 
                   
                     The
                     Diameter
                     of
                     a
                     Circle
                     being
                     given
                     to
                     find
                     the
                     Side
                     of
                     the
                     Square
                     ,
                     which
                     may
                     be
                     inscribed
                     within
                     the
                     same
                     Circle
                     .
                  
                
                 
                   The
                   Chord
                   or
                   Subtense
                   of
                   the
                   Fourth
                   Part
                   of
                   a
                   Circle
                   ,
                   whose
                   Diameter
                   is
                   an
                   Unite
                   ,
                   is
                   7071067
                   ,
                   and
                   therefore
                   ,
                   as
                   1.
                   to
                   7071067
                   :
                   so
                   is
                   the
                   Diameter
                   of
                   another
                   Circle
                   ,
                   to
                   the
                   Side
                   required
                   .
                   Example
                   ,
                   let
                   the
                   Diameter
                   given
                   be
                   13.25
                   to
                   find
                   the
                   side
                   of
                   a
                   Square
                   which
                   may
                   be
                   inscribed
                   in
                   that
                   Circle
                   :
                   I
                   say
                   ,
                
                 
                   As
                   1.
                   to
                   7071067
                   :
                   so
                   is
                   13.25
                   to
                   9.3691
                   the
                   side
                   required
                   .
                
              
               
                 
                 
                   Proposition
                   VIII
                   .
                
                 
                   
                     The
                     Circumference
                     of
                     a
                     Circle
                     being
                     given
                     ,
                     to
                     find
                     the
                     Side
                     of
                     the
                     Square
                     which
                     may
                     be
                     inscribed
                     in
                     the
                     same
                     Circle
                     .
                  
                
                 
                   As
                   the
                   Circumference
                   of
                   a
                   Circle
                   whose
                   Diameter
                   is
                   an
                   Unite
                   ,
                   is
                   to
                   the
                   side
                   inscribed
                   in
                   that
                   Circle
                   ;
                   so
                   is
                   the
                   Circumference
                   of
                   any
                   other
                   Circle
                   ,
                   to
                   the
                   side
                   of
                   the
                   Square
                   that
                   may
                   be
                   inscribed
                   therein
                   .
                   Therefore
                   an
                   Unite
                   being
                   made
                   the
                   Circumference
                   of
                   a
                   Circle
                   .
                
                 
                   As
                   3.14159
                   to
                   7071067
                   :
                   so
                   1.
                   to
                   225078.
                   
                
                 
                   And
                   therefore
                   the
                   Circumference
                   of
                   a
                   Circle
                   being
                   as
                   before
                   41.626
                   ,
                   to
                   find
                   the
                   side
                   of
                   the
                   Square
                   that
                   may
                   be
                   inscribed
                   :
                   I
                   say
                   ,
                
                 
                   As
                   1.
                   to
                   225078.
                   so
                   is
                   41.626
                   to
                   9.3691
                   the
                   side
                   inquired
                   .
                
              
               
                 
                   Proposition
                   IX
                   .
                
                 
                   
                     The
                     Axis
                     of
                     a
                     Sphere
                     or
                     Globe
                     being
                     given
                     ,
                     to
                     find
                     the
                     Superficial
                     Content
                     .
                  
                
                 
                   As
                   the
                   Square
                   of
                   the
                   Diameter
                   of
                   a
                   Circle
                   ,
                   which
                   is
                   Unity
                   ,
                   is
                   to
                   3.14159
                   the
                   Superficial
                   Content
                   ,
                   so
                   is
                   the
                   Square
                   of
                   any
                   other
                   Axis
                   given
                   ,
                   to
                   the
                   Superficial
                   Content
                   required
                   .
                   Example
                   ,
                   Let
                   13.25
                   be
                   the
                   Diameter
                   given
                   ,
                   to
                   find
                   the
                   Content
                   of
                   such
                   a
                   Globe
                   :
                   I
                   say
                   ,
                
                 
                   As
                   1.
                   to
                   3.14159
                   :
                   so
                   is
                   the
                   Square
                   of
                   13.25
                   to
                   551.54
                   the
                   Superficial
                   Content
                   required
                   .
                
              
               
                 
                 
                   Proposition
                   X.
                   
                
                 
                   
                     To
                     find
                     the
                     Area
                     of
                     an
                     Ellipsis
                     .
                  
                
                 
                   As
                   the
                   Square
                   of
                   the
                   Diameter
                   of
                   a
                   Circle
                   ,
                   is
                   to
                   the
                   Superficial
                   Content
                   of
                   that
                   Circle
                   ;
                   so
                   is
                   the
                   Rectangle
                   made
                   of
                   the
                   Conjugate
                   Diameters
                   in
                   an
                   Ellipsis
                   ,
                   to
                   the
                   Area
                   of
                   that
                   Ellipsis
                   ;
                   And
                   the
                   Diameter
                   of
                   a
                   Circle
                   being
                   one
                   ,
                   the
                   Area
                   is
                   7853975
                   ,
                   therefore
                   in
                   Fig.
                   26.
                   the
                   Diameters
                   AC8
                   and
                   BD5
                   being
                   given
                   ,
                   the
                   Area
                   of
                   the
                   
                     Ellipsis
                     ABCD
                  
                   may
                   thus
                   be
                   found
                   .
                
                 
                   As
                   1.
                   to
                   7853975
                   :
                   so
                   is
                   the
                   Rectangle
                   AC
                   in
                   BD40
                   to
                   3.1415900
                   ,
                   the
                   Area
                   of
                   the
                   Ellipsis
                   required
                   .
                
              
            
             
               
                 CHAP.
                 VIII
                 .
              
               
                 
                   Of
                   the
                   Measuring
                   of
                   Plain
                   Triangles
                   .
                
              
               
                 HAving
                 shewed
                 the
                 measuring
                 of
                 a
                 Circle
                 ,
                 and
                 Ellipsis
                 ,
                 we
                 come
                 now
                 to
                 Right
                 lined
                 Figures
                 ,
                 as
                 the
                 Triangle
                 ,
                 Quadrangle
                 ,
                 and
                 Multangled
                 Figures
                 ,
                 and
                 first
                 of
                 the
                 measuring
                 of
                 the
                 plain
                 Triangles
                 .
              
               
                 2.
                 
                 And
                 the
                 measuring
                 of
                 Plain
                 Triangles
                 is
                 either
                 in
                 the
                 measuring
                 of
                 the
                 Sides
                 and
                 Angles
                 ,
                 or
                 of
                 their
                 Area
                 and
                 Superficial
                 Content
                 .
              
               
                 3.
                 
                 Plain
                 Triangles
                 in
                 respect
                 of
                 their
                 Sides
                 and
                 Angles
                 are
                 to
                 be
                 measured
                 by
                 two
                 sorts
                 of
                 Lines
                 ,
                 the
                 one
                 is
                 a
                 Line
                 of
                 equal
                 Parts
                 ,
                 and
                 by
                 that
                 the
                 Sides
                 must
                 be
                 measured
                 ,
                 the
                 other
                 is
                 a
                 Line
                 of
                 Chords
                 ,
                 the
                 Construction
                 whereof
                 hath
                 
                 been
                 shewed
                 in
                 the
                 sixth
                 Chapter
                 ,
                 and
                 by
                 that
                 the
                 Angles
                 must
                 be
                 measured
                 ,
                 the
                 Angles
                 may
                 indeed
                 be
                 measured
                 by
                 the
                 Lines
                 of
                 Sines
                 ,
                 Tangents
                 or
                 Secants
                 ,
                 but
                 the
                 Line
                 of
                 Chords
                 being
                 not
                 only
                 sufficient
                 ,
                 but
                 most
                 ready
                 ,
                 it
                 shall
                 suffice
                 to
                 shew
                 how
                 any
                 Angle
                 may
                 be
                 protracted
                 by
                 a
                 Line
                 of
                 Chords
                 ,
                 or
                 the
                 Quantity
                 of
                 any
                 Angle
                 found
                 ,
                 which
                 is
                 protracted
                 .
              
               
                 4.
                 
                 And
                 first
                 to
                 protract
                 or
                 lay
                 down
                 an
                 Angle
                 to
                 the
                 Quantity
                 or
                 Number
                 of
                 Degrees
                 proposed
                 ,
                 do
                 thus
                 ,
                 draw
                 a
                 Line
                 at
                 pleasure
                 as
                 AD
                 in
                 Figure
                 5
                 ,
                 then
                 open
                 your
                 Compasses
                 to
                 the
                 Number
                 of
                 60
                 Degrees
                 in
                 the
                 Line
                 of
                 Chords
                 ,
                 and
                 setting
                 one
                 Foot
                 in
                 A
                 ,
                 with
                 the
                 other
                 describe
                 the
                 Arch
                 BG
                 ,
                 and
                 from
                 the
                 Point
                 A
                 let
                 it
                 be
                 required
                 to
                 make
                 an
                 Angle
                 of
                 36
                 Degrees
                 :
                 open
                 your
                 Compasses
                 to
                 that
                 extent
                 in
                 the
                 Line
                 of
                 Chords
                 ,
                 and
                 setting
                 one
                 Foot
                 in
                 B
                 ,
                 with
                 the
                 other
                 make
                 a
                 mark
                 at
                 G
                 ,
                 and
                 draw
                 the
                 Line
                 AG
                 ,
                 so
                 shall
                 the
                 Angle
                 BAG
                 contain
                 36
                 Degrees
                 ,
                 as
                 was
                 required
                 .
              
               
                 5.
                 
                 If
                 the
                 Quantity
                 of
                 an
                 Angle
                 were
                 required
                 ,
                 as
                 suppose
                 the
                 Angle
                 BAG
                 ,
                 open
                 your
                 Compasses
                 in
                 the
                 Line
                 of
                 Chords
                 to
                 the
                 extent
                 of
                 60
                 Degrees
                 ,
                 and
                 setting
                 one
                 Foot
                 in
                 A
                 ,
                 with
                 the
                 other
                 draw
                 the
                 Arch
                 BG
                 ,
                 then
                 take
                 in
                 your
                 Compasses
                 the
                 distance
                 of
                 BG
                 ,
                 and
                 apply
                 that
                 extent
                 to
                 the
                 Line
                 of
                 Chords
                 ,
                 and
                 it
                 will
                 shew
                 the
                 Number
                 of
                 Degrees
                 contained
                 in
                 that
                 Angle
                 ,
                 which
                 in
                 our
                 Example
                 is
                 36
                 Degrees
                 .
              
               
                 6.
                 
                 In
                 every
                 Plain
                 Triangle
                 ,
                 the
                 three
                 Angles
                 are
                 equal
                 to
                 two
                 right
                 or
                 180
                 Degrees
                 ,
                 therefore
                 one
                 Angle
                 being
                 given
                 ,
                 the
                 sum
                 of
                 the
                 other
                 two
                 is
                 also
                 given
                 ,
                 and
                 two
                 Angles
                 being
                 given
                 ,
                 the
                 third
                 is
                 given
                 also
                 .
              
               
               
                 7.
                 
                 Plain
                 Triangles
                 are
                 either
                 Right
                 Angled
                 or
                 Oblique
                 .
              
               
                 8.
                 
                 In
                 a
                 Right
                 Angled
                 Plain
                 Triangle
                 ,
                 one
                 of
                 the
                 Acute
                 Angles
                 is
                 the
                 Complement
                 of
                 the
                 other
                 to
                 a
                 Quadrant
                 or
                 90
                 Degrees
                 .
              
               
                 9.
                 
                 In
                 Right
                 Angled
                 Plain
                 Triangles
                 ,
                 the
                 Side
                 subtending
                 the
                 Right
                 Angle
                 we
                 call
                 the
                 Hypotenuse
                 ,
                 and
                 the
                 other
                 two
                 Sides
                 the
                 Legs
                 ,
                 thus
                 in
                 
                   Fig.
                   5
                   ▪
                   AE
                
                 is
                 the
                 Hypotenuse
                 ,
                 and
                 AD
                 and
                 ED
                 are
                 the
                 Legs
                 ;
                 these
                 things
                 premised
                 ,
                 the
                 several
                 cases
                 in
                 Right
                 Angled
                 and
                 Oblique
                 Angled
                 Plain
                 Triangles
                 may
                 be
                 resolved
                 ,
                 by
                 the
                 Propositions
                 following
                 .
              
               
                 
                   Proposition
                   I.
                   
                
                 
                   
                     In
                     a
                     Right
                     Angled
                     Plain
                     Triangle
                     ,
                     the
                     Angles
                     of
                     one
                     Leg
                     being
                     given
                     ,
                     to
                     find
                     the
                     Hypotenuse
                     and
                     the
                     other
                     Leg.
                     
                  
                
                 
                   In
                   the
                   Right
                   Angled
                   Plain
                   Triangle
                   ADE
                   in
                   Fig.
                   5.
                   
                   Let
                   the
                   given
                   Angles
                   be
                   DAE
                   36
                   ,
                   and
                   DEA
                   54
                   ,
                   and
                   let
                   the
                   given
                   Leg
                   be
                   AD
                   476
                   ;
                   to
                   find
                   the
                   
                     Hypotenuse
                     AE
                  
                   ,
                   and
                   the
                   other
                   Leg
                   ED.
                   
                
                 
                   Draw
                   a
                   Line
                   at
                   pleasure
                   ,
                   as
                   AD
                   ,
                   and
                   by
                   your
                   Scale
                   of
                   equal
                   Parts
                   set
                   from
                   A
                   to
                   D
                   476
                   the
                   Quantity
                   of
                   the
                   Leg
                   given
                   ,
                   then
                   erect
                   a
                   Perpendicular
                   upon
                   the
                   Point
                   D
                   ,
                   and
                   upon
                   the
                   Point
                   A
                   lay
                   down
                   your
                   given
                   Angle
                   DAE
                   36
                   by
                   the
                   fourth
                   hereof
                   ,
                   and
                   draw
                   the
                   Line
                   AE
                   till
                   it
                   cut
                   the
                   Perpendicular
                   DE
                   ,
                   then
                   measure
                   the
                   Lines
                   AE
                   and
                   DE
                   upon
                   your
                   Scale
                   of
                   Equal
                   Parts
                   ,
                   so
                   shall
                   AE
                   588.3
                   be
                   the
                   Hypotenuse
                   ,
                   and
                   DE
                   345.8
                   the
                   other
                   Leg.
                   
                
              
               
                 
                 
                   Proposition
                   II.
                   
                
                 
                   
                     The
                     Hypotenuse
                     and
                     Oblique
                     Angles
                     given
                     ,
                     to
                     find
                     the
                     Legs
                     .
                  
                
                 
                   Let
                   the
                   given
                   Hypotenuse
                   be
                   588
                   ,
                   and
                   one
                   of
                   the
                   Angles
                   36
                   degrees
                   ,
                   the
                   other
                   will
                   then
                   be
                   54
                   degrees
                   ,
                   Draw
                   a
                   Line
                   at
                   pleasure
                   ,
                   as
                   AD
                   ,
                   and
                   upon
                   the
                   Point
                   A
                   by
                   the
                   fourth
                   ▪
                   hereof
                   lay
                   down
                   one
                   of
                   the
                   given
                   Angles
                   suppose
                   the
                   less
                   ,
                   and
                   draw
                   the
                   Line
                   AC
                   ,
                   and
                   from
                   your
                   Scale
                   of
                   equal
                   Parts
                   ,
                   set
                   off
                   your
                   Hypotenuse
                   588
                   from
                   A
                   to
                   E
                   ,
                   and
                   from
                   the
                   Point
                   E
                   to
                   the
                   Line
                   AD
                   let
                   fall
                   the
                   Perpendicular
                   ED
                   ,
                   then
                   shall
                   AD
                   being
                   measured
                   upon
                   the
                   Scale
                   be
                   476
                   for
                   one
                   Leg
                   ,
                   and
                   ED
                   345.8
                   the
                   other
                   .
                
              
               
                 
                   Proposition
                   III.
                   
                
                 
                   
                     The
                     Hypotenuse
                     and
                     one
                     Leg
                     given
                     to
                     find
                     the
                     Angles
                     and
                     the
                     other
                     Leg.
                     
                  
                
                 
                   Let
                   the
                   given
                   Hypotenuse
                   be
                   588.
                   and
                   the
                   given
                   Leg
                   476.
                   
                   Draw
                   a
                   Line
                   at
                   pleasure
                   as
                   AD
                   ,
                   upon
                   which
                   set
                   the
                   given
                   Leg
                   from
                   A
                   to
                   D.
                   476
                   ,
                   and
                   upon
                   the
                   Point
                   D
                   ,
                   erect
                   the
                   Perpendicular
                   DE
                   ,
                   then
                   open
                   your
                   Compasses
                   in
                   the
                   Scale
                   of
                   Equal
                   Parts
                   to
                   the
                   Extent
                   of
                   your
                   given
                   Hypotenuse
                   588
                   ,
                   and
                   setting
                   one
                   Foot
                   of
                   that
                   Extent
                   in
                   A
                   ,
                   move
                   the
                   other
                   till
                   it
                   touch
                   the
                   Perpendicular
                   DE
                   ,
                   then
                   and
                   there
                   draw
                   AE
                   ,
                   so
                   shall
                   ED
                   be
                   345.8
                   the
                   Leg
                   inquired
                   ,
                   and
                   the
                   Angle
                   DAE
                   ,
                   will
                   be
                   found
                   by
                   the
                   Line
                   of
                   Chords
                   to
                   be
                   36
                   ▪
                   whose
                   Complement
                   is
                   the
                   Angle
                   DEA
                   .
                   54.
                   
                
              
               
                 
                 
                   Proposition
                   IV.
                   
                
                 
                   
                     The
                     Legs
                     given
                     to
                     find
                     the
                     Hypotenuse
                     ,
                     and
                     the
                     Oblique
                     Angles
                     .
                  
                
                 
                   Let
                   one
                   of
                   the
                   given
                   Legs
                   be
                   476
                   ,
                   and
                   the
                   other
                   345.8
                   ,
                   Draw
                   the
                   Line
                   AD
                   to
                   the
                   extent
                   of
                   476
                   ,
                   and
                   upon
                   the
                   Point
                   D
                   ,
                   erect
                   the
                   Perpendicular
                   DE
                   to
                   the
                   extent
                   of
                   345.8
                   ,
                   and
                   draw
                   the
                   Line
                   AE
                   ,
                   so
                   shall
                   AE
                   be
                   the
                   Hypotenuse
                   588
                   ,
                   and
                   the
                   Angle
                   DAE
                   will
                   by
                   the
                   Line
                   of
                   Chords
                   be
                   found
                   to
                   be
                   36
                   Degrees
                   ,
                   and
                   the
                   Angle
                   DEA
                   54
                   ,
                   as
                   before
                   .
                
                 
                   Hitherto
                   we
                   have
                   spoken
                   of
                   Right
                   angled
                   plain
                   Triangles
                   :
                   the
                   Propositions
                   following
                   concern
                   such
                   as
                   are
                   Oblique
                   .
                
              
               
                 
                   Proposition
                   V.
                   
                
                 
                   
                     Two
                     Angles
                     in
                     an
                     Oblique
                     angled
                     plain
                     Triangle
                     ,
                     being
                     given
                     ,
                     with
                     any
                     one
                     of
                     the
                     three
                     Sides
                     ,
                     to
                     find
                     the
                     other
                     two
                     Sides
                     .
                  
                
                 
                   In
                   any
                   Oblique
                   angled
                   plain
                   Triangle
                   ,
                   let
                   one
                   of
                   the
                   given
                   Angles
                   be
                   26.50
                   and
                   the
                   other
                   38.
                   and
                   let
                   the
                   given
                   Side
                   be
                   632
                   ,
                   the
                   Sum
                   of
                   the
                   two
                   given
                   Angles
                   being
                   deducted
                   from
                   a
                   Semi-circle
                   ,
                   leaveth
                   for
                   the
                   third
                   Angle
                   115.50
                   Degrees
                   ,
                   then
                   draw
                   the
                   Line
                   BC
                   632.
                   and
                   upon
                   the
                   Points
                   B
                   and
                   C
                   protract
                   the
                   given
                   Angles
                   ,
                   and
                   draw
                   the
                   Lines
                   BD
                   and
                   CD
                   ,
                   which
                   being
                   measured
                   upon
                   your
                   Scale
                   of
                   equal
                   Parts
                   BD
                   will
                   be
                   fou●d
                   to
                   be
                   312.43
                   ,
                   and
                   BD
                   431.09
                   ,
                
              
               
                 
                 
                   Proposition
                   VI.
                   
                
                 
                   
                     Two
                     Sides
                     in
                     an
                     Oblique
                     Angled
                     Triangle
                     being
                     given
                     ,
                     with
                     an
                     Angle
                     opposite
                     to
                     one
                     of
                     them
                     ,
                     to
                     find
                     the
                     other
                     Angles
                     and
                     the
                     third
                     Side
                     ,
                     if
                     it
                     be
                     known
                     whether
                     the
                     Angle
                     Opposite
                     to
                     the
                     other
                     Side
                     given
                     be
                     Acute
                     or
                     Obtuse
                     .
                  
                
                 
                   In
                   an
                   Oblique
                   Angled
                   Plain
                   Triangle
                   ,
                   let
                   the
                   given
                   Angle
                   be
                   38
                   Degrees
                   ,
                   and
                   let
                   the
                   Side
                   adjacent
                   to
                   that
                   Angle
                   be
                   632
                   ,
                   and
                   the
                   Side
                   opposite
                   431.
                   1.
                   upon
                   the
                   Line
                   BC
                   in
                   Fig.
                   25.
                   protract
                   the
                   given
                   Angle
                   38
                   Degrees
                   upon
                   the
                   Point
                   C
                   ,
                   and
                   draw
                   the
                   Line
                   DC
                   ,
                   then
                   open
                   your
                   Compasses
                   to
                   the
                   Extent
                   of
                   the
                   other
                   Side
                   given
                   431.
                   1.
                   and
                   setting
                   one
                   Foot
                   in
                   B
                   ,
                   turn
                   the
                   other
                   about
                   till
                   it
                   touch
                   the
                   Line
                   DC
                   ,
                   which
                   will
                   be
                   in
                   two
                   places
                   ,
                   in
                   the
                   Points
                   D
                   and
                   E
                   ;
                   if
                   therefore
                   the
                   Angle
                   at
                   B
                   be
                   Acute
                   the
                   third
                   Side
                   of
                   the
                   Triangle
                   will
                   he
                   CE
                   ,
                   according
                   therefore
                   to
                   the
                   Species
                   of
                   that
                   Angle
                   you
                   must
                   draw
                   the
                   Line
                   BD
                   or
                   BE
                   to
                   compleat
                   the
                   Triangle
                   ,
                   and
                   then
                   you
                   may
                   measure
                   the
                   other
                   Angles
                   ,
                   and
                   the
                   third
                   Side
                   as
                   hath
                   been
                   shewed
                   .
                
              
               
                 
                   Proposition
                   VII
                   .
                
                 
                   
                     Two
                     Sides
                     of
                     an
                     Oblique
                     Angled
                     Plain
                     Triangle
                     being
                     given
                     ,
                     with
                     the
                     Angle
                     comprehended
                     by
                     them
                     to
                     find
                     the
                     other
                     Angles
                     and
                     the
                     third
                     Side
                     .
                  
                
                 
                   Let
                   one
                   of
                   the
                   given
                   Sides
                   be
                   632
                   ,
                   and
                   the
                   other
                   431.1
                   ,
                   and
                   let
                   the
                   Angle
                   comprehended
                   by
                   them
                   be
                   Deg.
                   26.50
                   ,
                   draw
                   a
                   Line
                   at
                   pleasure
                   ,
                   
                   as
                   BC
                   ,
                   and
                   by
                   help
                   of
                   your
                   Scale
                   of
                   Equal
                   Parts
                   ,
                   set
                   off
                   one
                   of
                   your
                   given
                   Sides
                   from
                   B
                   to
                   C
                   632.
                   then
                   upon
                   the
                   Point
                   B
                   protract
                   the
                   given
                   Angle
                   26.
                   50.
                   and
                   draw
                   the
                   Line
                   BD
                   ,
                   and
                   from
                   B
                   to
                   D
                   ,
                   set
                   off
                   your
                   other
                   given
                   Side
                   431.
                   1.
                   and
                   draw
                   the
                   Line
                   DC
                   ,
                   so
                   have
                   you
                   constituted
                   the
                   Triangle
                   BDC
                   ,
                   in
                   which
                   you
                   may
                   measure
                   the
                   Angles
                   and
                   the
                   third
                   Side
                   ,
                   as
                   hath
                   been
                   shewed
                   .
                
              
               
                 
                   Proposition
                   VIII
                   .
                
                 
                   
                     The
                     three
                     Sides
                     of
                     an
                     Oblique
                     Angled
                     Triangle
                     being
                     given
                     ,
                     to
                     find
                     the
                     Angles
                     .
                  
                
                 
                   Let
                   the
                   length
                   of
                   one
                   of
                   the
                   given
                   Sides
                   be
                   632
                   ,
                   the
                   length
                   of
                   another
                   431.1
                   ,
                   and
                   the
                   length
                   of
                   the
                   third
                   312.4
                   ,
                   and
                   Draw
                   a
                   Line
                   at
                   pleasure
                   ,
                   as
                   BC
                   in
                   Fig.
                   25
                   ,
                   and
                   by
                   help
                   of
                   your
                   Scale
                   of
                   Equal
                   Parts
                   ,
                   set
                   off
                   the
                   greatest
                   Side
                   given
                   632
                   from
                   B
                   to
                   C.
                   then
                   open
                   your
                   Compasses
                   in
                   the
                   same
                   Scale
                   to
                   the
                   extent
                   of
                   either
                   of
                   the
                   other
                   Sides
                   ,
                   and
                   setting
                   one
                   Foot
                   of
                   your
                   Compasses
                   in
                   B
                   ,
                   with
                   the
                   other
                   describe
                   an
                   occult
                   Arch
                   ,
                   then
                   extend
                   your
                   Compasses
                   in
                   the
                   same
                   Scale
                   to
                   the
                   length
                   of
                   the
                   third
                   Side
                   ,
                   and
                   setting
                   one
                   Foot
                   in
                   C
                   with
                   the
                   other
                   describe
                   another
                   Arch
                   cutting
                   the
                   former
                   ,
                   and
                   from
                   the
                   Point
                   of
                   Intersection
                   draw
                   the
                   Lines
                   BD
                   and
                   DC
                   .
                   to
                   constitute
                   the
                   Triangle
                   BDC
                   ,
                   whose
                   Angles
                   may
                   be
                   measured
                   ,
                   as
                   hath
                   heen
                   shewed
                   .
                
                 
                   And
                   thus
                   may
                   all
                   the
                   Cases
                   of
                   Plain
                   Triangles
                   be
                   resolved
                   by
                   Scale
                   and
                   Compass
                   ,
                   he
                   that
                   desires
                   to
                   resolve
                   them
                   Arithmetically
                   ,
                   by
                   my
                   
                     Trigometria
                     Britannica
                  
                   ,
                   or
                   my
                   little
                   Geometrical
                   ,
                   Trigonometry
                   ;
                   only
                   one
                   Case
                   of
                   Right
                   Angled
                   Plain
                   
                   Triangles
                   which
                   I
                   shall
                   have
                   occasion
                   to
                   use
                   ,
                   in
                   the
                   finding
                   of
                   the
                   Area
                   of
                   the
                   Segment
                   of
                   a
                   Circle
                   I
                   will
                   here
                   shew
                   how
                   ,
                   to
                   resolve
                   by
                   Numbers
                   .
                
              
               
                 
                   Proposition
                   IX
                   .
                
                 
                   
                     In
                     a
                     Right
                     Angled
                     Plain
                     Angle
                     the
                     Hypotenuse
                     and
                     one
                     Leg
                     being
                     given
                     to
                     find
                     the
                     other
                     Leg.
                     
                  
                
                 
                   Take
                   the
                   Sums
                   and
                   difference
                   of
                   the
                   Hypotenuse
                   and
                   Leg
                   given
                   ,
                   then
                   multiply
                   the
                   Sum
                   by
                   the
                   Difference
                   ,
                   and
                   of
                   the
                   Product
                   extract
                   the
                   Square
                   Root
                   ,
                   which
                   Square
                   Root
                   shall
                   be
                   the
                   Leg
                   inquired
                   .
                
                 
                   Example
                   .
                   In
                   Fig.
                   5.
                   
                   Let
                   the
                   given
                   Hypotenuse
                   be
                   AE
                   588.3
                   ,
                   and
                   the
                   given
                   Leg
                   AD
                   476
                   ,
                   and
                   let
                   DE
                   be
                   the
                   Leg
                   inquired
                   .
                   The
                   Sum
                   of
                   AE
                   and
                   AD
                   is
                   1064.3
                   ,
                   and
                   their
                   Difference
                   is
                   112.3
                   ,
                   now
                   then
                   if
                   you
                   multiply
                   1064.3
                   by
                   112.3
                   ,
                   the
                   Product
                   will
                   be
                   119520.89
                   ,
                   whose
                   Square
                   Root
                   is
                   the
                   Leg
                   DE.
                   345.
                   8.
                   
                
              
               
                 
                   Proposition
                   X.
                   
                
                 
                   
                     The
                     Legs
                     of
                     a
                     Right
                     Angled
                     Plain
                     Triangle
                     being
                     gived
                     ,
                     to
                     find
                     the
                     Area
                     or
                     Superficial
                     Content
                     thereof
                     .
                  
                
                 
                   Multiply
                   one
                   Leg
                   by
                   the
                   other
                   ,
                   half
                   the
                   Product
                   shall
                   be
                   the
                   Content
                   .
                   Example
                   ,
                   In
                   the
                   Right
                   angled
                   plain
                   Triangle
                   ADE
                   ,
                   let
                   the
                   given
                   Legs
                   be
                   AD
                   476
                   ,
                   and
                   DE
                   345
                   ,
                   and
                   let
                   the
                   Area
                   of
                   that
                   Triangle
                   be
                   required
                   ,
                   if
                   you
                   multiply
                   476
                   by
                   345
                   the
                   Product
                   will
                   be
                   164220
                   ,
                   and
                   the
                   half
                   thereof
                   82110
                   is
                   the
                   Area
                   or
                   Superficial
                   Content
                   required
                   .
                
              
               
                 
                 
                   Proposition
                   XI
                   .
                
                 
                   
                     The
                     Sides
                     of
                     an
                     Oblique
                     angled
                     plain
                     Triangle
                     being
                     given
                     to
                     find
                     the
                     Area
                     or
                     Superficial
                     Content
                     thereof
                     .
                  
                
                 
                   Add
                   the
                   three
                   Sides
                   together
                   ,
                   and
                   from
                   the
                   half
                   Sum
                   subtract
                   each
                   Side
                   ,
                   and
                   note
                   their
                   Difference
                   ;
                   then
                   multiply
                   the
                   half
                   Sum
                   by
                   the
                   said
                   Differences
                   continually
                   ,
                   the
                   Square
                   Root
                   of
                   the
                   last
                   Product
                   ,
                   shall
                   be
                   the
                   Content
                   required
                   .
                
                 
                   Example
                   .
                   In
                   Fig.
                   9.
                   
                   Let
                   the
                   Sides
                   of
                   the
                   Triangle
                   ABC
                   be
                   
                     AB
                     20.
                     
                     AC
                  
                   13
                   ,
                   and
                   BC
                   11
                   the
                   Sum
                   of
                   these
                   three
                   Sides
                   is
                   44
                   ,
                   the
                   half
                   Sum
                   is
                   22
                   ,
                   from
                   whence
                   subtracting
                   AB
                   20
                   ,
                   the
                   Difference
                   is
                   2
                   ,
                   from
                   whence
                   also
                   if
                   you
                   substract
                   AC
                   13
                   ,
                   the
                   Difference
                   is
                   9
                   ,
                   and
                   lastly
                   ,
                   if
                   you
                   subtract
                   BC
                   11
                   from
                   the
                   half
                   Sum
                   22
                   ,
                   the
                   Difference
                   will
                   be
                   11.
                   
                   And
                   the
                   half
                   Sum
                   22
                   being
                   multiplied
                   by
                   the
                   first
                   Difference
                   2
                   ,
                   the
                   Product
                   is
                   44
                   ,
                   and
                   44
                   being
                   multiplied
                   by
                   the
                   Second
                   Difference
                   9
                   ,
                   the
                   Product
                   is
                   396
                   ,
                   and
                   396
                   being
                   multiplied
                   by
                   the
                   third
                   Difference
                   11
                   ,
                   the
                   Product
                   is
                   4356
                   ,
                   whose
                   Square
                   Root
                   66
                   ,
                   is
                   the
                   Content
                   required
                   .
                
                 
                   Or
                   thus
                   ,
                   from
                   the
                   Angle
                   C
                   let
                   fall
                   the
                   Perpendicular
                   DC
                   ,
                   so
                   is
                   the
                   Oblique
                   angled
                   Triangle
                   ABC
                   ,
                   turned
                   into
                   two
                   right
                   ,
                   now
                   then
                   if
                   you
                   measure
                   DC
                   upon
                   your
                   Scale
                   of
                   Equal
                   Parts
                   ,
                   the
                   length
                   thereof
                   will
                   be
                   found
                   to
                   be
                   6.6
                   ,
                   by
                   which
                   if
                   you
                   multiply
                   the
                   Base
                   AB
                   20
                   ,
                   the
                   Product
                   will
                   be
                   132.0
                   ,
                   whose
                   half
                   66
                   ,
                   is
                   the
                   Area
                   of
                   the
                   Triangle
                   ,
                   as
                   before
                   .
                
              
               
                 
                 
                   Proposition
                   XII
                   .
                
                 
                   
                     The
                     Sides
                     of
                     any
                     Oblique
                     angled
                     Quadrangle
                     being
                     given
                     ,
                     to
                     find
                     the
                     Area
                     or
                     Superficial
                     Content
                     thereof
                     .
                  
                
                 
                   Let
                   the
                   Sides
                   of
                   the
                   Oblique
                   angled
                   Quadrangle
                   ABED
                   in
                   Fig.
                   11.
                   be
                   given
                   ,
                   draw
                   the
                   Diagonal
                   AE
                   ,
                   and
                   also
                   the
                   Perpendiculars
                   DC
                   and
                   BF
                   ,
                   then
                   measuring
                   AE
                   upon
                   the
                   same
                   Scale
                   by
                   which
                   the
                   Quadrangular
                   Figure
                   was
                   protracted
                   ,
                   suppose
                   you
                   find
                   the
                   length
                   to
                   be
                   632
                   ,
                   the
                   length
                   of
                   
                     DC
                     112
                  
                   ,
                   and
                   the
                   length
                   of
                   BF
                   136
                   ,
                   if
                   you
                   multiply
                   AE
                   632
                   by
                   the
                   Half
                   of
                   DC
                   56
                   ,
                   the
                   Product
                   will
                   be
                   35392
                   the
                   Area
                   of
                   ACED
                   .
                   In
                   like
                   manner
                   if
                   you
                   multiply
                   AE
                   632
                   ,
                   by
                   the
                   half
                   of
                   BF
                   68
                   ,
                   the
                   Product
                   will
                   be
                   42976
                   the
                   Area
                   of
                   ACEB
                   ,
                   and
                   the
                   Sum
                   of
                   these
                   two
                   Products
                   is
                   the
                   Area
                   of
                   ABED
                   as
                   was
                   required
                   .
                
                 
                   Or
                   thus
                   ,
                   take
                   the
                   Sum
                   of
                   DC
                   112
                   ,
                   and
                   
                     BF
                     136
                  
                   ;
                   the
                   which
                   is
                   248
                   ,
                   and
                   multiply
                   AE
                   632
                   by
                   half
                   that
                   Sum
                   ,
                   that
                   is
                   by
                   124
                   ,
                   the
                   Product
                   will
                   be
                   78368
                   the
                   Area
                   of
                   the
                   Quadrangular
                   Figure
                   ABED
                   ,
                   as
                   before
                   .
                
              
               
                 
                   Proposition
                   XIII
                   .
                
                 
                   
                     The
                     Sides
                     of
                     a
                     plain
                     irregular
                     multangled
                     Figure
                     being
                     given
                     ,
                     to
                     find
                     the
                     Content
                     .
                  
                
                 
                   In
                   Fig.
                   26.
                   
                   Let
                   the
                   Sides
                   of
                   the
                   multangled
                   Figure
                   .
                   
                     A.
                     B.
                     C.
                     D.
                     E.
                     F.
                     G.
                     H.
                  
                   be
                   given
                   ,
                   and
                   let
                   the
                   Area
                   thereof
                   be
                   required
                   ,
                   by
                   Diagonals
                   drawn
                   from
                   the
                   opposite
                   Angles
                   reduce
                   the
                   Figure
                   given
                   ,
                   
                   into
                   Oblique
                   angled
                   plain
                   Triangles
                   ,
                   and
                   those
                   Oblique
                   angled
                   Triangles
                   ,
                   into
                   right
                   by
                   letting
                   fall
                   of
                   Perpendiculars
                   ,
                   then
                   measure
                   the
                   Diagonals
                   and
                   Perpendiculars
                   by
                   the
                   same
                   Scale
                   ,
                   by
                   which
                   the
                   Figure
                   it self
                   was
                   protracted
                   ,
                   the
                   Content
                   of
                   those
                   Triangles
                   being
                   computed
                   ,
                   as
                   hath
                   been
                   shewed
                   ,
                   shall
                   be
                   AF
                   the
                   Content
                   required
                   :
                   thus
                   by
                   the
                   Diagonals
                   
                     AG.
                     BE
                  
                   and
                   EC
                   the
                   multangled
                   Figure
                   propounded
                   is
                   converted
                   into
                   three
                   Oblique
                   angled
                   quadrangular
                   Figures
                   ,
                   
                     AFGH
                     .
                     AFEB
                  
                   and
                   BEDC
                   ,
                   and
                   each
                   of
                   these
                   are
                   divided
                   into
                   four
                   Right
                   angled
                   Triangles
                   ,
                   whose
                   several
                   Contents
                   may
                   be
                   thus
                   computed
                   .
                   Let
                   GA
                   94
                   be
                   multiplied
                   by
                   half
                   HL
                   27
                   more
                   Half
                   of
                   KF
                   29
                   ,
                   that
                   is
                   by
                   23
                   ,
                   the
                   Product
                   will
                   be
                   21
                   ,
                   be
                   the
                   Area
                   of
                   AHGF.
                   Secondly
                   ,
                   OB
                   is
                   11
                   ,
                   and
                   FN
                   13
                   ,
                   their
                   half
                   Sum
                   12
                   ,
                   by
                   which
                   if
                   you
                   multiply
                   AE
                   132
                   ,
                   the
                   Product
                   will
                   be
                   1584
                   the
                   Area
                   of
                   AFEB
                   .
                   Thirdly
                   ,
                   let
                   Bp
                   be
                   18
                   
                     m
                     D
                  
                   32
                   ,
                   the
                   half
                   Sum
                   is
                   25
                   ,
                   by
                   which
                   if
                   you
                   multiply
                   AEC
                   125
                   the
                   Product
                   will
                   be
                   3125
                   the
                   Area
                   of
                   BEDC
                   ,
                   and
                   the
                   Sum
                   of
                   these
                   Products
                   is
                   6871
                   the
                   Area
                   of
                   the
                   whole
                   irregular
                   Figure
                   .
                   ABCDEFGH
                   ,
                   as
                   was
                   required
                   .
                
              
               
                 
                   Proposition
                   XIV
                   .
                
                 
                   
                     The
                     Number
                     of
                     Degrees
                     in
                     the
                     Sector
                     of
                     a
                     Circle
                     being
                     given
                     ,
                     to
                     find
                     the
                     Area
                     thereof
                     .
                  
                
                 
                   In
                   
                     Fig.
                     27.
                     
                     ADEG
                  
                   is
                   the
                   Sector
                   of
                   a
                   Circle
                   ,
                   in
                   which
                   the
                   Arch
                   DEG
                   ,
                   is
                   Degrees
                   .
                   23.50
                   ,
                   and
                   by
                   1.
                   
                   Prop.
                   of
                   
                     Archimed
                     .
                     de
                     Dimensione
                     Circuli
                  
                   ,
                   the
                   length
                   of
                   half
                   the
                   Arch
                   is
                   equal
                   to
                   the
                   Area
                   of
                   the
                   Sector
                   of
                   the
                   double
                   Arch
                   ,
                   there
                   the
                   length
                   
                   of
                   DE
                   or
                   EG
                   is
                   equal
                   to
                   the
                   Area
                   of
                   the
                   
                     Sector
                     ADEG
                  
                   :
                   and
                   the
                   length
                   or
                   circumference
                   of
                   the
                   whole
                   Circle
                   whose
                   Diameter
                   is
                   1
                   according
                   to
                   
                     Van
                     Culen
                  
                   ,
                   is
                   3.14159265358979
                   ,
                   therefore
                   the
                   length
                   of
                   one
                   Centesme
                   of
                   a
                   Degree
                   ,
                   is
                   .
                   0.
                   01745329259.
                   
                   Now
                   then
                   to
                   find
                   the
                   length
                   of
                   any
                   Number
                   of
                   Degrees
                   and
                   Decimal
                   Parts
                   ,
                   you
                   must
                   multiply
                   the
                   aforesaid
                   length
                   of
                   one
                   Centesme
                   by
                   the
                   Degrees
                   and
                   Parts
                   given
                   ,
                   and
                   the
                   Product
                   shall
                   be
                   the
                   length
                   of
                   those
                   Degrees
                   and
                   Parts
                   required
                   ,
                   and
                   the
                   Area
                   of
                   a
                   Sector
                   containing
                   twice
                   those
                   Degrees
                   and
                   Parts
                   .
                   Example
                   ,
                   the
                   half
                   of
                   DEG
                   23.50
                   is
                   DE
                   or
                   EG
                   11.75
                   ,
                   by
                   which
                   if
                   you
                   multiply
                   0.01745329259
                   ,
                   the
                   Product
                   will
                   be
                   2050761879325
                   ,
                   the
                   length
                   of
                   the
                   Arch
                   DE
                   ,
                   and
                   the
                   Area
                   of
                   the
                   
                     Sector
                     ADEG
                  
                   .
                
              
               
                 
                   Proposition
                   XV.
                   
                
                 
                   
                     The
                     Number
                     of
                     Degrees
                     in
                     the
                     Segment
                     of
                     a
                     Circle
                     being
                     given
                     ,
                     to
                     find
                     the
                     Area
                     of
                     the
                     Segment
                     .
                  
                
                 
                   In
                   Fig.
                   27.
                   
                   Let
                   the
                   Area
                   of
                   the
                   Segment
                   DEGK
                   be
                   required
                   ,
                   in
                   which
                   let
                   the
                   Arch
                   DEG
                   be
                   Degrees
                   23.50
                   ,
                   then
                   is
                   the
                   Area
                   of
                   the
                   
                     Sector
                     ADEG
                  
                   2050761879325
                   by
                   the
                   last
                   aforegoing
                   ,
                   from
                   which
                   if
                   you
                   deduct
                   the
                   Area
                   of
                   the
                   Triangle
                   ADG
                   ,
                   the
                   remainer
                   will
                   be
                   the
                   Area
                   of
                   the
                   Segment
                   DEGK
                   .
                   And
                   the
                   Area
                   of
                   the
                   Triangle
                   ADG
                   may
                   thus
                   be
                   found
                   .
                   DK
                   is
                   the
                   Sine
                   of
                   DE
                   11.75
                   ,
                   which
                   being
                   sought
                   in
                   
                   Gellibrand's
                   Decimal
                   Canon
                   is
                   .
                   2036417511
                   ,
                   and
                   AK
                   is
                   the
                   Sine
                   of
                   DH
                   78.25
                   ,
                   or
                   the
                   Cosine
                   of
                   DE.
                   9790454724
                   ,
                   which
                   being
                   multiplied
                   by
                   the
                   Sine
                   of
                   DE
                   ,
                   the
                   Product
                   will
                   be
                   1993745344
                   ,
                   or
                   if
                   you
                   multiply
                   AG
                   
                   
                   
                   
                   the
                   Radius
                   by
                   half
                   DF
                   the
                   Sine
                   of
                   the
                   double
                   Arch
                   DEG
                   ,
                   the
                   Product
                   will
                   be
                   19937453445
                   as
                   before
                   ,
                   and
                   this
                   Product
                   being
                   deducted
                   from
                   the
                   Area
                   of
                   the
                   
                     Sector
                     ADEG
                  
                   2050761879325
                   ,
                   the
                   remainer
                   will
                   be
                   57016434875
                   the
                   Area
                   of
                   the
                   Segment
                   DEGL
                   ,
                   as
                   was
                   desired
                   .
                
              
               
                 
                   Proposition
                   XVI
                   .
                
                 
                   
                     The
                     Diameter
                     of
                     a
                     Circle
                     being
                     cut
                     into
                     any
                     Number
                     of
                     Equal
                     Parts
                     ,
                     to
                     find
                     the
                     Area
                     of
                     any
                     Segment
                     made
                     by
                     the
                     Chord
                     Line
                     drawn
                     at
                     Right
                     Angles
                     through
                     any
                     of
                     those
                     equal
                     Parts
                     of
                     the
                     Diameter
                     .
                  
                
                 
                   In
                   Fig.
                   28.
                   
                   The
                   
                     Radius
                     AD
                  
                   is
                   cut
                   into
                   five
                   Equal
                   Parts
                   ,
                   and
                   the
                   Segment
                   EDFL
                   is
                   made
                   by
                   the
                   Chord
                   Line
                   ELF
                   at
                   Right
                   Angles
                   to
                   AD
                   in
                   the
                   fourth
                   Equal
                   Part
                   ,
                   or
                   at
                   eight
                   tenths
                   thereof
                   :
                   now
                   then
                   to
                   find
                   the
                   Area
                   of
                   this
                   Segment
                   we
                   have
                   given
                   
                     AE
                     Radius
                  
                   ,
                   and
                   AL
                   8
                   ,
                   and
                   therefore
                   by
                   the
                   ninth
                   hereof
                   EL
                   will
                   be
                   found
                   to
                   be
                   606000
                   ,
                   the
                   Sine
                   of
                   ED
                   36.87
                   ,
                   by
                   which
                   if
                   you
                   multiply
                   0.0174532
                   ,
                   the
                   Product
                   is
                   the
                   Area
                   of
                   the
                   
                     Sector
                     AEDF
                  
                   64350286
                   ,
                   and
                   the
                   Area
                   of
                   the
                   Triangle
                   AEF
                   is
                   48
                   ,
                   which
                   being
                   deducted
                   from
                   the
                   Area
                   of
                   the
                   Sector
                   ,
                   the
                   Remainer
                   16350286
                   is
                   the
                   Area
                   of
                   the
                   
                     Sector
                     EDFL
                  
                   ,
                   as
                   was
                   required
                   .
                   And
                   in
                   this
                   manner
                   was
                   that
                   Table
                   of
                   Segments
                   made
                   by
                   the
                   Chord
                   Lines
                   cutting
                   the
                   Radius
                   into
                   100
                   Equal
                   Parts
                   .
                
                 
                   
                     Another
                     way
                  
                   .
                
                 
                   In
                   Fig.
                   28.
                   
                   Let
                   the
                   
                     Radius
                     AD
                  
                   be
                   cut
                   into
                   10.100
                   or
                   1000
                   Equal
                   Parts
                   ,
                   and
                   let
                   the
                   Area
                   of
                   
                   the
                   Segments
                   made
                   by
                   the
                   Chord
                   Lines
                   drawn
                   at
                   Right
                   Angles
                   through
                   all
                   those
                   Parts
                   be
                   required
                   :
                   first
                   find
                   the
                   Ordinates
                   GK
                   and
                   
                     M.
                     PN
                     .
                     EL
                  
                   ,
                   the
                   double
                   of
                   each
                   Ordinate
                   ,
                   will
                   be
                   the
                   Chords
                   of
                   the
                   several
                   Arches
                   ,
                   and
                   the
                   Sum
                   of
                   these
                   Chords
                   beginning
                   with
                   the
                   least
                   Ordinate
                   ,
                   will
                   orderly
                   give
                   you
                   the
                   Area
                   of
                   the
                   several
                   Segments
                   made
                   by
                   those
                   Chord
                   Lines
                   ,
                   but
                   the
                   Diameter
                   must
                   be
                   be
                   divided
                   into
                   100000
                   Equal
                   Parts
                   ,
                   because
                   of
                   the
                   unequal
                   differences
                   at
                   the
                   beginning
                   of
                   the
                   Diameter
                   :
                   but
                   taking
                   the
                   Area
                   of
                   the
                   Circle
                   to
                   be
                   3.
                   1415926535
                   ,
                   &c.
                   as
                   before
                   ,
                   the
                   Area
                   of
                   the
                   Semicircle
                   will
                   be
                   1.57079632
                   ,
                   from
                   which
                   if
                   you
                   deduct
                   the
                   Chord
                   GH1999999
                   ,
                   the
                   Chord
                   answering
                   to
                   999
                   Parts
                   of
                   the
                   Radius
                   ,
                   the
                   remainer
                   is
                   .
                   1.56879632
                   the
                   Area
                   of
                   the
                   Segment
                   GDH
                   .
                   And
                   in
                   this
                   manner
                   by
                   a
                   continual
                   deduction
                   of
                   the
                   Chord
                   Lines
                   from
                   the
                   Area
                   of
                   the
                   Segment
                   of
                   the
                   Circle
                   given
                   ,
                   was
                   made
                   that
                   Table
                   shewing
                   the
                   Area
                   of
                   the
                   Segments
                   of
                   a
                   Circle
                   to
                   the
                   thousandth
                   part
                   of
                   the
                   Radius
                   .
                
                 
                   And
                   because
                   a
                   Table
                   shewing
                   the
                   Area
                   of
                   the
                   Segments
                   of
                   a
                   Circle
                   to
                   the
                   thousandth
                   part
                   of
                   the
                   Radius
                   ,
                   whose
                   whole
                   Area
                   is
                   Unity
                   ,
                   is
                   yet
                   more
                   useful
                   in
                   Common
                   Practice
                   ,
                   therefore
                   from
                   this
                   Table
                   ,
                   was
                   that
                   Table
                   also
                   made
                   by
                   this
                   Proportion
                   .
                
                 
                   As
                   the
                   Area
                   of
                   the
                   Circle
                   whose
                   Diameter
                   is
                   .
                   Unity
                   ,
                   to
                   wit
                   3.14149
                   is
                   to
                   the
                   Area
                   of
                   any
                   part
                   of
                   that
                   Diameter
                   ,
                   so
                   is
                   Unity
                   the
                   supposed
                   Area
                   of
                   another
                   Circle
                   ,
                   to
                   the
                   like
                   part
                   of
                   that
                   Diameter
                   .
                   Example
                   ,
                   the
                   Area
                   answering
                   to
                   665
                   parts
                   of
                   the
                   Radius
                   of
                   a
                   Circlewhose
                   Area
                   is
                   3.14159
                   is
                   0.91354794
                   therefore
                   ,
                
                 
                 
              
            
             
               
                 CHAP.
                 IX
                 .
              
               
                 
                   Of
                   the
                   Measuring
                   of
                   Heights
                   and
                   Distances
                   .
                
              
               
                 HAving
                 shewed
                 in
                 the
                 former
                 Chapter
                 ,
                 how
                 all
                 plain
                 Triangles
                 may
                 be
                 measured
                 ,
                 not
                 only
                 in
                 respect
                 of
                 their
                 Sides
                 and
                 Angles
                 ,
                 but
                 in
                 respect
                 of
                 their
                 Area
                 ,
                 and
                 the
                 finding
                 of
                 the
                 Area
                 of
                 all
                 other
                 plain
                 Figures
                 also
                 ,
                 that
                 which
                 is
                 next
                 to
                 be
                 considered
                 ,
                 is
                 the
                 practical
                 use
                 of
                 those
                 Instructions
                 ,
                 in
                 the
                 measuring
                 of
                 Board
                 ,
                 Glass
                 ,
                 Wainscot
                 ,
                 Pavement
                 ,
                 and
                 such
                 like
                 ,
                 as
                 also
                 the
                 measuring
                 or
                 surveying
                 of
                 Land
                 ;
                 and
                 first
                 we
                 will
                 shew
                 the
                 measuring
                 of
                 Heights
                 and
                 Distances
                 .
              
               
                 2.
                 
                 And
                 in
                 the
                 measuring
                 of
                 Heights
                 and
                 Distances
                 ,
                 besides
                 a
                 Chain
                 of
                 50
                 or
                 100
                 Links
                 ,
                 each
                 Link
                 being
                 a
                 Foot
                 ,
                 it
                 is
                 necessary
                 to
                 have
                 a
                 Quadrant
                 of
                 four
                 or
                 five
                 Inches
                 Radius
                 ,
                 and
                 the
                 larger
                 the
                 Quadrant
                 is
                 ,
                 the
                 more
                 exactly
                 may
                 the
                 Angles
                 :
                 be
                 taken
                 ,
                 though
                 for
                 ordinary
                 Practice
                 ,
                 four
                 or
                 five
                 Inches
                 Radius
                 will
                 be
                 sufficient
                 .
              
               
                 Let
                 such
                 a
                 Quadrant
                 therefore
                 be
                 divided
                 in
                 the
                 Limb
                 into
                 90
                 Equal
                 Parts
                 or
                 Degrees
                 ,
                 and
                 numbred
                 from
                 the
                 left
                 hand
                 to
                 the
                 right
                 ,
                 at
                 every
                 tenth
                 Degree
                 ,
                 in
                 this
                 manner
                 10.
                 20.
                 30.
                 40.
                 50.
                 60.
                 70.
                 80.
                 90.
                 and
                 within
                 the
                 Limb
                 of
                 the
                 Quadrant
                 
                 draw
                 another
                 Arch
                 ,
                 which
                 being
                 divided
                 by
                 help
                 of
                 the
                 Limb
                 into
                 two
                 Equal
                 Parts
                 ,
                 in
                 the
                 Point
                 of
                 Interfection
                 set
                 the
                 Figure
                 1.
                 representing
                 the
                 Radius
                 or
                 Tangent
                 of
                 45
                 Degrees
                 ,
                 and
                 from
                 thence
                 both
                 ways
                 the
                 Tangents
                 of
                 63.44
                 Deg.
                 71.57
                 Deg.
                 75.97
                 Deg.
                 78.70
                 Deg.
                 80.54
                 Deg.
                 that
                 is
                 ,
                 2.
                 3.
                 4.
                 5
                 and
                 6
                 being
                 set
                 also
                 ,
                 your
                 Quadrant
                 will
                 be
                 fitted
                 for
                 the
                 taking
                 of
                 Heights
                 several
                 ways
                 ,
                 as
                 shall
                 be
                 explained
                 in
                 the
                 Propositions
                 following
                 .
              
               
                 
                   Proposition
                   I.
                   
                
                 
                   
                     To
                     find
                     the
                     Height
                     of
                     a
                     Tower
                     ,
                     Tree
                     ,
                     or
                     other
                     Object
                     at
                     one
                     Station
                     .
                  
                
                 
                   At
                   any
                   convenient
                   distance
                   from
                   the
                   Foot
                   of
                   the
                   Object
                   to
                   be
                   measured
                   ,
                   as
                   suppose
                   at
                   C
                   in
                   
                     Fig.
                     30.
                  
                   and
                   there
                   looking
                   through
                   the
                   Sights
                   of
                   your
                   Quadrant
                   till
                   you
                   espie
                   the
                   top
                   of
                   the
                   Object
                   at
                   A
                   ,
                   observe
                   what
                   Degrees
                   in
                   the
                   Limb
                   are
                   cut
                   by
                   the
                   Thread
                   ,
                   those
                   Degrees
                   from
                   the
                   left
                   Side
                   or
                   Edge
                   of
                   the
                   Quadrant
                   to
                   the
                   Right
                   ,
                   is
                   the
                   Quantity
                   of
                   the
                   Angle
                   ACB
                   ,
                   which
                   suppose
                   35
                   Degrees
                   ;
                   then
                   is
                   the
                   Angle
                   BAC
                   55
                   Degrees
                   ,
                   being
                   the
                   Complement
                   of
                   the
                   former
                   to
                   90
                   Degrees
                   .
                   This
                   done
                   with
                   your
                   Chain
                   or
                   otherwise
                   measure
                   the
                   distance
                   from
                   B
                   the
                   Foot
                   of
                   the
                   Object
                   ,
                   to
                   your
                   Station
                   at
                   C
                   ,
                   which
                   suppose
                   to
                   be
                   125
                   Foot.
                   Then
                   as
                   hath
                   been
                   shewed
                   in
                   the
                   1.
                   
                   
                     Prop.
                     Chap.
                  
                   8.
                   draw
                   a
                   Line
                   at
                   pleasure
                   as
                   BC
                   ,
                   and
                   by
                   your
                   Scale
                   of
                   Equal
                   Parts
                   ,
                   set
                   off
                   the
                   distance
                   measured
                   from
                   B
                   to
                   C
                   125
                   Foot
                   ,
                   and
                   upon
                   the
                   Point
                   C
                   lay
                   down
                   your
                   Angle
                   taken
                   by
                   observation
                   35
                   Degrees
                   ,
                   then
                   erect
                   a
                   Perpendicular
                   upon
                   
                   the
                   Point
                   B
                   ,
                   and
                   let
                   it
                   be
                   extended
                   till
                   it
                   cut
                   the
                   Hypothenusal
                   Line
                   AC
                   ,
                   so
                   shall
                   AB
                   measured
                   on
                   your
                   Scale
                   of
                   Equal
                   Parts
                   ,
                   be
                   87.5
                   Foot
                   for
                   the
                   Height
                   of
                   the
                   Object
                   above
                   the
                   Eye
                   ;
                   to
                   which
                   the
                   Height
                   of
                   the
                   Eye
                   from
                   the
                   Ground
                   being
                   added
                   ,
                   their
                   Sum
                   is
                   the
                   Height
                   required
                   .
                
                 
                   
                     Another
                     way
                  
                   .
                
                 
                   Let
                   AB
                   represent
                   a
                   Tower
                   whose
                   Altitude
                   you
                   would
                   take
                   ,
                   go
                   so
                   far
                   back
                   from
                   it
                   ,
                   that
                   looking
                   through
                   the
                   Sights
                   of
                   your
                   Quadrant
                   ,
                   to
                   the
                   top
                   of
                   the
                   Tower
                   at
                   A
                   the
                   Thread
                   may
                   cut
                   just
                   45
                   Degrees
                   in
                   the
                   Limb
                   ,
                   then
                   shall
                   the
                   distance
                   from
                   the
                   Foot
                   of
                   the
                   Tower
                   ,
                   to
                   your
                   Station
                   ,
                   be
                   the
                   Height
                   of
                   the
                   Tower
                   above
                   the
                   Eye
                   .
                
                 
                   Or
                   if
                   you
                   remove
                   your
                   Station
                   nearer
                   and
                   nearer
                   to
                   the
                   Object
                   ,
                   till
                   your
                   Thread
                   hang
                   over
                   the
                   Figures
                   2.
                   3.
                   4
                   or
                   5
                   in
                   the
                   Quadrant
                   ,
                   the
                   Height
                   of
                   the
                   Tower
                   at
                   2.
                   will
                   be
                   twice
                   as
                   much
                   as
                   the
                   distance
                   from
                   the
                   Tower
                   to
                   the
                   Station
                   ,
                   at
                   3.
                   it
                   will
                   be
                   thrice
                   as
                   much
                   ,
                   &c.
                   
                   As
                   if
                   removing
                   my
                   Station
                   from
                   C
                   to
                   D
                   ,
                   the
                   Thread
                   should
                   hang
                   over
                   2
                   in
                   the
                   Quadrant
                   ,
                   and
                   the
                   distance
                   BD
                   62
                   Foot
                   ,
                   then
                   will
                   124
                   Foot
                   be
                   the
                   Height
                   of
                   the
                   Tower
                   ,
                   above
                   the
                   Eye
                   .
                
                 
                   In
                   like
                   manner
                   if
                   you
                   remove
                   your
                   Station
                   backward
                   till
                   your
                   Thread
                   fall
                   upon
                   one
                   of
                   those
                   Figures
                   in
                   the
                   Quadrant
                   ;
                   between
                   45
                   and
                   90
                   Degrees
                   ,
                   the
                   distance
                   between
                   the
                   Foot
                   of
                   the
                   Tower
                   ,
                   and
                   your
                   Station
                   will
                   at
                   2.
                   be
                   twice
                   as
                   much
                   as
                   the
                   Height
                   ,
                   at
                   3.
                   thrice
                   as
                   much
                   ,
                   at
                   4.
                   four
                   times
                   so
                   much
                   ,
                   and
                   so
                   of
                   the
                   rest
                   .
                
                 
                 
                   
                     A
                     Third
                     way
                     by
                     a
                     Station
                     at
                     Random
                     .
                  
                
                 
                   Take
                   any
                   Station
                   at
                   pleasure
                   suppose
                   at
                   C
                   ,
                   and
                   looking
                   through
                   the
                   Sights
                   of
                   your
                   Quadrant
                   ,
                   observe
                   what
                   Parts
                   of
                   the
                   Quadrant
                   the
                   Thread
                   falls
                   upon
                   ,
                   and
                   then
                   measure
                   the
                   distance
                   between
                   the
                   Station
                   ,
                   and
                   the
                   Foot
                   of
                   the
                   Object
                   ,
                   that
                   distance
                   being
                   multiplied
                   by
                   the
                   parts
                   cut
                   in
                   the
                   Quadrant
                   ,
                   cutting
                   off
                   two
                   Figures
                   from
                   the
                   Product
                   shall
                   be
                   the
                   Height
                   of
                   the
                   Object
                   above
                   the
                   Eye
                   ?
                
                 
                   Example
                   ,
                   Suppose
                   I
                   standing
                   at
                   C
                   ,
                   that
                   the
                   Thread
                   hangs
                   upon
                   36
                   Degrees
                   ,
                   as
                   also
                   upon
                   72
                   in
                   the
                   Quadrant
                   which
                   is
                   the
                   Tangent
                   of
                   the
                   said
                   Arch
                   ,
                   and
                   let
                   the
                   measured
                   distance
                   be
                   CB
                   125
                   Foot
                   ,
                   which
                   being
                   multiplied
                   by
                   72
                   ,
                   the
                   Product
                   is
                   9000
                   ,
                   from
                   which
                   cutting
                   off
                   his
                   Figures
                   because
                   the
                   Radius
                   is
                   supposed
                   to
                   be
                   100
                   ,
                   the
                   Height
                   inquired
                   will
                   be
                   90
                   Foot
                   ,
                   he
                   that
                   desires
                   to
                   perform
                   this
                   work
                   with
                   more
                   exactness
                   ,
                   must
                   make
                   use
                   of
                   the
                   Table
                   of
                   Sines
                   and
                   Tangents
                   Natural
                   or
                   Artificial
                   ,
                   this
                   we
                   think
                   sufficient
                   for
                   our
                   present
                   purpose
                   .
                
              
               
                 
                   Proposition
                   II.
                   
                
                 
                   
                     To
                     find
                     an
                     inaccessible
                     Height
                     at
                     two
                     Stations
                     .
                  
                
                 
                   Take
                   any
                   Station
                   at
                   pleasure
                   as
                   at
                   D
                   ,
                   and
                   there
                   looking
                   through
                   the
                   Sights
                   of
                   your
                   Quadrant
                   to
                   the
                   top
                   of
                   the
                   Object
                   ,
                   observe
                   what
                   Degrees
                   are
                   cut
                   by
                   the
                   Thread
                   in
                   the
                   Limb
                   ,
                   which
                   admit
                   to
                   be
                   68
                   Degrees
                   ,
                   then
                   remove
                   backward
                   ,
                   till
                   the
                   Angle
                   taken
                   by
                   the
                   Quadrant
                   ,
                   be
                   but
                   half
                   so
                   much
                   
                   as
                   the
                   former
                   ,
                   that
                   is
                   34
                   Degrees
                   ,
                   then
                   is
                   the
                   distance
                   between
                   your
                   two
                   Stations
                   equal
                   to
                   the
                   Hypothenusal
                   Line
                   at
                   your
                   first
                   Station
                   ,
                   
                     viz.
                     AD.
                  
                   if
                   the
                   distance
                   between
                   your
                   two
                   Stations
                   were
                   326
                   foot
                   ,
                   then
                   draw
                   a
                   Line
                   at
                   pleasure
                   as
                   BD
                   ,
                   upon
                   the
                   Point
                   D
                   protract
                   ,
                   the
                   Angle
                   ADB
                   68
                   Degrees
                   ,
                   according
                   to
                   your
                   first
                   Observation
                   ,
                   and
                   from
                   your
                   Line
                   of
                   equal
                   parts
                   set
                   off
                   the
                   Hypothenusal
                   326
                   Foot
                   from
                   D
                   to
                   A
                   ,
                   and
                   from
                   the
                   Point
                   A
                   let
                   fall
                   the
                   Perpendicular
                   AB
                   which
                   being
                   measured
                   in
                   your
                   Scale
                   of
                   Equal
                   Parts
                   ,
                   shall
                   be
                   the
                   Altitude
                   of
                   the
                   Object
                   inquired
                   .
                
                 
                   Or
                   working
                   by
                   the
                   Table
                   of
                   Sines
                   and
                   Tangents
                   ,
                   the
                   Proportion
                   is
                   .
                
                 
                   As
                   the
                   Radius
                   ,
                   is
                   to
                   the
                   measured
                   distance
                   or
                   Hypothenusal
                   Line
                   AD
                   ;
                   so
                   is
                   the
                   Sine
                   of
                   the
                   Angle
                   ADE
                   ,
                   to
                   the
                   height
                   AB
                   inquired
                   .
                
                 
                   
                     Another
                     more
                     General
                     way
                     ,
                     by
                     any
                     two
                     Stations
                     taken
                     at
                     pleasure
                     .
                  
                
                 
                   Admit
                   the
                   first
                   Station
                   to
                   be
                   as
                   before
                   at
                   D
                   ,
                   and
                   the
                   Angle
                   by
                   observation
                   to
                   be
                   68
                   Degrees
                   ,
                   and
                   from
                   thence
                   at
                   pleasure
                   I
                   remove
                   to
                   C
                   ,
                   where
                   observing
                   aim
                   I
                   find
                   the
                   Angle
                   at
                   C
                   to
                   be
                   32
                   Degrees
                   ,
                   and
                   the
                   distance
                   between
                   the
                   Stations
                   150
                   Foot.
                   Draw
                   a
                   Line
                   at
                   pleasure
                   as
                   BC
                   ,
                   and
                   upon
                   Clay
                   down
                   your
                   last
                   observed
                   Angle
                   32
                   Degrees
                   ,
                   and
                   by
                   help
                   of
                   your
                   Scale
                   of
                   Equal
                   Parrs
                   ,
                   set
                   off
                   your
                   measured
                   distance
                   from
                   C
                   to
                   D
                   150
                   Foot
                   ,
                   then
                   upon
                   D
                   lay
                   down
                   your
                   Angle
                   of
                   68
                   Degrees
                   ,
                   according
                   to
                   your
                   first
                   Observation
                   ,
                   and
                   where
                   the
                   Lines
                   AD
                   and
                   AC
                   meet
                   ,
                   let
                   fall
                   the
                   Perpendicular
                   AB
                   ,
                   which
                   being
                   measured
                   in
                   your
                   Scale
                   of
                   Equal
                   Parts
                   ,
                   shall
                   be
                   the
                   height
                   of
                   the
                   Object
                   as
                   before
                   .
                
                 
                 
                   Or
                   working
                   by
                   the
                   Tables
                   of
                   Sines
                   and
                   Tangents
                   ,
                   the
                   Proportions
                   .
                
                 
                   1.
                   
                   As
                   the
                   Sine
                   of
                   DAC
                   to
                   the
                   Distance
                   DC
                   .
                   So
                   the
                   Sine
                   of
                   ACD
                   ,
                   to
                   the
                   Side
                   AD.
                   
                
                 
                   2.
                   
                   As
                   the
                   Radius
                   ,
                   to
                   the
                   Side
                   AD
                   ;
                   so
                   the
                   Sine
                   ADB
                   ,
                   to
                   the
                   Perpendicular
                   height
                   AB
                   inquired
                   .
                
                 
                   The
                   taking
                   of
                   Distances
                   is
                   much
                   after
                   the
                   same
                   manner
                   ,
                   but
                   because
                   there
                   is
                   required
                   either
                   some
                   alteration
                   in
                   the
                   sights
                   of
                   your
                   Quadrant
                   or
                   some
                   other
                   kind
                   of
                   Instrument
                   for
                   the
                   taking
                   of
                   Angles
                   ,
                   we
                   will
                   particularly
                   shew
                   ,
                   how
                   that
                   may
                   be
                   also
                   done
                   several
                   ways
                   ,
                   in
                   the
                   next
                   Chapter
                   .
                
              
            
             
               
                 CHAP.
                 X.
                 
              
               
                 
                   Of
                   the
                   taking
                   of
                   Distances
                   .
                
              
               
                 FOr
                 the
                 taking
                 of
                 Distances
                 some
                 make
                 use
                 of
                 a
                 Semicircle
                 ,
                 others
                 of
                 a
                 whole
                 Circle
                 ,
                 with
                 Ruler
                 and
                 Sights
                 rather
                 than
                 a
                 Quadrant
                 ,
                 and
                 although
                 the
                 matter
                 is
                 not
                 much
                 by
                 which
                 of
                 these
                 Instruments
                 the
                 Angles
                 be
                 taken
                 ,
                 yet
                 in
                 all
                 Cases
                 the
                 whole
                 Circle
                 is
                 somewhat
                 more
                 ready
                 ,
                 than
                 either
                 a
                 Semicircle
                 or
                 Quadrant
                 ,
                 the
                 which
                 with
                 its
                 Furniture
                 is
                 called
                 the
                 Theodolite
                 .
              
               
                 2.
                 
                 A
                 piece
                 of
                 Board
                 or
                 Brass
                 then
                 about
                 twelve
                 or
                 fourteen
                 Inches
                 Diameter
                 ,
                 being
                 made
                 Circular
                 like
                 a
                 round
                 Trencher
                 ,
                 must
                 be
                 divided
                 into
                 four
                 Quadrants
                 ,
                 and
                 each
                 Quadrant
                 divided
                 into
                 90
                 Degrees
                 ,
                 or
                 the
                 whole
                 Circle
                 into
                 360
                 ,
                 and
                 each
                 Degree
                 into
                 as
                 many
                 other
                 Equal
                 Parts
                 ,
                 as
                 the
                 largeness
                 of
                 the
                 Degrees
                 will
                 well
                 permit
                 :
                 let
                 your
                 Circle
                 be
                 numbred
                 both
                 ways
                 to
                 360
                 ,
                 that
                 is
                 from
                 the
                 right
                 hand
                 to
                 the
                 left
                 ,
                 and
                 from
                 the
                 left
                 to
                 the
                 right
                 .
              
               
               
                 3.
                 
                 Upon
                 the
                 backside
                 of
                 the
                 Circle
                 there
                 must
                 be
                 a
                 Socket
                 made
                 fast
                 ,
                 that
                 it
                 may
                 be
                 set
                 upon
                 a
                 three
                 legged
                 Staff
                 ,
                 to
                 bear
                 it
                 up
                 in
                 the
                 Field
                 .
              
               
                 4.
                 
                 You
                 must
                 also
                 have
                 a
                 Ruler
                 with
                 Sights
                 fixed
                 at
                 each
                 end
                 ,
                 for
                 making
                 of
                 Observation
                 ,
                 either
                 fixed
                 upon
                 the
                 Center
                 of
                 your
                 Circle
                 ,
                 or
                 loose
                 ,
                 as
                 you
                 shall
                 think
                 best
                 ;
                 your
                 Instrument
                 being
                 thus
                 made
                 ,
                 any
                 distance
                 whether
                 accessible
                 or
                 inaccessible
                 may
                 thus
                 be
                 taken
                 .
              
               
                 5.
                 
                 When
                 you
                 are
                 in
                 the
                 Field
                 ,
                 and
                 see
                 any
                 Church
                 ,
                 Tower
                 ,
                 or
                 other
                 Object
                 ,
                 whose
                 Distance
                 from
                 you
                 ,
                 you
                 desire
                 to
                 know
                 ,
                 choose
                 out
                 some
                 other
                 Station
                 in
                 the
                 same
                 Field
                 ,
                 from
                 whence
                 you
                 may
                 also
                 see
                 the
                 Object
                 ,
                 and
                 measure
                 the
                 distance
                 between
                 your
                 Stations
                 ;
                 then
                 setting
                 your
                 Ruler
                 upon
                 the
                 Diameter
                 of
                 your
                 Circle
                 ,
                 set
                 your
                 Instrument
                 so
                 ,
                 as
                 that
                 by
                 the
                 Sights
                 on
                 your
                 Ruler
                 ,
                 you
                 may
                 look
                 to
                 the
                 other
                 Station
                 ,
                 this
                 done
                 turn
                 your
                 Ruler
                 to
                 that
                 Object
                 whose
                 distance
                 you
                 desire
                 to
                 know
                 ,
                 and
                 observe
                 how
                 many
                 Degrees
                 of
                 the
                 Circle
                 are
                 cut
                 by
                 the
                 Ruler
                 ,
                 as
                 suppose
                 36
                 Degrees
                 ,
                 as
                 the
                 Angle
                 ACD
                 in
                 Fig.
                 30.
                 
                 Then
                 removing
                 your
                 Instrument
                 to
                 D
                 ,
                 lay
                 the
                 Ruler
                 on
                 the
                 Diameter
                 thereof
                 ,
                 and
                 then
                 turn
                 the
                 whole
                 Instrument
                 about
                 till
                 through
                 your
                 Sights
                 you
                 can
                 espy
                 the
                 mark
                 set
                 up
                 at
                 your
                 first
                 Station
                 at
                 C
                 ,
                 and
                 there
                 fix
                 your
                 Instrument
                 ,
                 and
                 then
                 upon
                 the
                 Centre
                 of
                 your
                 Circle
                 turn
                 your
                 Ruler
                 till
                 through
                 the
                 Sights
                 you
                 can
                 espy
                 the
                 Object
                 whose
                 distance
                 is
                 inquired
                 ,
                 suppose
                 at
                 A
                 ;
                 and
                 observe
                 the
                 Degrees
                 in
                 the
                 Circle
                 cut
                 by
                 the
                 Ruler
                 ,
                 which
                 let
                 be
                 112
                 ,
                 which
                 is
                 the
                 Angle
                 ADC
                 ,
                 and
                 let
                 the
                 distance
                 between
                 your
                 two
                 Stations
                 be
                 DC
                 326
                 Foot
                 ;
                 so
                 have
                 you
                 two
                 Angles
                 and
                 the
                 side
                 between
                 them
                 ,
                 in
                 a
                 plain
                 Triangle
                 given
                 ,
                 by
                 which
                 
                 to
                 find
                 the
                 other
                 sides
                 ,
                 the
                 which
                 by
                 protraction
                 may
                 be
                 done
                 as
                 hath
                 been
                 shewed
                 ,
                 in
                 the
                 fifth
                 Proposition
                 of
                 Chapter
                 8.
                 but
                 by
                 the
                 Table
                 of
                 Sines
                 and
                 Tangents
                 ,
                 the
                 Proportion
                 is
                 .
              
               
                 As
                 the
                 Sine
                 of
                 DAC
                 ,
                 is
                 to
                 DC
                 ;
                 so
                 is
                 the
                 Sine
                 of
                 ACD
                 to
                 the
                 Side
                 AD.
                 
              
               
                 Or
                 ,
                 as
                 the
                 Sine
                 of
                 DAC
                 ,
                 is
                 to
                 the
                 given
                 Side
                 DC
                 .
              
               
                 So
                 is
                 the
                 Sine
                 of
                 ADC
                 to
                 the
                 Side
                 AC
                 .
              
               
                 6.
                 
                 There
                 is
                 another
                 Instrument
                 called
                 the
                 plain
                 Table
                 ,
                 which
                 is
                 nothing
                 else
                 ,
                 but
                 a
                 piece
                 of
                 Board
                 ,
                 in
                 the
                 fashion
                 and
                 bigness
                 of
                 an
                 ordinary
                 sheet
                 of
                 paper
                 ,
                 with
                 a
                 little
                 frame
                 ,
                 to
                 fasten
                 a
                 sheet
                 of
                 paper
                 upon
                 it
                 ,
                 which
                 being
                 also
                 set
                 upon
                 a
                 Staff
                 ,
                 you
                 may
                 by
                 help
                 of
                 your
                 Ruler
                 ,
                 take
                 a
                 distance
                 therewith
                 in
                 this
                 manner
                 .
              
               
                 Having
                 measured
                 the
                 distance
                 between
                 your
                 two
                 Stations
                 at
                 D
                 and
                 C
                 ,
                 draw
                 upon
                 your
                 paper
                 a
                 Line
                 ,
                 on
                 which
                 having
                 set
                 off
                 your
                 distance
                 place
                 your
                 Instrument
                 at
                 your
                 first
                 Station
                 C
                 ,
                 and
                 laying
                 your
                 Ruler
                 upon
                 the
                 Line
                 so
                 drawn
                 thereon
                 ,
                 turn
                 your
                 Instrument
                 till
                 through
                 the
                 Sights
                 you
                 can
                 espy
                 the
                 Station
                 at
                 D
                 ,
                 then
                 laying
                 your
                 Ruler
                 upon
                 the
                 Point
                 C
                 ,
                 turn
                 the
                 same
                 about
                 till
                 through
                 the
                 Sights
                 you
                 can
                 espy
                 the
                 Object
                 at
                 A
                 ,
                 and
                 there
                 draw
                 a
                 Line
                 by
                 the
                 side
                 of
                 your
                 Ruler
                 ,
                 and
                 remove
                 your
                 Instrument
                 to
                 D
                 ,
                 and
                 laying
                 your
                 Ruler
                 upon
                 the
                 Line
                 DC
                 ,
                 turn
                 the
                 Instrument
                 about
                 ,
                 till
                 through
                 the
                 Sight
                 you
                 can
                 espy
                 the
                 Mark
                 at
                 C
                 ,
                 and
                 then
                 laying
                 your
                 Ruler
                 upon
                 the
                 Point
                 D
                 ,
                 turn
                 the
                 same
                 ,
                 till
                 through
                 the
                 Sights
                 you
                 can
                 espy
                 the
                 Object
                 at
                 A
                 ,
                 and
                 by
                 the
                 side
                 of
                 your
                 Ruler
                 draw
                 a
                 Line
                 ,
                 which
                 must
                 be
                 extended
                 till
                 it
                 meet
                 with
                 the
                 Line
                 AC
                 ,
                 so
                 shall
                 the
                 Line
                 AD
                 being
                 measured
                 upon
                 your
                 Scale
                 of
                 Equal
                 
                 Parts
                 ,
                 be
                 the
                 distance
                 of
                 the
                 Object
                 from
                 D
                 ,
                 and
                 the
                 Line
                 AC
                 shall
                 be
                 the
                 distance
                 thereof
                 from
                 C.
                 
              
               
                 7.
                 
                 And
                 in
                 this
                 manner
                 may
                 the
                 distance
                 of
                 two
                 ,
                 three
                 or
                 more
                 Objects
                 be
                 taken
                 ,
                 from
                 any
                 two
                 Stations
                 from
                 whence
                 the
                 several
                 Objects
                 may
                 be
                 seen
                 ,
                 and
                 that
                 either
                 by
                 the
                 plain
                 Table
                 ,
                 or
                 Theodolite
                 .
              
            
             
               
                 CHAP.
                 XI
                 .
              
               
                 
                   How
                   to
                   take
                   the
                   Plot
                   of
                   a
                   Field
                   at
                   one
                   Station
                   ,
                   from
                   whence
                   the
                   several
                   Angles
                   may
                   be
                   seen
                   .
                
              
               
                 ALthough
                 there
                 are
                 several
                 Instruments
                 by
                 which
                 the
                 Plat
                 of
                 a
                 Field
                 may
                 be
                 taken
                 ,
                 yet
                 do
                 I
                 think
                 it
                 sufficient
                 to
                 shew
                 the
                 use
                 of
                 these
                 two
                 ,
                 the
                 plain
                 Table
                 and
                 Theodolite
                 .
              
               
                 2.
                 
                 In
                 the
                 use
                 of
                 either
                 of
                 which
                 the
                 same
                 chain
                 which
                 is
                 used
                 in
                 taking
                 of
                 heights
                 and
                 distances
                 ,
                 is
                 not
                 so
                 proper
                 .
                 I
                 rather
                 commend
                 that
                 which
                 is
                 known
                 by
                 the
                 Name
                 of
                 
                 Gunter's
                 Chain
                 ,
                 which
                 is
                 four
                 Pole
                 divided
                 into
                 100
                 Links
                 ;
                 being
                 as
                 I
                 conceive
                 much
                 better
                 for
                 the
                 casting
                 up
                 the
                 Content
                 of
                 a
                 Piece
                 of
                 Ground
                 ,
                 than
                 any
                 other
                 Chain
                 that
                 I
                 have
                 yet
                 heard
                 of
                 ,
                 whose
                 easie
                 use
                 shall
                 be
                 explained
                 in
                 its
                 proper
                 place
                 .
              
               
                 3.
                 
                 When
                 you
                 are
                 therefore
                 entered
                 the
                 Field
                 with
                 your
                 Instrument
                 ,
                 whether
                 plain
                 Table
                 ,
                 or
                 Theodolite
                 ,
                 having
                 chosen
                 out
                 your
                 Station
                 ,
                 let
                 visible
                 Marks
                 be
                 set
                 up
                 in
                 all
                 the
                 Corners
                 thereof
                 ,
                 and
                 then
                 if
                 you
                 use
                 the
                 plain
                 Table
                 ,
                 make
                 a
                 mark
                 upon
                 your
                 paper
                 ,
                 representing
                 your
                 Station
                 ,
                 and
                 laying
                 your
                 Ruler
                 to
                 this
                 Point
                 ,
                 direct
                 
                 your
                 Sights
                 to
                 the
                 several
                 Corners
                 of
                 the
                 Field
                 ,
                 where
                 you
                 have
                 caused
                 Marks
                 to
                 be
                 set
                 up
                 ,
                 and
                 draw
                 Lines
                 by
                 the
                 side
                 of
                 the
                 Ruler
                 upon
                 the
                 paper
                 to
                 the
                 point
                 representing
                 your
                 station
                 ,
                 then
                 measure
                 the
                 distance
                 of
                 every
                 of
                 these
                 Marks
                 from
                 your
                 Instrument
                 ,
                 and
                 by
                 your
                 Scale
                 set
                 those
                 distances
                 upon
                 the
                 Lines
                 drawn
                 upon
                 the
                 paper
                 ,
                 making
                 small
                 marks
                 at
                 the
                 end
                 of
                 every
                 such
                 distance
                 ,
                 Lines
                 drawn
                 from
                 Point
                 to
                 Point
                 ,
                 shall
                 give
                 you
                 upon
                 your
                 paper
                 ,
                 the
                 Plot
                 of
                 the
                 Field
                 ,
                 by
                 which
                 Plot
                 so
                 taken
                 the
                 content
                 of
                 the
                 Field
                 may
                 easily
                 be
                 computed
                 .
              
               
                 Example
                 .
                 Let
                 Fig.
                 31.
                 represent
                 a
                 Field
                 whose
                 Plot
                 is
                 required
                 ;
                 your
                 Table
                 being
                 placed
                 with
                 a
                 sheet
                 of
                 paper
                 thereupon
                 ,
                 make
                 a
                 Mark
                 about
                 the
                 middle
                 of
                 your
                 Table
                 ,
                 as
                 at
                 A.
                 apply
                 your
                 Ruler
                 from
                 this
                 Mark
                 to
                 B
                 and
                 draw
                 the
                 Line
                 AB
                 ,
                 then
                 with
                 your
                 Chain
                 measure
                 the
                 distance
                 thereof
                 which
                 suppose
                 to
                 be
                 11
                 Chains
                 36
                 Links
                 ,
                 then
                 take
                 11
                 Chains
                 36
                 Links
                 from
                 your
                 Scale
                 ,
                 and
                 set
                 that
                 distance
                 from
                 A
                 to
                 B
                 ,
                 and
                 at
                 B
                 make
                 a
                 mark
                 .
              
               
                 Then
                 directing
                 the
                 Sights
                 to
                 C
                 ,
                 draw
                 a
                 Line
                 by
                 the
                 side
                 of
                 your
                 Ruler
                 as
                 before
                 ,
                 and
                 measure
                 the
                 distance
                 AC
                 ,
                 which
                 suppose
                 to
                 be
                 7
                 Chains
                 and
                 44
                 Links
                 ,
                 this
                 distance
                 must
                 be
                 taken
                 from
                 your
                 Scale
                 ,
                 and
                 set
                 from
                 A
                 to
                 C
                 upon
                 your
                 paper
                 .
              
               
                 And
                 in
                 this
                 manner
                 you
                 must
                 direct
                 your
                 Sights
                 from
                 Mark
                 to
                 Mark
                 ,
                 until
                 you
                 have
                 drawn
                 the
                 Lines
                 and
                 set
                 down
                 the
                 distances
                 ,
                 between
                 all
                 the
                 Angles
                 in
                 the
                 Field
                 and
                 your
                 station
                 ,
                 which
                 being
                 done
                 ,
                 you
                 must
                 draw
                 the
                 Lines
                 from
                 one
                 Point
                 to
                 another
                 ,
                 till
                 you
                 conclude
                 where
                 you
                 first
                 began
                 ,
                 so
                 will
                 those
                 Lines
                 
                   BC.
                   CD
                   .
                   DE.
                   FG.
                
                 and
                 GB
                 ,
                 give
                 you
                 the
                 exact
                 Figure
                 of
                 the
                 Field
                 .
              
               
                 4.
                 
                 To
                 do
                 this
                 by
                 the
                 Theodolite
                 ,
                 in
                 stead
                 of
                 
                 drawing
                 Lines
                 upon
                 your
                 paper
                 in
                 the
                 Field
                 ,
                 you
                 must
                 have
                 a
                 little
                 Book
                 ,
                 in
                 which
                 the
                 Pages
                 must
                 be
                 divided
                 into
                 five
                 Columns
                 ,
                 in
                 the
                 first
                 Column
                 whereof
                 you
                 must
                 set
                 several
                 Letters
                 to
                 signifie
                 the
                 several
                 Angles
                 in
                 the
                 Field
                 ,
                 from
                 which
                 Lines
                 are
                 to
                 be
                 drawn
                 to
                 your
                 place
                 of
                 standing
                 ,
                 in
                 the
                 second
                 and
                 third
                 Columns
                 the
                 degrees
                 and
                 parts
                 taken
                 by
                 your
                 Instrument
                 ,
                 and
                 the
                 fourth
                 and
                 fifth
                 ,
                 to
                 set
                 down
                 your
                 distances
                 Chains
                 and
                 Links
                 ,
                 this
                 being
                 in
                 readiness
                 ,
                 and
                 have
                 placed
                 your
                 Instrument
                 direct
                 your
                 Sights
                 to
                 the
                 first
                 mark
                 at
                 B
                 ,
                 and
                 observe
                 how
                 many
                 Degrees
                 are
                 comprehended
                 between
                 the
                 Diameter
                 of
                 your
                 Instrument
                 ,
                 and
                 the
                 Ruler
                 ,
                 and
                 set
                 them
                 in
                 the
                 second
                 and
                 third
                 Columns
                 of
                 your
                 Book
                 against
                 the
                 Letter
                 B
                 ,
                 which
                 stands
                 for
                 your
                 first
                 Mark
                 ,
                 then
                 measure
                 the
                 distance
                 AB
                 as
                 before
                 ,
                 and
                 set
                 that
                 down
                 ,
                 in
                 the
                 fourth
                 and
                 fifth
                 Columns
                 ,
                 and
                 so
                 proceed
                 from
                 Mark
                 to
                 Mark
                 ,
                 until
                 you
                 have
                 taken
                 all
                 the
                 Angles
                 and
                 Distances
                 in
                 the
                 Field
                 ,
                 which
                 suppose
                 to
                 be
                 ,
                 as
                 they
                 are
                 expressed
                 in
                 the
                 following
                 Table
                 .
              
               
                 
                   
                     
                        
                    
                     
                       Degr.
                       
                    
                     
                       Part
                    
                     
                       Chains
                    
                     
                       Links
                    
                  
                   
                     
                       B
                    
                     
                       39
                    
                     
                       75
                    
                     
                       11
                    
                     
                       56
                    
                  
                   
                     
                       C
                    
                     
                       40
                    
                     
                       75
                    
                     
                       7
                    
                     
                       44
                    
                  
                   
                     
                       D
                    
                     
                       96
                    
                     
                       00
                    
                     
                       7
                    
                     
                       48
                    
                  
                   
                     
                       E
                    
                     
                       43
                    
                     
                       25
                    
                     
                       8
                    
                     
                       92
                    
                  
                   
                     
                       F
                    
                     
                       80
                    
                     
                       00
                    
                     
                       6
                    
                     
                       08
                    
                  
                   
                     
                       G
                    
                     
                       59
                    
                     
                       25
                    
                     
                       9
                    
                     
                       73
                    
                  
                
              
               
                 5.
                 
                 Having
                 thus
                 taken
                 the
                 Angles
                 and
                 Distances
                 in
                 the
                 Field
                 ,
                 to
                 protract
                 the
                 same
                 on
                 Paper
                 or
                 
                 Parchment
                 ,
                 cannot
                 be
                 difficult
                 ;
                 for
                 if
                 you
                 draw
                 a
                 Line
                 at
                 pleasure
                 as
                 EB
                 representing
                 the
                 Diameter
                 of
                 your
                 Instrument
                 about
                 the
                 middle
                 thereof
                 ,
                 as
                 at
                 A
                 ,
                 mark
                 a
                 Mark
                 ,
                 and
                 opening
                 your
                 Compasses
                 to
                 60
                 Degrees
                 in
                 your
                 Line
                 of
                 Chords
                 ,
                 upon
                 A
                 as
                 a
                 Center
                 describe
                 a
                 Circle
                 ,
                 then
                 lay
                 your
                 Field
                 book
                 before
                 you
                 seeing
                 that
                 your
                 first
                 Observattion
                 cut
                 no
                 Degrees
                 ,
                 there
                 are
                 no
                 Degrees
                 to
                 be
                 marked
                 out
                 in
                 the
                 Circle
                 ,
                 but
                 the
                 Degrees
                 at
                 C
                 are
                 40.75
                 which
                 being
                 taken
                 from
                 your
                 Line
                 of
                 Chords
                 ,
                 you
                 must
                 set
                 them
                 from
                 H
                 to
                 I
                 ,
                 and
                 draw
                 the
                 Line
                 AI.
                 the
                 Degrees
                 at
                 D
                 are
                 96
                 which
                 must
                 in
                 like
                 manner
                 be
                 set
                 from
                 I
                 to
                 K
                 ,
                 and
                 so
                 the
                 rest
                 in
                 order
                 .
              
               
                 This
                 done
                 observe
                 by
                 your
                 Field-book
                 the
                 length
                 of
                 every
                 Line
                 ,
                 as
                 the
                 Line
                 AB
                 at
                 your
                 first
                 Observation
                 was
                 11
                 Chains
                 and
                 36
                 Links
                 ,
                 which
                 being
                 by
                 your
                 Scale
                 set
                 from
                 A
                 will
                 give
                 the
                 Point
                 B
                 in
                 the
                 Paper
                 ,
                 the
                 second
                 distance
                 being
                 set
                 upon
                 AI
                 will
                 give
                 the
                 Point
                 C
                 ,
                 and
                 so
                 proceeding
                 with
                 the
                 rest
                 ,
                 you
                 will
                 have
                 the
                 Points
                 BCDEF
                 and
                 G
                 ,
                 by
                 which
                 draw
                 the
                 Lines
                 
                   BC.
                   CD
                   .
                   DE
                   ;
                   EF.
                   FG
                
                 and
                 GB
                 ,
                 and
                 so
                 at
                 last
                 you
                 have
                 the
                 Figure
                 of
                 the
                 Field
                 upon
                 your
                 Paper
                 ,
                 as
                 was
                 required
                 .
              
               
                 And
                 what
                 is
                 here
                 done
                 at
                 one
                 station
                 ,
                 may
                 be
                 done
                 at
                 two
                 or
                 more
                 ,
                 by
                 measuring
                 one
                 or
                 two
                 distances
                 from
                 your
                 first
                 station
                 ,
                 taking
                 at
                 every
                 station
                 ,
                 the
                 Degrees
                 and
                 distances
                 to
                 as
                 many
                 Angles
                 ,
                 as
                 are
                 visible
                 at
                 each
                 station
                 .
              
               
                 And
                 as
                 for
                 taking
                 the
                 the
                 Plot
                 of
                 a-Field
                 by
                 Intersection
                 of
                 Lines
                 ,
                 he
                 that
                 doth
                 but
                 consider
                 how
                 the
                 distances
                 of
                 several
                 Objects
                 may
                 be
                 taken
                 at
                 two
                 stations
                 ,
                 will
                 be
                 able
                 to
                 do
                 the
                 other
                 also
                 ,
                 and
                 therefore
                 I
                 think
                 it
                 needless
                 ,
                 to
                 make
                 any
                 illustration
                 by
                 example
                 .
              
            
             
               
               
                 CHAP.
                 XII
                 .
              
               
                 
                   How
                   to
                   take
                   the
                   Plot
                   of
                   a
                   Wood
                   ,
                   Park
                   or
                   other
                   Champion
                   Plain
                   ,
                   by
                   going
                   round
                   the
                   same
                   ,
                   and
                   making
                   Observation
                   at
                   every
                   Angle
                   .
                
              
               
                 BY
                 these
                 Directions
                 which
                 have
                 been
                 already
                 given
                 ,
                 may
                 the
                 Plot
                 of
                 any
                 Field
                 or
                 Fields
                 be
                 taken
                 ,
                 when
                 the
                 Angles
                 may
                 be
                 seen
                 alone
                 or
                 more
                 stations
                 within
                 the
                 Field
                 ,
                 which
                 though
                 it
                 is
                 the
                 case
                 of
                 some
                 Grounds
                 ,
                 it
                 is
                 not
                 the
                 case
                 of
                 all
                 ;
                 now
                 where
                 observation
                 of
                 the
                 Angles
                 cannot
                 be
                 observed
                 within
                 ,
                 they
                 must
                 be
                 observed
                 without
                 ,
                 and
                 although
                 this
                 may
                 be
                 done
                 by
                 the
                 plain
                 Table
                 ,
                 yet
                 as
                 I
                 judge
                 it
                 may
                 be
                 more
                 conveniently
                 done
                 by
                 the
                 Theodolite
                 ,
                 in
                 these
                 cases
                 thereof
                 I
                 chiefly
                 commend
                 that
                 Instrument
                 ,
                 I
                 know
                 some
                 use
                 a
                 Mariners
                 Compass
                 ,
                 but
                 the
                 working
                 with
                 a
                 Needle
                 is
                 not
                 only
                 troublesom
                 ,
                 but
                 many
                 times
                 uncertain
                 ,
                 yet
                 if
                 a
                 Needle
                 be
                 joyned
                 with
                 the
                 Theodolite
                 the
                 joynt
                 Observations
                 of
                 the
                 Angles
                 may
                 serve
                 to
                 confirm
                 one
                 another
                 .
              
               
                 2.
                 
                 Suppose
                 the
                 Fig.
                 32.
                 to
                 be
                 a
                 large
                 Wood
                 whose
                 Plot
                 you
                 desire
                 to
                 take
                 ;
                 Having
                 placed
                 your
                 Instrument
                 at
                 the
                 Angle
                 A
                 ,
                 lay
                 your
                 Ruler
                 on
                 the
                 Diameter
                 thereof
                 ,
                 turning
                 the
                 whole
                 Instrument
                 till
                 through
                 the
                 Sights
                 you
                 espy
                 the
                 Angle
                 at
                 K
                 ,
                 then
                 fasten
                 it
                 there
                 ,
                 and
                 turn
                 your
                 Ruler
                 upon
                 the
                 Center
                 ,
                 till
                 through
                 the
                 Sights
                 you
                 espy
                 your
                 second
                 Mark
                 at
                 B
                 ,
                 the
                 Degrees
                 cut
                 by
                 the
                 Ruler
                 do
                 give
                 the
                 quantity
                 of
                 that
                 Angle
                 BAK
                 ,
                 suppose
                 125
                 Degrees
                 ,
                 and
                 the
                 Line
                 AB
                 6
                 Chains
                 ,
                 45
                 Links
                 ,
                 which
                 you
                 must
                 note
                 in
                 your
                 Field-book
                 ,
                 as
                 was
                 shewed
                 before
                 .
              
               
               
                 3.
                 
                 Then
                 remove
                 your
                 Instrument
                 to
                 B
                 ,
                 and
                 laying
                 your
                 Ruler
                 upon
                 the
                 Diameter
                 thereof
                 ,
                 turn
                 it
                 about
                 ,
                 till
                 through
                 the
                 Sights
                 you
                 can
                 espy
                 your
                 third
                 mark
                 at
                 C
                 ,
                 and
                 there
                 fasten
                 your
                 Instrument
                 ,
                 then
                 turn
                 the
                 Ruler
                 backward
                 till
                 through
                 the
                 Sights
                 you
                 see
                 the
                 Angle
                 at
                 A
                 ,
                 the
                 Degrees
                 cut
                 by
                 the
                 Ruler
                 being
                 106.25
                 the
                 quantity
                 of
                 the
                 Angle
                 ABC
                 ,
                 and
                 the
                 Line
                 BC
                 containing
                 8
                 Chains
                 and
                 30
                 Links
                 ,
                 which
                 note
                 in
                 your
                 Field-book
                 ,
                 as
                 before
                 .
              
               
                 4.
                 
                 Remove
                 your
                 Instrument
                 unto
                 C
                 ,
                 and
                 laying
                 the
                 Ruler
                 on
                 the
                 Diameter
                 thereof
                 ,
                 turn
                 the
                 Instrument
                 about
                 till
                 through
                 the
                 Sights
                 you
                 see
                 the
                 Angle
                 at
                 D
                 ,
                 and
                 fixing
                 of
                 it
                 there
                 ,
                 turn
                 the
                 Ruler
                 upon
                 the
                 Center
                 till
                 you
                 see
                 your
                 last
                 station
                 at
                 B
                 ,
                 and
                 observe
                 the
                 Degrees
                 cut
                 thereby
                 ,
                 which
                 suppose
                 to
                 be
                 134
                 Degrees
                 ,
                 and
                 the
                 Line
                 CD
                 6
                 Chains
                 65
                 Links
                 ,
                 which
                 must
                 be
                 entered
                 into
                 your
                 Field-book
                 also
                 ,
                 and
                 because
                 the
                 Angle
                 BCD
                 is
                 an
                 inward
                 Angle
                 ,
                 note
                 it
                 with
                 the
                 Mark
                 
                 for
                 your
                 better
                 remembrance
                 .
              
               
                 5.
                 
                 Remove
                 your
                 Instrument
                 unto
                 D
                 ,
                 and
                 Iaying
                 the
                 Ruler
                 on
                 the
                 Diameter
                 ,
                 turn
                 the
                 Instrument
                 about
                 ,
                 till
                 through
                 the
                 Sights
                 ,
                 you
                 see
                 the
                 Angle
                 at
                 E
                 ,
                 and
                 there
                 fixing
                 your
                 Instrument
                 ,
                 turn
                 your
                 Ruler
                 backward
                 till
                 you
                 espy
                 the
                 Mark
                 at
                 C
                 ,
                 where
                 the
                 Degrees
                 cut
                 are
                 ,
                 suppose
                 68.0
                 and
                 the
                 Line
                 DE
                 8
                 Chains
                 and
                 23
                 Links
                 .
              
               
                 6.
                 
                 Remove
                 your
                 Instrument
                 unto
                 E
                 ,
                 and
                 laying
                 the
                 Ruler
                 on
                 the
                 Diameter
                 ,
                 turn
                 the
                 Instrument
                 about
                 ,
                 till
                 through
                 the
                 Sights
                 you
                 see
                 the
                 Angle
                 at
                 F
                 ,
                 and
                 there
                 fix
                 it
                 ,
                 then
                 turn
                 the
                 Ruler
                 backward
                 till
                 you
                 see
                 the
                 Angle
                 at
                 D
                 ,
                 where
                 the
                 Degrees
                 cut
                 by
                 the
                 Ruler
                 suppose
                 to
                 be
                 125
                 and
                 the
                 Line
                 EF
                 7
                 Chains
                 and
                 45
                 Links
                 .
              
               
               
                 7.
                 
                 Remove
                 your
                 Instrument
                 unto
                 F
                 ,
                 and
                 laying
                 your
                 Ruler
                 upon
                 the
                 Diameter
                 ,
                 turn
                 the
                 Instrument
                 about
                 ,
                 till
                 through
                 the
                 Sights
                 ,
                 you
                 see
                 the
                 Angle
                 at
                 G
                 ,
                 where
                 fix
                 the
                 same
                 ,
                 and
                 turn
                 the
                 Ruler
                 backward
                 till
                 you
                 see
                 the
                 Angle
                 at
                 E
                 ,
                 where
                 the
                 Degrees
                 cut
                 by
                 the
                 Ruler
                 are
                 70
                 ,
                 and
                 the
                 Line
                 FG
                 4
                 Chains
                 15
                 Links
                 ,
                 which
                 must
                 be
                 set
                 down
                 with
                 this
                 
                 or
                 the
                 like
                 Mark
                 at
                 the
                 Angle
                 .
              
               
                 8.
                 
                 Remove
                 your
                 Instrument
                 unto
                 G
                 ,
                 and
                 laying
                 your
                 Ruler
                 upon
                 the
                 Diameter
                 ,
                 turn
                 the
                 Instrument
                 about
                 ,
                 till
                 through
                 the
                 Sights
                 you
                 see
                 the
                 Angle
                 at
                 H
                 ,
                 where
                 fix
                 the
                 same
                 ,
                 and
                 turn
                 the
                 Ruler
                 backward
                 till
                 you
                 see
                 the
                 Angle
                 at
                 F
                 ,
                 where
                 the
                 Degrees
                 cut
                 by
                 the
                 Ruler
                 are
                 65.25
                 ,
                 and
                 the
                 Line
                 GH
                 5
                 Chains
                 50
                 Links
                 .
              
               
                 9.
                 
                 Remove
                 your
                 Instrument
                 in
                 like
                 manner
                 to
                 H
                 and
                 K
                 ,
                 and
                 take
                 thereby
                 the
                 Angles
                 and
                 Distances
                 as
                 before
                 ,
                 and
                 having
                 thus
                 made
                 observation
                 at
                 every
                 Angle
                 in
                 the
                 Field
                 ,
                 set
                 them
                 down
                 in
                 your
                 Field-book
                 ,
                 as
                 was
                 before
                 directed
                 ,
                 the
                 which
                 in
                 our
                 present
                 Example
                 will
                 be
                 as
                 followeth
                 .
              
               
                 
                   
                     
                       A
                    
                     
                       151.00
                    
                     
                       6.45
                    
                  
                   
                     
                       B
                    
                     
                       106.25
                    
                     
                       8.30
                    
                  
                   
                     
                       C
                       
                    
                     
                       134.00
                    
                     
                       6.65
                    
                  
                   
                     
                       D
                    
                     
                       68.00
                    
                     
                       8.23
                    
                  
                   
                     
                       E
                    
                     
                       125.00
                    
                     
                       7.45
                    
                  
                   
                     
                       F
                       
                    
                     
                       70.25
                    
                     
                       4.15
                    
                  
                   
                     
                       G
                    
                     
                       65.25
                    
                     
                       5.50
                    
                  
                   
                     
                       H
                    
                     
                       130.00
                    
                     
                       6.50
                    
                  
                   
                     
                       K
                    
                     
                       140.00
                    
                     
                       11.00
                    
                  
                
              
               
                 The
                 taking
                 of
                 the
                 inward
                 Angles
                 BCD
                 and
                 EFG
                 was
                 more
                 for
                 Conformity
                 sake
                 than
                 any
                 
                 necessity
                 ,
                 you
                 might
                 have
                 removed
                 your
                 Instrument
                 from
                 B
                 to
                 D
                 ,
                 from
                 E
                 to
                 G
                 ,
                 the
                 Length
                 of
                 the
                 Lines
                 
                   BC.
                   CD
                   .
                   EF
                
                 and
                 G
                 ,
                 would
                 have
                 given
                 by
                 protraction
                 the
                 Plot
                 of
                 the
                 Field
                 without
                 taking
                 these
                 Angles
                 by
                 observation
                 ;
                 many
                 other
                 compendious
                 ways
                 of
                 working
                 there
                 are
                 ,
                 which
                 I
                 shall
                 leave
                 to
                 the
                 discretion
                 of
                 the
                 Ingenious
                 Practitioner
                 .
              
               
                 10.
                 
                 The
                 Angles
                 and
                 Sides
                 of
                 the
                 Field
                 being
                 thus
                 taken
                 ,
                 to
                 lay
                 down
                 the
                 same
                 upon
                 Paper
                 ,
                 Parchment
                 ,
                 another
                 Instrument
                 called
                 a
                 Protractor
                 is
                 convenient
                 ,
                 the
                 which
                 is
                 so
                 well
                 known
                 to
                 Instrument-makers
                 ,
                 that
                 I
                 shall
                 not
                 need
                 here
                 to
                 describe
                 it
                 ,
                 the
                 chief
                 use
                 is
                 to
                 lay
                 down
                 Angles
                 ,
                 and
                 is
                 much
                 more
                 ready
                 for
                 that
                 purpose
                 than
                 a
                 Line
                 of
                 Chords
                 ,
                 though
                 in
                 effect
                 it
                 be
                 the
                 same
                 .
              
               
                 11.
                 
                 Having
                 then
                 this
                 Instrument
                 in
                 a
                 readiness
                 draw
                 upon
                 your
                 Paper
                 or
                 Parchment
                 upon
                 which
                 you
                 mean
                 to
                 lay
                 down
                 the
                 Plot
                 of
                 that
                 Field
                 ,
                 a
                 Line
                 at
                 pleasure
                 as
                 AB
                 .
                 Then
                 place
                 the
                 Center
                 of
                 your
                 Protractor
                 upon
                 the
                 Point
                 A
                 ,
                 and
                 because
                 the
                 Angle
                 of
                 your
                 first
                 observation
                 at
                 A
                 was
                 115
                 Degrees
                 00
                 Parts
                 ,
                 turn
                 your
                 Protractor
                 about
                 till
                 the
                 Line
                 AK
                 lie
                 directly
                 under
                 the
                 115
                 Degree
                 ;
                 and
                 then
                 at
                 the
                 beginning
                 of
                 your
                 Protractor
                 make
                 a
                 Mark
                 ,
                 ând
                 draw
                 the
                 Line
                 AB
                 ,
                 setting
                 off
                 6
                 Chains
                 45
                 Links
                 from
                 A
                 to
                 B.
                 
              
               
                 12.
                 
                 Then
                 lay
                 the
                 Center
                 of
                 your
                 Protractor
                 upon
                 the
                 Point
                 B
                 ,
                 and
                 here
                 turn
                 your
                 Protractor
                 about
                 ,
                 till
                 the
                 line
                 AB
                 lie
                 under
                 106
                 Degrees
                 25
                 Parts
                 ,
                 and
                 draw
                 the
                 Line
                 BC
                 ,
                 setting
                 off
                 the
                 Distance
                 8
                 Chains
                 ,
                 30
                 Links
                 from
                 B
                 to
                 C.
                 
              
               
                 13.
                 
                 Then
                 lay
                 the
                 Center
                 of
                 your
                 Protractor
                 upon
                 the
                 Point
                 C
                 ,
                 and
                 turn
                 the
                 same
                 about
                 till
                 the
                 Line
                 BC
                 lie
                 under
                 134
                 Degrees
                 ,
                 but
                 remember
                 
                 to
                 make
                 it
                 an
                 inward
                 Angle
                 ,
                 as
                 it
                 is
                 marked
                 in
                 your
                 Field-Book
                 ,
                 and
                 there
                 make
                 a
                 Mark
                 ,
                 and
                 draw
                 the
                 Line
                 CD
                 ,
                 setting
                 off
                 6
                 Chains
                 ,
                 65
                 Links
                 from
                 C
                 to
                 D.
                 
              
               
                 And
                 thus
                 must
                 you
                 do
                 with
                 the
                 rest
                 of
                 the
                 Sides
                 and
                 Angles
                 ,
                 till
                 you
                 come
                 to
                 protract
                 your
                 last
                 Angle
                 at
                 H
                 ,
                 which
                 being
                 laid
                 down
                 according
                 to
                 the
                 former
                 Directions
                 the
                 Line
                 HK
                 will
                 cut
                 the
                 Line
                 AK
                 making
                 AK
                 11
                 Chains
                 and
                 HK
                 6
                 Chains
                 ,
                 50
                 Links
                 .
                 This
                 work
                 may
                 be
                 also
                 performed
                 by
                 protracting
                 your
                 last
                 observation
                 first
                 ;
                 for
                 having
                 drawn
                 the
                 Line
                 AK
                 ,
                 you
                 may
                 lay
                 the
                 Center
                 of
                 your
                 Protractor
                 upon
                 the
                 Point
                 K
                 ,
                 and
                 the
                 Diameter
                 upon
                 the
                 Line
                 AK
                 ;
                 and
                 because
                 your
                 Angle
                 at
                 K
                 by
                 observation
                 was
                 140
                 Degrees
                 ,
                 you
                 must
                 make
                 a
                 Mark
                 by
                 the
                 Side
                 of
                 your
                 Protractor
                 at
                 140
                 Degrees
                 ;
                 and
                 draw
                 the
                 Line
                 KH
                 ,
                 setting
                 off
                 6
                 Chains
                 ,
                 50
                 Links
                 from
                 K
                 to
                 H.
                 And
                 thus
                 proceeding
                 with
                 the
                 rest
                 of
                 the
                 Lines
                 and
                 Angles
                 ,
                 you
                 shall
                 find
                 the
                 Plot
                 of
                 your
                 Field
                 at
                 last
                 to
                 close
                 at
                 A
                 ,
                 as
                 before
                 it
                 did
                 at
                 K.
                 
              
            
             
               
                 CHAP.
                 XIII
                 .
              
               
                 
                   The
                   Plot
                   of
                   the
                   Field
                   being
                   taken
                   by
                   any
                   Instrument
                   ,
                   how
                   to
                   compute
                   the
                   Content
                   thereof
                   in
                   Acres
                   ,
                   Roods
                   ,
                   and
                   Perches
                   .
                
              
               
                 THe
                 measuring
                 of
                 many
                 sided
                 plain
                 Figures
                 hath
                 been
                 already
                 shewed
                 in
                 the
                 13
                 Proposition
                 of
                 the
                 8
                 Chapter
                 ,
                 which
                 being
                 but
                 well
                 considered
                 ,
                 to
                 compute
                 the
                 Content
                 of
                 a
                 Field
                 cannot
                 be
                 difficult
                 ;
                 It
                 must
                 be
                 remembred
                 indeed
                 that
                 40
                 square
                 Pearches
                 do
                 make
                 an
                 Acre
                 .
              
               
               
                 2.
                 
                 Now
                 then
                 if
                 the
                 Plot
                 be
                 taken
                 by
                 a
                 four
                 Pole
                 Chain
                 divided
                 into
                 100
                 Links
                 ,
                 as
                 16
                 square
                 Poles
                 are
                 the
                 tenth
                 part
                 of
                 an
                 Acre
                 ;
                 so
                 10.000
                 square
                 Links
                 of
                 such
                 a
                 Chain
                 are
                 equal
                 to
                 16
                 square
                 Pole
                 ,
                 or
                 Perches
                 ;
                 and
                 by
                 consequence
                 100.000
                 square
                 Links
                 are
                 equal
                 to
                 an
                 Acre
                 ,
                 or
                 the
                 square
                 Pearches
                 .
              
               
                 3.
                 
                 Having
                 then
                 converted
                 your
                 Plot
                 into
                 Triangles
                 ,
                 you
                 must
                 cast
                 up
                 the
                 Content
                 of
                 each
                 Triangle
                 as
                 hath
                 been
                 shewed
                 ,
                 and
                 then
                 add
                 the
                 several
                 Contents
                 into
                 one
                 Sum
                 ,
                 and
                 from
                 the
                 aggregate
                 cut
                 off
                 five
                 Figures
                 towards
                 the
                 right
                 hand
                 ;
                 the
                 remainer
                 of
                 the
                 Figures
                 towards
                 the
                 left
                 hand
                 are
                 Acres
                 ,
                 and
                 the
                 five
                 Figures
                 so
                 cut
                 off
                 towards
                 the
                 right
                 hand
                 are
                 parts
                 of
                 an
                 Acre
                 ,
                 which
                 being
                 multiplied
                 by
                 four
                 ,
                 if
                 you
                 cut
                 off
                 five
                 Figures
                 from
                 the
                 Product
                 ,
                 the
                 Figures
                 remaining
                 towards
                 the
                 left
                 hand
                 are
                 Roods
                 ,
                 and
                 the
                 five
                 Figures
                 cut
                 off
                 are
                 the
                 parts
                 of
                 a
                 Rood
                 ,
                 which
                 being
                 multiplied
                 by
                 forty
                 ,
                 if
                 you
                 cut
                 off
                 five
                 Figures
                 from
                 the
                 Product
                 ,
                 the
                 Figures
                 remaining
                 towards
                 the
                 left
                 hand
                 are
                 Perches
                 ,
                 and
                 the
                 Figures
                 cut
                 off
                 are
                 the
                 Parts
                 of
                 a
                 Pearch
                 .
              
               
                 Example
                 .
                 Let
                 258.94726
                 be
                 the
                 Sum
                 of
                 several
                 Triangles
                 ,
                 or
                 the
                 Content
                 of
                 a
                 Field
                 ready
                 cast
                 up
                 ,
                 the
                 three
                 Figures
                 towards
                 the
                 left
                 hand
                 258
                 are
                 the
                 Acres
                 ,
                 and
                 the
                 other
                 Figures
                 towards
                 the
                 right
                 hand
                 94726
                 are
                 the
                 Decimal
                 Parts
                 of
                 an
                 Acre
                 ,
                 which
                 being
                 multiplied
                 by
                 4
                 ,
                 the
                 Product
                 is
                 3.78904
                 ,
                 that
                 is
                 three
                 Roods
                 and
                 78904
                 Decimal
                 Parts
                 of
                 a
                 Rood
                 ,
                 which
                 being
                 multiplied
                 by
                 40
                 ,
                 the
                 product
                 is
                 31.56160
                 ,
                 that
                 is
                 31
                 Perches
                 and
                 56160
                 Decimal
                 Parts
                 of
                 a
                 Perch
                 ;
                 and
                 therefore
                 in
                 such
                 a
                 Field
                 there
                 are
                 Acres
                 258
                 ,
                 Roods
                 3
                 ,
                 Pearches
                 31
                 ,
                 and
                 56160
                 Decimal
                 Parts
                 of
                 a
                 Perch
                 .
              
            
             
               
               
                 CHAP.
                 XIV
                 .
              
               
                 
                   How
                   to
                   take
                   the
                   Plot
                   of
                   Mountainous
                   and
                   uneven
                   Grounds
                   ,
                   and
                   how
                   to
                   find
                   the
                   Content
                   .
                
              
               
                 VVHen
                 you
                 are
                 to
                 take
                 the
                 Plot
                 of
                 any
                 Mountainous
                 or
                 uneven
                 piece
                 of
                 Ground
                 ,
                 such
                 as
                 is
                 that
                 in
                 Figure
                 33
                 ,
                 you
                 must
                 first
                 place
                 your
                 Instrument
                 at
                 A
                 ,
                 and
                 direct
                 your
                 Sights
                 to
                 B
                 ,
                 measuring
                 the
                 Line
                 AB
                 ,
                 observing
                 the
                 Angle
                 GAB
                 ,
                 as
                 was
                 shewed
                 before
                 ,
                 and
                 so
                 proceed
                 from
                 B
                 to
                 C
                 ,
                 and
                 because
                 there
                 is
                 an
                 ascent
                 from
                 C
                 to
                 D
                 ,
                 you
                 must
                 measure
                 the
                 true
                 length
                 thereof
                 with
                 your
                 Chain
                 ,
                 and
                 set
                 that
                 down
                 in
                 your
                 Book
                 ,
                 but
                 your
                 Plot
                 must
                 he
                 drawn
                 according
                 to
                 the
                 length
                 of
                 the
                 Horizontal
                 Line
                 ,
                 which
                 must
                 be
                 taken
                 by
                 computing
                 the
                 Base
                 of
                 a
                 right
                 angled
                 Plain
                 Triangle
                 ,
                 as
                 hath
                 been
                 shewed
                 before
                 ,
                 and
                 so
                 proceed
                 from
                 Angle
                 to
                 Angle
                 until
                 you
                 have
                 gone
                 round
                 the
                 Field
                 ,
                 and
                 having
                 drawn
                 the
                 Figure
                 thereof
                 upon
                 your
                 Paper
                 ,
                 reduce
                 into
                 Triangles
                 and
                 Trapezias
                 ,
                 as
                 
                   ABC
                   .
                   CDE
                   .
                   ACEF
                
                 and
                 AFG
                 .
                 then
                 from
                 the
                 Angles
                 
                   B.
                   C.
                   D.
                   F
                
                 and
                 G
                 ;
                 let
                 fall
                 the
                 Perpendiculars
                 ,
                 
                   BK
                   .
                   CN
                   .
                   DL
                   .
                   FM
                   .
                
                 and
                 GH
                 .
                 This
                 done
                 you
                 must
                 measure
                 the
                 Field
                 again
                 from
                 Angle
                 to
                 Angle
                 ,
                 setting
                 down
                 the
                 Distance
                 taken
                 in
                 a
                 straight
                 Line
                 over
                 Hill
                 and
                 Dale
                 ,
                 and
                 so
                 likewise
                 the
                 several
                 Perpendiculars
                 ,
                 which
                 will
                 be
                 much
                 longer
                 than
                 the
                 streight
                 Lines
                 measured
                 on
                 your
                 Scale
                 ,
                 and
                 by
                 these
                 Lines
                 thus
                 measured
                 with
                 your
                 Chain
                 cast
                 up
                 the
                 Content
                 ;
                 which
                 will
                 be
                 much
                 more
                 than
                 the
                 Horizontal
                 Content
                 of
                 that
                 Field
                 according
                 to
                 the
                 Plot
                 ,
                 but
                 if
                 it
                 should
                 be
                 otherwise
                 plotted
                 than
                 by
                 the
                 Horizontal
                 
                 Lines
                 ,
                 the
                 Figure
                 thereof
                 could
                 not
                 be
                 contained
                 within
                 its
                 proper
                 limits
                 ,
                 but
                 being
                 laid
                 down
                 among
                 other
                 Grounds
                 ,
                 would
                 force
                 some
                 of
                 them
                 out
                 of
                 their
                 places
                 ,
                 and
                 therefore
                 such
                 Fields
                 as
                 these
                 must
                 be
                 shadowed
                 off
                 with
                 Hills
                 ,
                 if
                 it
                 be
                 but
                 to
                 shew
                 that
                 the
                 Content
                 thereof
                 is
                 computed
                 according
                 to
                 the
                 true
                 length
                 of
                 the
                 Lines
                 from
                 Corner
                 to
                 Corner
                 ,
                 and
                 not
                 according
                 to
                 their
                 Distance
                 measured
                 by
                 Scale
                 in
                 the
                 Plot.
                 
              
            
             
               
                 CHAP.
                 XV.
                 
              
               
                 
                   How
                   to
                   reduce
                   Statute
                   Measure
                   into
                   Customary
                   ,
                   and
                   the
                   contrary
                   .
                
              
               
                 VVHereas
                 an
                 Acre
                 of
                 Ground
                 by
                 Statute
                 Measure
                 is
                 to
                 contain
                 160
                 square
                 Perches
                 ,
                 measured
                 by
                 the
                 Pole
                 or
                 Perch
                 of
                 sixteen
                 foot
                 and
                 a
                 half
                 :
                 In
                 many
                 places
                 of
                 this
                 Nation
                 ,
                 the
                 Pole
                 or
                 Perch
                 doth
                 by
                 custom
                 contain
                 18
                 foot
                 ,
                 in
                 some
                 20.
                 24.
                 28
                 
                 Foot
                 ;
                 it
                 will
                 be
                 therefore
                 required
                 to
                 give
                 the
                 Content
                 of
                 a
                 Field
                 according
                 to
                 such
                 several
                 quantities
                 of
                 the
                 Pole
                 or
                 Perch
                 .
              
               
                 2.
                 
                 To
                 do
                 this
                 you
                 must
                 consider
                 how
                 many
                 square
                 Feet
                 there
                 is
                 in
                 a
                 Pole
                 according
                 to
                 these
                 several
                 Quantities
                 .
              
               
                 
                   In
                   16.5
                   to
                   the
                   Pole
                   ,
                   there
                   are
                   272.25
                   sq.
                   feet
                   .
                
                 
                   In
                   18
                   to
                   the
                   Pole
                   there
                   are
                   324
                   square
                   feet
                   .
                
                 
                   In
                   20
                   to
                   the
                   Pole
                   there
                   are
                   400
                   square
                   feet
                   .
                
                 
                   In
                   24
                   to
                   the
                   Pole
                   there
                   are
                   576
                   square
                   feet
                   .
                
                 
                   In
                   28
                   to
                   the
                   Pole
                   there
                   are
                   784
                   square
                   feet
                   .
                
              
               
                 Now
                 then
                 if
                 it
                 were
                 desired
                 to
                 reduce
                 7
                 Acres
                 ,
                 3
                 Roods
                 ,
                 27
                 Perches
                 ,
                 according
                 to
                 Statute
                 Measure
                 ,
                 into
                 Perches
                 of
                 18
                 Foot
                 to
                 the
                 Perch
                 ;
                 first
                 reduce
                 
                 your
                 given
                 quantity
                 ,
                 7
                 Acres
                 .
                 3
                 Rods
                 ,
                 27
                 Poles
                 into
                 Perches
                 ,
                 and
                 they
                 make
                 1267
                 Perches
                 .
              
               
                 Then
                 say
                 ,
                 as
                 324.
                 to
                 272.
                 25.
                 so
                 is
                 1267
                 to
                 1065.
                 6.
                 that
                 is
                 1065
                 Perches
                 ,
                 and
                 6
                 tenths
                 of
                 a
                 Perch
                 .
                 But
                 to
                 reduce
                 customary
                 Measure
                 into
                 statute
                 measure
                 ,
                 say
                 as
                 272.
                 25.
                 is
                 to
                 324
                 so
                 is
                 1267
                 Perches
                 in
                 customary
                 measure
                 ,
                 to
                 1507.
                 8
                 that
                 is
                 1507
                 Perches
                 and
                 8
                 tenths
                 of
                 a
                 Perch
                 in
                 statute
                 measure
                 ,
                 the
                 like
                 may
                 be
                 done
                 ,
                 with
                 the
                 customary
                 measures
                 of
                 20.24
                 and
                 28
                 or
                 any
                 other
                 measure
                 that
                 shall
                 be
                 propounded
                 .
              
            
             
               
                 CHAP.
                 XVI
                 .
              
               
                 
                   Of
                   the
                   Measuring
                   of
                   solid
                   Bodies
                   .
                
              
               
                 HAving
                 shewed
                 how
                 the
                 content
                 of
                 all
                 plains
                 may
                 be
                 computed
                 ,
                 we
                 are
                 now
                 come
                 to
                 the
                 measuring
                 of
                 solid
                 Bodies
                 ,
                 as
                 Prisms
                 ,
                 Pyramids
                 and
                 Spheres
                 ,
                 the
                 which
                 shall
                 be
                 explained
                 in
                 the
                 Propositions
                 following
                 .
              
               
                 
                   Proposition
                   .
                   I.
                   
                
                 
                   
                     The
                     base
                     of
                     a
                     Prism
                     or
                     Cylinder
                     being
                     given
                     ,
                     to
                     find
                     the
                     solid
                     content
                     .
                  
                
                 
                   The
                   base
                   of
                   
                     a
                     Prism
                  
                   is
                   either
                   Triangular
                   ,
                   as
                   the
                   Pentahedron
                   ;
                   Quadrangular
                   ,
                   as
                   the
                   Hexahedron
                   ,
                   or
                   Multangular
                   ,
                   or
                   the
                   Polyhedron
                   Prism
                   ,
                   all
                   which
                   must
                   be
                   computed
                   as
                   hath
                   been
                   shewed
                   ,
                   which
                   done
                   if
                   you
                   multiply
                   the
                   base
                   given
                   by
                   the
                   altitude
                   ,
                   the
                   product
                   shall
                   be
                   the
                   solid
                   content
                   required
                   .
                
                 
                   Example
                   .
                   In
                   an
                   Hexahedron
                   Prism
                   ,
                   whose
                   base
                   
                   is
                   quadrangular
                   ,
                   one
                   side
                   of
                   the
                   Base
                   being
                   65
                   foot
                   and
                   the
                   other
                   43
                   ,
                   the
                   Superficies
                   or
                   Base
                   will
                   be
                   27.
                   95.
                   
                   Which
                   being
                   multiplyed
                   by
                   the
                   Altitude
                   ,
                   suppose
                   12.
                   5.
                   the
                   product
                   .
                   359.
                   375.
                   is
                   the
                   solid
                   content
                   required
                   .
                
                 
                   In
                   like
                   manner
                   the
                   Base
                   of
                   a
                   Cylinder
                   being
                   45.
                   6.
                   and
                   the
                   altitude
                   15.
                   4.
                   the
                   content
                   will
                   be
                   702.
                   24.
                   
                
                 
                   And
                   in
                   this
                   manner
                   may
                   Timber
                   be
                   measured
                   whether
                   round
                   or
                   squared
                   ,
                   be
                   the
                   sides
                   of
                   the
                   squared
                   Timber
                   equal
                   or
                   unequal
                   .
                
                 
                   Example
                   .
                   Let
                   the
                   Diameter
                   of
                   a
                   round
                   piece
                   of
                   Timber
                   be
                   2.
                   75
                   foot
                   .
                   Then
                   ,
                   As
                   1
                   it
                   to
                   785397.
                   so
                   is
                   the
                   square
                   of
                   the
                   Diameter
                   2.
                   75.
                   to
                   5.9395
                   the
                   Superficial
                   content
                   of
                   that
                   Circle
                   .
                
                 
                   Or
                   if
                   the
                   circumference
                   had
                   been
                   given
                   8.
                   64.
                   then
                   ,
                   As
                   1
                   is
                   to
                   079578
                   ,
                   so
                   is
                   the
                   square
                   of
                   8.
                   64.
                   to
                   5.9404
                   the
                   superficial
                   content
                   .
                
                 
                   Now
                   then
                   if
                   you
                   multiply
                   this
                   Base
                   5.
                   94.
                   by
                   the
                   length
                   ,
                   suppose
                   21
                   foot
                   ,
                   the
                   content
                   will
                   be
                   124.
                   74.
                   
                
                 
                   If
                   the
                   side
                   of
                   a
                   piece
                   of
                   Timber
                   perfectly
                   square
                   be
                   1.15
                   this
                   side
                   being
                   multiplyed
                   by
                   it self
                   ,
                   the
                   product
                   will
                   be
                   1.3225
                   the
                   superficial
                   content
                   ,
                   or
                   content
                   of
                   the
                   Base
                   ,
                   which
                   being
                   multiplyed
                   by
                   21
                   the
                   length
                   ,
                   the
                   content
                   will
                   be
                   27.
                   7745.
                   
                
                 
                   Or
                   if
                   a
                   piece
                   of
                   Timber
                   were
                   in
                   breadth
                   1.
                   15.
                   in
                   depth
                   1.5
                   the
                   content
                   of
                   the
                   Base
                   would
                   be
                   1.725
                   which
                   being
                   multiplied
                   by
                   21
                   the
                   length
                   ,
                   the
                   content
                   will
                   be
                   .
                   36.
                   225.
                   
                
              
               
                 
                   Proposition
                   .
                   II.
                   
                
                 
                   
                     The
                     Base
                     and
                     Altitude
                     of
                     a
                     Pyramid
                     or
                     Cone
                     being
                     given
                     ,
                     to
                     find
                     the
                     solid
                     content
                     .
                  
                
                 
                 
                   Multiply
                   the
                   Altitude
                   by
                   a
                   third
                   part
                   of
                   the
                   Base
                   ,
                   or
                   the
                   whole
                   Base
                   by
                   a
                   third
                   part
                   of
                   the
                   Altitude
                   ,
                   the
                   Product
                   shall
                   be
                   the
                   solid
                   content
                   required
                   .
                
                 
                   Example
                   .
                   In
                   a
                   Pyramid
                   having
                   a
                   Quadrangular
                   Base
                   as
                   in
                   Fig.
                   22.
                   
                   The
                   side
                   
                     CF
                     17.
                     
                     CD
                  
                   9.
                   5.
                   the
                   Product
                   is
                   the
                   Base
                   CDEF
                   .
                   161.
                   5
                   ,
                   which
                   being
                   multiplyed
                   by
                   10.5
                   the
                   third
                   of
                   the
                   Altitude
                   AB
                   31.5
                   the
                   Product
                   is
                   1695.75
                   the
                   content
                   .
                   Or
                   the
                   third
                   of
                   the
                   Base
                   .
                   viz.
                   53.
                   &
                   3
                   being
                   multiplied
                   by
                   the
                   whole
                   Altitude
                   AB
                   31.5
                   the
                   Product
                   will
                   be
                   the
                   content
                   as
                   before
                   .
                
                 
                   2.
                   
                   Example
                   .
                   In
                   Fig.
                   21.
                   
                   Let
                   there
                   be
                   given
                   the
                   Diameter
                   of
                   the
                   Cone
                   AB
                   3.
                   5.
                   
                   The
                   Base
                   will
                   be
                   96.
                   25.
                   whose
                   Altitude
                   let
                   be
                   CD
                   16.92
                   the
                   third
                   part
                   thereof
                   is
                   5.64
                   &
                   96.25
                   being
                   multiplied
                   by
                   5.64
                   ,
                   the
                   Product
                   542.85
                   is
                   the
                   solid
                   content
                   required
                   .
                
              
               
                 
                   Proposition
                   .
                   III.
                   
                
                 
                   
                     The
                     Axis
                     of
                     a
                     Sphere
                     being
                     given
                     ,
                     to
                     find
                     the
                     solid
                     content
                     .
                  
                
                 
                   If
                   you
                   multiply
                   the
                   Cube
                   of
                   the
                   Axis
                   given
                   by
                   523598
                   the
                   solid
                   content
                   of
                   a
                   Sphere
                   whose
                   Axis
                   is
                   an
                   unite
                   ,
                   the
                   Product
                   shall
                   be
                   the
                   solid
                   content
                   required
                   .
                
                 
                   Example
                   .
                   Let
                   the
                   Axis
                   given
                   be
                   ●
                   ,
                   the
                   Cube
                   thereof
                   is
                   27
                   ,
                   by
                   which
                   if
                   you
                   multiply
                   .
                   523598
                   ,
                   the
                   Product
                   14.137166
                   is
                   the
                   solid
                   content
                   required
                   .
                
              
               
                 
                 
                   Proposition
                   .
                   IV.
                   
                
                 
                   
                     The
                     Basis
                     and
                     Altitude
                     of
                     the
                     Frustum
                     of
                     a
                     Pyramid
                     or
                     Cone
                     being
                     given
                     ,
                     to
                     find
                     the
                     content
                     .
                  
                
                 
                   If
                   the
                   aggregate
                   of
                   both
                   the
                   Bases
                   of
                   the
                   Frustan
                   and
                   the
                   mean
                   proportional
                   betwe●n
                   them
                   ,
                   shall
                   be
                   multiplied
                   by
                   the
                   third
                   part
                   of
                   the
                   Altitude
                   ,
                   the
                   Product
                   shall
                   be
                   the
                   solid
                   content
                   of
                   the
                   Frustum
                   .
                
                 
                   Example
                   .
                   In
                   Fig.
                   22.
                   
                   Let
                   CDEF
                   represent
                   the
                   greater
                   Base
                   of
                   a
                   Pyramid
                   ,
                   whose
                   superficial
                   content
                   let
                   be
                   1.
                   92
                   ,
                   and
                   let
                   the
                   lesser
                   Base
                   be
                   HGLKO
                   .
                   85
                   the
                   mean
                   proportional
                   between
                   them
                   is
                   .
                   1.
                   2775
                   and
                   the
                   aggregate
                   of
                   these
                   three
                   numbers
                   is
                   .
                   4.
                   0475.
                   
                   Let
                   the
                   given
                   Altitude
                   be
                   15.
                   the
                   third
                   part
                   thereof
                   is
                   .
                   5
                   by
                   which
                   if
                   you
                   multiply
                   4.0475
                   the
                   Product
                   20.
                   2375
                   is
                   the
                   content
                   of
                   the
                   Frustum
                   Pyramid
                   .
                
                 
                   And
                   to
                   find
                   the
                   content
                   of
                   the
                   Frustum
                   Cone
                   .
                   I
                   say
                   .
                
                 
                   As.
                   1.
                   ro
                   78539.
                   so
                   20.23
                   to
                   15.
                   884397
                   ,
                   the
                   content
                   of
                   the
                   Cone
                   required
                   .
                
                 
                   But
                   if
                   the
                   Bases
                   of
                   the
                   Frustum
                   Pyramid
                   shall
                   be
                   square
                   ,
                   you
                   may
                   find
                   the
                   content
                   in
                   this
                   manner
                   .
                
                 
                   Multiply
                   each
                   Diameter
                   by
                   it self
                   and
                   by
                   one
                   another
                   ,
                   and
                   the
                   aggregate
                   of
                   these
                   Products
                   ,
                   by
                   the
                   third
                   part
                   of
                   the
                   altitude
                   ,
                   the
                   last
                   Product
                   shall
                   be
                   the
                   content
                   of
                   the
                   Frustum
                   Pyramid
                   .
                
                 
                   Example
                   .
                   Let
                   the
                   Diameter
                   of
                   the
                   greater
                   Base
                   be
                   144
                   ,
                   the
                   Diameter
                   of
                   the
                   lesser
                   Base
                   108
                   ,
                   and
                   the
                   altitude
                   60.
                   
                
                 
                   
                   
                     The
                     Square
                     of
                     144
                     is
                  
                   
                     20736
                  
                   
                     The
                     Square
                     of
                     108
                     is
                  
                   
                     11664
                  
                   
                     The
                     Product
                     of
                     1444108
                     is
                  
                   
                     15552
                  
                   
                     The
                     Sum
                     of
                     these
                     3
                     Products
                     is
                  
                   
                     47952
                  
                
                 
                   Which
                   being
                   multiplyed
                   by
                   20
                   the
                   third
                   part
                   of
                   the
                   Altitude
                   ,
                   the
                   Product
                   959040
                   is
                   the
                   content
                   of
                   the
                   Frustum
                   Pyramid
                   .
                
                 
                   And
                   this
                   content
                   being
                   multiplied
                   by
                   .785
                   39
                   the
                   content
                   of
                   the
                   Frustum
                   Cone
                   will
                   be
                   .753
                   .228
                   .
                
                 
                   
                     Another
                     way
                  
                   .
                
                 
                   Find
                   the
                   content
                   of
                   the
                   whole
                   Pyramid
                   of
                   the
                   greater
                   and
                   lesser
                   Diameter
                   ,
                   the
                   lesser
                   content
                   deducted
                   from
                   the
                   greater
                   ,
                   the
                   remain
                   shall
                   be
                   the
                   content
                   of
                   the
                   Frustum
                   .
                   To
                   find
                   the
                   content
                   of
                   the
                   whole
                   Pyramid
                   ,
                   you
                   must
                   first
                   find
                   their
                   several
                   Altitudes
                   in
                   this
                   manner
                   .
                
                 
                   As
                   the
                   difference
                   between
                   the
                   Diameters
                   ,
                
                 
                   Is
                   to
                   the
                   lesser
                   Diameter
                   .
                
                 
                   So
                   is
                   the
                   Altitude
                   given
                   ,
                   to
                   the
                   Altitude
                   cut
                   off
                   .
                
                 
                   Example
                   .
                   The
                   difference
                   between
                   the
                   former
                   Diameter
                   .
                   144.
                   and
                   108
                   is
                   36
                   ,
                   the
                   Altitude
                   60.
                   now
                   then
                   As
                   36.
                   108
                   
                   ∷
                   60.
                   108.
                   the
                   altitude
                   cut
                   off
                   .
                
                 
                   Now
                   then
                   if
                   you
                   mnltiply
                   the
                   lesser
                   Base
                   1
                   1664
                   by
                   60
                   the
                   third
                   part
                   of
                   180
                   the
                   Product
                   699840
                   is
                   the
                   content
                   of
                   that
                   Pyramid
                   .
                
                 
                   And
                   adding
                   60
                   to
                   180
                   the
                   Altitude
                   of
                   the
                   greater
                   Pyramid
                   is
                   240
                   ,
                   the
                   third
                   part
                   whereof
                   is
                   80
                   ,
                   by
                   which
                   if
                   you
                   multiply
                   the
                   greater
                   Base
                   before
                   found
                   ,
                   70736
                   ,
                   the
                   Product
                   is
                   the
                   content
                   of
                   the
                   
                   greater
                   Pyramid
                   .
                   1658880
                   ,
                   from
                   which
                   if
                   you
                   deduct
                   the
                   lesser
                   699840
                   the
                   remainer
                   959040
                   is
                   the
                   content
                   of
                   the
                   Frustum
                   Pyramid
                   as
                   before
                   .
                
                 
                   And
                   upon
                   these
                   grounds
                   may
                   the
                   content
                   of
                   Taper
                   Timber
                   ,
                   whether
                   round
                   or
                   square
                   ,
                   and
                   of
                   Brewers
                   Tuns
                   ,
                   whether
                   Circular
                   or
                   Elliptical
                   ,
                   be
                   computed
                   ,
                   as
                   by
                   the
                   following
                   Propositions
                   shall
                   be
                   explained
                   .
                
              
               
                 
                   Proposition
                   .
                   V.
                   
                
                 
                   
                     The
                     breadth
                     and
                     depth
                     of
                     a
                     Taper
                     piece
                     of
                     Squared
                     Timber
                     ,
                     both
                     ends
                     being
                     given
                     together
                     with
                     the
                     length
                     ,
                     to
                     find
                     the
                     content
                     .
                  
                
                 
                   
                     Let
                     the
                     given
                     Dimensions
                     .
                  
                   
                     At
                     the
                     Bottom
                     be
                     A.
                     5.75
                     and
                     B
                     2.34
                  
                   
                     At
                     the
                     Top.
                     C.
                     2.16
                     and
                     D.
                     1.83
                     .
                  
                   
                     And
                     let
                     the
                     given
                     length
                     be
                     24
                     Foot.
                     
                  
                
                 
                   According
                   to
                   the
                   last
                   Proposition
                   ,
                   find
                   the
                   Area
                   or
                   Superficial
                   content
                   of
                   the
                   Tree
                   at
                   both
                   ends
                   thus
                   .
                
                 
                   
                     
                       
                         Multiply
                         the
                         breadth
                      
                       
                         3.75
                      
                       
                         0.574031
                      
                    
                     
                       
                         By
                         the
                         depth
                      
                       
                         2.34
                      
                       
                         0.369215
                      
                    
                     
                       
                         The
                         Product
                      
                       
                         8.7750
                      
                       
                         0.943246
                      
                    
                     
                       
                         2.
                         
                         Multiply
                         the
                         breadth
                      
                       
                         2.16
                      
                       
                         0.334453
                      
                    
                     
                       
                         By
                         the
                         depth
                      
                       
                         1.82
                      
                       
                         0.262451
                      
                    
                     
                       
                         The
                         Product
                         is
                      
                       
                         3.9528
                      
                       
                         0.596904
                      
                    
                     
                       
                         
                         3.
                         
                         Multiply
                         the
                         1.
                         
                         Content
                         .
                      
                       
                         87750
                      
                       
                         0.943246
                      
                    
                     
                       
                         by
                         the
                         second
                         content
                         .
                      
                       
                         3.9528
                      
                       
                         0.596904
                      
                    
                     
                       
                         And
                         find
                         the
                         square
                         root
                      
                       
                         5.8986
                      
                       
                         1.540150
                      
                    
                     
                       
                          
                      
                       
                          
                      
                       
                         0.770075
                      
                    
                  
                
                 
                   The
                   Sum
                   of
                   these
                   18.6264
                   being
                   multiplyed
                   by
                   8
                   one
                   third
                   of
                   the
                   length
                   ,
                   the
                   content
                   will
                   be
                   found
                   to
                   be
                   149.
                   0112.
                   
                   Thus
                   by
                   the
                   Table
                   of
                   Logarithms
                   the
                   mean
                   proportional
                   between
                   the
                   two
                   Bases
                   is
                   easily
                   found
                   ,
                   and
                   without
                   extracting
                   the
                   square
                   Root
                   ,
                   may
                   by
                   natural
                   Arithmetick
                   be
                   found
                   thus
                   .
                
                 
                   
                     A
                     4
                     2
                     /
                     2
                     CX
                  
                   A
                   half
                   C
                   multiplyed
                   by
                   B
                   :
                   And
                   C
                   more
                   half
                   A
                   multiplyed
                   by
                   D
                   being
                   added
                   together
                   and
                   multiplyed
                   by
                   30
                   ,
                   the
                   length
                   shall
                   give
                   the
                   content
                   .
                   Example
                   .
                
                 
                   
                     
                       
                         A.
                         3.75
                      
                       
                         C
                         2.16
                      
                    
                     
                       
                         1
                         /
                         2
                         C.
                         1.08
                      
                       
                         1
                         /
                         2
                         A
                         1.875
                      
                    
                     
                       
                         Sum
                         4.83
                      
                       
                         Sum.
                         4.035
                      
                    
                     
                       
                         B
                         -
                         2.34
                      
                       
                         D.
                         1.83
                      
                    
                     
                       
                         1932
                      
                       
                         12105
                      
                    
                     
                       
                         1449
                      
                       
                         32280
                      
                    
                     
                       
                         966
                      
                       
                         4035
                      
                    
                     
                       
                         11.3022
                      
                       
                         7.38405
                      
                    
                     
                       
                          
                      
                       
                         11.30220
                      
                    
                     
                       
                         The
                         sum
                         of
                         the
                         Products
                      
                       
                         18.68625
                      
                    
                  
                
                 
                   Being
                   multiplyed
                   by
                   8
                   the
                   third
                   of
                   the
                   length
                   ,
                   the
                   content
                   will
                   be
                   .
                   149.
                   49000.
                   
                   The
                   like
                   may
                   be
                   done
                   for
                   any
                   other
                   .
                
              
               
                 
                 
                   Proposition
                   VI.
                   
                
                 
                   
                     The
                     Diameters
                     of
                     a
                     piece
                     of
                     Timber
                     being
                     given
                     at
                     the
                     Top
                     and
                     and
                     Bottom
                     ,
                     together
                     with
                     the
                     length
                     ,
                     to
                     find
                     the
                     content
                     .
                  
                
                 
                   The
                   Proposition
                   may
                   be
                   resolved
                   either
                   by
                   the
                   Squares
                   of
                   the
                   Diameters
                   ,
                   or
                   by
                   the
                   Areas
                   of
                   the
                   Circles
                   answering
                   to
                   the
                   Diameters
                   given
                   ,
                   for
                   which
                   purpose
                   I
                   have
                   here
                   annexed
                   not
                   only
                   a
                   Table
                   of
                   the
                   Squares
                   of
                   all
                   numbers
                   under
                   a
                   thousand
                   ,
                   but
                   a
                   Table
                   sharing
                   the
                   third
                   part
                   of
                   the
                   Areas
                   of
                   Circles
                   in
                   full
                   measure
                   ,
                   to
                   any
                   Diameter
                   given
                   under
                   3
                   foot
                   .
                
                 
                   And
                   therefore
                   putting
                   S
                   =
                   The
                   Sum
                   of
                   the
                   Tabular
                   numbers
                   answering
                   to
                   the
                   Diameters
                   at
                   each
                   end
                   .
                
                 
                   X
                   =
                   The
                   difference
                   between
                   these
                   Diameters
                   .
                
                 
                   L
                   =
                   the
                   length
                   of
                   the
                   Timber
                   ,
                   C
                   =
                   The
                   content
                   .
                
                 
                   Then
                   1
                   ½
                   S
                   =
                   ½
                   -
                   
                     XX.
                     +
                     L.
                     =
                     C.
                  
                   
                
                 
                   If
                   you
                   work
                   by
                   the
                   Table
                   of
                   the
                   squares
                   of
                   Numbers
                   .
                   you
                   must
                   multiply
                   the
                   less
                   side
                   of
                   the
                   Equation
                   ,
                   by
                   0.26179
                   the
                   third
                   part
                   of
                   0.78539
                   the
                   Product
                   being
                   multiplyed
                   by
                   the
                   length
                   ,
                   will
                   give
                   the
                   content
                   .
                
                 
                   But
                   if
                   you
                   work
                   by
                   the
                   Table
                   of
                   the
                   third
                   parts
                   of
                   the
                   Areas
                   of
                   Circles
                   in
                   full
                   measure
                   ,
                   the
                   tabular
                   Numbers
                   being
                   multiplyed
                   by
                   the
                   length
                   will
                   give
                   the
                   content
                   .
                   Only
                   instead
                   of
                   the
                   square
                   of
                   the
                   difference
                   of
                   the
                   Diameter
                   ,
                   you
                   must
                   take
                   half
                   the
                   Tabular
                   number
                   answering
                   to
                   that
                   Difference
                   ,
                   and
                   you
                   shall
                   have
                   the
                   content
                   as
                   before
                   .
                   Example
                   .
                
                 
                 
                   
                     
                       Let
                       the
                       greatest
                       Diameter
                       by
                       2.75
                       ,
                       and
                       the
                       less
                       1.
                       93.
                       
                    
                     
                       Their
                       difference
                       is
                       0.83
                    
                     
                       The
                       square
                       of
                       2.75
                       is
                    
                     
                       7.5625
                    
                     
                       The
                       square
                       of
                       1.93
                       is
                    
                     
                       3.7249
                       .
                    
                     
                       The
                       Sum
                       of
                       the
                       Squares
                    
                     
                       11.2874
                    
                     
                       The
                       half
                       Sum
                    
                     
                       5.6437
                    
                     
                       The
                       Sum
                       of
                       them
                       is
                    
                     
                       16.9311
                    
                     
                       Half
                       the
                       square
                       of
                       0.82
                       deduct
                       .
                    
                     
                       0.3362
                    
                     
                       The
                       Difference
                       is
                    
                     
                       16.5949
                    
                     
                       Which
                       being
                       multiplyed
                       by
                    
                     
                       26179
                    
                     
                        
                    
                     
                       1493541
                    
                     
                        
                    
                     
                       1161643
                    
                     
                        
                    
                     
                       165949
                    
                     
                        
                    
                     
                       995694
                    
                     
                        
                    
                     
                       331898
                    
                     
                       The
                       Product
                       will
                       be
                       .
                    
                     
                       4.344378871
                    
                  
                   
                     
                     
                       Or
                       by
                       the
                       Table
                       of
                       Areas
                       .
                    
                     
                       The
                       Area
                       of
                       2.75
                       is
                    
                     
                       1.979857
                    
                     
                       The
                       Area
                       of
                       1.93
                       is
                    
                     
                       0.975176
                    
                     
                       The
                       Sum
                    
                     
                       2.955033
                    
                     
                       The
                       half
                       Sum
                    
                     
                       1.477516
                    
                     
                       The
                       Sum
                       of
                       them
                    
                     
                       4.432549
                    
                     
                       Half
                       the
                       Area
                       of
                       0.82
                       deduct
                    
                     
                       0.088016
                    
                     
                       The
                       former
                       Product
                    
                     
                       4.344533
                    
                     
                       Which
                       being
                       multiplyed
                       by
                    
                     
                       24
                    
                     
                        
                    
                     
                       17378132
                    
                     
                        
                    
                     
                       8689066
                    
                     
                       The
                       content
                       is
                    
                     
                       104268792
                    
                  
                
                 
                   But
                   because
                   that
                   in
                   measuring
                   of
                   round
                   Timber
                   the
                   circumference
                   is
                   usually
                   given
                   and
                   not
                   the
                   Diameter
                   ,
                   I
                   have
                   added
                   another
                   Table
                   by
                   which
                   the
                   circumference
                   being
                   given
                   ,
                   the
                   Diameter
                   may
                   be
                   found
                   .
                
                 
                   Example
                   .
                   Let
                   the
                   circumference
                   of
                   a
                   piece
                   of
                   Timber
                   be
                   8325220
                   looking
                   this
                   Number
                   in
                   the
                   second
                   column
                   of
                   that
                   Table
                   ,
                   I
                   find
                   the
                   next
                   less
                   to
                   be
                   8.168140
                   and
                   thence
                   proceeding
                   in
                   a
                   streight
                   Line
                   ,
                   I
                   find
                   that
                   in
                   the
                   seventh
                   Column
                   the
                   Number
                   given
                   ,
                   and
                   the
                   Diameter
                   answering
                   thereunto
                   to
                   be
                   2.
                   65.
                   and
                   thus
                   may
                   any
                   other
                   Diameter
                   be
                   found
                   not
                   exceeding
                   the
                   three
                   foot
                   .
                   The
                   Proportion
                   by
                   which
                   the
                   Table
                   was
                   made
                   ,
                   is
                   thus
                   .
                   As
                   1.
                   to
                   3.14159
                   so
                   is
                   the
                   Diameter
                   given
                   ,
                   to
                   the
                   circumference
                   required
                   .
                
                 
                 
                 
                   Or
                   the
                   Circumference
                   being
                   given
                   ,
                   to
                   find
                   the
                   Diameter
                   ,
                   say
                   :
                   As.
                   1.
                   to
                   0.3183
                   ,
                   so
                   is
                   the
                   Circumference
                   given
                   to
                   the
                   Diameter
                   required
                   .
                
                 
                   And
                   although
                   by
                   these
                   two
                   Tables
                   all
                   round
                   Timber
                   may
                   be
                   easily
                   measured
                   ,
                   yet
                   it
                   being
                   more
                   usual
                   to
                   take
                   the
                   Circumference
                   of
                   a
                   Tree
                   ,
                   then
                   the
                   Diameter
                   ,
                   I
                   have
                   here
                   added
                   a
                   third
                   Table
                   ,
                   shewing
                   the
                   third
                   part
                   of
                   the
                   Areas
                   of
                   Circles
                   answering
                   to
                   any
                   circumference
                   under
                   10
                   foot
                   ,
                   and
                   that
                   in
                   Natural
                   and
                   Artificial
                   numbers
                   ,
                   the
                   use
                   of
                   which
                   Table
                   shall
                   be
                   explained
                   in
                   the
                   Proposition
                   following
                   .
                
              
               
                 
                   Proposition
                   .
                   VII
                   .
                
                 
                   
                     The
                     Circumference
                     of
                     a
                     piece
                     of
                     round
                     Timber
                     at
                     both
                     ends
                     ,
                     with
                     the
                     length
                     being
                     given
                     ,
                     to
                     find
                     the
                     content
                     .
                  
                
                 
                   The
                   Circumference
                   of
                   a
                   Circle
                   being
                   given
                   ,
                   the
                   Area
                   thereof
                   may
                   be
                   found
                   as
                   hath
                   been
                   shewed
                   ,
                   in
                   the
                   7
                   Chapter
                   ,
                   Proposition
                   4.
                   and
                   by
                   the
                   first
                   Proposition
                   of
                   this
                   ;
                   and
                   to
                   find
                   the
                   third
                   part
                   of
                   the
                   Area
                   ,
                   which
                   is
                   more
                   convenient
                   for
                   our
                   purpose
                   I
                   took
                   a
                   third
                   part
                   of
                   the
                   number
                   given
                   by
                   which
                   to
                   find
                   the
                   whole
                   ,
                   that
                   is
                   a
                   third
                   part
                   of
                   07957747
                   that
                   is
                   0.02652582
                   and
                   having
                   by
                   the
                   multiplying
                   this
                   number
                   by
                   the
                   square
                   of
                   the
                   Circumference
                   computed
                   three
                   or
                   four
                   of
                   the
                   first
                   numbers
                   ,
                   the
                   rest
                   were
                   found
                   by
                   the
                   first
                   and
                   second
                   differences
                   .
                
                 
                   The
                   Artificial
                   numbers
                   were
                   computed
                   by
                   adding
                   the
                   Logarithms
                   of
                   the
                   Squares
                   of
                   the
                   circumference
                   ,
                   to
                   8.42966891
                   the
                   Logarithm
                   of
                   0.
                   02652582.
                   
                
                 
                   And
                   by
                   these
                   Natural
                   and
                   Artificial
                   numbers
                   
                   the
                   content
                   of
                   round
                   Timber
                   may
                   be
                   found
                   two
                   ways
                
                 
                   By
                   the
                   Natural
                   numbers
                   in
                   the
                   same
                   manner
                   as
                   the
                   content
                   was
                   computed
                   ,
                   the
                   Diameters
                   being
                   given
                   ,
                   and
                   by
                   the
                   Natural
                   and
                   Artificial
                   numbers
                   both
                   ,
                   by
                   finding
                   a
                   mean
                   proportional
                   between
                   the
                   two
                   Areas
                   at
                   the
                   top
                   and
                   bottom
                   of
                   the
                   Tree
                   ,
                   as
                   by
                   Example
                   shall
                   be
                   explained
                   .
                
                 
                   Let
                   the
                   given
                   Diamensions
                   ,
                   or
                   Circumferences
                   be
                   At
                   the
                   Bottom
                   9.95
                   Their
                   difference
                   is
                   6.20
                   At
                   the
                   Top
                   3.75
                
                 
                   
                     
                       The
                       tabular
                       Numbers
                       .
                    
                     
                       
                          
                      
                       
                         Natural
                      
                       
                         Artificial
                         .
                      
                    
                     
                       
                         Answering
                         to
                         9.95
                      
                       
                         2.626162
                      
                       
                         0.418931
                      
                    
                     
                       
                         And
                         to
                         3.75
                      
                       
                         0.373019
                      
                       
                         9.571731
                      
                    
                  
                
                 
                   
                     The
                     Sum
                     of
                     the
                     Logarith
                     .
                  
                   
                     9.990662
                  
                   
                     The
                     half
                     Sum
                     or
                     Logarith
                     .
                     989300
                  
                   
                     9.995331
                  
                   
                     The
                     Sum
                     of
                     the
                     Number
                     is
                  
                   
                     3.988481
                  
                   
                     The
                     Sum
                     of
                     the
                     Natural
                     Numbers
                     is
                  
                   
                     2
                     .
                     9●9181
                  
                   
                     The
                     half
                     Sum
                  
                   
                     ●
                     .
                     499190
                  
                   
                     The
                     Sum
                     of
                     them
                  
                   
                     4.498771
                  
                   
                     Half
                     the
                     number
                     answer
                     .
                     to
                     .
                     6.
                     20
                     is
                  
                   
                     0.509826
                  
                   
                     The
                     remainer
                     is
                  
                   
                     3.988945
                  
                
                 
                   Which
                   being
                   multiplyed
                   by
                   the
                   length
                   24
                   ,
                   the
                   content
                   will
                   be
                   95.
                   73468.
                   
                
                 
                   Mr.
                   Darling
                   in
                   his
                   Carpenters
                   Rule
                   made
                   easie
                   ,
                   doth
                   propound
                   a
                   shorter
                   way
                   ,
                   but
                   not
                   so
                   exact
                   ,
                   which
                   is
                   by
                   the
                   Circumference
                   given
                   in
                   the
                   middle
                   of
                   the
                   piece
                   to
                   find
                   the
                   side
                   of
                   the
                   Square
                   ,
                   namely
                   
                   by
                   multiplying
                   the
                   Circumference
                   given
                   by
                   28209
                   ,
                   or
                   2821.
                   which
                   side
                   of
                   the
                   Square
                   being
                   computed
                   in
                   Inches
                   ,
                   and
                   lookt
                   in
                   his
                   Table
                   of
                   Timber
                   measure
                   ,
                   doth
                   give
                   the
                   content
                   of
                   the
                   Tree
                   not
                   exceeding
                   31
                   foot
                   in
                   length
                   ,
                   the
                   which
                   way
                   of
                   measuring
                   may
                   be
                   as
                   easily
                   performed
                   by
                   this
                   Table
                   .
                   Example
                   .
                
                 
                   The
                   circumference
                   at
                   the
                   top
                   and
                   bottom
                   of
                   the
                   Tree
                   being
                   given
                   9.95
                   and
                   3.75
                   the
                   Sum
                   is
                   13.70
                   The
                   half
                   thereof
                   is
                   the
                   mean
                   circumfer
                   .
                   6.85
                   Which
                   sought
                   in
                   the
                   Table
                   ,
                   the
                   Numbers
                   are
                   .
                
                 
                   The
                   Natural
                   number
                   is
                   1.244657
                   ,
                   which
                   being
                   multiplyed
                   by
                   3
                   the
                   Product
                   is
                   3.733971
                   ,
                   which
                   multiplyed
                   by
                   the
                   length
                   24
                   ,
                   the
                   content
                   is
                   89.
                   615304.
                   
                
                 
                   
                     The
                     Artificial
                     number
                     is
                  
                   
                     0.095049
                  
                   
                     The
                     Logarithm
                     of
                     24
                     is
                  
                   
                     1.380211
                  
                   
                     The
                     Absolute
                     Number
                     29.871
                  
                   
                     1.475260
                  
                   
                     Which
                     multiplyed
                     by
                     3
                     ,
                     the
                     Product
                     is
                  
                   
                     89613
                  
                
              
               
                 
                   Proposition
                   .
                   VIII
                   .
                
                 
                   
                     The
                     Diameters
                     of
                     a
                     Brewers
                     Tun
                     at
                     top
                     and
                     bottom
                     being
                     given
                     with
                     the
                     height
                     thereof
                     ,
                     to
                     find
                     the
                     content
                     .
                  
                
                 
                   In
                   Fig.
                   29.
                   
                   Let
                   the
                   given
                   Diameter
                   .
                
                 
                   At
                   the
                   top
                   be
                   
                     AC
                     136
                     BD
                  
                   128
                
                 
                   At
                   the
                   bottom
                   .
                   
                     KG
                     152
                     HF
                  
                   144
                   Altit
                   .
                   51
                   Inches
                   .
                
                 
                   The
                   which
                   by
                   the
                   5
                   Proposition
                   of
                   this
                   Chap.
                   may
                   thus
                   be
                   computed
                   .
                   
                     AC
                     139
                     +
                     ½
                     KG
                     76
                     =
                     212
                     ×
                     BD
                  
                   128
                   the
                   Product
                   is
                   27136.
                   
                
                 
                 
                   And
                   
                     KG
                     1524
                     ½
                     AC
                     68
                     =
                     220
                     ×
                     HF
                  
                   144
                   the
                   Product
                   is
                   31680.
                   the
                   Sum
                   of
                   these
                   2
                   Products
                   is
                   58816
                   which
                   being
                   multiplyed
                   by
                   onethird
                   of
                   51
                   ,
                   that
                   is
                   by
                   17
                   ,
                   and
                   that
                   Product
                   multiplyed
                   by
                   26179
                   the
                   third
                   of
                   78539
                   will
                   give
                   the
                   content
                   .
                
                 
                   
                     The
                     Logarithm
                     of
                     58816.
                     is
                  
                   
                     54.76949
                  
                   
                     The
                     Logarithm
                     of
                     17
                     is
                  
                   
                     1.230449
                  
                   
                     The
                     Product
                  
                   
                     1.999944
                  
                   
                     The
                     Logarithm
                     of
                     .
                     26179
                  
                   
                     9.417968
                  
                   
                     The
                     content
                     is
                     .
                     261765
                  
                   
                     5.417912
                  
                
                 
                   Thus
                   the
                   content
                   of
                   a
                   Tun
                   may
                   be
                   found
                   in
                   Inches
                   ,
                   which
                   being
                   divided
                   282
                   the
                   number
                   of
                   Inches
                   in
                   an
                   Ale
                   Gallon
                   ,
                   the
                   quotient
                   will
                   be
                   the
                   content
                   in
                   Gallons
                   .
                
                 
                   Or
                   thus
                   ;
                   divide
                   the
                   former
                   .
                   26179
                   by
                   282
                   the
                   quotient
                   will
                   be
                   00092836.
                   by
                   which
                   the
                   content
                   may
                   be
                   found
                   in
                   Ale
                   Gallons
                   in
                   this
                   manner
                   .
                
                 
                   
                     The
                     former
                     Product
                  
                   
                     5.999944
                  
                   
                     The
                     Logarithm
                     of
                     0.00092836
                  
                   
                     6.967719
                  
                   
                     The
                     content
                     in
                     Gallons
                     928.24
                  
                   
                     2.967663
                  
                
              
               
                 
                   Proposition
                   .
                   IX
                   .
                
                 
                   
                     The
                     Diameters
                     of
                     a
                     close
                     Cask
                     ,
                     at
                     head
                     and
                     bung
                     with
                     the
                     length
                     given
                     ,
                     to
                     find
                     the
                     content
                     .
                  
                
                 
                   In
                   the
                   resolving
                   of
                   this
                   Proposition
                   ,
                   we
                   are
                   to
                   consider
                   the
                   several
                   forms
                   of
                   Casks
                   ,
                   as
                   will
                   as
                   the
                   kind
                   of
                   the
                   Liquor
                   ,
                   with
                   which
                   it
                   is
                   filled
                   ,
                   for
                   one
                   and
                   the
                   same
                   Rule
                   will
                   not
                   find
                   the
                   content
                   in
                   all
                   Cask
                   .
                
                 
                 
                   And
                   a
                   Coopers
                   Cask
                   is
                   commonly
                   taken
                   ,
                   either
                   for
                   the
                   middle
                   Frustum
                   of
                   a
                   Spheroid
                   ,
                   the
                   middle
                   Frustum
                   of
                   a
                   Parabolical
                   Spindle
                   ,
                   the
                   middle
                   Frustum
                   of
                   two
                   Parabolick
                   Conoids
                   ,
                   or
                   for
                   the
                   middle
                   Frustum
                   of
                   two
                   Cones
                   abutting
                   upon
                   one
                   common
                   Base
                   .
                
                 
                   And
                   the
                   content
                   of
                   these
                   several
                   Casks
                   may
                   be
                   found
                   either
                   by
                   equating
                   the
                   Diameters
                   ,
                   or
                   by
                   equating
                   the
                   Circles
                   .
                   for
                   the
                   one
                   ,
                   a
                   Table
                   of
                   Squares
                   is
                   necessary
                   ,
                   and
                   a
                   Table
                   shewing
                   the
                   third
                   part
                   of
                   the
                   Areas
                   of
                   a
                   Circle
                   to
                   all
                   Diameters
                   .
                   The
                   making
                   of
                   the
                   Table
                   of
                   Squares
                   ,
                   every
                   one
                   knows
                   ,
                   to
                   be
                   nothing
                   else
                   but
                   the
                   Product
                   of
                   a
                   Number
                   multiplyed
                   ,
                   by
                   it self
                   ,
                   thus
                   the
                   Square
                   of
                   3
                   is
                   9.
                   the
                   Square
                   of
                   8
                   is
                   64
                   and
                   so
                   of
                   the
                   rest
                   .
                
                 
                   And
                   the
                   Area
                   of
                   a
                   Circle
                   to
                   any
                   given
                   Diameter
                   may
                   be
                   found
                   ,
                   as
                   hath
                   been
                   shewed
                   ,
                   in
                   Chap.
                   7
                   Proposition
                   2.
                   
                   But
                   here
                   the
                   Area
                   of
                   a
                   Circle
                   in
                   Inches
                   ,
                   will
                   not
                   suffice
                   ,
                   it
                   will
                   be
                   more
                   fit
                   for
                   use
                   ,
                   if
                   the
                   third
                   part
                   of
                   the
                   Area
                   be
                   found
                   in
                   Ale
                   and
                   Wine
                   Gallons
                   both
                   ,
                   the
                   which
                   may
                   indeed
                   be
                   done
                   by
                   dividing
                   the
                   whole
                   Area
                   in
                   Inches
                   by
                   3
                   and
                   the
                   quotient
                   by
                   282
                   to
                   make
                   the
                   Table
                   for
                   Ale-measure
                   ,
                   and
                   by
                   231
                   to
                   make
                   the
                   Table
                   for
                   Wine-measure
                   ;
                   but
                   yet
                   these
                   Tables
                   
                     (
                     as
                     I
                     think
                  
                   )
                   may
                   be
                   more
                   readily
                   made
                   in
                   this
                   manner
                   .
                
                 
                   The
                   Square
                   of
                   any
                   Diameter
                   in
                   Inches
                   ,
                   being
                   divided
                   by
                   3.81972
                   will
                   give
                   the
                   Area
                   of
                   the
                   Circle
                   in
                   Inches
                   :
                   And
                   this
                   Division
                   being
                   multiplyed
                   by
                   282
                   will
                   give
                   you
                   1077.161
                   for
                   a
                   common
                   Division
                   ,
                   by
                   which
                   to
                   find
                   the
                   Area
                   in
                   Ale-Gallons
                   ,
                   or
                   being
                   multiplyed
                   by
                   231
                   the
                   Product
                   ,
                   882.355
                   will
                   be
                   a
                   commou
                   Division
                   by
                   which
                   to
                   find
                   the
                   Area
                   in
                   Wine-Gallons
                   .
                
                 
                   But
                   because
                   it
                   is
                   easier
                   to
                   multiply
                   then
                   divide
                   :
                   
                   If
                   you
                   multiply
                   the
                   several
                   Squares
                   by
                   26178
                   the
                   third
                   part
                   of
                   78539
                   the
                   Product
                   will
                   give
                   the
                   Area
                   in
                   Inches
                   ,
                   or
                   if
                   you
                   divide
                   .
                   26179
                   by
                   282
                   the
                   quotient
                   will
                   be
                   .
                   00092886
                   for
                   a
                   common
                   Multiplicator
                   ,
                   by
                   which
                   to
                   find
                   the
                   Area
                   in
                   Ale-Gallons
                   ,
                   or
                   being
                   divided
                   by
                   231
                   the
                   quotient
                   will
                   be
                   0011333
                   a
                   common
                   Multiplicator
                   ,
                   by
                   which
                   to
                   find
                   the
                   content
                   in
                   Wine-Gallons
                   .
                   An
                   Example
                   or
                   two
                   will
                   be
                   sufficient
                   for
                   illustration
                   .
                   Let
                   the
                   Diameter
                   given
                   be
                   32
                   Inches
                   ,
                   the
                   Square
                   thereof
                   1024
                   being
                   divided
                   by
                   3.81970
                   the
                   quotient
                   is
                   268.083
                   ,
                   and
                   the
                   same
                   Square
                   1024
                   being
                   multiplyed
                   by
                   261799
                   ,
                   the
                   Product
                   will
                   be
                   268.
                   082.
                   
                
                 
                   Again
                   if
                   you
                   divide
                   1024
                   by
                   1077.161
                   the
                   quotient
                   will
                   be
                   9508
                   ,
                   or
                   being
                   multiplied
                   by
                   00092836
                   ,
                   the
                   Product
                   will
                   be
                   9508.
                   
                
                 
                   Lastly
                   if
                   you
                   divide
                   1024
                   by
                   882.755
                   ,
                   the
                   quotient
                   will
                   be
                   1.1605
                   ,
                   or
                   being
                   multiplied
                   by
                   00113333
                   the
                   Product
                   is
                   1.1605
                   ,
                
                 
                   And
                   in
                   this
                   manner
                   may
                   the
                   Tables
                   be
                   made
                   for
                   Wine
                   and
                   Beer-measure
                   ,
                   but
                   the
                   second
                   differences
                   in
                   these
                   Numbers
                   being
                   equal
                   ,
                   three
                   or
                   four
                   Numbers
                   in
                   each
                   Table
                   being
                   thus
                   computed
                   ,
                   the
                   rest
                   may
                   be
                   found
                   by
                   Addition
                   only
                   .
                
                 
                   Thus
                   the
                   Squares
                   of
                   1.
                   2.
                   3.
                   and
                   4
                   Inches
                   are
                   .
                   1.
                   4.
                   9
                   and
                   16
                   by
                   which
                   if
                   you
                   multiply
                   00113333
                   ,
                   the
                   several
                   Products
                   will
                   be
                   third
                   part
                   of
                   the
                   Area
                   ,
                   of
                   the
                   Circles
                   answering
                   to
                   those
                   Diameters
                   in
                   Wine-Gallons
                   .
                   Or
                   00092836
                   being
                   multiplied
                   by
                   those
                   Squares
                   ,
                   the
                   several
                   Products
                   ,
                   will
                   be
                   the
                   third
                   part
                   of
                   the
                   Areas
                   of
                   the
                   Circles
                   answering
                   to
                   those
                   Diameters
                   in
                   Ale-Gallons
                   ;
                   the
                   which
                   with
                   their
                   first
                   and
                   second
                   differences
                   are
                   as
                   followeth
                   .
                
                 
                 
                   
                     
                       The
                       Products
                       or
                       Areas
                       in
                       Wine-Gallons
                       :
                    
                     
                       
                         1.
                         
                      
                       
                         00113333
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         2.
                         
                      
                       
                         00453332
                      
                       
                         33999
                      
                       
                         226666
                      
                    
                     
                       
                         3.
                         
                      
                       
                         01019997
                      
                       
                         566665
                      
                       
                         226666
                      
                    
                     
                       
                         4.
                         
                      
                       
                         01813328
                      
                       
                         796331
                      
                       
                          
                      
                    
                  
                
                 
                   
                     
                       The
                       Products
                       in
                       Ale-Gallons
                       .
                    
                     
                       
                         1.
                         
                      
                       
                         00092836
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         2.
                         
                      
                       
                         00371344
                      
                       
                         278508
                      
                       
                         185672
                      
                    
                     
                       
                         3.
                         
                      
                       
                         00835524
                      
                       
                         464180
                      
                       
                         185672
                      
                    
                     
                       
                         4.
                         
                      
                       
                         01485376
                      
                       
                         649852
                      
                       
                          
                      
                    
                  
                
                 
                   And
                   by
                   the
                   continual
                   addition
                   of
                   the
                   second
                   differences
                   to
                   the
                   first
                   ,
                   and
                   the
                   first
                   differences
                   to
                   the
                   products
                   before
                   found
                   ,
                   the
                   Table
                   may
                   be
                   continued
                   as
                   far
                   as
                   you
                   please
                   .
                
                 
                   The
                   construction
                   of
                   the
                   Tables
                   being
                   thus
                   shewed
                   :
                   We
                   will
                   now
                   shew
                   their
                   use
                   in
                   finding
                   the
                   content
                   of
                   any
                   Cask
                   .
                
                 
                   Let
                   S
                   =
                   the
                   Sum
                   of
                   the
                   Tabular
                   Numbers
                   answering
                   to
                   the
                   Diameters
                   at
                   the
                   Head
                   and
                   Bung.
                   D
                   =
                   their
                   difference
                   X
                   =
                   the
                   difference
                   of
                   the
                   Diameters
                   themselves
                   .
                   L
                   =
                   the
                   length
                   of
                   the
                   Vessel
                   ,
                   and
                   C
                   =
                   the
                   content
                   thereof
                   .
                
                 
                   1.
                   
                   If
                   a
                   Cask
                   be
                   taken
                   for
                   the
                   middle
                   Frustum
                   of
                   a
                   Spheroid
                   ,
                   intercepted
                   between
                   two
                   Planes
                   parallel
                   ,
                   cutting
                   the
                   Axis
                   at
                   right
                   Angles
                   :
                   Then
                   1
                   ½
                   
                     S
                     +
                     ½
                     D
                     ×
                     L
                     =
                     C.
                     
                  
                
                 
                   2.
                   
                   If
                   a
                   Cask
                   be
                   taken
                   for
                   the
                   middle
                   Frustum
                   of
                   a
                   parabolical
                   Spindle
                   ,
                   intercepted
                   between
                   two
                   planes
                   parallel
                   cutting
                   the
                   Axis
                   at
                   right
                   Angles
                   .
                   Then
                   1
                   ½
                   S
                   +
                   ½
                   
                     D
                     ×
                     L
                     =
                     C.
                  
                   
                
                 
                 
                   3.
                   
                   If
                   a
                   Cask
                   be
                   taken
                   for
                   the
                   middle
                   Frustum
                   of
                   two
                   Parabolick
                   Conoids
                   ,
                   abutting
                   upon
                   one
                   common
                   Base
                   ,
                   intercepted
                   between
                   two
                   Planes
                   parallel
                   ,
                   cutting
                   the
                   Axis
                   at
                   right
                   Angle
                   :
                   Then
                   1
                   ½
                   S
                   :
                   ×
                   
                     L
                     =
                     C.
                  
                   
                
                 
                   4.
                   
                   If
                   a
                   Cask
                   be
                   taken
                   for
                   the
                   middle
                   Frustum
                   of
                   two
                   Cones
                   ,
                   abutting
                   upon
                   one
                   common
                   bafe
                   ,
                   intercepted
                   between
                   two
                   Planes
                   parallel
                   cutting
                   the
                   Axis
                   at
                   Right
                   Angles
                   .
                   Then
                   1
                   ½
                   
                     S
                     —
                     ⅓
                     XX.
                     ×
                     L
                     =
                     C.
                     
                  
                
                 
                   In
                   all
                   these
                   four
                   Equations
                   ,
                   if
                   you
                   work
                   by
                   the
                   Table
                   of
                   Squares
                   of
                   numbers
                   ,
                   you
                   must
                   multiply
                   the
                   less
                   side
                   of
                   the
                   Equation
                   by
                   262
                   ,
                   if
                   you
                   would
                   have
                   the
                   content
                   in
                   Cubical
                   Inches
                   ;
                   by
                   001133
                   if
                   you
                   would
                   have
                   the
                   content
                   in
                   Wine-Gallons
                   ;
                   and
                   by
                   000928
                   ,
                   if
                   you
                   would
                   have
                   the
                   content
                   in
                   Ale-Gallons
                   .
                
                 
                   But
                   if
                   you
                   work
                   by
                   the
                   Tables
                   of
                   the
                   third
                   parts
                   of
                   the
                   Areas
                   Circle
                   ,
                   the
                   Tabular
                   Numbers
                   being
                   multiplyed
                   by
                   the
                   length
                   only
                   will
                   give
                   the
                   content
                   required
                   ,
                   only
                   in
                   the
                   fourth
                   Equation
                   instead
                   of
                   half
                   the
                   Square
                   of
                   the
                   Difference
                   of
                   the
                   Diameters
                   ,
                   take
                   half
                   the
                   Tabular
                   Number
                   answering
                   to
                   that
                   difference
                   ,
                   and
                   you
                   shall
                   have
                   the
                   content
                   required
                   ;
                   as
                   by
                   the
                   following
                   Examples
                   will
                   better
                   appear
                   ,
                   then
                   by
                   many
                   words
                   .
                
                 
                   Examples
                   in
                   Wine-measure
                   by
                   the
                   Table
                   of
                   the
                   Squares
                   of
                   Numbers
                   .
                
                 
                   The
                   Diameter
                   of
                   a
                   Vessel
                
                 
                   At
                   the
                   Bung
                   being
                   32
                   Inches
                   .
                
                 
                   At
                   the
                   Head
                   22
                   Inches
                   .
                
                 
                   The
                   difference
                   of
                   the
                   Diameters
                   10
                   Inches
                   .
                
                 
                   And
                   the
                   length
                   of
                   the
                   Vessel
                   44
                   Inches
                   .
                
                 
                 
                   
                     
                       
                         Spheroid
                         .
                      
                       
                         Parabolick
                         Spindle
                         .
                      
                    
                     
                       
                         1024
                      
                       
                         1024
                      
                    
                     
                       
                         484
                      
                       
                         484
                      
                    
                     
                       
                         1508
                      
                       
                         1508
                      
                    
                     
                       
                         754
                      
                       
                         754
                      
                    
                     
                       
                         270
                      
                       
                         540
                      
                    
                     
                       
                         2532
                      
                       
                         23160
                      
                    
                     
                       
                         2532
                      
                       
                         23160
                      
                    
                     
                       
                         7596
                      
                       
                         69480
                      
                    
                     
                       
                         7596
                      
                       
                         69480
                      
                    
                     
                       
                         7596
                      
                       
                         69480
                      
                    
                     
                       
                         28695156
                      
                       
                         262472280
                      
                    
                     
                       
                         44
                      
                       
                         44
                      
                    
                     
                       
                         114780624
                      
                       
                         104988912
                      
                    
                     
                       
                         114780624
                      
                       
                         104988912
                      
                    
                     
                       
                         126.2586864
                      
                       
                         115.4878032
                      
                    
                  
                
                 
                 
                   
                     
                       
                         Parabolick
                         Conoid
                      
                       
                         Cone
                         .
                      
                    
                     
                       
                         1024
                      
                       
                         1024
                      
                    
                     
                       
                         484
                      
                       
                         484
                      
                    
                     
                       
                         1508
                      
                       
                         1508
                      
                    
                     
                       
                         754
                      
                       
                         754
                      
                    
                     
                       
                          
                      
                       
                         50
                      
                    
                     
                       
                         2262
                      
                       
                         2212
                      
                    
                     
                       
                         2262
                      
                       
                         2212
                      
                    
                     
                       
                         6786
                      
                       
                         6636
                      
                    
                     
                       
                         6786
                      
                       
                         6636
                      
                    
                     
                       
                         6786
                      
                       
                         6636
                      
                    
                     
                       
                         25635246
                      
                       
                         25068596
                      
                    
                     
                       
                         44
                      
                       
                         44
                      
                    
                     
                       
                         102540984
                      
                       
                         200274384
                      
                    
                     
                       
                         102540984
                      
                       
                         100274384
                      
                    
                     
                       
                         112.79508241
                      
                       
                         110.30182224
                      
                    
                  
                
                 
                 
                   This
                   which
                   hath
                   been
                   done
                   by
                   the
                   Table
                   of
                   Squares
                   may
                   be
                   more
                   easily
                   performed
                   ,
                   by
                   the
                   Table
                   of
                   the
                   third
                   part
                   of
                   the
                   Areas
                   of
                   Circles
                   ,
                   ready
                   reduced
                   to
                   Wine-Gallons
                   .
                
                 
                   
                     
                       
                         Spheroid
                      
                       
                         Parabolick
                         Spindle
                         .
                      
                    
                     
                       
                         1.16053
                      
                       
                         1.16053
                      
                    
                     
                       
                         0.54853
                      
                       
                         0.54853
                      
                    
                     
                       
                         1.70906
                      
                       
                         1.70906
                      
                    
                     
                       
                         85453
                      
                       
                         85453
                      
                    
                     
                       
                         30600
                      
                       
                         61200
                      
                    
                     
                       
                         2.86959
                      
                       
                         2.624790
                      
                    
                     
                       
                         44
                      
                       
                         44
                      
                    
                     
                       
                         1147836
                      
                       
                         1049916
                      
                    
                     
                       
                         1147836
                      
                       
                         10499160
                      
                    
                     
                       
                         126.26196
                      
                       
                         115.490760
                      
                    
                  
                
                 
                 
                   
                     
                       
                         Parabolick
                         Conoid
                      
                       
                         Cone
                         .
                      
                    
                     
                       
                         1.16053
                      
                       
                         1.16053
                      
                    
                     
                       
                         0.54853
                      
                       
                         0.54853
                      
                    
                     
                       
                         1.70906
                      
                       
                         1.70906
                      
                    
                     
                       
                         85453
                      
                       
                         85453
                      
                    
                     
                       
                          
                      
                       
                         56666
                      
                    
                     
                       
                         2.56359
                      
                       
                         2.506924
                      
                    
                     
                       
                         44
                      
                       
                         44
                      
                    
                     
                       
                         1025436
                      
                       
                         10027696
                      
                    
                     
                       
                         1025436
                      
                       
                         10027696
                      
                    
                     
                       
                         112.79796
                      
                       
                         110.304656
                      
                    
                  
                
                 
                 
                   Examples
                   in
                   Ale-measure
                   by
                   the
                   Table
                   of
                   the
                   Squares
                   of
                   Numbers
                   .
                
                 
                   
                     
                       
                         Spheroid
                         .
                      
                       
                         Parabolick
                         Spindle
                         .
                      
                    
                     
                       
                         1024
                      
                       
                         1024
                      
                    
                     
                       
                         484
                      
                       
                         484
                      
                    
                     
                       
                         1508
                      
                       
                         1508
                      
                    
                     
                       
                         754
                      
                       
                         754
                      
                    
                     
                       
                         270
                      
                       
                         540
                      
                    
                     
                       
                         2532
                      
                       
                         2316.0
                      
                    
                     
                       
                         00092836
                      
                       
                         00092836
                      
                    
                     
                       
                         22758
                      
                       
                         20844
                      
                    
                     
                       
                         5064
                      
                       
                         4632
                      
                    
                     
                       
                         20256
                      
                       
                         18528
                      
                    
                     
                       
                         7596
                      
                       
                         6948
                      
                    
                     
                       
                         15192
                      
                       
                         138960
                      
                    
                     
                       
                         235660752
                      
                       
                         2.150081760
                      
                    
                     
                       
                         44
                      
                       
                         44
                      
                    
                     
                       
                         948623008
                      
                       
                         860032704
                      
                    
                     
                       
                         940643008
                      
                       
                         860032704
                      
                    
                     
                       
                         103.22673088
                      
                       
                         94.60359744
                      
                    
                  
                
                 
                 
                   
                     
                       
                         Parabolick
                         Conoid
                      
                       
                         Cone
                         .
                      
                    
                     
                       
                         1024
                      
                       
                         1024
                      
                    
                     
                       
                         484
                      
                       
                         484
                      
                    
                     
                       
                         1508
                      
                       
                         1508
                      
                    
                     
                       
                         754
                      
                       
                         754
                      
                    
                     
                       
                          
                      
                       
                         50
                      
                    
                     
                       
                         2262
                      
                       
                         2212
                      
                    
                     
                       
                         20358
                      
                       
                         19909
                      
                    
                     
                       
                         4524
                      
                       
                         4424
                      
                    
                     
                       
                         18096
                      
                       
                         17696
                      
                    
                     
                       
                         6786
                      
                       
                         6636
                      
                    
                     
                       
                         13527
                      
                       
                         13272
                      
                    
                     
                       
                         2.09995032
                      
                       
                         2.05423232
                      
                    
                     
                       
                         44
                      
                       
                         44
                      
                    
                     
                       
                         8.39980128
                      
                       
                         821692928
                      
                    
                     
                       
                         839980128
                      
                       
                         821692928
                      
                    
                     
                       
                         92.39781408
                      
                       
                         90.38622208
                      
                    
                  
                
                 
                 
                   
                     
                       By
                       the
                       Areas
                       of
                       Circles
                       .
                    
                     
                       
                         Spheroid
                         .
                      
                       
                         Parabolick
                         Spindle
                         .
                      
                    
                     
                       
                         0.95052
                      
                       
                         0.95052
                      
                    
                     
                       
                         0.44930
                      
                       
                         0.44930
                      
                    
                     
                       
                         1.39982
                      
                       
                         1.39982
                      
                    
                     
                       
                         .69991
                      
                       
                         69991
                      
                    
                     
                       
                         .25061
                      
                       
                         050122
                      
                    
                     
                       
                         2.35034
                      
                       
                         2.149852
                      
                    
                     
                       
                         34
                      
                       
                         44
                      
                    
                     
                       
                         940136
                      
                       
                         8599408
                      
                    
                     
                       
                         940136
                      
                       
                         8599408
                      
                    
                     
                       
                         103.41496
                      
                       
                         94.593488
                      
                    
                  
                
                 
                 
                   
                     
                       
                         Parabolick
                         Conoid
                         .
                      
                       
                         Cone
                         .
                      
                    
                     
                       
                         0.95052
                      
                       
                         0.95052
                      
                    
                     
                       
                         0.44930
                      
                       
                         0.44930
                      
                    
                     
                       
                         1.39982
                      
                       
                         1.39982
                      
                    
                     
                       
                         69991
                      
                       
                         .69991
                      
                    
                     
                       
                          
                      
                       
                         46425
                      
                    
                     
                       
                         209973
                      
                       
                         2.053305
                      
                    
                     
                       
                         44
                      
                       
                         44
                      
                    
                     
                       
                         839892
                      
                       
                         8213220
                      
                    
                     
                       
                         839892
                      
                       
                         8213220
                      
                    
                     
                       
                         90.345420
                      
                       
                         90.345420
                      
                    
                  
                
                 
                   And
                   here
                   for
                   the
                   Singularity
                   of
                   the
                   Example
                   ,
                   I
                   will
                   set
                   the
                   Dimensions
                   of
                   a
                   Cask
                   lately
                   made
                   in
                   Herefordshire
                   ,
                   for
                   that
                   excellent
                   Liquor
                   of
                   Red
                   streak
                   Cyder
                   ,
                   the
                   like
                   whereof
                   either
                   for
                   the
                   largeness
                   of
                   the
                   Cask
                   ,
                   or
                   incomparable
                   goodness
                   of
                   that
                   kind
                   of
                   Drink
                   ,
                   is
                   not
                   to
                   be
                   found
                   in
                   all
                   England
                   ,
                   nay
                   and
                   perhaps
                   not
                   in
                   the
                   World.
                   
                
                 
                   The
                   length
                   of
                   the
                   Cask
                   is
                   104
                   Inches
                   .
                
                 
                   The
                   Diameter
                   at
                   the
                   Bung
                   92
                   Inches
                   .
                
                 
                   And
                   the
                   Diameter
                   at
                   the
                   Head
                   74
                   Inches
                   .
                
                 
                 
                   The
                   Numbers
                   in
                   the
                   Table
                   of
                   Ale-Gallons
                   answering
                   to
                   these
                   Dimensions
                   are
                   .
                
                 
                   
                     
                       
                         Spheroid
                      
                       
                         Parabolick
                         Spindle
                         .
                      
                    
                     
                       
                         Bung.
                         92
                         7.859639
                      
                       
                         7.859639
                      
                    
                     
                       
                         Head.
                         74
                         5.083699
                      
                       
                         5.083699
                      
                    
                     
                       
                         12.941338
                      
                       
                         12.941338
                      
                    
                     
                       
                         6.470669
                      
                       
                         6.470669
                      
                    
                     
                       
                         1.386770
                      
                       
                         .277394
                      
                    
                     
                       
                         20.798777
                      
                       
                         19.689401
                      
                    
                     
                       
                         104
                      
                       
                         104
                      
                    
                     
                       
                         83195108
                      
                       
                         78.757604
                      
                    
                     
                       
                         20798777
                      
                       
                         19689401
                      
                    
                     
                       
                         Con.
                         2163.072808
                      
                       
                         2047.697704
                      
                    
                  
                
                 
                 
                   
                     
                       
                         Parabolick
                         Conoid
                         .
                      
                       
                         Cone
                         .
                      
                    
                     
                       
                         7.857639
                      
                       
                         7.857639
                      
                    
                     
                       
                         5.083699
                      
                       
                         5.083699
                      
                    
                     
                       
                         12.941338
                      
                       
                         12.941338
                      
                    
                     
                       
                         6.470669
                      
                       
                         6.470669
                      
                    
                     
                       
                          
                      
                       
                         0.150394
                      
                    
                     
                       
                         19.412007
                      
                       
                         19.261613
                      
                    
                     
                       
                         104
                      
                       
                         104
                      
                    
                     
                       
                         77648028
                      
                       
                         77046452
                      
                    
                     
                       
                         19412007
                      
                       
                         19261613
                      
                    
                     
                       
                         201.
                         8.
                         848728
                      
                       
                         2003.207752
                      
                    
                  
                
                 
                   And
                   thus
                   you
                   have
                   the
                   content
                   of
                   this
                   Cask
                   by
                   four
                   several
                   Ways
                   of
                   Gauging
                   ,
                   but
                   that
                   which
                   doth
                   best
                   agree
                   with
                   the
                   true
                   content
                   ,
                   found
                   by
                   these
                   that
                   filled
                   the
                   same
                   is
                   the
                   second
                   way
                   or
                   that
                   which
                   takes
                   a
                   Cask
                   to
                   be
                   the
                   middle
                   Frustum
                   of
                   a
                   Parabolick
                   Spindle
                   ,
                   according
                   to
                   which
                   the
                   content
                   is
                   2047
                   Gallons
                   .
                   That
                   is
                   allowing
                   64
                   Gallons
                   to
                   the
                   Hogshead
                   .
                   32
                   Hogsheads
                   very
                   near
                   .
                
              
               
                 
                 
                   Proposition
                   .
                   X.
                   
                
                 
                   
                     If
                     a
                     Cask
                     be
                     not
                     full
                     ,
                     to
                     find
                     the
                     quantity
                     of
                     Liquor
                     contained
                     in
                     it
                     ,
                     the
                     Axis
                     being
                     posited
                     parallel
                     to
                     the
                     Horizon
                     .
                  
                
                 
                   To
                   resolve
                   this
                   Proposition
                   ,
                   there
                   must
                   be
                   given
                   the
                   whole
                   content
                   of
                   the
                   Cask
                   ,
                   the
                   Diameter
                   at
                   the
                   Bung
                   ,
                   and
                   the
                   wet
                   Portion
                   thereof
                   ,
                   then
                   by
                   help
                   of
                   the
                   Table
                   of
                   Segments
                   ,
                   whose
                   Area
                   is
                   unity
                   ,
                   and
                   the
                   Diameter
                   divided
                   into
                   10.000
                   equal
                   parts
                   ,
                   the
                   content
                   may
                   thus
                   be
                   found
                   .
                
                 
                   As
                   the
                   whole
                   Diameter
                   ,
                   is
                   to
                   its
                   wet
                   Portion
                   .
                
                 
                   So
                   is
                   the
                   Diameter
                   in
                   the
                   Table
                   .
                   10.000
                   to
                   its
                   like
                   Portion
                   ,
                   which
                   being
                   sought
                   in
                   the
                   Table
                   of
                   Segments
                   ,
                   gives
                   you
                   a
                   Segment
                   ,
                   by
                   which
                   if
                   you
                   multiply
                   the
                   whole
                   content
                   of
                   the
                   Cask
                   ,
                   the
                   Product
                   is
                   the
                   content
                   of
                   the
                   Liquor
                   remaining
                   in
                   the
                   Cask
                   .
                
                 
                   But
                   in
                   the
                   Table
                   of
                   Segments
                   in
                   this
                   Book
                   ,
                   you
                   have
                   the
                   Area
                   ,
                   to
                   the
                   equal
                   parts
                   of
                   one
                   half
                   of
                   the
                   Diameter
                   only
                   ,
                   when
                   the
                   Cask
                   therefore
                   is
                   more
                   then
                   half
                   full
                   ,
                   you
                   must
                   make
                   use
                   of
                   the
                   dry
                   part
                   of
                   the
                   Diameter
                   instead
                   of
                   the
                   wet
                   ,
                   so
                   shall
                   you
                   find
                   what
                   quantity
                   of
                   Liquor
                   is
                   wanting
                   to
                   fill
                   up
                   the
                   Cask
                   ,
                   which
                   being
                   deducted
                   from
                   the
                   whole
                   content
                   of
                   the
                   Cask
                   ;
                   the
                   remainer
                   is
                   the
                   quantity
                   of
                   Liquor
                   yet
                   remaining
                   ,
                   an
                   Example
                   in
                   each
                   will
                   be
                   sufficient
                   ,
                   to
                   explane
                   the
                   use
                   of
                   this
                   Table
                   .
                
                 
                   1.
                   
                   Example
                   ,
                   In
                   a
                   Wine
                   Cask
                   not
                   half
                   full
                   ,
                   let
                   the
                   great
                   Diameter
                   be
                   as
                   before
                   32
                   Inches
                   ,
                   the
                   
                   content
                   126.25
                   Gallons
                   ,
                   and
                   let
                   the
                   wet
                   part
                   of
                   the
                   Diameter
                   be
                   12
                   Inches
                   ,
                   First
                   I
                   say
                   .
                
                 
                   As
                   the
                   whole
                   Diameter
                   32.
                   is
                   to
                   the
                   wet
                   part
                   12.
                   so
                   is
                   10.000
                   to
                   3750
                   ,
                   which
                   being
                   sought
                   in
                   the
                   Table
                   ,
                   I
                   find
                   ,
                   the
                   Area
                   of
                   that
                   Segment
                   to
                   be
                   .
                   342518
                   which
                   being
                   multiplyed
                   by
                   the
                   whole
                   content
                   of
                   the
                   Cask
                   126.25
                   ,
                   the
                   Product
                   is
                   43.24289750
                   and
                   therefore
                   there
                   is
                   remaining
                   in
                   the
                   Cask
                   43
                   &
                   1
                   /
                   4
                   ferè
                   .
                
                 
                   2.
                   
                   Example
                   .
                   In
                   the
                   same
                   Cask
                   let
                   the
                   wet
                   part
                   of
                   the
                   Diameter
                   be
                   18
                   Inches
                   .
                   I
                   say
                   .
                
                 
                   As
                   32.18
                   :
                   :
                   10000.5625
                   whos
                   's
                   Complement
                   to
                   10000
                   is
                   4375
                   which
                   being
                   sought
                   in
                   the
                   Table
                   ,
                   I
                   find
                   the
                   Area
                   answering
                   thereto
                   to
                   be
                   420630
                   ;
                   now
                   then
                   I
                   say
                   .
                
                 
                   As
                   the
                   whole
                   Area
                   of
                   the
                   Circle
                   1000000
                   is
                   to
                   the
                   whole
                   content
                   of
                   the
                   Cask
                   126.
                   25.
                   
                
                 
                   So
                   is
                   the
                   Area
                   of
                   the
                   Segment
                   sought
                   .
                   420630
                   ,
                   to
                   the
                   content
                   53.1044375
                   which
                   is
                   in
                   this
                   case
                   the
                   content
                   of
                   the
                   Liquor
                   that
                   is
                   wanting
                   ,
                   this
                   therefore
                   being
                   deducted
                   from
                   the
                   content
                   of
                   the
                   whole
                   Cask
                   ,
                   136.
                   25.
                   the
                   part
                   remaining
                   in
                   the
                   Vessel
                   is
                   .
                   73.
                   1455625.
                   
                
                 
                   Thus
                   may
                   Casks
                   be
                   gauged
                   in
                   whole
                   or
                   in
                   part
                   ,
                   in
                   which
                   a
                   Table
                   of
                   Squares
                   is
                   sometimes
                   necessary
                   ,
                   as
                   being
                   the
                   Foundation
                   ,
                   from
                   whom
                   the
                   other
                   Tables
                   are
                   deduced
                   ;
                   such
                   a
                   Table
                   therefore
                   is
                   here
                   exhibited
                   ,
                   for
                   all
                   Numbers
                   under
                   1000
                   ,
                   by
                   help
                   whereof
                   the
                   Square
                   of
                   any
                   Number
                   under
                   10.000
                   may
                   easily
                   be
                   found
                   in
                   this
                   manner
                   .
                
                 
                   The
                   Rectangle
                   made
                   of
                   the
                   Sum
                   and
                   Difference
                   of
                   any
                   two
                   Numbers
                   ,
                   is
                   equal
                   to
                   the
                   Difference
                   of
                   the
                   Squares
                   of
                   these
                   Numbers
                   .
                
                 
                   Example
                   ,
                   Let
                   the
                   given
                   Numbers
                   be
                   36
                   and
                   85
                   
                   their
                   Sum
                   is
                   121
                   ,
                   their
                   difference
                   49
                   ,
                   by
                   which
                   if
                   you
                   multiply
                   121
                   ,
                   the
                   Product
                   will
                   be
                   5929.
                   
                   The
                   Square
                   of
                   36
                   is
                   1296
                   ,
                   and
                   the
                   Square
                   of
                   85
                   is
                   7225
                   ,
                   the
                   difference
                   between
                   which
                   Squares
                   is
                   5929
                   as
                   before
                   .
                
                 
                   And
                   hence
                   the
                   Square
                   of
                   any
                   Number
                   under
                   10.000
                   may
                   thus
                   be
                   found
                   ,
                   the
                   Squares
                   of
                   all
                   Numbers
                   under
                   1000
                   being
                   given
                   .
                
                 
                   Example
                   .
                   Let
                   the
                   Square
                   of
                   5715
                   be
                   required
                   .
                   The
                   Square
                   of
                   571
                   by
                   the
                   Table
                   is
                   326041
                   ,
                   therefore
                   the
                   Square
                   of
                   5710
                   is
                   32604100
                   :
                   the
                   Sum
                   of
                   5710
                   and
                   5715
                   is
                   11425
                   ,
                   and
                   the
                   difference
                   5
                   ,
                   by
                   which
                   if
                   you
                   multiple
                   11425
                   ,
                   the
                   Product
                   is
                   52125
                   which
                   being
                   added
                   unto
                   32604100
                   the
                   Sum
                   32656325
                   is
                   the
                   Square
                   of
                   5715.
                   
                   The
                   like
                   may
                   be
                   done
                   for
                   any
                   other
                   .
                
              
            
          
        
      
       
         
           
             
             
             
               TABLES
               FOR
               THE
               Measuring
               OF
               TIMBER
               ,
               AND
               THE
               GAUGING
               OF
               CASKS
               AND
               Brevvers
               Tuns
               .
            
             
               LONDON
               ,
               Printed
               for
               
                 Thomas
                 Passinger
              
               at
               the
               three
               Bibles
               on
               London-Bridge
               .
               1679.
               
            
          
        
         
           
             
             
             
               
                 
                   A
                   Table
                   of
                   Squares
                   .
                
                 
                   
                     1
                  
                   
                     1
                  
                   
                     3
                  
                
                 
                   
                     2
                  
                   
                     4
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     09
                  
                   
                     5
                  
                
                 
                   
                     4
                  
                   
                     16
                  
                   
                     7
                  
                
                 
                   
                     5
                  
                   
                     25
                  
                   
                     9
                  
                
                 
                   
                     6
                  
                   
                     36
                  
                   
                     11
                  
                
                 
                   
                     7
                  
                   
                     49
                  
                   
                     13
                  
                
                 
                   
                     8
                  
                   
                     64
                  
                   
                     15
                  
                
                 
                   
                     9
                  
                   
                     81
                  
                   
                     17
                  
                
                 
                   
                     10
                  
                   
                     100
                  
                   
                     19
                  
                
                 
                   
                     11
                  
                   
                     121
                  
                   
                     21
                  
                
                 
                   
                     12
                  
                   
                     144
                  
                   
                     23
                  
                
                 
                   
                     13
                  
                   
                     160
                  
                   
                     25
                  
                
                 
                   
                     14
                  
                   
                     196
                  
                   
                     27
                  
                
                 
                   
                     15
                  
                   
                     225
                  
                   
                     29
                  
                
                 
                   
                     16
                  
                   
                     256
                  
                   
                     31
                  
                
                 
                   
                     17
                  
                   
                     287
                  
                   
                     33
                  
                
                 
                   
                     18
                  
                   
                     324
                  
                   
                     35
                  
                
                 
                   
                     19
                  
                   
                     361
                  
                   
                     37
                  
                
                 
                   
                     20
                  
                   
                     400
                  
                   
                     39
                  
                
                 
                   
                     21
                  
                   
                     441
                  
                   
                     41
                  
                
                 
                   
                     22
                  
                   
                     484
                  
                   
                     43
                  
                
                 
                   
                     23
                  
                   
                     529
                  
                   
                     45
                  
                
                 
                   
                     24
                  
                   
                     576
                  
                   
                     47
                  
                
                 
                   
                     25
                  
                   
                     625
                  
                   
                     49
                  
                
                 
                   
                     26
                  
                   
                     676
                  
                   
                     51
                  
                
                 
                   
                     27
                  
                   
                     729
                  
                   
                     53
                  
                
                 
                   
                     28
                  
                   
                     784
                  
                   
                     55
                  
                
                 
                   
                     29
                  
                   
                     841
                  
                   
                     57
                  
                
                 
                   
                     30
                  
                   
                     900
                  
                   
                     59
                  
                
                 
                   
                     31
                  
                   
                     961
                  
                   
                     61
                  
                
                 
                   
                     32
                  
                   
                     1024
                  
                   
                     63
                  
                
                 
                   
                     33
                  
                   
                     1089
                  
                   
                     65
                  
                
                 
                   
                     34
                  
                   
                     1156
                  
                   
                     67
                  
                
                 
                   
                     34
                  
                   
                     1156
                  
                   
                     69
                  
                
                 
                   
                     35
                  
                   
                     1225
                  
                   
                     71
                  
                
                 
                   
                     36
                  
                   
                     1206
                  
                   
                     73
                  
                
                 
                   
                     37
                  
                   
                     1369
                  
                   
                     75
                  
                
                 
                   
                     38
                  
                   
                     1444
                  
                   
                     77
                  
                
                 
                   
                     39
                  
                   
                     1521
                  
                   
                     79
                  
                
                 
                   
                     40
                  
                   
                     1600
                  
                   
                     81
                  
                
                 
                   
                     41
                  
                   
                     1681
                  
                   
                     83
                  
                
                 
                   
                     42
                  
                   
                     1764
                  
                   
                     85
                  
                
                 
                   
                     43
                  
                   
                     1841
                  
                   
                     87
                  
                
                 
                   
                     44
                  
                   
                     1936
                  
                   
                     89
                  
                
                 
                   
                     45
                  
                   
                     2025
                  
                   
                     91
                  
                
                 
                   
                     46
                  
                   
                     2116
                  
                   
                     93
                  
                
                 
                   
                     47
                  
                   
                     2209
                  
                   
                     95
                  
                
                 
                   
                     48
                  
                   
                     2304
                  
                   
                     97
                  
                
                 
                   
                     49
                  
                   
                     2401
                  
                   
                     99
                  
                
                 
                   
                     50
                  
                   
                     2500
                  
                   
                     101
                  
                
                 
                   
                     51
                  
                   
                     2601
                  
                   
                     103
                  
                
                 
                   
                     52
                  
                   
                     2704
                  
                   
                     105
                  
                
                 
                   
                     53
                  
                   
                     2809
                  
                   
                     107
                  
                
                 
                   
                     54
                  
                   
                     2916
                  
                   
                     109
                  
                
                 
                   
                     55
                  
                   
                     3025
                  
                   
                     111
                  
                
                 
                   
                     56
                  
                   
                     3136
                  
                   
                     113
                  
                
                 
                   
                     57
                  
                   
                     3249
                  
                   
                     115
                  
                
                 
                   
                     58
                  
                   
                     3364
                  
                   
                     117
                  
                
                 
                   
                     59
                  
                   
                     3481
                  
                   
                     119
                  
                
                 
                   
                     60
                  
                   
                     3600
                  
                   
                     121
                  
                
                 
                   
                     61
                  
                   
                     3721
                  
                   
                     123
                  
                
                 
                   
                     62
                  
                   
                     3844
                  
                   
                     125
                  
                
                 
                   
                     63
                  
                   
                     3969
                  
                   
                     127
                  
                
                 
                   
                     64
                  
                   
                     4096
                  
                   
                     129
                  
                
                 
                   
                     65
                  
                   
                     4225
                  
                   
                     131
                  
                
                 
                   
                     66
                  
                   
                     4356
                  
                   
                     133
                  
                
                 
                   
                     67
                  
                   
                     4489
                  
                   
                     135
                  
                
                 
                   
                     67
                  
                   
                     4489
                  
                   
                     135
                  
                
                 
                   
                     68
                  
                   
                     4624
                  
                   
                     137
                  
                
                 
                   
                     60
                  
                   
                     4761
                  
                   
                     139
                  
                
                 
                   
                     70
                  
                   
                     4900
                  
                   
                     141
                  
                
                 
                   
                     71
                  
                   
                     5041
                  
                   
                     143
                  
                
                 
                   
                     72
                  
                   
                     5184
                  
                   
                     145
                  
                
                 
                   
                     73
                  
                   
                     5329
                  
                   
                     147
                  
                
                 
                   
                     74
                  
                   
                     5476
                  
                   
                     149
                  
                
                 
                   
                     75
                  
                   
                     5625
                  
                   
                     151
                  
                
                 
                   
                     76
                  
                   
                     5776
                  
                   
                     153
                  
                
                 
                   
                     77
                  
                   
                     5929
                  
                   
                     155
                  
                
                 
                   
                     78
                  
                   
                     6084
                  
                   
                     157
                  
                
                 
                   
                     79
                  
                   
                     6241
                  
                   
                     159
                  
                
                 
                   
                     80
                  
                   
                     6400
                  
                   
                     161
                  
                
                 
                   
                     81
                  
                   
                     6561
                  
                   
                     163
                  
                
                 
                   
                     82
                  
                   
                     6724
                  
                   
                     165
                  
                
                 
                   
                     83
                  
                   
                     6889
                  
                   
                     167
                  
                
                 
                   
                     84
                  
                   
                     7056
                  
                   
                     169
                  
                
                 
                   
                     05
                  
                   
                     7225
                  
                   
                     171
                  
                
                 
                   
                     06
                  
                   
                     7396
                  
                   
                     173
                  
                
                 
                   
                     87
                  
                   
                     7559
                  
                   
                     175
                  
                
                 
                   
                     88
                  
                   
                     7744
                  
                   
                     177
                  
                
                 
                   
                     89
                  
                   
                     7921
                  
                   
                     179
                  
                
                 
                   
                     90
                  
                   
                     8100
                  
                   
                     181
                  
                
                 
                   
                     91
                  
                   
                     8281
                  
                   
                     183
                  
                
                 
                   
                     92
                  
                   
                     8464
                  
                   
                     185
                  
                
                 
                   
                     93
                  
                   
                     8649
                  
                   
                     187
                  
                
                 
                   
                     94
                  
                   
                     8836
                  
                   
                     189
                  
                
                 
                   
                     95
                  
                   
                     9025
                  
                   
                     191
                  
                
                 
                   
                     96
                  
                   
                     9216
                  
                   
                     193
                  
                
                 
                   
                     97
                  
                   
                     9409
                  
                   
                     195
                  
                
                 
                   
                     98
                  
                   
                     9604
                  
                   
                     197
                  
                
                 
                   
                     99
                  
                   
                     9801
                  
                   
                     199
                  
                
                 
                   
                     100
                  
                   
                     10000
                  
                   
                     201
                  
                
                 
                   
                     
                     101
                  
                   
                     10201
                  
                   
                     203
                  
                
                 
                   
                     102
                  
                   
                     10404
                  
                   
                     205
                  
                
                 
                   
                     103
                  
                   
                     10609
                  
                   
                     207
                  
                
                 
                   
                     104
                  
                   
                     10816
                  
                   
                     209
                  
                
                 
                   
                     105
                  
                   
                     11025
                  
                   
                     211
                  
                
                 
                   
                     106
                  
                   
                     11236
                  
                   
                     213
                  
                
                 
                   
                     107
                  
                   
                     11449
                  
                   
                     215
                  
                
                 
                   
                     108
                  
                   
                     11664
                  
                   
                     217
                  
                
                 
                   
                     109
                  
                   
                     11881
                  
                   
                     219
                  
                
                 
                   
                     110
                  
                   
                     12100
                  
                   
                     221
                  
                
                 
                   
                     111
                  
                   
                     12321
                  
                   
                     223
                  
                
                 
                   
                     112
                  
                   
                     12544
                  
                   
                     225
                  
                
                 
                   
                     113
                  
                   
                     12769
                  
                   
                     227
                  
                
                 
                   
                     114
                  
                   
                     12996
                  
                   
                     229
                  
                
                 
                   
                     115
                  
                   
                     13225
                  
                   
                     231
                  
                
                 
                   
                     116
                  
                   
                     13456
                  
                   
                     233
                  
                
                 
                   
                     117
                  
                   
                     13689
                  
                   
                     235
                  
                
                 
                   
                     118
                  
                   
                     13924
                  
                   
                     237
                  
                
                 
                   
                     119
                  
                   
                     14161
                  
                   
                     239
                  
                
                 
                   
                     120
                  
                   
                     14400
                  
                   
                     241
                  
                
                 
                   
                     121
                  
                   
                     14641
                  
                   
                     243
                  
                
                 
                   
                     122
                  
                   
                     14884
                  
                   
                     245
                  
                
                 
                   
                     123
                  
                   
                     15129
                  
                   
                     247
                  
                
                 
                   
                     124
                  
                   
                     15376
                  
                   
                     249
                  
                
                 
                   
                     125
                  
                   
                     15625
                  
                   
                     251
                  
                
                 
                   
                     126
                  
                   
                     15876
                  
                   
                     253
                  
                
                 
                   
                     127
                  
                   
                     16129
                  
                   
                     255
                  
                
                 
                   
                     128
                  
                   
                     16384
                  
                   
                     257
                  
                
                 
                   
                     129
                  
                   
                     16641
                  
                   
                     259
                  
                
                 
                   
                     130
                  
                   
                     16900
                  
                   
                     261
                  
                
                 
                   
                     131
                  
                   
                     17161
                  
                   
                     263
                  
                
                 
                   
                     132
                  
                   
                     17424
                  
                   
                     265
                  
                
                 
                   
                     133
                  
                   
                     17689
                  
                   
                     267
                  
                
                 
                   
                     134
                  
                   
                     17956
                  
                   
                     269
                  
                
                 
                   
                     134
                  
                   
                     17956
                  
                   
                     269
                  
                
                 
                   
                     135
                  
                   
                     18225
                  
                   
                     271
                  
                
                 
                   
                     136
                  
                   
                     18496
                  
                   
                     273
                  
                
                 
                   
                     137
                  
                   
                     18769
                  
                   
                     275
                  
                
                 
                   
                     138
                  
                   
                     19044
                  
                   
                     277
                  
                
                 
                   
                     139
                  
                   
                     19321
                  
                   
                     279
                  
                
                 
                   
                     140
                  
                   
                     19600
                  
                   
                     281
                  
                
                 
                   
                     141
                  
                   
                     19881
                  
                   
                     283
                  
                
                 
                   
                     142
                  
                   
                     20164
                  
                   
                     285
                  
                
                 
                   
                     143
                  
                   
                     20449
                  
                   
                     287
                  
                
                 
                   
                     144
                  
                   
                     20736
                  
                   
                     289
                  
                
                 
                   
                     145
                  
                   
                     21025
                  
                   
                     291
                  
                
                 
                   
                     146
                  
                   
                     21316
                  
                   
                     293
                  
                
                 
                   
                     147
                  
                   
                     21609
                  
                   
                     295
                  
                
                 
                   
                     148
                  
                   
                     21904
                  
                   
                     297
                  
                
                 
                   
                     149
                  
                   
                     22201
                  
                   
                     299
                  
                
                 
                   
                     150
                  
                   
                     22500
                  
                   
                     301
                  
                
                 
                   
                     151
                  
                   
                     22801
                  
                   
                     303
                  
                
                 
                   
                     152
                  
                   
                     23104
                  
                   
                     305
                  
                
                 
                   
                     153
                  
                   
                     23409
                  
                   
                     307
                  
                
                 
                   
                     154
                  
                   
                     23716
                  
                   
                     309
                  
                
                 
                   
                     155
                  
                   
                     24025
                  
                   
                     311
                  
                
                 
                   
                     156
                  
                   
                     24336
                  
                   
                     313
                  
                
                 
                   
                     157
                  
                   
                     24649
                  
                   
                     315
                  
                
                 
                   
                     158
                  
                   
                     24964
                  
                   
                     317
                  
                
                 
                   
                     159
                  
                   
                     25281
                  
                   
                     319
                  
                
                 
                   
                     160
                  
                   
                     25600
                  
                   
                     321
                  
                
                 
                   
                     161
                  
                   
                     25921
                  
                   
                     323
                  
                
                 
                   
                     162
                  
                   
                     26244
                  
                   
                     325
                  
                
                 
                   
                     163
                  
                   
                     26569
                  
                   
                     327
                  
                
                 
                   
                     164
                  
                   
                     26896
                  
                   
                     329
                  
                
                 
                   
                     165
                  
                   
                     27225
                  
                   
                     331
                  
                
                 
                   
                     166
                  
                   
                     27556
                  
                   
                     333
                  
                
                 
                   
                     167
                  
                   
                     27889
                  
                   
                     335
                  
                
                 
                   
                     
                     167
                  
                   
                     27889
                  
                   
                     335
                  
                
                 
                   
                     168
                  
                   
                     28224
                  
                   
                     337
                  
                
                 
                   
                     169
                  
                   
                     28561
                  
                   
                     339
                  
                
                 
                   
                     170
                  
                   
                     28900
                  
                   
                     341
                  
                
                 
                   
                     171
                  
                   
                     29241
                  
                   
                     343
                  
                
                 
                   
                     172
                  
                   
                     29584
                  
                   
                     345
                  
                
                 
                   
                     173
                  
                   
                     29929
                  
                   
                     347
                  
                
                 
                   
                     174
                  
                   
                     30276
                  
                   
                     349
                  
                
                 
                   
                     175
                  
                   
                     30625
                  
                   
                     351
                  
                
                 
                   
                     176
                  
                   
                     30976
                  
                   
                     353
                  
                
                 
                   
                     177
                  
                   
                     31329
                  
                   
                     355
                  
                
                 
                   
                     178
                  
                   
                     31684
                  
                   
                     357
                  
                
                 
                   
                     179
                  
                   
                     32041
                  
                   
                     359
                  
                
                 
                   
                     180
                  
                   
                     32400
                  
                   
                     361
                  
                
                 
                   
                     181
                  
                   
                     32761
                  
                   
                     363
                  
                
                 
                   
                     182
                  
                   
                     33124
                  
                   
                     365
                  
                
                 
                   
                     183
                  
                   
                     33489
                  
                   
                     367
                  
                
                 
                   
                     184
                  
                   
                     33856
                  
                   
                     369
                  
                
                 
                   
                     185
                  
                   
                     34225
                  
                   
                     371
                  
                
                 
                   
                     186
                  
                   
                     34596
                  
                   
                     373
                  
                
                 
                   
                     187
                  
                   
                     34969
                  
                   
                     375
                  
                
                 
                   
                     188
                  
                   
                     35344
                  
                   
                     377
                  
                
                 
                   
                     189
                  
                   
                     35721
                  
                   
                     379
                  
                
                 
                   
                     190
                  
                   
                     36100
                  
                   
                     381
                  
                
                 
                   
                     191
                  
                   
                     36481
                  
                   
                     383
                  
                
                 
                   
                     192
                  
                   
                     36864
                  
                   
                     385
                  
                
                 
                   
                     193
                  
                   
                     37249
                  
                   
                     387
                  
                
                 
                   
                     194
                  
                   
                     37636
                  
                   
                     389
                  
                
                 
                   
                     195
                  
                   
                     38025
                  
                   
                     391
                  
                
                 
                   
                     196
                  
                   
                     38416
                  
                   
                     393
                  
                
                 
                   
                     197
                  
                   
                     38809
                  
                   
                     395
                  
                
                 
                   
                     198
                  
                   
                     39204
                  
                   
                     397
                  
                
                 
                   
                     199
                  
                   
                     39601
                  
                   
                     399
                  
                
                 
                   
                     200
                  
                   
                     40000
                  
                   
                     401
                  
                
                 
                   
                     201
                  
                   
                     40401
                  
                   
                     403
                  
                
                 
                   
                     202
                  
                   
                     40804
                  
                   
                     405
                  
                
                 
                   
                     203
                  
                   
                     41209
                  
                   
                     407
                  
                
                 
                   
                     204
                  
                   
                     41616
                  
                   
                     409
                  
                
                 
                   
                     205
                  
                   
                     42025
                  
                   
                     411
                  
                
                 
                   
                     206
                  
                   
                     42436
                  
                   
                     413
                  
                
                 
                   
                     207
                  
                   
                     42849
                  
                   
                     415
                  
                
                 
                   
                     208
                  
                   
                     43264
                  
                   
                     417
                  
                
                 
                   
                     209
                  
                   
                     43681
                  
                   
                     419
                  
                
                 
                   
                     210
                  
                   
                     44100
                  
                   
                     421
                  
                
                 
                   
                     211
                  
                   
                     44521
                  
                   
                     423
                  
                
                 
                   
                     212
                  
                   
                     44944
                  
                   
                     425
                  
                
                 
                   
                     213
                  
                   
                     45369
                  
                   
                     427
                  
                
                 
                   
                     214
                  
                   
                     45796
                  
                   
                     429
                  
                
                 
                   
                     215
                  
                   
                     46255
                  
                   
                     431
                  
                
                 
                   
                     216
                  
                   
                     46656
                  
                   
                     433
                  
                
                 
                   
                     217
                  
                   
                     47089
                  
                   
                     435
                  
                
                 
                   
                     218
                  
                   
                     47524
                  
                   
                     437
                  
                
                 
                   
                     219
                  
                   
                     47961
                  
                   
                     439
                  
                
                 
                   
                     220
                  
                   
                     48400
                  
                   
                     441
                  
                
                 
                   
                     221
                  
                   
                     48841
                  
                   
                     443
                  
                
                 
                   
                     222
                  
                   
                     49284
                  
                   
                     445
                  
                
                 
                   
                     223
                  
                   
                     49729
                  
                   
                     447
                  
                
                 
                   
                     224
                  
                   
                     50176
                  
                   
                     449
                  
                
                 
                   
                     225
                  
                   
                     50625
                  
                   
                     451
                  
                
                 
                   
                     226
                  
                   
                     51076
                  
                   
                     453
                  
                
                 
                   
                     227
                  
                   
                     51529
                  
                   
                     455
                  
                
                 
                   
                     228
                  
                   
                     51984
                  
                   
                     457
                  
                
                 
                   
                     229
                  
                   
                     52441
                  
                   
                     459
                  
                
                 
                   
                     230
                  
                   
                     52900
                  
                   
                     461
                  
                
                 
                   
                     231
                  
                   
                     53361
                  
                   
                     463
                  
                
                 
                   
                     232
                  
                   
                     53824
                  
                   
                     465
                  
                
                 
                   
                     233
                  
                   
                     54289
                  
                   
                     467
                  
                
                 
                   
                     234
                  
                   
                     54756
                  
                   
                     469
                  
                
                 
                   
                     
                     234
                  
                   
                     54756
                  
                   
                     469
                  
                
                 
                   
                     235
                  
                   
                     55225
                  
                   
                     471
                  
                
                 
                   
                     236
                  
                   
                     55696
                  
                   
                     473
                  
                
                 
                   
                     237
                  
                   
                     56169
                  
                   
                     475
                  
                
                 
                   
                     238
                  
                   
                     56644
                  
                   
                     477
                  
                
                 
                   
                     239
                  
                   
                     57121
                  
                   
                     479
                  
                
                 
                   
                     240
                  
                   
                     57600
                  
                   
                     481
                  
                
                 
                   
                     241
                  
                   
                     58081
                  
                   
                     483
                  
                
                 
                   
                     242
                  
                   
                     58564
                  
                   
                     485
                  
                
                 
                   
                     143
                  
                   
                     59049
                  
                   
                     487
                  
                
                 
                   
                     244
                  
                   
                     59536
                  
                   
                     489
                  
                
                 
                   
                     245
                  
                   
                     60025
                  
                   
                     491
                  
                
                 
                   
                     246
                  
                   
                     60516
                  
                   
                     493
                  
                
                 
                   
                     247
                  
                   
                     61009
                  
                   
                     495
                  
                
                 
                   
                     248
                  
                   
                     61504
                  
                   
                     497
                  
                
                 
                   
                     249
                  
                   
                     62001
                  
                   
                     499
                  
                
                 
                   
                     250
                  
                   
                     62500
                  
                   
                     501
                  
                
                 
                   
                     251
                  
                   
                     63001
                  
                   
                     503
                  
                
                 
                   
                     252
                  
                   
                     63504
                  
                   
                     505
                  
                
                 
                   
                     253
                  
                   
                     64009
                  
                   
                     507
                  
                
                 
                   
                     254
                  
                   
                     64516
                  
                   
                     509
                  
                
                 
                   
                     255
                  
                   
                     65025
                  
                   
                     511
                  
                
                 
                   
                     256
                  
                   
                     65536
                  
                   
                     513
                  
                
                 
                   
                     257
                  
                   
                     66049
                  
                   
                     515
                  
                
                 
                   
                     258
                  
                   
                     66564
                  
                   
                     517
                  
                
                 
                   
                     259
                  
                   
                     67071
                  
                   
                     519
                  
                
                 
                   
                     260
                  
                   
                     67600
                  
                   
                     621
                  
                
                 
                   
                     261
                  
                   
                     68121
                  
                   
                     523
                  
                
                 
                   
                     262
                  
                   
                     68644
                  
                   
                     525
                  
                
                 
                   
                     263
                  
                   
                     69169
                  
                   
                     527
                  
                
                 
                   
                     264
                  
                   
                     69696
                  
                   
                     529
                  
                
                 
                   
                     265
                  
                   
                     70225
                  
                   
                     531
                  
                
                 
                   
                     266
                  
                   
                     70756
                  
                   
                     533
                  
                
                 
                   
                     277
                  
                   
                     71289
                  
                   
                     535
                  
                
                 
                   
                     267
                  
                   
                     71289
                  
                   
                     535
                  
                
                 
                   
                     268
                  
                   
                     71824
                  
                   
                     537
                  
                
                 
                   
                     269
                  
                   
                     72361
                  
                   
                     539
                  
                
                 
                   
                     270
                  
                   
                     72900
                  
                   
                     541
                  
                
                 
                   
                     271
                  
                   
                     73441
                  
                   
                     543
                  
                
                 
                   
                     272
                  
                   
                     73984
                  
                   
                     545
                  
                
                 
                   
                     273
                  
                   
                     74529
                  
                   
                     547
                  
                
                 
                   
                     274
                  
                   
                     75076
                  
                   
                     549
                  
                
                 
                   
                     275
                  
                   
                     75625
                  
                   
                     551
                  
                
                 
                   
                     276
                  
                   
                     76176
                  
                   
                     553
                  
                
                 
                   
                     277
                  
                   
                     76729
                  
                   
                     555
                  
                
                 
                   
                     278
                  
                   
                     77284
                  
                   
                     557
                  
                
                 
                   
                     279
                  
                   
                     77841
                  
                   
                     559
                  
                
                 
                   
                     280
                  
                   
                     78400
                  
                   
                     561
                  
                
                 
                   
                     281
                  
                   
                     78961
                  
                   
                     563
                  
                
                 
                   
                     282
                  
                   
                     79524
                  
                   
                     565
                  
                
                 
                   
                     283
                  
                   
                     80089
                  
                   
                     567
                  
                
                 
                   
                     284
                  
                   
                     80616
                  
                   
                     569
                  
                
                 
                   
                     285
                  
                   
                     81225
                  
                   
                     571
                  
                
                 
                   
                     286
                  
                   
                     81796
                  
                   
                     573
                  
                
                 
                   
                     287
                  
                   
                     82369
                  
                   
                     575
                  
                
                 
                   
                     288
                  
                   
                     82944
                  
                   
                     577
                  
                
                 
                   
                     289
                  
                   
                     83521
                  
                   
                     579
                  
                
                 
                   
                     290
                  
                   
                     84100
                  
                   
                     581
                  
                
                 
                   
                     291
                  
                   
                     84681
                  
                   
                     583
                  
                
                 
                   
                     292
                  
                   
                     85264
                  
                   
                     585
                  
                
                 
                   
                     293
                  
                   
                     85849
                  
                   
                     587
                  
                
                 
                   
                     294
                  
                   
                     86436
                  
                   
                     589
                  
                
                 
                   
                     295
                  
                   
                     87025
                  
                   
                     591
                  
                
                 
                   
                     296
                  
                   
                     87616
                  
                   
                     593
                  
                
                 
                   
                     297
                  
                   
                     88200
                  
                   
                     595
                  
                
                 
                   
                     298
                  
                   
                     88804
                  
                   
                     597
                  
                
                 
                   
                     299
                  
                   
                     89401
                  
                   
                     599
                  
                
                 
                   
                     300
                  
                   
                     90000
                  
                   
                     601
                  
                
                 
                   
                     
                     301
                  
                   
                     090601
                  
                   
                     603
                  
                
                 
                   
                     302
                  
                   
                     091204
                  
                   
                     605
                  
                
                 
                   
                     303
                  
                   
                     091809
                  
                   
                     607
                  
                
                 
                   
                     304
                  
                   
                     092416
                  
                   
                     609
                  
                
                 
                   
                     305
                  
                   
                     093025
                  
                   
                     611
                  
                
                 
                   
                     306
                  
                   
                     093636
                  
                   
                     613
                  
                
                 
                   
                     307
                  
                   
                     094249
                  
                   
                     615
                  
                
                 
                   
                     308
                  
                   
                     094864
                  
                   
                     617
                  
                
                 
                   
                     309
                  
                   
                     095481
                  
                   
                     619
                  
                
                 
                   
                     310
                  
                   
                     096109
                  
                   
                     621
                  
                
                 
                   
                     311
                  
                   
                     096721
                  
                   
                     623
                  
                
                 
                   
                     312
                  
                   
                     97344
                  
                   
                     625
                  
                
                 
                   
                     313
                  
                   
                     97969
                  
                   
                     627
                  
                
                 
                   
                     314
                  
                   
                     98596
                  
                   
                     629
                  
                
                 
                   
                     315
                  
                   
                     99325
                  
                   
                     631
                  
                
                 
                   
                     316
                  
                   
                     99856
                  
                   
                     633
                  
                
                 
                   
                     317
                  
                   
                     100487
                  
                   
                     645
                  
                
                 
                   
                     318
                  
                   
                     101124
                  
                   
                     637
                  
                
                 
                   
                     319
                  
                   
                     101761
                  
                   
                     639
                  
                
                 
                   
                     320
                  
                   
                     102400
                  
                   
                     641
                  
                
                 
                   
                     321
                  
                   
                     103041
                  
                   
                     643
                  
                
                 
                   
                     322
                  
                   
                     103684
                  
                   
                     645
                  
                
                 
                   
                     323
                  
                   
                     104329
                  
                   
                     647
                  
                
                 
                   
                     324
                  
                   
                     104976
                  
                   
                     649
                  
                
                 
                   
                     325
                  
                   
                     105625
                  
                   
                     651
                  
                
                 
                   
                     326
                  
                   
                     106276
                  
                   
                     653
                  
                
                 
                   
                     327
                  
                   
                     106929
                  
                   
                     655
                  
                
                 
                   
                     328
                  
                   
                     107584
                  
                   
                     657
                  
                
                 
                   
                     329
                  
                   
                     108241
                  
                   
                     659
                  
                
                 
                   
                     330
                  
                   
                     108900
                  
                   
                     661
                  
                
                 
                   
                     331
                  
                   
                     109561
                  
                   
                     663
                  
                
                 
                   
                     332
                  
                   
                     110224
                  
                   
                     665
                  
                
                 
                   
                     333
                  
                   
                     110889
                  
                   
                     667
                  
                
                 
                   
                     334
                  
                   
                     111556
                  
                   
                     669
                  
                
                 
                   
                     334
                  
                   
                     111556
                  
                   
                     669
                  
                
                 
                   
                     335
                  
                   
                     112225
                  
                   
                     671
                  
                
                 
                   
                     336
                  
                   
                     112896
                  
                   
                     673
                  
                
                 
                   
                     337
                  
                   
                     113569
                  
                   
                     675
                  
                
                 
                   
                     338
                  
                   
                     114244
                  
                   
                     677
                  
                
                 
                   
                     339
                  
                   
                     114921
                  
                   
                     679
                  
                
                 
                   
                     340
                  
                   
                     115600
                  
                   
                     681
                  
                
                 
                   
                     341
                  
                   
                     116281
                  
                   
                     683
                  
                
                 
                   
                     342
                  
                   
                     116964
                  
                   
                     685
                  
                
                 
                   
                     343
                  
                   
                     117649
                  
                   
                     687
                  
                
                 
                   
                     344
                  
                   
                     118336
                  
                   
                     689
                  
                
                 
                   
                     345
                  
                   
                     119025
                  
                   
                     691
                  
                
                 
                   
                     346
                  
                   
                     119716
                  
                   
                     693
                  
                
                 
                   
                     347
                  
                   
                     120409
                  
                   
                     695
                  
                
                 
                   
                     348
                  
                   
                     121104
                  
                   
                     697
                  
                
                 
                   
                     349
                  
                   
                     121801
                  
                   
                     699
                  
                
                 
                   
                     350
                  
                   
                     122500
                  
                   
                     701
                  
                
                 
                   
                     351
                  
                   
                     123201
                  
                   
                     703
                  
                
                 
                   
                     352
                  
                   
                     123904
                  
                   
                     705
                  
                
                 
                   
                     353
                  
                   
                     124609
                  
                   
                     707
                  
                
                 
                   
                     354
                  
                   
                     125316
                  
                   
                     709
                  
                
                 
                   
                     355
                  
                   
                     126025
                  
                   
                     711
                  
                
                 
                   
                     356
                  
                   
                     126736
                  
                   
                     713
                  
                
                 
                   
                     357
                  
                   
                     127449
                  
                   
                     715
                  
                
                 
                   
                     358
                  
                   
                     128164
                  
                   
                     717
                  
                
                 
                   
                     359
                  
                   
                     128881
                  
                   
                     719
                  
                
                 
                   
                     360
                  
                   
                     129600
                  
                   
                     721
                  
                
                 
                   
                     361
                  
                   
                     138321
                  
                   
                     723
                  
                
                 
                   
                     362
                  
                   
                     131044
                  
                   
                     725
                  
                
                 
                   
                     363
                  
                   
                     131769
                  
                   
                     727
                  
                
                 
                   
                     364
                  
                   
                     132496
                  
                   
                     729
                  
                
                 
                   
                     365
                  
                   
                     133225
                  
                   
                     731
                  
                
                 
                   
                     366
                  
                   
                     133956
                  
                   
                     733
                  
                
                 
                   
                     367
                  
                   
                     134689
                  
                   
                     735
                  
                
                 
                   
                     
                     367
                  
                   
                     134689
                  
                   
                     735
                  
                
                 
                   
                     368
                  
                   
                     135424
                  
                   
                     737
                  
                
                 
                   
                     369
                  
                   
                     136161
                  
                   
                     739
                  
                
                 
                   
                     370
                  
                   
                     136900
                  
                   
                     741
                  
                
                 
                   
                     371
                  
                   
                     137641
                  
                   
                     743
                  
                
                 
                   
                     372
                  
                   
                     138384
                  
                   
                     745
                  
                
                 
                   
                     373
                  
                   
                     139129
                  
                   
                     747
                  
                
                 
                   
                     374
                  
                   
                     139876
                  
                   
                     749
                  
                
                 
                   
                     375
                  
                   
                     140625
                  
                   
                     751
                  
                
                 
                   
                     376
                  
                   
                     141376
                  
                   
                     753
                  
                
                 
                   
                     377
                  
                   
                     142129
                  
                   
                     755
                  
                
                 
                   
                     378
                  
                   
                     142884
                  
                   
                     757
                  
                
                 
                   
                     379
                  
                   
                     143641
                  
                   
                     759
                  
                
                 
                   
                     380
                  
                   
                     144400
                  
                   
                     761
                  
                
                 
                   
                     381
                  
                   
                     145161
                  
                   
                     763
                  
                
                 
                   
                     382
                  
                   
                     145924
                  
                   
                     765
                  
                
                 
                   
                     383
                  
                   
                     146689
                  
                   
                     767
                  
                
                 
                   
                     384
                  
                   
                     147456
                  
                   
                     769
                  
                
                 
                   
                     385
                  
                   
                     148225
                  
                   
                     771
                  
                
                 
                   
                     386
                  
                   
                     148996
                  
                   
                     773
                  
                
                 
                   
                     387
                  
                   
                     149769
                  
                   
                     775
                  
                
                 
                   
                     388
                  
                   
                     150544
                  
                   
                     777
                  
                
                 
                   
                     389
                  
                   
                     151321
                  
                   
                     779
                  
                
                 
                   
                     390
                  
                   
                     152100
                  
                   
                     781
                  
                
                 
                   
                     391
                  
                   
                     152881
                  
                   
                     783
                  
                
                 
                   
                     392
                  
                   
                     153664
                  
                   
                     785
                  
                
                 
                   
                     393
                  
                   
                     154449
                  
                   
                     787
                  
                
                 
                   
                     394
                  
                   
                     155236
                  
                   
                     789
                  
                
                 
                   
                     395
                  
                   
                     156025
                  
                   
                     791
                  
                
                 
                   
                     396
                  
                   
                     156816
                  
                   
                     793
                  
                
                 
                   
                     397
                  
                   
                     157609
                  
                   
                     795
                  
                
                 
                   
                     398
                  
                   
                     158404
                  
                   
                     797
                  
                
                 
                   
                     399
                  
                   
                     159201
                  
                   
                     799
                  
                
                 
                   
                     400
                  
                   
                     160000
                  
                   
                     801
                  
                
                 
                   
                     401
                  
                   
                     160801
                  
                   
                     803
                  
                
                 
                   
                     402
                  
                   
                     161604
                  
                   
                     805
                  
                
                 
                   
                     403
                  
                   
                     162409
                  
                   
                     807
                  
                
                 
                   
                     404
                  
                   
                     163216
                  
                   
                     809
                  
                
                 
                   
                     405
                  
                   
                     164025
                  
                   
                     811
                  
                
                 
                   
                     406
                  
                   
                     164836
                  
                   
                     813
                  
                
                 
                   
                     407
                  
                   
                     165649
                  
                   
                     815
                  
                
                 
                   
                     408
                  
                   
                     166464
                  
                   
                     817
                  
                
                 
                   
                     409
                  
                   
                     167281
                  
                   
                     819
                  
                
                 
                   
                     410
                  
                   
                     168100
                  
                   
                     821
                  
                
                 
                   
                     411
                  
                   
                     168921
                  
                   
                     823
                  
                
                 
                   
                     412
                  
                   
                     169744
                  
                   
                     825
                  
                
                 
                   
                     413
                  
                   
                     170569
                  
                   
                     827
                  
                
                 
                   
                     414
                  
                   
                     171396
                  
                   
                     829
                  
                
                 
                   
                     415
                  
                   
                     172225
                  
                   
                     831
                  
                
                 
                   
                     416
                  
                   
                     173056
                  
                   
                     833
                  
                
                 
                   
                     417
                  
                   
                     173889
                  
                   
                     835
                  
                
                 
                   
                     418
                  
                   
                     174724
                  
                   
                     837
                  
                
                 
                   
                     419
                  
                   
                     175561
                  
                   
                     839
                  
                
                 
                   
                     420
                  
                   
                     176400
                  
                   
                     841
                  
                
                 
                   
                     421
                  
                   
                     177241
                  
                   
                     843
                  
                
                 
                   
                     422
                  
                   
                     178084
                  
                   
                     845
                  
                
                 
                   
                     423
                  
                   
                     178929
                  
                   
                     847
                  
                
                 
                   
                     424
                  
                   
                     179776
                  
                   
                     849
                  
                
                 
                   
                     425
                  
                   
                     180625
                  
                   
                     851
                  
                
                 
                   
                     426
                  
                   
                     181476
                  
                   
                     853
                  
                
                 
                   
                     427
                  
                   
                     182329
                  
                   
                     855
                  
                
                 
                   
                     428
                  
                   
                     183184
                  
                   
                     857
                  
                
                 
                   
                     429
                  
                   
                     184041
                  
                   
                     859
                  
                
                 
                   
                     430
                  
                   
                     184900
                  
                   
                     861
                  
                
                 
                   
                     431
                  
                   
                     185761
                  
                   
                     863
                  
                
                 
                   
                     432
                  
                   
                     186624
                  
                   
                     865
                  
                
                 
                   
                     433
                  
                   
                     187489
                  
                   
                     867
                  
                
                 
                   
                     434
                  
                   
                     188356
                  
                   
                     869
                  
                
                 
                   
                     
                     434
                  
                   
                     188356
                  
                   
                     869
                  
                
                 
                   
                     435
                  
                   
                     189225
                  
                   
                     871
                  
                
                 
                   
                     436
                  
                   
                     190096
                  
                   
                     873
                  
                
                 
                   
                     437
                  
                   
                     190969
                  
                   
                     875
                  
                
                 
                   
                     438
                  
                   
                     191844
                  
                   
                     877
                  
                
                 
                   
                     439
                  
                   
                     192721
                  
                   
                     879
                  
                
                 
                   
                     440
                  
                   
                     193600
                  
                   
                     881
                  
                
                 
                   
                     441
                  
                   
                     194481
                  
                   
                     883
                  
                
                 
                   
                     442
                  
                   
                     195364
                  
                   
                     885
                  
                
                 
                   
                     443
                  
                   
                     196249
                  
                   
                     887
                  
                
                 
                   
                     444
                  
                   
                     197136
                  
                   
                     889
                  
                
                 
                   
                     445
                  
                   
                     198025
                  
                   
                     891
                  
                
                 
                   
                     446
                  
                   
                     198916
                  
                   
                     893
                  
                
                 
                   
                     447
                  
                   
                     199809
                  
                   
                     895
                  
                
                 
                   
                     448
                  
                   
                     200704
                  
                   
                     897
                  
                
                 
                   
                     449
                  
                   
                     201601
                  
                   
                     899
                  
                
                 
                   
                     450
                  
                   
                     202500
                  
                   
                     901
                  
                
                 
                   
                     451
                  
                   
                     203401
                  
                   
                     903
                  
                
                 
                   
                     452
                  
                   
                     204304
                  
                   
                     905
                  
                
                 
                   
                     453
                  
                   
                     205209
                  
                   
                     907
                  
                
                 
                   
                     454
                  
                   
                     206116
                  
                   
                     909
                  
                
                 
                   
                     455
                  
                   
                     207025
                  
                   
                     911
                  
                
                 
                   
                     456
                  
                   
                     207936
                  
                   
                     913
                  
                
                 
                   
                     457
                  
                   
                     208849
                  
                   
                     915
                  
                
                 
                   
                     458
                  
                   
                     209764
                  
                   
                     917
                  
                
                 
                   
                     459
                  
                   
                     210681
                  
                   
                     919
                  
                
                 
                   
                     460
                  
                   
                     211600
                  
                   
                     921
                  
                
                 
                   
                     461
                  
                   
                     212521
                  
                   
                     923
                  
                
                 
                   
                     462
                  
                   
                     213444
                  
                   
                     925
                  
                
                 
                   
                     463
                  
                   
                     214369
                  
                   
                     927
                  
                
                 
                   
                     464
                  
                   
                     215296
                  
                   
                     929
                  
                
                 
                   
                     465
                  
                   
                     216225
                  
                   
                     931
                  
                
                 
                   
                     466
                  
                   
                     217156
                  
                   
                     933
                  
                
                 
                   
                     467
                  
                   
                     218089
                  
                   
                     935
                  
                
                 
                   
                     467
                  
                   
                     218089
                  
                   
                     935
                  
                
                 
                   
                     468
                  
                   
                     219024
                  
                   
                     937
                  
                
                 
                   
                     469
                  
                   
                     219961
                  
                   
                     939
                  
                
                 
                   
                     470
                  
                   
                     220900
                  
                   
                     941
                  
                
                 
                   
                     471
                  
                   
                     221841
                  
                   
                     943
                  
                
                 
                   
                     472
                  
                   
                     222784
                  
                   
                     945
                  
                
                 
                   
                     473
                  
                   
                     223729
                  
                   
                     947
                  
                
                 
                   
                     474
                  
                   
                     224676
                  
                   
                     949
                  
                
                 
                   
                     475
                  
                   
                     225625
                  
                   
                     951
                  
                
                 
                   
                     476
                  
                   
                     226576
                  
                   
                     953
                  
                
                 
                   
                     477
                  
                   
                     227529
                  
                   
                     955
                  
                
                 
                   
                     478
                  
                   
                     228484
                  
                   
                     957
                  
                
                 
                   
                     479
                  
                   
                     229441
                  
                   
                     959
                  
                
                 
                   
                     480
                  
                   
                     230400
                  
                   
                     961
                  
                
                 
                   
                     481
                  
                   
                     231361
                  
                   
                     963
                  
                
                 
                   
                     482
                  
                   
                     232324
                  
                   
                     965
                  
                
                 
                   
                     483
                  
                   
                     233289
                  
                   
                     967
                  
                
                 
                   
                     484
                  
                   
                     234256
                  
                   
                     969
                  
                
                 
                   
                     485
                  
                   
                     235225
                  
                   
                     971
                  
                
                 
                   
                     486
                  
                   
                     236196
                  
                   
                     973
                  
                
                 
                   
                     487
                  
                   
                     237169
                  
                   
                     975
                  
                
                 
                   
                     488
                  
                   
                     238144
                  
                   
                     977
                  
                
                 
                   
                     489
                  
                   
                     239121
                  
                   
                     979
                  
                
                 
                   
                     490
                  
                   
                     240100
                  
                   
                     981
                  
                
                 
                   
                     491
                  
                   
                     241081
                  
                   
                     983
                  
                
                 
                   
                     492
                  
                   
                     242064
                  
                   
                     985
                  
                
                 
                   
                     493
                  
                   
                     243049
                  
                   
                     987
                  
                
                 
                   
                     494
                  
                   
                     244036
                  
                   
                     989
                  
                
                 
                   
                     495
                  
                   
                     245025
                  
                   
                     991
                  
                
                 
                   
                     496
                  
                   
                     246016
                  
                   
                     993
                  
                
                 
                   
                     497
                  
                   
                     247009
                  
                   
                     995
                  
                
                 
                   
                     498
                  
                   
                     248004
                  
                   
                     997
                  
                
                 
                   
                     499
                  
                   
                     249001
                  
                   
                     999
                  
                
                 
                   
                     500
                  
                   
                     250000
                  
                   
                     1001
                  
                
                 
                   
                     
                     501
                  
                   
                     251001
                  
                   
                     1003
                  
                
                 
                   
                     502
                  
                   
                     252004
                  
                   
                     1005
                  
                
                 
                   
                     503
                  
                   
                     253009
                  
                   
                     1007
                  
                
                 
                   
                     504
                  
                   
                     254016
                  
                   
                     1009
                  
                
                 
                   
                     505
                  
                   
                     255025
                  
                   
                     1011
                  
                
                 
                   
                     506
                  
                   
                     256036
                  
                   
                     1013
                  
                
                 
                   
                     507
                  
                   
                     257049
                  
                   
                     1015
                  
                
                 
                   
                     508
                  
                   
                     258064
                  
                   
                     1017
                  
                
                 
                   
                     509
                  
                   
                     259081
                  
                   
                     1019
                  
                
                 
                   
                     510
                  
                   
                     260100
                  
                   
                     1021
                  
                
                 
                   
                     511
                  
                   
                     261121
                  
                   
                     1023
                  
                
                 
                   
                     512
                  
                   
                     262144
                  
                   
                     1025
                  
                
                 
                   
                     513
                  
                   
                     263169
                  
                   
                     1027
                  
                
                 
                   
                     514
                  
                   
                     264196
                  
                   
                     1029
                  
                
                 
                   
                     515
                  
                   
                     265225
                  
                   
                     1031
                  
                
                 
                   
                     516
                  
                   
                     266256
                  
                   
                     1033
                  
                
                 
                   
                     517
                  
                   
                     267289
                  
                   
                     1035
                  
                
                 
                   
                     518
                  
                   
                     268324
                  
                   
                     1037
                  
                
                 
                   
                     519
                  
                   
                     269361
                  
                   
                     1039
                  
                
                 
                   
                     520
                  
                   
                     270400
                  
                   
                     1041
                  
                
                 
                   
                     521
                  
                   
                     271441
                  
                   
                     1043
                  
                
                 
                   
                     522
                  
                   
                     272484
                  
                   
                     1045
                  
                
                 
                   
                     523
                  
                   
                     273529
                  
                   
                     1047
                  
                
                 
                   
                     524
                  
                   
                     274576
                  
                   
                     1049
                  
                
                 
                   
                     525
                  
                   
                     275625
                  
                   
                     1051
                  
                
                 
                   
                     526
                  
                   
                     276676
                  
                   
                     1053
                  
                
                 
                   
                     527
                  
                   
                     277729
                  
                   
                     1055
                  
                
                 
                   
                     528
                  
                   
                     278784
                  
                   
                     1057
                  
                
                 
                   
                     529
                  
                   
                     279841
                  
                   
                     1050
                  
                
                 
                   
                     530
                  
                   
                     288900
                  
                   
                     1061
                  
                
                 
                   
                     531
                  
                   
                     281961
                  
                   
                     1063
                  
                
                 
                   
                     532
                  
                   
                     283024
                  
                   
                     1065
                  
                
                 
                   
                     533
                  
                   
                     284089
                  
                   
                     1067
                  
                
                 
                   
                     534
                  
                   
                     285156
                  
                   
                     1069
                  
                
                 
                   
                     534
                  
                   
                     285156
                  
                   
                     1069
                  
                
                 
                   
                     535
                  
                   
                     286225
                  
                   
                     1071
                  
                
                 
                   
                     536
                  
                   
                     287296
                  
                   
                     1073
                  
                
                 
                   
                     537
                  
                   
                     288369
                  
                   
                     1075
                  
                
                 
                   
                     538
                  
                   
                     289444
                  
                   
                     1077
                  
                
                 
                   
                     539
                  
                   
                     290521
                  
                   
                     1079
                  
                
                 
                   
                     540
                  
                   
                     291600
                  
                   
                     1081
                  
                
                 
                   
                     541
                  
                   
                     292681
                  
                   
                     1083
                  
                
                 
                   
                     542
                  
                   
                     293764
                  
                   
                     1085
                  
                
                 
                   
                     543
                  
                   
                     294849
                  
                   
                     1087
                  
                
                 
                   
                     544
                  
                   
                     295936
                  
                   
                     1089
                  
                
                 
                   
                     545
                  
                   
                     297025
                  
                   
                     1091
                  
                
                 
                   
                     546
                  
                   
                     298116
                  
                   
                     1093
                  
                
                 
                   
                     547
                  
                   
                     299209
                  
                   
                     1095
                  
                
                 
                   
                     548
                  
                   
                     300324
                  
                   
                     1097
                  
                
                 
                   
                     549
                  
                   
                     301401
                  
                   
                     1099
                  
                
                 
                   
                     550
                  
                   
                     302500
                  
                   
                     1101
                  
                
                 
                   
                     551
                  
                   
                     303601
                  
                   
                     1103
                  
                
                 
                   
                     552
                  
                   
                     304704
                  
                   
                     1105
                  
                
                 
                   
                     553
                  
                   
                     305809
                  
                   
                     1107
                  
                
                 
                   
                     554
                  
                   
                     306916
                  
                   
                     1109
                  
                
                 
                   
                     555
                  
                   
                     308025
                  
                   
                     1111
                  
                
                 
                   
                     556
                  
                   
                     309136
                  
                   
                     1113
                  
                
                 
                   
                     557
                  
                   
                     310249
                  
                   
                     1115
                  
                
                 
                   
                     558
                  
                   
                     311364
                  
                   
                     1117
                  
                
                 
                   
                     559
                  
                   
                     312481
                  
                   
                     1119
                  
                
                 
                   
                     560
                  
                   
                     313600
                  
                   
                     1121
                  
                
                 
                   
                     561
                  
                   
                     314721
                  
                   
                     1123
                  
                
                 
                   
                     562
                  
                   
                     315844
                  
                   
                     1125
                  
                
                 
                   
                     563
                  
                   
                     316969
                  
                   
                     1127
                  
                
                 
                   
                     564
                  
                   
                     318096
                  
                   
                     1129
                  
                
                 
                   
                     565
                  
                   
                     319225
                  
                   
                     1131
                  
                
                 
                   
                     566
                  
                   
                     320356
                  
                   
                     1133
                  
                
                 
                   
                     567
                  
                   
                     321489
                  
                   
                     1135
                  
                
                 
                   
                     
                     567
                  
                   
                     321489
                  
                   
                     1135
                  
                
                 
                   
                     568
                  
                   
                     322624
                  
                   
                     1137
                  
                
                 
                   
                     569
                  
                   
                     323761
                  
                   
                     1139
                  
                
                 
                   
                     570
                  
                   
                     324900
                  
                   
                     1141
                  
                
                 
                   
                     571
                  
                   
                     326041
                  
                   
                     1143
                  
                
                 
                   
                     572
                  
                   
                     327184
                  
                   
                     1145
                  
                
                 
                   
                     573
                  
                   
                     328329
                  
                   
                     1147
                  
                
                 
                   
                     574
                  
                   
                     329476
                  
                   
                     1149
                  
                
                 
                   
                     575
                  
                   
                     330625
                  
                   
                     1151
                  
                
                 
                   
                     576
                  
                   
                     331776
                  
                   
                     1153
                  
                
                 
                   
                     577
                  
                   
                     332929
                  
                   
                     1155
                  
                
                 
                   
                     578
                  
                   
                     334084
                  
                   
                     1157
                  
                
                 
                   
                     579
                  
                   
                     335241
                  
                   
                     1159
                  
                
                 
                   
                     580
                  
                   
                     336400
                  
                   
                     1161
                  
                
                 
                   
                     581
                  
                   
                     337561
                  
                   
                     1163
                  
                
                 
                   
                     582
                  
                   
                     338724
                  
                   
                     1165
                  
                
                 
                   
                     583
                  
                   
                     339889
                  
                   
                     1167
                  
                
                 
                   
                     584
                  
                   
                     341056
                  
                   
                     1169
                  
                
                 
                   
                     585
                  
                   
                     342225
                  
                   
                     1171
                  
                
                 
                   
                     586
                  
                   
                     343396
                  
                   
                     1173
                  
                
                 
                   
                     587
                  
                   
                     344569
                  
                   
                     1175
                  
                
                 
                   
                     588
                  
                   
                     345744
                  
                   
                     1177
                  
                
                 
                   
                     589
                  
                   
                     346921
                  
                   
                     1179
                  
                
                 
                   
                     590
                  
                   
                     348100
                  
                   
                     1181
                  
                
                 
                   
                     591
                  
                   
                     349281
                  
                   
                     1183
                  
                
                 
                   
                     592
                  
                   
                     350464
                  
                   
                     1185
                  
                
                 
                   
                     593
                  
                   
                     351649
                  
                   
                     1187
                  
                
                 
                   
                     594
                  
                   
                     352836
                  
                   
                     1189
                  
                
                 
                   
                     595
                  
                   
                     354025
                  
                   
                     1191
                  
                
                 
                   
                     596
                  
                   
                     355216
                  
                   
                     1193
                  
                
                 
                   
                     597
                  
                   
                     356409
                  
                   
                     1195
                  
                
                 
                   
                     598
                  
                   
                     357604
                  
                   
                     1197
                  
                
                 
                   
                     599
                  
                   
                     358801
                  
                   
                     1199
                  
                
                 
                   
                     600
                  
                   
                     369000
                  
                   
                     1201
                  
                
                 
                   
                     601
                  
                   
                     361201
                  
                   
                     1203
                  
                
                 
                   
                     602
                  
                   
                     362404
                  
                   
                     1205
                  
                
                 
                   
                     603
                  
                   
                     963609
                  
                   
                     1207
                  
                
                 
                   
                     604
                  
                   
                     364816
                  
                   
                     1209
                  
                
                 
                   
                     605
                  
                   
                     366025
                  
                   
                     1211
                  
                
                 
                   
                     606
                  
                   
                     367236
                  
                   
                     1213
                  
                
                 
                   
                     607
                  
                   
                     368449
                  
                   
                     1215
                  
                
                 
                   
                     608
                  
                   
                     369664
                  
                   
                     1217
                  
                
                 
                   
                     609
                  
                   
                     370881
                  
                   
                     1219
                  
                
                 
                   
                     610
                  
                   
                     372100
                  
                   
                     1221
                  
                
                 
                   
                     611
                  
                   
                     373321
                  
                   
                     1223
                  
                
                 
                   
                     612
                  
                   
                     374544
                  
                   
                     1225
                  
                
                 
                   
                     613
                  
                   
                     375769
                  
                   
                     1227
                  
                
                 
                   
                     614
                  
                   
                     376996
                  
                   
                     1229
                  
                
                 
                   
                     615
                  
                   
                     378225
                  
                   
                     1231
                  
                
                 
                   
                     616
                  
                   
                     379456
                  
                   
                     1233
                  
                
                 
                   
                     617
                  
                   
                     380689
                  
                   
                     1235
                  
                
                 
                   
                     618
                  
                   
                     381924
                  
                   
                     1237
                  
                
                 
                   
                     619
                  
                   
                     383161
                  
                   
                     1239
                  
                
                 
                   
                     620
                  
                   
                     384400
                  
                   
                     1241
                  
                
                 
                   
                     621
                  
                   
                     385641
                  
                   
                     1243
                  
                
                 
                   
                     622
                  
                   
                     386834
                  
                   
                     1245
                  
                
                 
                   
                     623
                  
                   
                     388129
                  
                   
                     1247
                  
                
                 
                   
                     624
                  
                   
                     389376
                  
                   
                     1249
                  
                
                 
                   
                     625
                  
                   
                     390625
                  
                   
                     1251
                  
                
                 
                   
                     626
                  
                   
                     391876
                  
                   
                     1253
                  
                
                 
                   
                     627
                  
                   
                     393129
                  
                   
                     1255
                  
                
                 
                   
                     628
                  
                   
                     394385
                  
                   
                     1257
                  
                
                 
                   
                     629
                  
                   
                     395641
                  
                   
                     1259
                  
                
                 
                   
                     630
                  
                   
                     396900
                  
                   
                     1261
                  
                
                 
                   
                     631
                  
                   
                     398161
                  
                   
                     1263
                  
                
                 
                   
                     632
                  
                   
                     399424
                  
                   
                     1265
                  
                
                 
                   
                     633
                  
                   
                     400689
                  
                   
                     1267
                  
                
                 
                   
                     634
                  
                   
                     401956
                  
                   
                     1269
                  
                
                 
                   
                     
                     634
                  
                   
                     401956
                  
                   
                     1269
                  
                
                 
                   
                     635
                  
                   
                     403225
                  
                   
                     1271
                  
                
                 
                   
                     636
                  
                   
                     404496
                  
                   
                     1273
                  
                
                 
                   
                     637
                  
                   
                     405769
                  
                   
                     1275
                  
                
                 
                   
                     638
                  
                   
                     407044
                  
                   
                     1277
                  
                
                 
                   
                     639
                  
                   
                     408321
                  
                   
                     1279
                  
                
                 
                   
                     640
                  
                   
                     409600
                  
                   
                     1281
                  
                
                 
                   
                     641
                  
                   
                     410881
                  
                   
                     1283
                  
                
                 
                   
                     642
                  
                   
                     412164
                  
                   
                     1285
                  
                
                 
                   
                     643
                  
                   
                     413449
                  
                   
                     1287
                  
                
                 
                   
                     644
                  
                   
                     414736
                  
                   
                     1289
                  
                
                 
                   
                     645
                  
                   
                     416025
                  
                   
                     1291
                  
                
                 
                   
                     646
                  
                   
                     417316
                  
                   
                     1293
                  
                
                 
                   
                     647
                  
                   
                     418609
                  
                   
                     1295
                  
                
                 
                   
                     648
                  
                   
                     419904
                  
                   
                     1297
                  
                
                 
                   
                     649
                  
                   
                     421201
                  
                   
                     1299
                  
                
                 
                   
                     650
                  
                   
                     422500
                  
                   
                     1301
                  
                
                 
                   
                     651
                  
                   
                     423801
                  
                   
                     1303
                  
                
                 
                   
                     652
                  
                   
                     425104
                  
                   
                     1305
                  
                
                 
                   
                     653
                  
                   
                     426409
                  
                   
                     1307
                  
                
                 
                   
                     654
                  
                   
                     427716
                  
                   
                     1309
                  
                
                 
                   
                     655
                  
                   
                     429025
                  
                   
                     1311
                  
                
                 
                   
                     656
                  
                   
                     430336
                  
                   
                     1313
                  
                
                 
                   
                     657
                  
                   
                     431649
                  
                   
                     1315
                  
                
                 
                   
                     658
                  
                   
                     432964
                  
                   
                     1317
                  
                
                 
                   
                     659
                  
                   
                     434281
                  
                   
                     1319
                  
                
                 
                   
                     660
                  
                   
                     435600
                  
                   
                     1321
                  
                
                 
                   
                     661
                  
                   
                     436921
                  
                   
                     1323
                  
                
                 
                   
                     662
                  
                   
                     438244
                  
                   
                     1325
                  
                
                 
                   
                     663
                  
                   
                     439569
                  
                   
                     1327
                  
                
                 
                   
                     664
                  
                   
                     440896
                  
                   
                     1329
                  
                
                 
                   
                     665
                  
                   
                     442225
                  
                   
                     1331
                  
                
                 
                   
                     666
                  
                   
                     443556
                  
                   
                     1333
                  
                
                 
                   
                     667
                  
                   
                     444889
                  
                   
                     1335
                  
                
                 
                   
                     667
                  
                   
                     444889
                  
                   
                     1335
                  
                
                 
                   
                     668
                  
                   
                     446224
                  
                   
                     1337
                  
                
                 
                   
                     669
                  
                   
                     447561
                  
                   
                     1339
                  
                
                 
                   
                     670
                  
                   
                     448900
                  
                   
                     1341
                  
                
                 
                   
                     671
                  
                   
                     450241
                  
                   
                     1343
                  
                
                 
                   
                     672
                  
                   
                     451584
                  
                   
                     1345
                  
                
                 
                   
                     673
                  
                   
                     452929
                  
                   
                     1347
                  
                
                 
                   
                     674
                  
                   
                     454276
                  
                   
                     1349
                  
                
                 
                   
                     675
                  
                   
                     455625
                  
                   
                     1351
                  
                
                 
                   
                     676
                  
                   
                     456976
                  
                   
                     1353
                  
                
                 
                   
                     677
                  
                   
                     458329
                  
                   
                     1355
                  
                
                 
                   
                     678
                  
                   
                     459684
                  
                   
                     1357
                  
                
                 
                   
                     679
                  
                   
                     461041
                  
                   
                     1359
                  
                
                 
                   
                     680
                  
                   
                     462400
                  
                   
                     1361
                  
                
                 
                   
                     681
                  
                   
                     463761
                  
                   
                     1363
                  
                
                 
                   
                     682
                  
                   
                     465124
                  
                   
                     1365
                  
                
                 
                   
                     683
                  
                   
                     466489
                  
                   
                     1367
                  
                
                 
                   
                     684
                  
                   
                     467856
                  
                   
                     1369
                  
                
                 
                   
                     685
                  
                   
                     469225
                  
                   
                     1371
                  
                
                 
                   
                     686
                  
                   
                     470596
                  
                   
                     1373
                  
                
                 
                   
                     687
                  
                   
                     471969
                  
                   
                     1375
                  
                
                 
                   
                     688
                  
                   
                     473344
                  
                   
                     1377
                  
                
                 
                   
                     689
                  
                   
                     474721
                  
                   
                     1379
                  
                
                 
                   
                     690
                  
                   
                     476100
                  
                   
                     1381
                  
                
                 
                   
                     691
                  
                   
                     477481
                  
                   
                     1383
                  
                
                 
                   
                     692
                  
                   
                     478864
                  
                   
                     1385
                  
                
                 
                   
                     693
                  
                   
                     480249
                  
                   
                     1387
                  
                
                 
                   
                     694
                  
                   
                     481636
                  
                   
                     1389
                  
                
                 
                   
                     695
                  
                   
                     483025
                  
                   
                     1391
                  
                
                 
                   
                     696
                  
                   
                     484416
                  
                   
                     1393
                  
                
                 
                   
                     697
                  
                   
                     485809
                  
                   
                     1395
                  
                
                 
                   
                     698
                  
                   
                     487204
                  
                   
                     1397
                  
                
                 
                   
                     699
                  
                   
                     488601
                  
                   
                     1399
                  
                
                 
                   
                     700
                  
                   
                     490000
                  
                   
                     1401
                  
                
                 
                   
                     
                     701
                  
                   
                     491401
                  
                   
                     1403
                  
                
                 
                   
                     702
                  
                   
                     492804
                  
                   
                     1405
                  
                
                 
                   
                     703
                  
                   
                     494209
                  
                   
                     1407
                  
                
                 
                   
                     704
                  
                   
                     495616
                  
                   
                     1409
                  
                
                 
                   
                     705
                  
                   
                     497025
                  
                   
                     1411
                  
                
                 
                   
                     706
                  
                   
                     498436
                  
                   
                     1413
                  
                
                 
                   
                     707
                  
                   
                     499849
                  
                   
                     1415
                  
                
                 
                   
                     708
                  
                   
                     501264
                  
                   
                     1417
                  
                
                 
                   
                     709
                  
                   
                     502681
                  
                   
                     1419
                  
                
                 
                   
                     710
                  
                   
                     504100
                  
                   
                     1421
                  
                
                 
                   
                     711
                  
                   
                     505521
                  
                   
                     1423
                  
                
                 
                   
                     712
                  
                   
                     506944
                  
                   
                     1425
                  
                
                 
                   
                     713
                  
                   
                     508369
                  
                   
                     1427
                  
                
                 
                   
                     714
                  
                   
                     509796
                  
                   
                     1429
                  
                
                 
                   
                     715
                  
                   
                     511225
                  
                   
                     1431
                  
                
                 
                   
                     716
                  
                   
                     512656
                  
                   
                     1433
                  
                
                 
                   
                     717
                  
                   
                     514089
                  
                   
                     1435
                  
                
                 
                   
                     718
                  
                   
                     515524
                  
                   
                     1437
                  
                
                 
                   
                     719
                  
                   
                     516961
                  
                   
                     1439
                  
                
                 
                   
                     720
                  
                   
                     518400
                  
                   
                     1441
                  
                
                 
                   
                     721
                  
                   
                     519841
                  
                   
                     1443
                  
                
                 
                   
                     722
                  
                   
                     521284
                  
                   
                     1445
                  
                
                 
                   
                     723
                  
                   
                     522729
                  
                   
                     1447
                  
                
                 
                   
                     724
                  
                   
                     524176
                  
                   
                     1449
                  
                
                 
                   
                     725
                  
                   
                     525625
                  
                   
                     1451
                  
                
                 
                   
                     726
                  
                   
                     527076
                  
                   
                     1453
                  
                
                 
                   
                     727
                  
                   
                     528529
                  
                   
                     1455
                  
                
                 
                   
                     728
                  
                   
                     529984
                  
                   
                     1457
                  
                
                 
                   
                     729
                  
                   
                     531441
                  
                   
                     1459
                  
                
                 
                   
                     730
                  
                   
                     532900
                  
                   
                     1461
                  
                
                 
                   
                     731
                  
                   
                     534361
                  
                   
                     1463
                  
                
                 
                   
                     732
                  
                   
                     535824
                  
                   
                     1465
                  
                
                 
                   
                     733
                  
                   
                     537289
                  
                   
                     1467
                  
                
                 
                   
                     734
                  
                   
                     538756
                  
                   
                     1469
                  
                
                 
                   
                     734
                  
                   
                     538756
                  
                   
                     1469
                  
                
                 
                   
                     735
                  
                   
                     540225
                  
                   
                     1471
                  
                
                 
                   
                     736
                  
                   
                     541696
                  
                   
                     1473
                  
                
                 
                   
                     737
                  
                   
                     543169
                  
                   
                     1475
                  
                
                 
                   
                     738
                  
                   
                     544644
                  
                   
                     1477
                  
                
                 
                   
                     739
                  
                   
                     546121
                  
                   
                     1479
                  
                
                 
                   
                     740
                  
                   
                     547600
                  
                   
                     1481
                  
                
                 
                   
                     741
                  
                   
                     549081
                  
                   
                     1483
                  
                
                 
                   
                     742
                  
                   
                     550564
                  
                   
                     1485
                  
                
                 
                   
                     743
                  
                   
                     552049
                  
                   
                     1487
                  
                
                 
                   
                     744
                  
                   
                     553536
                  
                   
                     1489
                  
                
                 
                   
                     745
                  
                   
                     555025
                  
                   
                     1491
                  
                
                 
                   
                     746
                  
                   
                     556516
                  
                   
                     1493
                  
                
                 
                   
                     747
                  
                   
                     558009
                  
                   
                     1495
                  
                
                 
                   
                     748
                  
                   
                     559504
                  
                   
                     1497
                  
                
                 
                   
                     749
                  
                   
                     561001
                  
                   
                     1499
                  
                
                 
                   
                     750
                  
                   
                     562500
                  
                   
                     1501
                  
                
                 
                   
                     751
                  
                   
                     564001
                  
                   
                     1503
                  
                
                 
                   
                     752
                  
                   
                     565504
                  
                   
                     1505
                  
                
                 
                   
                     753
                  
                   
                     567009
                  
                   
                     1507
                  
                
                 
                   
                     754
                  
                   
                     568516
                  
                   
                     1509
                  
                
                 
                   
                     755
                  
                   
                     570025
                  
                   
                     1511
                  
                
                 
                   
                     756
                  
                   
                     571536
                  
                   
                     1513
                  
                
                 
                   
                     757
                  
                   
                     573049
                  
                   
                     1515
                  
                
                 
                   
                     758
                  
                   
                     574564
                  
                   
                     1517
                  
                
                 
                   
                     759
                  
                   
                     576081
                  
                   
                     1519
                  
                
                 
                   
                     760
                  
                   
                     577600
                  
                   
                     1521
                  
                
                 
                   
                     761
                  
                   
                     579121
                  
                   
                     1523
                  
                
                 
                   
                     762
                  
                   
                     580644
                  
                   
                     1525
                  
                
                 
                   
                     763
                  
                   
                     582169
                  
                   
                     1527
                  
                
                 
                   
                     764
                  
                   
                     583696
                  
                   
                     1529
                  
                
                 
                   
                     765
                  
                   
                     585225
                  
                   
                     1531
                  
                
                 
                   
                     766
                  
                   
                     586756
                  
                   
                     1533
                  
                
                 
                   
                     767
                  
                   
                     588289
                  
                   
                     1535
                  
                
                 
                   
                     
                     767
                  
                   
                     588289
                  
                   
                     1535
                  
                
                 
                   
                     768
                  
                   
                     589824
                  
                   
                     1537
                  
                
                 
                   
                     769
                  
                   
                     591361
                  
                   
                     1539
                  
                
                 
                   
                     770
                  
                   
                     592900
                  
                   
                     1541
                  
                
                 
                   
                     771
                  
                   
                     594441
                  
                   
                     1543
                  
                
                 
                   
                     772
                  
                   
                     595984
                  
                   
                     1545
                  
                
                 
                   
                     773
                  
                   
                     597529
                  
                   
                     1547
                  
                
                 
                   
                     774
                  
                   
                     599076
                  
                   
                     1549
                  
                
                 
                   
                     775
                  
                   
                     600625
                  
                   
                     1551
                  
                
                 
                   
                     776
                  
                   
                     602176
                  
                   
                     1553
                  
                
                 
                   
                     777
                  
                   
                     603726
                  
                   
                     1555
                  
                
                 
                   
                     778
                  
                   
                     605284
                  
                   
                     1557
                  
                
                 
                   
                     779
                  
                   
                     606841
                  
                   
                     1559
                  
                
                 
                   
                     780
                  
                   
                     608400
                  
                   
                     1561
                  
                
                 
                   
                     781
                  
                   
                     609961
                  
                   
                     1563
                  
                
                 
                   
                     782
                  
                   
                     611524
                  
                   
                     1565
                  
                
                 
                   
                     783
                  
                   
                     613089
                  
                   
                     1567
                  
                
                 
                   
                     784
                  
                   
                     614656
                  
                   
                     1569
                  
                
                 
                   
                     785
                  
                   
                     616225
                  
                   
                     1571
                  
                
                 
                   
                     786
                  
                   
                     617796
                  
                   
                     1573
                  
                
                 
                   
                     787
                  
                   
                     619369
                  
                   
                     1575
                  
                
                 
                   
                     788
                  
                   
                     620944
                  
                   
                     1577
                  
                
                 
                   
                     789
                  
                   
                     622521
                  
                   
                     1579
                  
                
                 
                   
                     790
                  
                   
                     624100
                  
                   
                     1581
                  
                
                 
                   
                     791
                  
                   
                     625681
                  
                   
                     1583
                  
                
                 
                   
                     792
                  
                   
                     627264
                  
                   
                     1585
                  
                
                 
                   
                     793
                  
                   
                     628849
                  
                   
                     1587
                  
                
                 
                   
                     794
                  
                   
                     630436
                  
                   
                     1589
                  
                
                 
                   
                     795
                  
                   
                     632025
                  
                   
                     1591
                  
                
                 
                   
                     796
                  
                   
                     633616
                  
                   
                     1593
                  
                
                 
                   
                     797
                  
                   
                     635209
                  
                   
                     1595
                  
                
                 
                   
                     798
                  
                   
                     636804
                  
                   
                     1597
                  
                
                 
                   
                     799
                  
                   
                     638401
                  
                   
                     1599
                  
                
                 
                   
                     800
                  
                   
                     640000
                  
                   
                     1601
                  
                
                 
                   
                     801
                  
                   
                     641601
                  
                   
                     1603
                  
                
                 
                   
                     802
                  
                   
                     643204
                  
                   
                     1605
                  
                
                 
                   
                     893
                  
                   
                     644809
                  
                   
                     1607
                  
                
                 
                   
                     804
                  
                   
                     646416
                  
                   
                     1609
                  
                
                 
                   
                     805
                  
                   
                     648025
                  
                   
                     1611
                  
                
                 
                   
                     806
                  
                   
                     649636
                  
                   
                     1613
                  
                
                 
                   
                     807
                  
                   
                     651249
                  
                   
                     1615
                  
                
                 
                   
                     808
                  
                   
                     652864
                  
                   
                     1617
                  
                
                 
                   
                     809
                  
                   
                     654481
                  
                   
                     1619
                  
                
                 
                   
                     010
                  
                   
                     656100
                  
                   
                     1621
                  
                
                 
                   
                     811
                  
                   
                     657721
                  
                   
                     1623
                  
                
                 
                   
                     812
                  
                   
                     659344
                  
                   
                     2625
                  
                
                 
                   
                     813
                  
                   
                     560969
                  
                   
                     1627
                  
                
                 
                   
                     814
                  
                   
                     562596
                  
                   
                     1629
                  
                
                 
                   
                     815
                  
                   
                     564225
                  
                   
                     1631
                  
                
                 
                   
                     816
                  
                   
                     565856
                  
                   
                     1633
                  
                
                 
                   
                     817
                  
                   
                     567489
                  
                   
                     1635
                  
                
                 
                   
                     818
                  
                   
                     569124
                  
                   
                     1637
                  
                
                 
                   
                     819
                  
                   
                     570761
                  
                   
                     1639
                  
                
                 
                   
                     820
                  
                   
                     672400
                  
                   
                     1641
                  
                
                 
                   
                     821
                  
                   
                     674041
                  
                   
                     1643
                  
                
                 
                   
                     822
                  
                   
                     675684
                  
                   
                     1645
                  
                
                 
                   
                     823
                  
                   
                     677329
                  
                   
                     1647
                  
                
                 
                   
                     824
                  
                   
                     678976
                  
                   
                     1649
                  
                
                 
                   
                     825
                  
                   
                     680625
                  
                   
                     1651
                  
                
                 
                   
                     826
                  
                   
                     682276
                  
                   
                     1653
                  
                
                 
                   
                     827
                  
                   
                     683929
                  
                   
                     1655
                  
                
                 
                   
                     828
                  
                   
                     685584
                  
                   
                     1657
                  
                
                 
                   
                     829
                  
                   
                     687241
                  
                   
                     1659
                  
                
                 
                   
                     830
                  
                   
                     688900
                  
                   
                     1661
                  
                
                 
                   
                     831
                  
                   
                     690561
                  
                   
                     1663
                  
                
                 
                   
                     832
                  
                   
                     692224
                  
                   
                     1665
                  
                
                 
                   
                     833
                  
                   
                     693889
                  
                   
                     1667
                  
                
                 
                   
                     834
                  
                   
                     695556
                  
                   
                     1669
                  
                
                 
                   
                     
                     834
                  
                   
                     695556
                  
                   
                     1669
                  
                
                 
                   
                     835
                  
                   
                     697225
                  
                   
                     1671
                  
                
                 
                   
                     836
                  
                   
                     668869
                  
                   
                     1673
                  
                
                 
                   
                     837
                  
                   
                     700569
                  
                   
                     1675
                  
                
                 
                   
                     838
                  
                   
                     702244
                  
                   
                     1677
                  
                
                 
                   
                     839
                  
                   
                     703921
                  
                   
                     1679
                  
                
                 
                   
                     840
                  
                   
                     705600
                  
                   
                     1681
                  
                
                 
                   
                     841
                  
                   
                     707281
                  
                   
                     1683
                  
                
                 
                   
                     842
                  
                   
                     708964
                  
                   
                     1685
                  
                
                 
                   
                     853
                  
                   
                     710649
                  
                   
                     1687
                  
                
                 
                   
                     844
                  
                   
                     712336
                  
                   
                     1689
                  
                
                 
                   
                     845
                  
                   
                     714025
                  
                   
                     1691
                  
                
                 
                   
                     846
                  
                   
                     715716
                  
                   
                     1693
                  
                
                 
                   
                     847
                  
                   
                     717409
                  
                   
                     1695
                  
                
                 
                   
                     848
                  
                   
                     719104
                  
                   
                     1697
                  
                
                 
                   
                     849
                  
                   
                     729801
                  
                   
                     1699
                  
                
                 
                   
                     850
                  
                   
                     722500
                  
                   
                     1701
                  
                
                 
                   
                     851
                  
                   
                     724201
                  
                   
                     1703
                  
                
                 
                   
                     852
                  
                   
                     725904
                  
                   
                     1705
                  
                
                 
                   
                     853
                  
                   
                     727609
                  
                   
                     1707
                  
                
                 
                   
                     854
                  
                   
                     729316
                  
                   
                     1709
                  
                
                 
                   
                     855
                  
                   
                     731025
                  
                   
                     1711
                  
                
                 
                   
                     856
                  
                   
                     732736
                  
                   
                     1713
                  
                
                 
                   
                     857
                  
                   
                     734449
                  
                   
                     1715
                  
                
                 
                   
                     858
                  
                   
                     736164
                  
                   
                     1717
                  
                
                 
                   
                     859
                  
                   
                     737881
                  
                   
                     1719
                  
                
                 
                   
                     860
                  
                   
                     739600
                  
                   
                     1721
                  
                
                 
                   
                     861
                  
                   
                     741321
                  
                   
                     1723
                  
                
                 
                   
                     862
                  
                   
                     743044
                  
                   
                     1725
                  
                
                 
                   
                     863
                  
                   
                     744769
                  
                   
                     1727
                  
                
                 
                   
                     864
                  
                   
                     746596
                  
                   
                     1729
                  
                
                 
                   
                     865
                  
                   
                     748225
                  
                   
                     1731
                  
                
                 
                   
                     866
                  
                   
                     749956
                  
                   
                     1733
                  
                
                 
                   
                     867
                  
                   
                     751689
                  
                   
                     1735
                  
                
                 
                   
                     867
                  
                   
                     751689
                  
                   
                     1735
                  
                
                 
                   
                     868
                  
                   
                     753424
                  
                   
                     1737
                  
                
                 
                   
                     869
                  
                   
                     755161
                  
                   
                     1739
                  
                
                 
                   
                     870
                  
                   
                     756900
                  
                   
                     1741
                  
                
                 
                   
                     871
                  
                   
                     658641
                  
                   
                     1743
                  
                
                 
                   
                     872
                  
                   
                     760384
                  
                   
                     1745
                  
                
                 
                   
                     873
                  
                   
                     762129
                  
                   
                     1747
                  
                
                 
                   
                     874
                  
                   
                     763876
                  
                   
                     1749
                  
                
                 
                   
                     875
                  
                   
                     765625
                  
                   
                     1751
                  
                
                 
                   
                     876
                  
                   
                     767376
                  
                   
                     1753
                  
                
                 
                   
                     877
                  
                   
                     769529
                  
                   
                     1755
                  
                
                 
                   
                     878
                  
                   
                     770884
                  
                   
                     1757
                  
                
                 
                   
                     879
                  
                   
                     772641
                  
                   
                     1759
                  
                
                 
                   
                     880
                  
                   
                     774400
                  
                   
                     1761
                  
                
                 
                   
                     881
                  
                   
                     776161
                  
                   
                     1763
                  
                
                 
                   
                     882
                  
                   
                     777924
                  
                   
                     1765
                  
                
                 
                   
                     883
                  
                   
                     779689
                  
                   
                     1767
                  
                
                 
                   
                     884
                  
                   
                     781456
                  
                   
                     1769
                  
                
                 
                   
                     885
                  
                   
                     783225
                  
                   
                     1771
                  
                
                 
                   
                     886
                  
                   
                     754996
                  
                   
                     1773
                  
                
                 
                   
                     887
                  
                   
                     786709
                  
                   
                     1775
                  
                
                 
                   
                     888
                  
                   
                     786544
                  
                   
                     1777
                  
                
                 
                   
                     889
                  
                   
                     790321
                  
                   
                     1779
                  
                
                 
                   
                     890
                  
                   
                     792100
                  
                   
                     1781
                  
                
                 
                   
                     891
                  
                   
                     793881
                  
                   
                     1783
                  
                
                 
                   
                     892
                  
                   
                     795664
                  
                   
                     1785
                  
                
                 
                   
                     893
                  
                   
                     797449
                  
                   
                     1787
                  
                
                 
                   
                     894
                  
                   
                     799236
                  
                   
                     1789
                  
                
                 
                   
                     895
                  
                   
                     801025
                  
                   
                     1791
                  
                
                 
                   
                     896
                  
                   
                     802816
                  
                   
                     1793
                  
                
                 
                   
                     897
                  
                   
                     894609
                  
                   
                     1795
                  
                
                 
                   
                     808
                  
                   
                     806404
                  
                   
                     1797
                  
                
                 
                   
                     899
                  
                   
                     808281
                  
                   
                     1799
                  
                
                 
                   
                     900
                  
                   
                     810000
                  
                   
                     1801
                  
                
                 
                   
                     
                     901
                  
                   
                     811801
                  
                   
                     1803
                  
                
                 
                   
                     902
                  
                   
                     813604
                  
                   
                     1805
                  
                
                 
                   
                     903
                  
                   
                     815409
                  
                   
                     1807
                  
                
                 
                   
                     904
                  
                   
                     817216
                  
                   
                     1809
                  
                
                 
                   
                     905
                  
                   
                     819025
                  
                   
                     1811
                  
                
                 
                   
                     906
                  
                   
                     820836
                  
                   
                     1813
                  
                
                 
                   
                     907
                  
                   
                     822649
                  
                   
                     1815
                  
                
                 
                   
                     908
                  
                   
                     824464
                  
                   
                     1817
                  
                
                 
                   
                     909
                  
                   
                     826281
                  
                   
                     1819
                  
                
                 
                   
                     910
                  
                   
                     828100
                  
                   
                     1821
                  
                
                 
                   
                     911
                  
                   
                     829921
                  
                   
                     1823
                  
                
                 
                   
                     912
                  
                   
                     831744
                  
                   
                     1825
                  
                
                 
                   
                     913
                  
                   
                     833569
                  
                   
                     1827
                  
                
                 
                   
                     914
                  
                   
                     835396
                  
                   
                     1829
                  
                
                 
                   
                     915
                  
                   
                     837225
                  
                   
                     1831
                  
                
                 
                   
                     916
                  
                   
                     839056
                  
                   
                     1833
                  
                
                 
                   
                     917
                  
                   
                     840889
                  
                   
                     1835
                  
                
                 
                   
                     918
                  
                   
                     842724
                  
                   
                     1837
                  
                
                 
                   
                     919
                  
                   
                     844561
                  
                   
                     1839
                  
                
                 
                   
                     920
                  
                   
                     846400
                  
                   
                     1841
                  
                
                 
                   
                     921
                  
                   
                     848241
                  
                   
                     1843
                  
                
                 
                   
                     922
                  
                   
                     850084
                  
                   
                     1845
                  
                
                 
                   
                     923
                  
                   
                     851929
                  
                   
                     1847
                  
                
                 
                   
                     924
                  
                   
                     853776
                  
                   
                     1849
                  
                
                 
                   
                     925
                  
                   
                     855625
                  
                   
                     1851
                  
                
                 
                   
                     926
                  
                   
                     857476
                  
                   
                     1853
                  
                
                 
                   
                     927
                  
                   
                     859329
                  
                   
                     1855
                  
                
                 
                   
                     928
                  
                   
                     861184
                  
                   
                     1857
                  
                
                 
                   
                     929
                  
                   
                     863041
                  
                   
                     1859
                  
                
                 
                   
                     930
                  
                   
                     864900
                  
                   
                     1861
                  
                
                 
                   
                     931
                  
                   
                     866761
                  
                   
                     1863
                  
                
                 
                   
                     932
                  
                   
                     868624
                  
                   
                     1865
                  
                
                 
                   
                     933
                  
                   
                     870489
                  
                   
                     1867
                  
                
                 
                   
                     934
                  
                   
                     872356
                  
                   
                     1869
                  
                
                 
                   
                     934
                  
                   
                     872356
                  
                   
                     1869
                  
                
                 
                   
                     935
                  
                   
                     874225
                  
                   
                     1871
                  
                
                 
                   
                     936
                  
                   
                     876096
                  
                   
                     1873
                  
                
                 
                   
                     937
                  
                   
                     877969
                  
                   
                     1875
                  
                
                 
                   
                     938
                  
                   
                     879844
                  
                   
                     1877
                  
                
                 
                   
                     939
                  
                   
                     881721
                  
                   
                     1879
                  
                
                 
                   
                     940
                  
                   
                     883600
                  
                   
                     1881
                  
                
                 
                   
                     941
                  
                   
                     885481
                  
                   
                     1883
                  
                
                 
                   
                     942
                  
                   
                     887364
                  
                   
                     1885
                  
                
                 
                   
                     943
                  
                   
                     889249
                  
                   
                     1887
                  
                
                 
                   
                     944
                  
                   
                     891136
                  
                   
                     1889
                  
                
                 
                   
                     945
                  
                   
                     893025
                  
                   
                     1891
                  
                
                 
                   
                     946
                  
                   
                     894916
                  
                   
                     1893
                  
                
                 
                   
                     947
                  
                   
                     896809
                  
                   
                     1895
                  
                
                 
                   
                     948
                  
                   
                     898704
                  
                   
                     1897
                  
                
                 
                   
                     949
                  
                   
                     900601
                  
                   
                     1899
                  
                
                 
                   
                     950
                  
                   
                     902500
                  
                   
                     1901
                  
                
                 
                   
                     951
                  
                   
                     904401
                  
                   
                     1903
                  
                
                 
                   
                     952
                  
                   
                     906304
                  
                   
                     1905
                  
                
                 
                   
                     953
                  
                   
                     908209
                  
                   
                     1907
                  
                
                 
                   
                     954
                  
                   
                     910116
                  
                   
                     1909
                  
                
                 
                   
                     955
                  
                   
                     912025
                  
                   
                     1911
                  
                
                 
                   
                     956
                  
                   
                     913936
                  
                   
                     1913
                  
                
                 
                   
                     957
                  
                   
                     915849
                  
                   
                     1915
                  
                
                 
                   
                     958
                  
                   
                     917764
                  
                   
                     1917
                  
                
                 
                   
                     959
                  
                   
                     919681
                  
                   
                     1919
                  
                
                 
                   
                     960
                  
                   
                     921600
                  
                   
                     1921
                  
                
                 
                   
                     961
                  
                   
                     923521
                  
                   
                     1923
                  
                
                 
                   
                     962
                  
                   
                     925444
                  
                   
                     1925
                  
                
                 
                   
                     963
                  
                   
                     927369
                  
                   
                     1927
                  
                
                 
                   
                     964
                  
                   
                     929296
                  
                   
                     1929
                  
                
                 
                   
                     965
                  
                   
                     931225
                  
                   
                     1931
                  
                
                 
                   
                     966
                  
                   
                     933156
                  
                   
                     1933
                  
                
                 
                   
                     967
                  
                   
                     935089
                  
                   
                     1935
                  
                
                 
                   
                     
                     967
                  
                   
                     935089
                  
                   
                     1935
                  
                
                 
                   
                     968
                  
                   
                     937024
                  
                   
                     1937
                  
                
                 
                   
                     969
                  
                   
                     938961
                  
                   
                     1939
                  
                
                 
                   
                     970
                  
                   
                     940900
                  
                   
                     1941
                  
                
                 
                   
                     971
                  
                   
                     942841
                  
                   
                     1943
                  
                
                 
                   
                     972
                  
                   
                     944784
                  
                   
                     1945
                  
                
                 
                   
                     973
                  
                   
                     946729
                  
                   
                     1947
                  
                
                 
                   
                     974
                  
                   
                     948676
                  
                   
                     1949
                  
                
                 
                   
                     975
                  
                   
                     950625
                  
                   
                     1951
                  
                
                 
                   
                     976
                  
                   
                     952576
                  
                   
                     1953
                  
                
                 
                   
                     977
                  
                   
                     954529
                  
                   
                     1955
                  
                
                 
                   
                     978
                  
                   
                     956484
                  
                   
                     1957
                  
                
                 
                   
                     979
                  
                   
                     958441
                  
                   
                     1959
                  
                
                 
                   
                     980
                  
                   
                     960400
                  
                   
                     1961
                  
                
                 
                   
                     981
                  
                   
                     962361
                  
                   
                     1963
                  
                
                 
                   
                     982
                  
                   
                     964324
                  
                   
                     1965
                  
                
                 
                   
                     983
                  
                   
                     966289
                  
                   
                     1967
                  
                
                 
                   
                     984
                  
                   
                     968256
                  
                   
                     1969
                  
                
                 
                   
                     985
                  
                   
                     970225
                  
                   
                     1971
                  
                
                 
                   
                     986
                  
                   
                     972196
                  
                   
                     1973
                  
                
                 
                   
                     987
                  
                   
                     974169
                  
                   
                     1975
                  
                
                 
                   
                     988
                  
                   
                     976144
                  
                   
                     1977
                  
                
                 
                   
                     989
                  
                   
                     978121
                  
                   
                     1979
                  
                
                 
                   
                     990
                  
                   
                     980100
                  
                   
                     1981
                  
                
                 
                   
                     991
                  
                   
                     982081
                  
                   
                     1983
                  
                
                 
                   
                     992
                  
                   
                     984064
                  
                   
                     1985
                  
                
                 
                   
                     993
                  
                   
                     986049
                  
                   
                     1987
                  
                
                 
                   
                     994
                  
                   
                     988036
                  
                   
                     1989
                  
                
                 
                   
                     995
                  
                   
                     990025
                  
                   
                     1991
                  
                
                 
                   
                     996
                  
                   
                     992016
                  
                   
                     1993
                  
                
                 
                   
                     997
                  
                   
                     994009
                  
                   
                     1995
                  
                
                 
                   
                     998
                  
                   
                     996004
                  
                   
                     1997
                  
                
                 
                   
                     999
                  
                   
                     998001
                  
                   
                     1999
                  
                
                 
                   
                     1000
                  
                   
                     1000000
                  
                   
                     2001
                  
                
              
            
             
             
               
                 
                   
                      
                  
                   
                     0
                  
                   
                     1
                  
                   
                     2
                  
                   
                     3
                  
                   
                     4
                  
                   
                     5
                  
                   
                     6
                  
                   
                     7
                  
                   
                     8
                  
                   
                     9
                  
                
                 
                   
                     1
                  
                   
                     0.001133
                  
                   
                     001371
                  
                   
                     001631
                  
                   
                     001915
                  
                   
                     002221
                  
                   
                     002549
                  
                   
                     002901
                  
                   
                     003275
                  
                   
                     003671
                  
                   
                     004091
                  
                
                 
                   
                     2
                  
                   
                     0.004533
                  
                   
                     004997
                  
                   
                     005485
                  
                   
                     005995
                  
                   
                     006527
                  
                   
                     007083
                  
                   
                     007661
                  
                   
                     008261
                  
                   
                     008885
                  
                   
                     009531
                  
                
                 
                   
                     3
                  
                   
                     0.010199
                  
                   
                     010891
                  
                   
                     011605
                  
                   
                     012341
                  
                   
                     013101
                  
                   
                     013883
                  
                   
                     014687
                  
                   
                     015515
                  
                   
                     016365
                  
                   
                     017237
                  
                
                 
                   
                     4
                  
                   
                     0.018133
                  
                   
                     019051
                  
                   
                     019991
                  
                   
                     020955
                  
                   
                     021941
                  
                   
                     022949
                  
                   
                     023981
                  
                   
                     025035
                  
                   
                     026111
                  
                   
                     027211
                  
                
                 
                   
                     5
                  
                   
                     0.028333
                  
                   
                     029477
                  
                   
                     030645
                  
                   
                     031835
                  
                   
                     033047
                  
                   
                     034283
                  
                   
                     035541
                  
                   
                     036825
                  
                   
                     038125
                  
                   
                     039451
                  
                
                 
                   
                     6
                  
                   
                     0.040799
                  
                   
                     042171
                  
                   
                     043565
                  
                   
                     044981
                  
                   
                     046421
                  
                   
                     047883
                  
                   
                     049367
                  
                   
                     050875
                  
                   
                     052405
                  
                   
                     053957
                  
                
                 
                   
                     7
                  
                   
                     0.051533
                  
                   
                     057131
                  
                   
                     058751
                  
                   
                     060395
                  
                   
                     062061
                  
                   
                     063749
                  
                   
                     065461
                  
                   
                     067195
                  
                   
                     068951
                  
                   
                     070731
                  
                
                 
                   
                     8
                  
                   
                     0.072533
                  
                   
                     074357
                  
                   
                     076205
                  
                   
                     078075
                  
                   
                     079967
                  
                   
                     681883
                  
                   
                     083821
                  
                   
                     085781
                  
                   
                     087765
                  
                   
                     089771
                  
                
                 
                   
                     9
                  
                   
                     0.091799
                  
                   
                     093851
                  
                   
                     095925
                  
                   
                     098021
                  
                   
                     100141
                  
                   
                     102283
                  
                   
                     104447
                  
                   
                     106635
                  
                   
                     108845
                  
                   
                     111077
                  
                
                 
                   
                     10
                  
                   
                     0.113333
                  
                   
                     115610
                  
                   
                     117911
                  
                   
                     120234
                  
                   
                     122580
                  
                   
                     124949
                  
                   
                     127340
                  
                   
                     129754
                  
                   
                     132191
                  
                   
                     134650
                  
                
                 
                   
                     11
                  
                   
                     0.137132
                  
                   
                     139637
                  
                   
                     142164
                  
                   
                     144714
                  
                   
                     147287
                  
                   
                     149882
                  
                   
                     152500
                  
                   
                     155141
                  
                   
                     157804
                  
                   
                     160490
                  
                
                 
                   
                     12
                  
                   
                     0.163199
                  
                   
                     165930
                  
                   
                     168684
                  
                   
                     171461
                  
                   
                     174266
                  
                   
                     177082
                  
                   
                     179927
                  
                   
                     182794
                  
                   
                     185684
                  
                   
                     188597
                  
                
                 
                   
                     13
                  
                   
                     0.191532
                  
                   
                     194490
                  
                   
                     197471
                  
                   
                     200474
                  
                   
                     203500
                  
                   
                     206549
                  
                   
                     229620
                  
                   
                     212714
                  
                   
                     215831
                  
                   
                     218970
                  
                
                 
                   
                     14
                  
                   
                     0.222132
                  
                   
                     225317
                  
                   
                     228524
                  
                   
                     231754
                  
                   
                     235007
                  
                   
                     238282
                  
                   
                     241589
                  
                   
                     244901
                  
                   
                     248244
                  
                   
                     251610
                  
                
                 
                   
                     15
                  
                   
                     0.254999
                  
                   
                     258410
                  
                   
                     261844
                  
                   
                     265301
                  
                   
                     268780
                  
                   
                     272282
                  
                   
                     275807
                  
                   
                     279354
                  
                   
                     282924
                  
                   
                     286517
                  
                
                 
                   
                     16
                  
                   
                     0.290132
                  
                   
                     293770
                  
                   
                     297431
                  
                   
                     301114
                  
                   
                     304820
                  
                   
                     308549
                  
                   
                     312300
                  
                   
                     316074
                  
                   
                     319871
                  
                   
                     323690
                  
                
                 
                   
                     17
                  
                   
                     0.327532
                  
                   
                     331397
                  
                   
                     335284
                  
                   
                     339194
                  
                   
                     343126
                  
                   
                     374082
                  
                   
                     351060
                  
                   
                     355060
                  
                   
                     359084
                  
                   
                     363130
                  
                
                 
                   
                     18
                  
                   
                     0.367198
                  
                   
                     371290
                  
                   
                     375404
                  
                   
                     379540
                  
                   
                     383700
                  
                   
                     387882
                  
                   
                     392086
                  
                   
                     396314
                  
                   
                     400564
                  
                   
                     404836
                  
                
                 
                   
                     19
                  
                   
                     0.409132
                  
                   
                     413450
                  
                   
                     417790
                  
                   
                     422154
                  
                   
                     426540
                  
                   
                     430948
                  
                   
                     435380
                  
                   
                     439834
                  
                   
                     444310
                  
                   
                     448810
                  
                
                 
                   
                     20
                  
                   
                     0.453332
                  
                   
                     457876
                  
                   
                     462443
                  
                   
                     467033
                  
                   
                     471646
                  
                   
                     476281
                  
                   
                     480939
                  
                   
                     485620
                  
                   
                     490323
                  
                   
                     495049
                  
                
                 
                   
                     21
                  
                   
                     0.499798
                  
                   
                     504569
                  
                   
                     509363
                  
                   
                     514180
                  
                   
                     519019
                  
                   
                     523881
                  
                   
                     528766
                  
                   
                     533673
                  
                   
                     538603
                  
                   
                     543556
                  
                
                 
                   
                     22
                  
                   
                     0.548531
                  
                   
                     553529
                  
                   
                     558550
                  
                   
                     563593
                  
                   
                     568659
                  
                   
                     573748
                  
                   
                     578859
                  
                   
                     583993
                  
                   
                     589150
                  
                   
                     594329
                  
                
                 
                   
                     23
                  
                   
                     0.599531
                  
                   
                     604756
                  
                   
                     610003
                  
                   
                     615273
                  
                   
                     620566
                  
                   
                     625881
                  
                   
                     631219
                  
                   
                     696580
                  
                   
                     641963
                  
                   
                     647369
                  
                
                 
                   
                     24
                  
                   
                     0.652798
                  
                   
                     658249
                  
                   
                     663723
                  
                   
                     669220
                  
                   
                     674739
                  
                   
                     680281
                  
                   
                     685845
                  
                   
                     691433
                  
                   
                     697043
                  
                   
                     702675
                  
                
                 
                   
                     25
                  
                   
                     0.708331
                  
                   
                     714009
                  
                   
                     719709
                  
                   
                     725233
                  
                   
                     731179
                  
                   
                     736947
                  
                   
                     742739
                  
                   
                     748553
                  
                   
                     754389
                  
                   
                     760249
                  
                
                 
                   
                     26
                  
                   
                     0.766131
                  
                   
                     772035
                  
                   
                     777963
                  
                   
                     783913
                  
                   
                     789885
                  
                   
                     795880
                  
                   
                     801898
                  
                   
                     807939
                  
                   
                     814002
                  
                   
                     820088
                  
                
                 
                   
                     27
                  
                   
                     0.826197
                  
                   
                     832328
                  
                   
                     838482
                  
                   
                     844659
                  
                   
                     850858
                  
                   
                     857080
                  
                   
                     863325
                  
                   
                     869592
                  
                   
                     875882
                  
                   
                     882195
                  
                
                 
                   
                     28
                  
                   
                     0.888530
                  
                   
                     894888
                  
                   
                     901269
                  
                   
                     907672
                  
                   
                     914098
                  
                   
                     920547
                  
                   
                     927018
                  
                   
                     933512
                  
                   
                     940029
                  
                   
                     946568
                  
                
                 
                   
                     29
                  
                   
                     0.953130
                  
                   
                     959715
                  
                   
                     966322
                  
                   
                     972952
                  
                   
                     979605
                  
                   
                     986280
                  
                   
                     992978
                  
                   
                     999699
                  
                   
                     006442
                  
                   
                     013208
                  
                
                 
                   
                     30
                  
                   
                     1.019997
                  
                   
                     026808
                  
                   
                     033642
                  
                   
                     040498
                  
                   
                     047378
                  
                   
                     054280
                  
                   
                     061204
                  
                   
                     068152
                  
                   
                     075122
                  
                   
                     082114
                  
                
                 
                   
                     31
                  
                   
                     1.089130
                  
                   
                     096168
                  
                   
                     103228
                  
                   
                     110312
                  
                   
                     117418
                  
                   
                     124546
                  
                   
                     131698
                  
                   
                     138871
                  
                   
                     146068
                  
                   
                     153287
                  
                
                 
                   
                     32
                  
                   
                     1.160529
                  
                   
                     167794
                  
                   
                     175081
                  
                   
                     182391
                  
                   
                     189724
                  
                   
                     197079
                  
                   
                     204457
                  
                   
                     211858
                  
                   
                     219281
                  
                   
                     226727
                  
                
                 
                   
                     33
                  
                   
                     1.234196
                  
                   
                     241687
                  
                   
                     249201
                  
                   
                     256738
                  
                   
                     264297
                  
                   
                     271879
                  
                   
                     279484
                  
                   
                     287111
                  
                   
                     294761
                  
                   
                     302434
                  
                
                 
                   
                     34
                  
                   
                     1.310129
                  
                   
                     317847
                  
                   
                     325588
                  
                   
                     333351
                  
                   
                     341137
                  
                   
                     348946
                  
                   
                     356777
                  
                   
                     364631
                  
                   
                     372507
                  
                   
                     380467
                  
                
                 
                   
                     
                     34
                  
                   
                     1.310129
                  
                   
                     317847
                  
                   
                     325588
                  
                   
                     333351
                  
                   
                     341137
                  
                   
                     348946
                  
                   
                     356777
                  
                   
                     364631
                  
                   
                     372507
                  
                   
                     380467
                  
                
                 
                   
                     35
                  
                   
                     1.388329
                  
                   
                     396273
                  
                   
                     404241
                  
                   
                     412231
                  
                   
                     420243
                  
                   
                     428279
                  
                   
                     436337
                  
                   
                     444417
                  
                   
                     452521
                  
                   
                     460647
                  
                
                 
                   
                     36
                  
                   
                     1.468795
                  
                   
                     476966
                  
                   
                     485160
                  
                   
                     493377
                  
                   
                     501616
                  
                   
                     509878
                  
                   
                     518163
                  
                   
                     526470
                  
                   
                     534800
                  
                   
                     543153
                  
                
                 
                   
                     37
                  
                   
                     1.551528
                  
                   
                     559926
                  
                   
                     568347
                  
                   
                     576790
                  
                   
                     585256
                  
                   
                     593745
                  
                   
                     602256
                  
                   
                     610790
                  
                   
                     619347
                  
                   
                     627926
                  
                
                 
                   
                     38
                  
                   
                     1.636528
                  
                   
                     645153
                  
                   
                     653800
                  
                   
                     662470
                  
                   
                     671163
                  
                   
                     679878
                  
                   
                     688616
                  
                   
                     697577
                  
                   
                     706160
                  
                   
                     714966
                  
                
                 
                   
                     39
                  
                   
                     1.723794
                  
                   
                     732646
                  
                   
                     741520
                  
                   
                     750416
                  
                   
                     759336
                  
                   
                     768278
                  
                   
                     777242
                  
                   
                     786230
                  
                   
                     795240
                  
                   
                     804272
                  
                
                 
                   
                     40
                  
                   
                     1.813328
                  
                   
                     822405
                  
                   
                     831506
                  
                   
                     840629
                  
                   
                     849775
                  
                   
                     858944
                  
                   
                     868135
                  
                   
                     877349
                  
                   
                     886586
                  
                   
                     895845
                  
                
                 
                   
                     41
                  
                   
                     1.905127
                  
                   
                     914432
                  
                   
                     923759
                  
                   
                     933109
                  
                   
                     942482
                  
                   
                     951877
                  
                   
                     961295
                  
                   
                     970736
                  
                   
                     980199
                  
                   
                     989685
                  
                
                 
                   
                     42
                  
                   
                     1.999194
                  
                   
                     008725
                  
                   
                     018279
                  
                   
                     027856
                  
                   
                     037455
                  
                   
                     047077
                  
                   
                     056721
                  
                   
                     066389
                  
                   
                     076079
                  
                   
                     085791
                  
                
                 
                   
                     43
                  
                   
                     2.095527
                  
                   
                     105285
                  
                   
                     115065
                  
                   
                     124869
                  
                   
                     134695
                  
                   
                     144543
                  
                   
                     154414
                  
                   
                     164308
                  
                   
                     174225
                  
                   
                     184164
                  
                
                 
                   
                     44
                  
                   
                     2.194126
                  
                   
                     204111
                  
                   
                     214118
                  
                   
                     224148
                  
                   
                     234201
                  
                   
                     244276
                  
                   
                     254374
                  
                   
                     264495
                  
                   
                     274638
                  
                   
                     284804
                  
                
                 
                   
                     45
                  
                   
                     2.294993
                  
                   
                     305204
                  
                   
                     315438
                  
                   
                     325695
                  
                   
                     335974
                  
                   
                     346276
                  
                   
                     356601
                  
                   
                     366948
                  
                   
                     377318
                  
                   
                     387710
                  
                
                 
                   
                     46
                  
                   
                     2.398126
                  
                   
                     408564
                  
                   
                     419024
                  
                   
                     429508
                  
                   
                     440014
                  
                   
                     450542
                  
                   
                     461094
                  
                   
                     471668
                  
                   
                     482264
                  
                   
                     492884
                  
                
                 
                   
                     47
                  
                   
                     2.503525
                  
                   
                     514190
                  
                   
                     524877
                  
                   
                     535587
                  
                   
                     546310
                  
                   
                     557075
                  
                   
                     567853
                  
                   
                     578654
                  
                   
                     589477
                  
                   
                     600323
                  
                
                 
                   
                     48
                  
                   
                     2.611192
                  
                   
                     622083
                  
                   
                     632997
                  
                   
                     643934
                  
                   
                     654893
                  
                   
                     665875
                  
                   
                     676880
                  
                   
                     697907
                  
                   
                     698957
                  
                   
                     710030
                  
                
                 
                   
                     49
                  
                   
                     2.721125
                  
                   
                     732243
                  
                   
                     743383
                  
                   
                     754547
                  
                   
                     765733
                  
                   
                     776941
                  
                   
                     788173
                  
                   
                     799427
                  
                   
                     810703
                  
                   
                     822003
                  
                
                 
                   
                     50
                  
                   
                     2.833325
                  
                   
                     844669
                  
                   
                     856036
                  
                   
                     867426
                  
                   
                     878839
                  
                   
                     890274
                  
                   
                     901732
                  
                   
                     913213
                  
                   
                     924716
                  
                   
                     936242
                  
                
                 
                   
                     51
                  
                   
                     2.947791
                  
                   
                     959362
                  
                   
                     970956
                  
                   
                     982573
                  
                   
                     994212
                  
                   
                     005874
                  
                   
                     017559
                  
                   
                     029266
                  
                   
                     040996
                  
                   
                     052749
                  
                
                 
                   
                     52
                  
                   
                     3.064524
                  
                   
                     076322
                  
                   
                     088142
                  
                   
                     099986
                  
                   
                     111852
                  
                   
                     123740
                  
                   
                     135652
                  
                   
                     147586
                  
                   
                     159542
                  
                   
                     171522
                  
                
                 
                   
                     53
                  
                   
                     3.183523
                  
                   
                     195548
                  
                   
                     207595
                  
                   
                     219665
                  
                   
                     231758
                  
                   
                     243872
                  
                   
                     256011
                  
                   
                     268172
                  
                   
                     280355
                  
                   
                     292561
                  
                
                 
                   
                     54
                  
                   
                     3.304790
                  
                   
                     317041
                  
                   
                     329315
                  
                   
                     341612
                  
                   
                     353931
                  
                   
                     366273
                  
                   
                     378638
                  
                   
                     391025
                  
                   
                     403435
                  
                   
                     415867
                  
                
                 
                   
                     55
                  
                   
                     3.428323
                  
                   
                     440801
                  
                   
                     453301
                  
                   
                     465825
                  
                   
                     478371
                  
                   
                     490939
                  
                   
                     503531
                  
                   
                     516544
                  
                   
                     528781
                  
                   
                     541440
                  
                
                 
                   
                     56
                  
                   
                     3.554122
                  
                   
                     566827
                  
                   
                     579554
                  
                   
                     592304
                  
                   
                     605077
                  
                   
                     617872
                  
                   
                     630690
                  
                   
                     643531
                  
                   
                     856394
                  
                   
                     669280
                  
                
                 
                   
                     57
                  
                   
                     3.682189
                  
                   
                     695120
                  
                   
                     708074
                  
                   
                     721051
                  
                   
                     734050
                  
                   
                     747072
                  
                   
                     760116
                  
                   
                     773184
                  
                   
                     786274
                  
                   
                     799386
                  
                
                 
                   
                     58
                  
                   
                     3.812522
                  
                   
                     825980
                  
                   
                     838860
                  
                   
                     852064
                  
                   
                     865289
                  
                   
                     878530
                  
                   
                     891809
                  
                   
                     905103
                  
                   
                     918420
                  
                   
                     931759
                  
                
                 
                   
                     59
                  
                   
                     3.945121
                  
                   
                     958506
                  
                   
                     971913
                  
                   
                     985343
                  
                   
                     998796
                  
                   
                     012271
                  
                   
                     025769
                  
                   
                     039290
                  
                   
                     252833
                  
                   
                     066399
                  
                
                 
                   
                     60
                  
                   
                     4●079988
                  
                   
                     093599
                  
                   
                     107233
                  
                   
                     120889
                  
                   
                     134569
                  
                   
                     148271
                  
                   
                     161195
                  
                   
                     175743
                  
                   
                     189513
                  
                   
                     203305
                  
                
                 
                   
                     61
                  
                   
                     4.217120
                  
                   
                     230958
                  
                   
                     244819
                  
                   
                     258702
                  
                   
                     272608
                  
                   
                     286537
                  
                   
                     300488
                  
                   
                     314462
                  
                   
                     328459
                  
                   
                     342478
                  
                
                 
                   
                     62
                  
                   
                     4.356520
                  
                   
                     370585
                  
                   
                     384672
                  
                   
                     398782
                  
                   
                     412915
                  
                   
                     427070
                  
                   
                     441248
                  
                   
                     455448
                  
                   
                     469672
                  
                   
                     483918
                  
                
                 
                   
                     63
                  
                   
                     4.498186
                  
                   
                     512778
                  
                   
                     526792
                  
                   
                     541128
                  
                   
                     555487
                  
                   
                     569869
                  
                   
                     584274
                  
                   
                     598701
                  
                   
                     613151
                  
                   
                     627624
                  
                
                 
                   
                     64
                  
                   
                     4.642119
                  
                   
                     656637
                  
                   
                     671178
                  
                   
                     685741
                  
                   
                     700327
                  
                   
                     714936
                  
                   
                     729567
                  
                   
                     744221
                  
                   
                     758898
                  
                   
                     773597
                  
                
                 
                   
                     65
                  
                   
                     4.788319
                  
                   
                     80●06●
                  
                   
                     81●831
                  
                   
                     832621
                  
                   
                     84773●
                  
                   
                     862269
                  
                   
                     877126
                  
                   
                     892007
                  
                   
                     906910
                  
                   
                     921836
                  
                
                 
                   
                     66
                  
                   
                     4.936785
                  
                   
                     951756
                  
                   
                     966750
                  
                   
                     981767
                  
                   
                     996806
                  
                   
                     011868
                  
                   
                     026953
                  
                   
                     042060
                  
                   
                     057190
                  
                   
                     072341
                  
                
                 
                   
                     67
                  
                   
                     5.087518
                  
                   
                     102716
                  
                   
                     117936
                  
                   
                     133180
                  
                   
                     148446
                  
                   
                     163734
                  
                   
                     179046
                  
                   
                     194380
                  
                   
                     209736
                  
                   
                     225115
                  
                
                 
                   
                     
                     67
                  
                   
                     5.087518
                  
                   
                     102716
                  
                   
                     117936
                  
                   
                     133180
                  
                   
                     148446
                  
                   
                     163734
                  
                   
                     179046
                  
                   
                     194380
                  
                   
                     209736
                  
                   
                     225115
                  
                
                 
                   
                     68
                  
                   
                     5.240517
                  
                   
                     255942
                  
                   
                     271389
                  
                   
                     286859
                  
                   
                     302352
                  
                   
                     317567
                  
                   
                     333405
                  
                   
                     348966
                  
                   
                     364549
                  
                   
                     380155
                  
                
                 
                   
                     69
                  
                   
                     5.395784
                  
                   
                     411435
                  
                   
                     427109
                  
                   
                     442805
                  
                   
                     458525
                  
                   
                     474267
                  
                   
                     490031
                  
                   
                     505819
                  
                   
                     521629
                  
                   
                     537461
                  
                
                 
                   
                     70
                  
                   
                     5.553317
                  
                   
                     569194
                  
                   
                     585095
                  
                   
                     601018
                  
                   
                     616964
                  
                   
                     632933
                  
                   
                     648924
                  
                   
                     664938
                  
                   
                     680975
                  
                   
                     697034
                  
                
                 
                   
                     71
                  
                   
                     5.713116
                  
                   
                     729221
                  
                   
                     745348
                  
                   
                     761498
                  
                   
                     777601
                  
                   
                     793868
                  
                   
                     810084
                  
                   
                     826324
                  
                   
                     842588
                  
                   
                     858874
                  
                
                 
                   
                     72
                  
                   
                     5.875182
                  
                   
                     891514
                  
                   
                     907867
                  
                   
                     924244
                  
                   
                     940643
                  
                   
                     957065
                  
                   
                     973510
                  
                   
                     989977
                  
                   
                     006467
                  
                   
                     022980
                  
                
                 
                   
                     73
                  
                   
                     6.039555
                  
                   
                     056073
                  
                   
                     072654
                  
                   
                     089257
                  
                   
                     105883
                  
                   
                     122531
                  
                   
                     139203
                  
                   
                     155897
                  
                   
                     172613
                  
                   
                     189353
                  
                
                 
                   
                     74
                  
                   
                     6.206115
                  
                   
                     222899
                  
                   
                     239706
                  
                   
                     256536
                  
                   
                     273389
                  
                   
                     290264
                  
                   
                     307162
                  
                   
                     324083
                  
                   
                     341026
                  
                   
                     357992
                  
                
                 
                   
                     75
                  
                   
                     6.374981
                  
                   
                     391992
                  
                   
                     409026
                  
                   
                     426083
                  
                   
                     443162
                  
                   
                     460264
                  
                   
                     477388
                  
                   
                     494536
                  
                   
                     511706
                  
                   
                     528898
                  
                
                 
                   
                     76
                  
                   
                     6.546114
                  
                   
                     563352
                  
                   
                     580612
                  
                   
                     597895
                  
                   
                     615201
                  
                   
                     632530
                  
                   
                     649881
                  
                   
                     667255
                  
                   
                     684652
                  
                   
                     702071
                  
                
                 
                   
                     77
                  
                   
                     6.719513
                  
                   
                     736978
                  
                   
                     754465
                  
                   
                     771975
                  
                   
                     789508
                  
                   
                     807063
                  
                   
                     824641
                  
                   
                     842241
                  
                   
                     859865
                  
                   
                     877511
                  
                
                 
                   
                     78
                  
                   
                     6.895179
                  
                   
                     912871
                  
                   
                     930584
                  
                   
                     948321
                  
                   
                     966080
                  
                   
                     983862
                  
                   
                     001667
                  
                   
                     019494
                  
                   
                     037344
                  
                   
                     055117
                  
                
                 
                   
                     79
                  
                   
                     7.073112
                  
                   
                     091030
                  
                   
                     108971
                  
                   
                     126934
                  
                   
                     144920
                  
                   
                     162928
                  
                   
                     180960
                  
                   
                     199012
                  
                   
                     217090
                  
                   
                     235190
                  
                
                 
                   
                     80
                  
                   
                     7.253312
                  
                   
                     271456
                  
                   
                     289623
                  
                   
                     307813
                  
                   
                     326026
                  
                   
                     344261
                  
                   
                     362519
                  
                   
                     380800
                  
                   
                     399103
                  
                   
                     417429
                  
                
                 
                   
                     81
                  
                   
                     7.455778
                  
                   
                     454149
                  
                   
                     472543
                  
                   
                     490959
                  
                   
                     509399
                  
                   
                     527861
                  
                   
                     546345
                  
                   
                     564853
                  
                   
                     583383
                  
                   
                     601935
                  
                
                 
                   
                     82
                  
                   
                     7.620510
                  
                   
                     639108
                  
                   
                     657729
                  
                   
                     676372
                  
                   
                     695038
                  
                   
                     713727
                  
                   
                     732438
                  
                   
                     751172
                  
                   
                     769929
                  
                   
                     788708
                  
                
                 
                   
                     83
                  
                   
                     7.807510
                  
                   
                     826334
                  
                   
                     845182
                  
                   
                     864052
                  
                   
                     882944
                  
                   
                     901860
                  
                   
                     920798
                  
                   
                     939758
                  
                   
                     958741
                  
                   
                     977747
                  
                
                 
                   
                     84
                  
                   
                     7.996776
                  
                   
                     015827
                  
                   
                     034901
                  
                   
                     053998
                  
                   
                     073117
                  
                   
                     092259
                  
                   
                     111424
                  
                   
                     130611
                  
                   
                     149821
                  
                   
                     169053
                  
                
                 
                   
                     85
                  
                   
                     8.188309
                  
                   
                     207587
                  
                   
                     226887
                  
                   
                     246211
                  
                   
                     265557
                  
                   
                     284925
                  
                   
                     304316
                  
                   
                     323730
                  
                   
                     343167
                  
                   
                     362626
                  
                
                 
                   
                     86
                  
                   
                     8.382108
                  
                   
                     401613
                  
                   
                     421140
                  
                   
                     440690
                  
                   
                     460263
                  
                   
                     479858
                  
                   
                     499476
                  
                   
                     519116
                  
                   
                     538780
                  
                   
                     558466
                  
                
                 
                   
                     87
                  
                   
                     8.578174
                  
                   
                     597906
                  
                   
                     617659
                  
                   
                     637436
                  
                   
                     657235
                  
                   
                     677057
                  
                   
                     696902
                  
                   
                     716769
                  
                   
                     736659
                  
                   
                     756572
                  
                
                 
                   
                     88
                  
                   
                     8.776507
                  
                   
                     796465
                  
                   
                     816446
                  
                   
                     836449
                  
                   
                     856475
                  
                   
                     876523
                  
                   
                     896595
                  
                   
                     916689
                  
                   
                     936805
                  
                   
                     936944
                  
                
                 
                   
                     89
                  
                   
                     8.977106
                  
                   
                     997291
                  
                   
                     017498
                  
                   
                     037728
                  
                   
                     057981
                  
                   
                     078256
                  
                   
                     098554
                  
                   
                     118875
                  
                   
                     139218
                  
                   
                     159584
                  
                
                 
                   
                     90
                  
                   
                     9.179973
                  
                   
                     200384
                  
                   
                     220818
                  
                   
                     241274
                  
                   
                     261754
                  
                   
                     282256
                  
                   
                     302780
                  
                   
                     323327
                  
                   
                     343897
                  
                   
                     364490
                  
                
                 
                   
                     91
                  
                   
                     9.385105
                  
                   
                     405743
                  
                   
                     426404
                  
                   
                     447087
                  
                   
                     467793
                  
                   
                     488522
                  
                   
                     509273
                  
                   
                     530047
                  
                   
                     550843
                  
                   
                     571663
                  
                
                 
                   
                     92
                  
                   
                     9.592505
                  
                   
                     613369
                  
                   
                     634256
                  
                   
                     655166
                  
                   
                     676099
                  
                   
                     897054
                  
                   
                     718032
                  
                   
                     739033
                  
                   
                     760056
                  
                   
                     781102
                  
                
                 
                   
                     93
                  
                   
                     9.802171
                  
                   
                     823262
                  
                   
                     844376
                  
                   
                     865512
                  
                   
                     886672
                  
                   
                     907854
                  
                   
                     929058
                  
                   
                     950286
                  
                   
                     971536
                  
                   
                     992808
                  
                
                 
                   
                     94
                  
                   
                     10.014103
                  
                   
                     035421
                  
                   
                     056762
                  
                   
                     078125
                  
                   
                     099511
                  
                   
                     120920
                  
                   
                     142351
                  
                   
                     163805
                  
                   
                     185282
                  
                   
                     206781
                  
                
                 
                   
                     95
                  
                   
                     10.228303
                  
                   
                     249847
                  
                   
                     271415
                  
                   
                     293005
                  
                   
                     314617
                  
                   
                     336252
                  
                   
                     337910
                  
                   
                     379591
                  
                   
                     401294
                  
                   
                     423020
                  
                
                 
                   
                     96
                  
                   
                     10.444769
                  
                   
                     466540
                  
                   
                     488334
                  
                   
                     510151
                  
                   
                     531990
                  
                   
                     553852
                  
                   
                     575736
                  
                   
                     597644
                  
                   
                     619574
                  
                   
                     641526
                  
                
                 
                   
                     97
                  
                   
                     10.663501
                  
                   
                     685499
                  
                   
                     707520
                  
                   
                     729563
                  
                   
                     751629
                  
                   
                     773718
                  
                   
                     795829
                  
                   
                     817963
                  
                   
                     840120
                  
                   
                     862299
                  
                
                 
                   
                     98
                  
                   
                     10.884501
                  
                   
                     906725
                  
                   
                     928973
                  
                   
                     951243
                  
                   
                     973535
                  
                   
                     995850
                  
                   
                     018188
                  
                   
                     040549
                  
                   
                     062932
                  
                   
                     085338
                  
                
                 
                   
                     99
                  
                   
                     11.107767
                  
                   
                     130218
                  
                   
                     152692
                  
                   
                     175189
                  
                   
                     197708
                  
                   
                     220250
                  
                   
                     242814
                  
                   
                     265402
                  
                   
                     288012
                  
                   
                     310644
                  
                
                 
                   
                     100
                  
                   
                     11.333300
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                
              
               
                 
                   
                     
                  
                   
                     0
                  
                   
                     1
                  
                   
                     2
                  
                   
                     3
                  
                   
                     4
                  
                   
                     5
                  
                   
                     6
                  
                   
                     7
                  
                   
                     8
                  
                   
                     9
                  
                
                 
                   
                     1
                  
                   
                     0.000928
                  
                   
                     001127
                  
                   
                     001336
                  
                   
                     001569
                  
                   
                     001819
                  
                   
                     002089
                  
                   
                     002376
                  
                   
                     002683
                  
                   
                     003008
                  
                   
                     003351
                  
                
                 
                   
                     2
                  
                   
                     0.003713
                  
                   
                     004094
                  
                   
                     004493
                  
                   
                     004911
                  
                   
                     005347
                  
                   
                     005802
                  
                   
                     006275
                  
                   
                     006767
                  
                   
                     007278
                  
                   
                     007807
                  
                
                 
                   
                     3
                  
                   
                     0.008355
                  
                   
                     008921
                  
                   
                     009506
                  
                   
                     010109
                  
                   
                     010731
                  
                   
                     011372
                  
                   
                     012031
                  
                   
                     012709
                  
                   
                     013405
                  
                   
                     014120
                  
                
                 
                   
                     4
                  
                   
                     0.014855
                  
                   
                     015605
                  
                   
                     016376
                  
                   
                     017165
                  
                   
                     017973
                  
                   
                     018799
                  
                   
                     019644
                  
                   
                     020507
                  
                   
                     021389
                  
                   
                     022289
                  
                
                 
                   
                     5
                  
                   
                     0.023209
                  
                   
                     024146
                  
                   
                     025102
                  
                   
                     026077
                  
                   
                     027070
                  
                   
                     028082
                  
                   
                     029113
                  
                   
                     030162
                  
                   
                     031230
                  
                   
                     032316
                  
                
                 
                   
                     6
                  
                   
                     0.033420
                  
                   
                     034544
                  
                   
                     035686
                  
                   
                     036846
                  
                   
                     038025
                  
                   
                     039223
                  
                   
                     040439
                  
                   
                     041674
                  
                   
                     042927
                  
                   
                     044199
                  
                
                 
                   
                     7
                  
                   
                     0.045489
                  
                   
                     046798
                  
                   
                     048126
                  
                   
                     049472
                  
                   
                     050836
                  
                   
                     052220
                  
                   
                     053322
                  
                   
                     055042
                  
                   
                     056481
                  
                   
                     057938
                  
                
                 
                   
                     8
                  
                   
                     0.059415
                  
                   
                     060909
                  
                   
                     062422
                  
                   
                     063954
                  
                   
                     065505
                  
                   
                     067074
                  
                   
                     068661
                  
                   
                     070267
                  
                   
                     071892
                  
                   
                     073535
                  
                
                 
                   
                     9
                  
                   
                     0.075197
                  
                   
                     076877
                  
                   
                     078576
                  
                   
                     080293
                  
                   
                     082029
                  
                   
                     083784
                  
                   
                     085557
                  
                   
                     087349
                  
                   
                     089159
                  
                   
                     090988
                  
                
                 
                   
                     10
                  
                   
                     0.092836
                  
                   
                     094702
                  
                   
                     096586
                  
                   
                     098489
                  
                   
                     100411
                  
                   
                     102351
                  
                   
                     104310
                  
                   
                     106287
                  
                   
                     108283
                  
                   
                     110298
                  
                
                 
                   
                     11
                  
                   
                     0.112331
                  
                   
                     114383
                  
                   
                     116453
                  
                   
                     118542
                  
                   
                     120649
                  
                   
                     122775
                  
                   
                     124920
                  
                   
                     127083
                  
                   
                     129264
                  
                   
                     131465
                  
                
                 
                   
                     12
                  
                   
                     0.133683
                  
                   
                     135921
                  
                   
                     138177
                  
                   
                     140451
                  
                   
                     142744
                  
                   
                     145056
                  
                   
                     147386
                  
                   
                     149735
                  
                   
                     152102
                  
                   
                     154489
                  
                
                 
                   
                     13
                  
                   
                     0.156892
                  
                   
                     159315
                  
                   
                     161757
                  
                   
                     164217
                  
                   
                     166696
                  
                   
                     169193
                  
                   
                     171709
                  
                   
                     174243
                  
                   
                     176796
                  
                   
                     179368
                  
                
                 
                   
                     14
                  
                   
                     0.181958
                  
                   
                     184567
                  
                   
                     187194
                  
                   
                     189840
                  
                   
                     192504
                  
                   
                     195187
                  
                   
                     197889
                  
                   
                     200609
                  
                   
                     203347
                  
                   
                     206105
                  
                
                 
                   
                     15
                  
                   
                     0.208881
                  
                   
                     211675
                  
                   
                     214488
                  
                   
                     217319
                  
                   
                     220169
                  
                   
                     223038
                  
                   
                     225925
                  
                   
                     228831
                  
                   
                     231755
                  
                   
                     234698
                  
                
                 
                   
                     16
                  
                   
                     0.237660
                  
                   
                     240640
                  
                   
                     243638
                  
                   
                     246655
                  
                   
                     249691
                  
                   
                     252746
                  
                   
                     255818
                  
                   
                     258910
                  
                   
                     262020
                  
                   
                     265148
                  
                
                 
                   
                     17
                  
                   
                     0.268296
                  
                   
                     271461
                  
                   
                     274646
                  
                   
                     277848
                  
                   
                     281070
                  
                   
                     284310
                  
                   
                     287568
                  
                   
                     290845
                  
                   
                     294141
                  
                   
                     297455
                  
                
                 
                   
                     18
                  
                   
                     0.300788
                  
                   
                     304140
                  
                   
                     307509
                  
                   
                     310898
                  
                   
                     314305
                  
                   
                     317731
                  
                   
                     321175
                  
                   
                     324638
                  
                   
                     328119
                  
                   
                     331619
                  
                
                 
                   
                     19
                  
                   
                     0.335137
                  
                   
                     338675
                  
                   
                     342230
                  
                   
                     345804
                  
                   
                     349397
                  
                   
                     353008
                  
                   
                     356638
                  
                   
                     360287
                  
                   
                     363954
                  
                   
                     367639
                  
                
                 
                   
                     20
                  
                   
                     0.371344
                  
                   
                     375066
                  
                   
                     378808
                  
                   
                     382567
                  
                   
                     386346
                  
                   
                     390143
                  
                   
                     393958
                  
                   
                     397792
                  
                   
                     401645
                  
                   
                     405516
                  
                
                 
                   
                     21
                  
                   
                     0.409406
                  
                   
                     413315
                  
                   
                     417242
                  
                   
                     421174
                  
                   
                     425151
                  
                   
                     429134
                  
                   
                     433135
                  
                   
                     437155
                  
                   
                     441193
                  
                   
                     445250
                  
                
                 
                   
                     22
                  
                   
                     0.449326
                  
                   
                     463420
                  
                   
                     457532
                  
                   
                     461664
                  
                   
                     465813
                  
                   
                     469982
                  
                   
                     474169
                  
                   
                     478374
                  
                   
                     482598
                  
                   
                     486841
                  
                
                 
                   
                     23
                  
                   
                     0.491102
                  
                   
                     495382
                  
                   
                     499680
                  
                   
                     503997
                  
                   
                     508338
                  
                   
                     512686
                  
                   
                     517059
                  
                   
                     521450
                  
                   
                     525860
                  
                   
                     530288
                  
                
                 
                   
                     24
                  
                   
                     0.534735
                  
                   
                     539200
                  
                   
                     543684
                  
                   
                     548187
                  
                   
                     552708
                  
                   
                     557248
                  
                   
                     561806
                  
                   
                     566383
                  
                   
                     570978
                  
                   
                     575592
                  
                
                 
                   
                     25
                  
                   
                     0.580225
                  
                   
                     584876
                  
                   
                     589545
                  
                   
                     594233
                  
                   
                     598940
                  
                   
                     603666
                  
                   
                     608410
                  
                   
                     613172
                  
                   
                     617953
                  
                   
                     622753
                  
                
                 
                   
                     26
                  
                   
                     0.627570
                  
                   
                     632408
                  
                   
                     637263
                  
                   
                     642137
                  
                   
                     647029
                  
                   
                     651940
                  
                   
                     656870
                  
                   
                     661818
                  
                   
                     666785
                  
                   
                     671770
                  
                
                 
                   
                     27
                  
                   
                     0.676774
                  
                   
                     681796
                  
                   
                     686837
                  
                   
                     691897
                  
                   
                     696975
                  
                   
                     702072
                  
                   
                     707187
                  
                   
                     712321
                  
                   
                     717473
                  
                   
                     722644
                  
                
                 
                   
                     28
                  
                   
                     0.727834
                  
                   
                     733042
                  
                   
                     738269
                  
                   
                     743514
                  
                   
                     748778
                  
                   
                     754060
                  
                   
                     759361
                  
                   
                     764680
                  
                   
                     770018
                  
                   
                     775375
                  
                
                 
                   
                     29
                  
                   
                     0.780750
                  
                   
                     786144
                  
                   
                     791556
                  
                   
                     796987
                  
                   
                     802437
                  
                   
                     807905
                  
                   
                     813391
                  
                   
                     818897
                  
                   
                     824420
                  
                   
                     829963
                  
                
                 
                   
                     30
                  
                   
                     0.835524
                  
                   
                     841103
                  
                   
                     846701
                  
                   
                     852318
                  
                   
                     857953
                  
                   
                     863606
                  
                   
                     869279
                  
                   
                     874970
                  
                   
                     880679
                  
                   
                     886407
                  
                
                 
                   
                     31
                  
                   
                     0.892133
                  
                   
                     897919
                  
                   
                     903702
                  
                   
                     909505
                  
                   
                     915325
                  
                   
                     921165
                  
                   
                     927023
                  
                   
                     932899
                  
                   
                     938794
                  
                   
                     944708
                  
                
                 
                   
                     32
                  
                   
                     0.950640
                  
                   
                     956591
                  
                   
                     962560
                  
                   
                     968548
                  
                   
                     974555
                  
                   
                     980580
                  
                   
                     986623
                  
                   
                     992686
                  
                   
                     998766
                  
                   
                     004866
                  
                
                 
                   
                     33
                  
                   
                     1.010984
                  
                   
                     017120
                  
                   
                     023275
                  
                   
                     029449
                  
                   
                     035641
                  
                   
                     041852
                  
                   
                     048081
                  
                   
                     054329
                  
                   
                     060595
                  
                   
                     066880
                  
                
                 
                   
                     34
                  
                   
                     1.073184
                  
                   
                     079●06
                  
                   
                     085846
                  
                   
                     092206
                  
                   
                     098584
                  
                   
                     104980
                  
                   
                     111395
                  
                   
                     117828
                  
                   
                     124281
                  
                   
                     130751
                  
                
                 
                   
                     
                     34
                  
                   
                     1.073184
                  
                   
                     079506
                  
                   
                     085846
                  
                   
                     092206
                  
                   
                     098584
                  
                   
                     104980
                  
                   
                     111395
                  
                   
                     117828
                  
                   
                     124281
                  
                   
                     130751
                  
                
                 
                   
                     35
                  
                   
                     1.137241
                  
                   
                     143748
                  
                   
                     150275
                  
                   
                     156820
                  
                   
                     163383
                  
                   
                     169965
                  
                   
                     176566
                  
                   
                     183185
                  
                   
                     189823
                  
                   
                     196479
                  
                
                 
                   
                     36
                  
                   
                     1.203154
                  
                   
                     209848
                  
                   
                     216560
                  
                   
                     223290
                  
                   
                     230039
                  
                   
                     236807
                  
                   
                     243593
                  
                   
                     250398
                  
                   
                     257222
                  
                   
                     264064
                  
                
                 
                   
                     37
                  
                   
                     1.270924
                  
                   
                     277803
                  
                   
                     284701
                  
                   
                     291617
                  
                   
                     298852
                  
                   
                     305506
                  
                   
                     312478
                  
                   
                     319468
                  
                   
                     326477
                  
                   
                     333505
                  
                
                 
                   
                     38
                  
                   
                     1.340551
                  
                   
                     347616
                  
                   
                     354700
                  
                   
                     361802
                  
                   
                     368922
                  
                   
                     376061
                  
                   
                     383219
                  
                   
                     390395
                  
                   
                     397590
                  
                   
                     404803
                  
                
                 
                   
                     39
                  
                   
                     1.412035
                  
                   
                     419286
                  
                   
                     426555
                  
                   
                     433842
                  
                   
                     441148
                  
                   
                     448473
                  
                   
                     455817
                  
                   
                     463178
                  
                   
                     470549
                  
                   
                     477958
                  
                
                 
                   
                     40
                  
                   
                     1.485376
                  
                   
                     492812
                  
                   
                     500266
                  
                   
                     507740
                  
                   
                     515232
                  
                   
                     522742
                  
                   
                     530271
                  
                   
                     537819
                  
                   
                     545385
                  
                   
                     552969
                  
                
                 
                   
                     41
                  
                   
                     1.560573
                  
                   
                     568194
                  
                   
                     575835
                  
                   
                     583494
                  
                   
                     591171
                  
                   
                     598868
                  
                   
                     606582
                  
                   
                     614315
                  
                   
                     622067
                  
                   
                     629838
                  
                
                 
                   
                     42
                  
                   
                     1.637627
                  
                   
                     645434
                  
                   
                     653260
                  
                   
                     661105
                  
                   
                     668968
                  
                   
                     676850
                  
                   
                     684750
                  
                   
                     692669
                  
                   
                     700606
                  
                   
                     708563
                  
                
                 
                   
                     43
                  
                   
                     1.716537
                  
                   
                     724530
                  
                   
                     732542
                  
                   
                     740572
                  
                   
                     748621
                  
                   
                     756689
                  
                   
                     764775
                  
                   
                     772879
                  
                   
                     781002
                  
                   
                     789144
                  
                
                 
                   
                     44
                  
                   
                     1.797304
                  
                   
                     805483
                  
                   
                     813681
                  
                   
                     821897
                  
                   
                     830131
                  
                   
                     838384
                  
                   
                     846656
                  
                   
                     854946
                  
                   
                     863255
                  
                   
                     871583
                  
                
                 
                   
                     45
                  
                   
                     1.879929
                  
                   
                     888293
                  
                   
                     896676
                  
                   
                     905078
                  
                   
                     913498
                  
                   
                     921937
                  
                   
                     930394
                  
                   
                     938870
                  
                   
                     947365
                  
                   
                     955878
                  
                
                 
                   
                     46
                  
                   
                     1.964409
                  
                   
                     972959
                  
                   
                     981528
                  
                   
                     990116
                  
                   
                     998721
                  
                   
                     007346
                  
                   
                     015989
                  
                   
                     024651
                  
                   
                     033331
                  
                   
                     042029
                  
                
                 
                   
                     47
                  
                   
                     2.050747
                  
                   
                     059483
                  
                   
                     068237
                  
                   
                     077010
                  
                   
                     085802
                  
                   
                     094612
                  
                   
                     103440
                  
                   
                     112288
                  
                   
                     121154
                  
                   
                     130038
                  
                
                 
                   
                     48
                  
                   
                     2.138941
                  
                   
                     147862
                  
                   
                     156803
                  
                   
                     165761
                  
                   
                     174739
                  
                   
                     183734
                  
                   
                     192749
                  
                   
                     201782
                  
                   
                     210833
                  
                   
                     219903
                  
                
                 
                   
                     49
                  
                   
                     2.228992
                  
                   
                     238099
                  
                   
                     247225
                  
                   
                     256369
                  
                   
                     265532
                  
                   
                     274714
                  
                   
                     283914
                  
                   
                     293132
                  
                   
                     302369
                  
                   
                     311625
                  
                
                 
                   
                     50
                  
                   
                     2.32090
                  
                   
                     330192
                  
                   
                     339504
                  
                   
                     348834
                  
                   
                     358182
                  
                   
                     267550
                  
                   
                     376935
                  
                   
                     386340
                  
                   
                     395762
                  
                   
                     405204
                  
                
                 
                   
                     51
                  
                   
                     2.414664
                  
                   
                     424142
                  
                   
                     433640
                  
                   
                     443155
                  
                   
                     452689
                  
                   
                     462242
                  
                   
                     471814
                  
                   
                     481404
                  
                   
                     491012
                  
                   
                     508639
                  
                
                 
                   
                     52
                  
                   
                     2.510285
                  
                   
                     519949
                  
                   
                     529632
                  
                   
                     539333
                  
                   
                     549053
                  
                   
                     558792
                  
                   
                     568549
                  
                   
                     578324
                  
                   
                     588119
                  
                   
                     597931
                  
                
                 
                   
                     53
                  
                   
                     2.607763
                  
                   
                     617613
                  
                   
                     627481
                  
                   
                     637368
                  
                   
                     647274
                  
                   
                     657198
                  
                   
                     667141
                  
                   
                     677102
                  
                   
                     687082
                  
                   
                     697080
                  
                
                 
                   
                     54
                  
                   
                     2.707097
                  
                   
                     717133
                  
                   
                     727187
                  
                   
                     737260
                  
                   
                     747351
                  
                   
                     757461
                  
                   
                     767589
                  
                   
                     777736
                  
                   
                     787902
                  
                   
                     798086
                  
                
                 
                   
                     55
                  
                   
                     2.808289
                  
                   
                     818510
                  
                   
                     828750
                  
                   
                     839008
                  
                   
                     849285
                  
                   
                     859580
                  
                   
                     869894
                  
                   
                     880227
                  
                   
                     890578
                  
                   
                     900948
                  
                
                 
                   
                     56
                  
                   
                     2.911336
                  
                   
                     921743
                  
                   
                     932169
                  
                   
                     942613
                  
                   
                     953076
                  
                   
                     963557
                  
                   
                     974056
                  
                   
                     984575
                  
                   
                     995112
                  
                   
                     005667
                  
                
                 
                   
                     57
                  
                   
                     3.016241
                  
                   
                     026834
                  
                   
                     037445
                  
                   
                     048075
                  
                   
                     058723
                  
                   
                     069390
                  
                   
                     080075
                  
                   
                     090779
                  
                   
                     101502
                  
                   
                     112243
                  
                
                 
                   
                     58
                  
                   
                     3.123003
                  
                   
                     133781
                  
                   
                     144578
                  
                   
                     155393
                  
                   
                     166227
                  
                   
                     177080
                  
                   
                     187951
                  
                   
                     198840
                  
                   
                     209748
                  
                   
                     220675
                  
                
                 
                   
                     59
                  
                   
                     3.231621
                  
                   
                     242585
                  
                   
                     253567
                  
                   
                     264568
                  
                   
                     275588
                  
                   
                     286626
                  
                   
                     297683
                  
                   
                     308758
                  
                   
                     319852
                  
                   
                     330964
                  
                
                 
                   
                     60
                  
                   
                     3.342096
                  
                   
                     353245
                  
                   
                     364413
                  
                   
                     375600
                  
                   
                     386805
                  
                   
                     398029
                  
                   
                     409272
                  
                   
                     420533
                  
                   
                     431812
                  
                   
                     443110
                  
                
                 
                   
                     61
                  
                   
                     3.454427
                  
                   
                     465762
                  
                   
                     477116
                  
                   
                     488489
                  
                   
                     499880
                  
                   
                     511289
                  
                   
                     522717
                  
                   
                     534164
                  
                   
                     545629
                  
                   
                     557113
                  
                
                 
                   
                     62
                  
                   
                     3.568615
                  
                   
                     580136
                  
                   
                     591676
                  
                   
                     603234
                  
                   
                     614811
                  
                   
                     626406
                  
                   
                     638020
                  
                   
                     649652
                  
                   
                     661303
                  
                   
                     672972
                  
                
                 
                   
                     63
                  
                   
                     3.684660
                  
                   
                     696367
                  
                   
                     708092
                  
                   
                     719836
                  
                   
                     731598
                  
                   
                     743379
                  
                   
                     755179
                  
                   
                     766997
                  
                   
                     778838
                  
                   
                     790688
                  
                
                 
                   
                     64
                  
                   
                     3.802562
                  
                   
                     814454
                  
                   
                     826365
                  
                   
                     838295
                  
                   
                     850243
                  
                   
                     862209
                  
                   
                     874194
                  
                   
                     886198
                  
                   
                     898220
                  
                   
                     910261
                  
                
                 
                   
                     65
                  
                   
                     3.922321
                  
                   
                     934398
                  
                   
                     946495
                  
                   
                     958610
                  
                   
                     970744
                  
                   
                     982896
                  
                   
                     995067
                  
                   
                     007256
                  
                   
                     919464
                  
                   
                     031691
                  
                
                 
                   
                     66
                  
                   
                     4.043936
                  
                   
                     056199
                  
                   
                     068481
                  
                   
                     080782
                  
                   
                     093102
                  
                   
                     105440
                  
                   
                     117796
                  
                   
                     130171
                  
                   
                     142565
                  
                   
                     154977
                  
                
                 
                   
                     67
                  
                   
                     4.167408
                  
                   
                     179857
                  
                   
                     192325
                  
                   
                     204811
                  
                   
                     217316
                  
                   
                     229840
                  
                   
                     242382
                  
                   
                     254943
                  
                   
                     267522
                  
                   
                     280120
                  
                
                 
                   
                     
                     67
                  
                   
                     4.167408
                  
                   
                     179857
                  
                   
                     192325
                  
                   
                     204811
                  
                   
                     217316
                  
                   
                     229840
                  
                   
                     242382
                  
                   
                     254943
                  
                   
                     267522
                  
                   
                     280122
                  
                
                 
                   
                     68
                  
                   
                     4.292736
                  
                   
                     305371
                  
                   
                     318025
                  
                   
                     330697
                  
                   
                     343387
                  
                   
                     356097
                  
                   
                     368825
                  
                   
                     381571
                  
                   
                     394336
                  
                   
                     407119
                  
                
                 
                   
                     69
                  
                   
                     4.419921
                  
                   
                     432742
                  
                   
                     445581
                  
                   
                     458439
                  
                   
                     471315
                  
                   
                     484210
                  
                   
                     497124
                  
                   
                     510056
                  
                   
                     523007
                  
                   
                     535976
                  
                
                 
                   
                     70
                  
                   
                     4.548964
                  
                   
                     561970
                  
                   
                     574995
                  
                   
                     588038
                  
                   
                     601100
                  
                   
                     614181
                  
                   
                     627280
                  
                   
                     670398
                  
                   
                     653534
                  
                   
                     666789
                  
                
                 
                   
                     71
                  
                   
                     4.679862
                  
                   
                     693054
                  
                   
                     706265
                  
                   
                     819494
                  
                   
                     732724
                  
                   
                     746008
                  
                   
                     759293
                  
                   
                     772596
                  
                   
                     785918
                  
                   
                     799259
                  
                
                 
                   
                     72
                  
                   
                     4.812618
                  
                   
                     825995
                  
                   
                     839392
                  
                   
                     852806
                  
                   
                     866240
                  
                   
                     879692
                  
                   
                     893162
                  
                   
                     906651
                  
                   
                     920159
                  
                   
                     933685
                  
                
                 
                   
                     73
                  
                   
                     4.947230
                  
                   
                     960793
                  
                   
                     974375
                  
                   
                     987976
                  
                   
                     001595
                  
                   
                     015232
                  
                   
                     028888
                  
                   
                     042563
                  
                   
                     056257
                  
                   
                     069968
                  
                
                 
                   
                     74
                  
                   
                     5.083699
                  
                   
                     097448
                  
                   
                     111215
                  
                   
                     125002
                  
                   
                     138806
                  
                   
                     152630
                  
                   
                     166471
                  
                   
                     180332
                  
                   
                     194211
                  
                   
                     208108
                  
                
                 
                   
                     75
                  
                   
                     5.222025
                  
                   
                     235959
                  
                   
                     249912
                  
                   
                     263884
                  
                   
                     277875
                  
                   
                     291884
                  
                   
                     305911
                  
                   
                     319957
                  
                   
                     334022
                  
                   
                     348105
                  
                
                 
                   
                     76
                  
                   
                     5.362207
                  
                   
                     376327
                  
                   
                     390466
                  
                   
                     404624
                  
                   
                     418800
                  
                   
                     432994
                  
                   
                     447208
                  
                   
                     461439
                  
                   
                     475690
                  
                   
                     489958
                  
                
                 
                   
                     77
                  
                   
                     5.504246
                  
                   
                     518552
                  
                   
                     532877
                  
                   
                     547220
                  
                   
                     561581
                  
                   
                     575962
                  
                   
                     590361
                  
                   
                     604778
                  
                   
                     619214
                  
                   
                     633669
                  
                
                 
                   
                     78
                  
                   
                     5.648142
                  
                   
                     662633
                  
                   
                     677144
                  
                   
                     691673
                  
                   
                     706220
                  
                   
                     720786
                  
                   
                     735370
                  
                   
                     479974
                  
                   
                     764595
                  
                   
                     779235
                  
                
                 
                   
                     79
                  
                   
                     5.793894
                  
                   
                     808572
                  
                   
                     823268
                  
                   
                     837982
                  
                   
                     852715
                  
                   
                     867467
                  
                   
                     882237
                  
                   
                     897026
                  
                   
                     911833
                  
                   
                     926659
                  
                
                 
                   
                     80
                  
                   
                     5.941504
                  
                   
                     956367
                  
                   
                     971248
                  
                   
                     986148
                  
                   
                     001067
                  
                   
                     016004
                  
                   
                     030960
                  
                   
                     045935
                  
                   
                     060928
                  
                   
                     075939
                  
                
                 
                   
                     81
                  
                   
                     6.090969
                  
                   
                     106018
                  
                   
                     121085
                  
                   
                     136171
                  
                   
                     151276
                  
                   
                     166399
                  
                   
                     181540
                  
                   
                     196700
                  
                   
                     211879
                  
                   
                     227076
                  
                
                 
                   
                     82
                  
                   
                     6.242292
                  
                   
                     257527
                  
                   
                     272779
                  
                   
                     288051
                  
                   
                     303341
                  
                   
                     318650
                  
                   
                     333977
                  
                   
                     349323
                  
                   
                     364687
                  
                   
                     380070
                  
                
                 
                   
                     83
                  
                   
                     6.395472
                  
                   
                     410892
                  
                   
                     426330
                  
                   
                     441787
                  
                   
                     457263
                  
                   
                     472758
                  
                   
                     488270
                  
                   
                     503802
                  
                   
                     519352
                  
                   
                     534920
                  
                
                 
                   
                     84
                  
                   
                     6.550508
                  
                   
                     566113
                  
                   
                     581738
                  
                   
                     597381
                  
                   
                     613042
                  
                   
                     628722
                  
                   
                     644421
                  
                   
                     660138
                  
                   
                     675873
                  
                   
                     691628
                  
                
                 
                   
                     85
                  
                   
                     6.707401
                  
                   
                     723192
                  
                   
                     739002
                  
                   
                     754830
                  
                   
                     770678
                  
                   
                     786543
                  
                   
                     802427
                  
                   
                     818330
                  
                   
                     834252
                  
                   
                     850192
                  
                
                 
                   
                     86
                  
                   
                     6.866150
                  
                   
                     882127
                  
                   
                     898123
                  
                   
                     914137
                  
                   
                     930170
                  
                   
                     946221
                  
                   
                     962291
                  
                   
                     978380
                  
                   
                     994487
                  
                   
                     010612
                  
                
                 
                   
                     87
                  
                   
                     7.026756
                  
                   
                     042919
                  
                   
                     059100
                  
                   
                     075300
                  
                   
                     091519
                  
                   
                     107756
                  
                   
                     124011
                  
                   
                     140285
                  
                   
                     156578
                  
                   
                     172889
                  
                
                 
                   
                     88
                  
                   
                     7.189219
                  
                   
                     205568
                  
                   
                     221935
                  
                   
                     239320
                  
                   
                     254724
                  
                   
                     271147
                  
                   
                     287588
                  
                   
                     304048
                  
                   
                     320527
                  
                   
                     337024
                  
                
                 
                   
                     89
                  
                   
                     7.353539
                  
                   
                     370073
                  
                   
                     386626
                  
                   
                     403197
                  
                   
                     419787
                  
                   
                     436395
                  
                   
                     453022
                  
                   
                     469668
                  
                   
                     486332
                  
                   
                     503014
                  
                
                 
                   
                     90
                  
                   
                     7.519716
                  
                   
                     536435
                  
                   
                     553174
                  
                   
                     569930
                  
                   
                     586706
                  
                   
                     603500
                  
                   
                     620313
                  
                   
                     637144
                  
                   
                     653993
                  
                   
                     670862
                  
                
                 
                   
                     91
                  
                   
                     7.687749
                  
                   
                     704654
                  
                   
                     721578
                  
                   
                     738521
                  
                   
                     755482
                  
                   
                     772462
                  
                   
                     789460
                  
                   
                     806477
                  
                   
                     823512
                  
                   
                     840566
                  
                
                 
                   
                     92
                  
                   
                     7.857639
                  
                   
                     874730
                  
                   
                     891839
                  
                   
                     908968
                  
                   
                     926114
                  
                   
                     943280
                  
                   
                     960464
                  
                   
                     977666
                  
                   
                     994887
                  
                   
                     012127
                  
                
                 
                   
                     93
                  
                   
                     8.029385
                  
                   
                     046662
                  
                   
                     063957
                  
                   
                     081271
                  
                   
                     098604
                  
                   
                     115955
                  
                   
                     133324
                  
                   
                     150713
                  
                   
                     168119
                  
                   
                     185545
                  
                
                 
                   
                     94
                  
                   
                     8.202988
                  
                   
                     220451
                  
                   
                     237932
                  
                   
                     255432
                  
                   
                     272950
                  
                   
                     290486
                  
                   
                     308042
                  
                   
                     325616
                  
                   
                     343208
                  
                   
                     360819
                  
                
                 
                   
                     95
                  
                   
                     8.378449
                  
                   
                     396097
                  
                   
                     413763
                  
                   
                     431449
                  
                   
                     449152
                  
                   
                     466875
                  
                   
                     484616
                  
                   
                     502375
                  
                   
                     520153
                  
                   
                     537950
                  
                
                 
                   
                     96
                  
                   
                     8.555765
                  
                   
                     573599
                  
                   
                     591451
                  
                   
                     609322
                  
                   
                     627212
                  
                   
                     645120
                  
                   
                     663047
                  
                   
                     680992
                  
                   
                     698956
                  
                   
                     716938
                  
                
                 
                   
                     97
                  
                   
                     8.734939
                  
                   
                     752958
                  
                   
                     770996
                  
                   
                     789053
                  
                   
                     807128
                  
                   
                     825222
                  
                   
                     843334
                  
                   
                     861465
                  
                   
                     879614
                  
                   
                     897782
                  
                
                 
                   
                     98
                  
                   
                     8.915969
                  
                   
                     934174
                  
                   
                     952398
                  
                   
                     970640
                  
                   
                     988901
                  
                   
                     007180
                  
                   
                     025478
                  
                   
                     043795
                  
                   
                     062130
                  
                   
                     080484
                  
                
                 
                   
                     99
                  
                   
                     9.098856
                  
                   
                     117247
                  
                   
                     135656
                  
                   
                     154084
                  
                   
                     172531
                  
                   
                     190996
                  
                   
                     209479
                  
                   
                     227981
                  
                   
                     246502
                  
                   
                     265042
                  
                
                 
                   
                     100
                  
                   
                     9.283600
                  
                   
                     302176
                  
                   
                     320771
                  
                   
                     339385
                  
                   
                     358017
                  
                   
                     376668
                  
                   
                     395337
                  
                   
                     414025
                  
                   
                     432731
                  
                   
                     451456
                  
                
                 
                   
                     
                     100
                  
                   
                     9.283600
                  
                   
                     302176
                  
                   
                     302771
                  
                   
                     339385
                  
                   
                     358017
                  
                   
                     376668
                  
                   
                     395337
                  
                   
                     414025
                  
                   
                     432731
                  
                   
                     451456
                  
                
                 
                   
                     101
                  
                   
                     9.470200
                  
                   
                     488962
                  
                   
                     507743
                  
                   
                     526524
                  
                   
                     545360
                  
                   
                     564196
                  
                   
                     583051
                  
                   
                     601925
                  
                   
                     620817
                  
                   
                     639728
                  
                
                 
                   
                     102
                  
                   
                     9.658657
                  
                   
                     677605
                  
                   
                     696574
                  
                   
                     715556
                  
                   
                     734560
                  
                   
                     753582
                  
                   
                     772622
                  
                   
                     791682
                  
                   
                     810759
                  
                   
                     829856
                  
                
                 
                   
                     103
                  
                   
                     9.848971
                  
                   
                     868104
                  
                   
                     887256
                  
                   
                     906427
                  
                   
                     925616
                  
                   
                     944824
                  
                   
                     964050
                  
                   
                     983295
                  
                   
                     ●02559
                  
                   
                     021841
                  
                
                 
                   
                     104
                  
                   
                     10.041141
                  
                   
                     060460
                  
                   
                     079798
                  
                   
                     099154
                  
                   
                     118529
                  
                   
                     137923
                  
                   
                     157335
                  
                   
                     176765
                  
                   
                     196215
                  
                   
                     215682
                  
                
                 
                   
                     105
                  
                   
                     10.235169
                  
                   
                     254673
                  
                   
                     274197
                  
                   
                     293739
                  
                   
                     323299
                  
                   
                     332878
                  
                   
                     352476
                  
                   
                     372092
                  
                   
                     391727
                  
                   
                     411381
                  
                
                 
                   
                     106
                  
                   
                     10.431052
                  
                   
                     450743
                  
                   
                     470452
                  
                   
                     490180
                  
                   
                     509926
                  
                   
                     529691
                  
                   
                     549474
                  
                   
                     569276
                  
                   
                     589096
                  
                   
                     608936
                  
                
                 
                   
                     107
                  
                   
                     10.628793
                  
                   
                     648669
                  
                   
                     668564
                  
                   
                     688477
                  
                   
                     708409
                  
                   
                     728360
                  
                   
                     748329
                  
                   
                     768316
                  
                   
                     788323
                  
                   
                     808347
                  
                
                 
                   
                     108
                  
                   
                     10.828391
                  
                   
                     848452
                  
                   
                     868533
                  
                   
                     888632
                  
                   
                     908749
                  
                   
                     928886
                  
                   
                     949040
                  
                   
                     969213
                  
                   
                     989405
                  
                   
                     009616
                  
                
                 
                   
                     109
                  
                   
                     11.029845
                  
                   
                     050092
                  
                   
                     070358
                  
                   
                     090643
                  
                   
                     110946
                  
                   
                     131268
                  
                   
                     151608
                  
                   
                     171967
                  
                   
                     192345
                  
                   
                     212741
                  
                
                 
                   
                     110
                  
                   
                     11.233156
                  
                   
                     253589
                  
                   
                     274040
                  
                   
                     294511
                  
                   
                     315000
                  
                   
                     335507
                  
                   
                     356033
                  
                   
                     376578
                  
                   
                     397141
                  
                   
                     417723
                  
                
                 
                   
                     111
                  
                   
                     11.438323
                  
                   
                     458942
                  
                   
                     479579
                  
                   
                     500235
                  
                   
                     520910
                  
                   
                     541603
                  
                   
                     562315
                  
                   
                     583045
                  
                   
                     603794
                  
                   
                     624561
                  
                
                 
                   
                     112
                  
                   
                     11.645347
                  
                   
                     666152
                  
                   
                     686975
                  
                   
                     707817
                  
                   
                     728677
                  
                   
                     749556
                  
                   
                     770453
                  
                   
                     791369
                  
                   
                     812304
                  
                   
                     833257
                  
                
                 
                   
                     113
                  
                   
                     11.854228
                  
                   
                     875219
                  
                   
                     896227
                  
                   
                     917255
                  
                   
                     938301
                  
                   
                     959365
                  
                   
                     980448
                  
                   
                     001550
                  
                   
                     022670
                  
                   
                     043809
                  
                
                 
                   
                     114
                  
                   
                     12.064966
                  
                   
                     086142
                  
                   
                     107336
                  
                   
                     128549
                  
                   
                     149781
                  
                   
                     171031
                  
                   
                     192300
                  
                   
                     213587
                  
                   
                     234893
                  
                   
                     256218
                  
                
                 
                   
                     115
                  
                   
                     12.277561
                  
                   
                     298922
                  
                   
                     320302
                  
                   
                     341701
                  
                   
                     363118
                  
                   
                     384554
                  
                   
                     406008
                  
                   
                     427481
                  
                   
                     448973
                  
                   
                     470483
                  
                
                 
                   
                     116
                  
                   
                     12.492012
                  
                   
                     513559
                  
                   
                     535125
                  
                   
                     556709
                  
                   
                     578312
                  
                   
                     509934
                  
                   
                     621574
                  
                   
                     643232
                  
                   
                     664909
                  
                   
                     686605
                  
                
                 
                   
                     117
                  
                   
                     12.708320
                  
                   
                     730052
                  
                   
                     751804
                  
                   
                     773574
                  
                   
                     795363
                  
                   
                     817170
                  
                   
                     838995
                  
                   
                     860840
                  
                   
                     882703
                  
                   
                     904584
                  
                
                 
                   
                     118
                  
                   
                     12.926484
                  
                   
                     948403
                  
                   
                     970340
                  
                   
                     992296
                  
                   
                     014270
                  
                   
                     036263
                  
                   
                     058274
                  
                   
                     080304
                  
                   
                     102353
                  
                   
                     124420
                  
                
                 
                   
                     119
                  
                   
                     13.146505
                  
                   
                     168610
                  
                   
                     190733
                  
                   
                     212874
                  
                   
                     235034
                  
                   
                     257212
                  
                   
                     279409
                  
                   
                     301625
                  
                   
                     323859
                  
                   
                     346112
                  
                
                 
                   
                     120
                  
                   
                     13.368384
                  
                   
                     390673
                  
                   
                     412982
                  
                   
                     435309
                  
                   
                     457655
                  
                   
                     480019
                  
                   
                     502402
                  
                   
                     524803
                  
                   
                     547223
                  
                   
                     569661
                  
                
                 
                   
                     121
                  
                   
                     13.592118
                  
                   
                     614594
                  
                   
                     637088
                  
                   
                     659601
                  
                   
                     682132
                  
                   
                     704682
                  
                   
                     727250
                  
                   
                     749837
                  
                   
                     772443
                  
                   
                     795067
                  
                
                 
                   
                     122
                  
                   
                     13.817710
                  
                   
                     840371
                  
                   
                     863051
                  
                   
                     885749
                  
                   
                     908466
                  
                   
                     931202
                  
                   
                     953956
                  
                   
                     976729
                  
                   
                     999520
                  
                   
                     022320
                  
                
                 
                   
                     123
                  
                   
                     14.045158
                  
                   
                     068005
                  
                   
                     090870
                  
                   
                     113754
                  
                   
                     136657
                  
                   
                     159578
                  
                   
                     182518
                  
                   
                     205476
                  
                   
                     228453
                  
                   
                     251449
                  
                
                 
                   
                     124
                  
                   
                     14.274463
                  
                   
                     297495
                  
                   
                     320547
                  
                   
                     343616
                  
                   
                     366705
                  
                   
                     389812
                  
                   
                     412937
                  
                   
                     436081
                  
                   
                     459244
                  
                   
                     482425
                  
                
                 
                   
                     125
                  
                   
                     14.505625
                  
                   
                     528843
                  
                   
                     552080
                  
                   
                     575335
                  
                   
                     598609
                  
                   
                     621902
                  
                   
                     645213
                  
                   
                     668542
                  
                   
                     691891
                  
                   
                     715257
                  
                
                 
                   
                     126
                  
                   
                     14.738643
                  
                   
                     762047
                  
                   
                     785469
                  
                   
                     808910
                  
                   
                     832370
                  
                   
                     855848
                  
                   
                     879345
                  
                   
                     902860
                  
                   
                     926394
                  
                   
                     949947
                  
                
                 
                   
                     127
                  
                   
                     14.973518
                  
                   
                     997108
                  
                   
                     020716
                  
                   
                     044343
                  
                   
                     067988
                  
                   
                     091652
                  
                   
                     115334
                  
                   
                     139035
                  
                   
                     162755
                  
                   
                     186493
                  
                
                 
                   
                     128
                  
                   
                     15.210250
                  
                   
                     234025
                  
                   
                     257819
                  
                   
                     281631
                  
                   
                     305462
                  
                   
                     329312
                  
                   
                     353180
                  
                   
                     377067
                  
                   
                     400972
                  
                   
                     424896
                  
                
                 
                   
                     129
                  
                   
                     15.448838
                  
                   
                     472799
                  
                   
                     496779
                  
                   
                     520777
                  
                   
                     544794
                  
                   
                     568829
                  
                   
                     592883
                  
                   
                     616955
                  
                   
                     641046
                  
                   
                     665155
                  
                
                 
                   
                     130
                  
                   
                     15.689284
                  
                   
                     713430
                  
                   
                     737595
                  
                   
                     761779
                  
                   
                     785981
                  
                   
                     810202
                  
                   
                     834442
                  
                   
                     858700
                  
                   
                     882977
                  
                   
                     907272
                  
                
                 
                   
                     131
                  
                   
                     15.931585
                  
                   
                     955918
                  
                   
                     982269
                  
                   
                     004638
                  
                   
                     029026
                  
                   
                     053433
                  
                   
                     077858
                  
                   
                     102302
                  
                   
                     126764
                  
                   
                     151245
                  
                
                 
                   
                     132
                  
                   
                     16.175744
                  
                   
                     200262
                  
                   
                     224799
                  
                   
                     249354
                  
                   
                     273927
                  
                   
                     298520
                  
                   
                     323131
                  
                   
                     347760
                  
                   
                     372408
                  
                   
                     497074
                  
                
                 
                   
                     133
                  
                   
                     16.421760
                  
                   
                     446463
                  
                   
                     471185
                  
                   
                     495926
                  
                   
                     502686
                  
                   
                     545464
                  
                   
                     570260
                  
                   
                     595075
                  
                   
                     619909
                  
                   
                     644761
                  
                
                 
                   
                     
                     134
                  
                   
                     16.669632
                  
                   
                     694521
                  
                   
                     719429
                  
                   
                     744355
                  
                   
                     769300
                  
                   
                     794264
                  
                   
                     819242
                  
                   
                     844247
                  
                   
                     869266
                  
                   
                     894304
                  
                
                 
                   
                     135
                  
                   
                     16.919361
                  
                   
                     944436
                  
                   
                     969529
                  
                   
                     994641
                  
                   
                     019772
                  
                   
                     044921
                  
                   
                     070089
                  
                   
                     095275
                  
                   
                     120489
                  
                   
                     145704
                  
                
                 
                   
                     136
                  
                   
                     17.170946
                  
                   
                     196207
                  
                   
                     221486
                  
                   
                     246784
                  
                   
                     272100
                  
                   
                     297435
                  
                   
                     322789
                  
                   
                     348161
                  
                   
                     373551
                  
                   
                     398961
                  
                
                 
                   
                     137
                  
                   
                     17.424388
                  
                   
                     449835
                  
                   
                     475300
                  
                   
                     500783
                  
                   
                     526285
                  
                   
                     551806
                  
                   
                     577345
                  
                   
                     602903
                  
                   
                     628479
                  
                   
                     654074
                  
                
                 
                   
                     138
                  
                   
                     17.679687
                  
                   
                     705319
                  
                   
                     730970
                  
                   
                     756639
                  
                   
                     782327
                  
                   
                     808033
                  
                   
                     833758
                  
                   
                     859501
                  
                   
                     885263
                  
                   
                     911044
                  
                
                 
                   
                     139
                  
                   
                     17.936843
                  
                   
                     962661
                  
                   
                     988497
                  
                   
                     014352
                  
                   
                     040225
                  
                   
                     066117
                  
                   
                     092028
                  
                   
                     117957
                  
                   
                     143904
                  
                   
                     169871
                  
                
                 
                   
                     140
                  
                   
                     18.195856
                  
                   
                     221859
                  
                   
                     247881
                  
                   
                     273921
                  
                   
                     299980
                  
                   
                     326058
                  
                   
                     325154
                  
                   
                     378269
                  
                   
                     404402
                  
                   
                     430554
                  
                
                 
                   
                     141
                  
                   
                     18.456725
                  
                   
                     482914
                  
                   
                     509121
                  
                   
                     535347
                  
                   
                     561592
                  
                   
                     587856
                  
                   
                     614137
                  
                   
                     640438
                  
                   
                     666757
                  
                   
                     693094
                  
                
                 
                   
                     142
                  
                   
                     18.719451
                  
                   
                     745825
                  
                   
                     772219
                  
                   
                     798630
                  
                   
                     825061
                  
                   
                     851510
                  
                   
                     877977
                  
                   
                     904463
                  
                   
                     930968
                  
                   
                     957491
                  
                
                 
                   
                     143
                  
                   
                     18.984033
                  
                   
                     010059
                  
                   
                     037172
                  
                   
                     063770
                  
                   
                     090386
                  
                   
                     117021
                  
                   
                     143674
                  
                   
                     170346
                  
                   
                     197036
                  
                   
                     223745
                  
                
                 
                   
                     144
                  
                   
                     19.250472
                  
                   
                     277219
                  
                   
                     303983
                  
                   
                     330766
                  
                   
                     357568
                  
                   
                     384388
                  
                   
                     411227
                  
                   
                     438085
                  
                   
                     464961
                  
                   
                     491855
                  
                
                 
                   
                     145
                  
                   
                     19.518769
                  
                   
                     545700
                  
                   
                     527651
                  
                   
                     599619
                  
                   
                     626607
                  
                   
                     653613
                  
                   
                     680637
                  
                   
                     707680
                  
                   
                     734742
                  
                   
                     761822
                  
                
                 
                   
                     146
                  
                   
                     19.788921
                  
                   
                     816039
                  
                   
                     843175
                  
                   
                     870329
                  
                   
                     897502
                  
                   
                     924694
                  
                   
                     951904
                  
                   
                     979133
                  
                   
                     006380
                  
                   
                     033646
                  
                
                 
                   
                     147
                  
                   
                     20.060931
                  
                   
                     088234
                  
                   
                     115555
                  
                   
                     142896
                  
                   
                     170254
                  
                   
                     197632
                  
                   
                     225028
                  
                   
                     252442
                  
                   
                     279875
                  
                   
                     307327
                  
                
                 
                   
                     148
                  
                   
                     20.334797
                  
                   
                     362286
                  
                   
                     389793
                  
                   
                     417319
                  
                   
                     444863
                  
                   
                     472426
                  
                   
                     500008
                  
                   
                     527608
                  
                   
                     555227
                  
                   
                     582864
                  
                
                 
                   
                     149
                  
                   
                     20.610520
                  
                   
                     638194
                  
                   
                     665887
                  
                   
                     693599
                  
                   
                     721329
                  
                   
                     749078
                  
                   
                     776845
                  
                   
                     804631
                  
                   
                     832435
                  
                   
                     860258
                  
                
                 
                   
                     150
                  
                   
                     20.888100
                  
                   
                     915960
                  
                   
                     943838
                  
                   
                     971735
                  
                   
                     999651
                  
                   
                     027586
                  
                   
                     055539
                  
                   
                     083510
                  
                   
                     111500
                  
                   
                     139509
                  
                
                 
                   
                     151
                  
                   
                     21.167536
                  
                   
                     195582
                  
                   
                     223646
                  
                   
                     251729
                  
                   
                     279830
                  
                   
                     307950
                  
                   
                     336089
                  
                   
                     364246
                  
                   
                     392422
                  
                   
                     420616
                  
                
                 
                   
                     152
                  
                   
                     21.448829
                  
                   
                     477060
                  
                   
                     505310
                  
                   
                     533579
                  
                   
                     561866
                  
                   
                     590172
                  
                   
                     618496
                  
                   
                     646839
                  
                   
                     675200
                  
                   
                     703580
                  
                
                 
                   
                     153
                  
                   
                     21.731979
                  
                   
                     760396
                  
                   
                     788832
                  
                   
                     817286
                  
                   
                     845759
                  
                   
                     874250
                  
                   
                     902760
                  
                   
                     931288
                  
                   
                     959835
                  
                   
                     988401
                  
                
                 
                   
                     154
                  
                   
                     22.016985
                  
                   
                     045588
                  
                   
                     074209
                  
                   
                     102849
                  
                   
                     131508
                  
                   
                     130185
                  
                   
                     188880
                  
                   
                     217595
                  
                   
                     246327
                  
                   
                     275079
                  
                
                 
                   
                     155
                  
                   
                     22.303849
                  
                   
                     332637
                  
                   
                     361444
                  
                   
                     390270
                  
                   
                     419114
                  
                   
                     447976
                  
                   
                     476858
                  
                   
                     505758
                  
                   
                     534676
                  
                   
                     563613
                  
                
                 
                   
                     156
                  
                   
                     22.592568
                  
                   
                     621543
                  
                   
                     650535
                  
                   
                     679547
                  
                   
                     708576
                  
                   
                     737625
                  
                   
                     766692
                  
                   
                     795777
                  
                   
                     824881
                  
                   
                     854004
                  
                
                 
                   
                     157
                  
                   
                     22.883145
                  
                   
                     912305
                  
                   
                     941483
                  
                   
                     970680
                  
                   
                     999896
                  
                   
                     029130
                  
                   
                     058382
                  
                   
                     087654
                  
                   
                     116943
                  
                   
                     146252
                  
                
                 
                   
                     158
                  
                   
                     23.175579
                  
                   
                     204924
                  
                   
                     234288
                  
                   
                     263671
                  
                   
                     293072
                  
                   
                     322492
                  
                   
                     351930
                  
                   
                     381387
                  
                   
                     410862
                  
                   
                     440356
                  
                
                 
                   
                     159
                  
                   
                     23.469869
                  
                   
                     499400
                  
                   
                     528949
                  
                   
                     558515
                  
                   
                     588105
                  
                   
                     617710
                  
                   
                     647334
                  
                   
                     676976
                  
                   
                     706638
                  
                   
                     736317
                  
                
                 
                   
                     160
                  
                   
                     23.766016
                  
                   
                     795732
                  
                   
                     825468
                  
                   
                     855222
                  
                   
                     884994
                  
                   
                     914785
                  
                   
                     944595
                  
                   
                     974423
                  
                   
                     004270
                  
                   
                     034135
                  
                
                 
                   
                     161
                  
                   
                     24.064019
                  
                   
                     093922
                  
                   
                     123843
                  
                   
                     153782
                  
                   
                     183740
                  
                   
                     213717
                  
                   
                     243712
                  
                   
                     273726
                  
                   
                     303759
                  
                   
                     333810
                  
                
                 
                   
                     162
                  
                   
                     24.363879
                  
                   
                     393967
                  
                   
                     424074
                  
                   
                     454199
                  
                   
                     484343
                  
                   
                     514506
                  
                   
                     544687
                  
                   
                     574886
                  
                   
                     605104
                  
                   
                     635341
                  
                
                 
                   
                     163
                  
                   
                     24.665596
                  
                   
                     695870
                  
                   
                     726163
                  
                   
                     756474
                  
                   
                     786803
                  
                   
                     817151
                  
                   
                     847518
                  
                   
                     877903
                  
                   
                     908307
                  
                   
                     938729
                  
                
                 
                   
                     164
                  
                   
                     24.969170
                  
                   
                     999630
                  
                   
                     030108
                  
                   
                     060604
                  
                   
                     091119
                  
                   
                     121653
                  
                   
                     152206
                  
                   
                     182776
                  
                   
                     213366
                  
                   
                     243974
                  
                
                 
                   
                     165
                  
                   
                     25.274601
                  
                   
                     305246
                  
                   
                     335909
                  
                   
                     366592
                  
                   
                     397293
                  
                   
                     428012
                  
                   
                     458750
                  
                   
                     489507
                  
                   
                     520282
                  
                   
                     551075
                  
                
                 
                   
                     166
                  
                   
                     25.581888
                  
                   
                     612718
                  
                   
                     643568
                  
                   
                     674436
                  
                   
                     705322
                  
                   
                     736228
                  
                   
                     767151
                  
                   
                     798093
                  
                   
                     829054
                  
                   
                     860034
                  
                
                 
                   
                     167
                  
                   
                     25
                     .
                     89103●
                  
                   
                     922048
                  
                   
                     95308
                  
                   
                     984137
                  
                   
                     915209
                  
                   
                     046300
                  
                   
                     077409
                  
                   
                     108537
                  
                   
                     139683
                  
                   
                     170849
                  
                
                 
                   
                     
                     167
                  
                   
                     25.891032
                  
                   
                     922048
                  
                   
                     953083
                  
                   
                     984137
                  
                   
                     015209
                  
                   
                     046300
                  
                   
                     077409
                  
                   
                     108537
                  
                   
                     139683
                  
                   
                     170849
                  
                
                 
                   
                     168
                  
                   
                     26.202032
                  
                   
                     233234
                  
                   
                     264455
                  
                   
                     295694
                  
                   
                     326952
                  
                   
                     358229
                  
                   
                     389524
                  
                   
                     420837
                  
                   
                     452169
                  
                   
                     483520
                  
                
                 
                   
                     169
                  
                   
                     26.514689
                  
                   
                     546277
                  
                   
                     577684
                  
                   
                     609109
                  
                   
                     640552
                  
                   
                     672014
                  
                   
                     703495
                  
                   
                     734994
                  
                   
                     766512
                  
                   
                     798049
                  
                
                 
                   
                     170
                  
                   
                     26.829604
                  
                   
                     861177
                  
                   
                     892769
                  
                   
                     924380
                  
                   
                     956009
                  
                   
                     987657
                  
                   
                     019323
                  
                   
                     051008
                  
                   
                     082712
                  
                   
                     114432
                  
                
                 
                   
                     171
                  
                   
                     27.146174
                  
                   
                     177933
                  
                   
                     209711
                  
                   
                     241508
                  
                   
                     273322
                  
                   
                     305156
                  
                   
                     337008
                  
                   
                     368879
                  
                   
                     400768
                  
                   
                     432675
                  
                
                 
                   
                     172
                  
                   
                     27.464602
                  
                   
                     496547
                  
                   
                     528510
                  
                   
                     560492
                  
                   
                     592493
                  
                   
                     624512
                  
                   
                     656549
                  
                   
                     688606
                  
                   
                     720681
                  
                   
                     752774
                  
                
                 
                   
                     173
                  
                   
                     27.784886
                  
                   
                     817016
                  
                   
                     849166
                  
                   
                     881333
                  
                   
                     913520
                  
                   
                     945724
                  
                   
                     977948
                  
                   
                     010190
                  
                   
                     042450
                  
                   
                     074729
                  
                
                 
                   
                     174
                  
                   
                     28.107027
                  
                   
                     139343
                  
                   
                     171678
                  
                   
                     204031
                  
                   
                     236403
                  
                   
                     268794
                  
                   
                     301213
                  
                   
                     333630
                  
                   
                     366076
                  
                   
                     398541
                  
                
                 
                   
                     175
                  
                   
                     28.431025
                  
                   
                     463526
                  
                   
                     496047
                  
                   
                     528586
                  
                   
                     561142
                  
                   
                     593720
                  
                   
                     626314
                  
                   
                     658928
                  
                   
                     691559
                  
                   
                     724210
                  
                
                 
                   
                     176
                  
                   
                     28.756879
                  
                   
                     789566
                  
                   
                     822273
                  
                   
                     854997
                  
                   
                     881740
                  
                   
                     920502
                  
                   
                     953283
                  
                   
                     986082
                  
                   
                     018899
                  
                   
                     051735
                  
                
                 
                   
                     177
                  
                   
                     29.084590
                  
                   
                     117463
                  
                   
                     150355
                  
                   
                     183265
                  
                   
                     216194
                  
                   
                     249142
                  
                   
                     282108
                  
                   
                     315092
                  
                   
                     348096
                  
                   
                     381117
                  
                
                 
                   
                     178
                  
                   
                     29.414158
                  
                   
                     447217
                  
                   
                     480294
                  
                   
                     513390
                  
                   
                     546505
                  
                   
                     579638
                  
                   
                     612790
                  
                   
                     645960
                  
                   
                     679149
                  
                   
                     712356
                  
                
                 
                   
                     179
                  
                   
                     29.745582
                  
                   
                     778827
                  
                   
                     812090
                  
                   
                     845372
                  
                   
                     878672
                  
                   
                     919991
                  
                   
                     945328
                  
                   
                     978684
                  
                   
                     012059
                  
                   
                     045452
                  
                
                 
                   
                     180
                  
                   
                     30.078864
                  
                   
                     112294
                  
                   
                     145743
                  
                   
                     179210
                  
                   
                     212696
                  
                   
                     246200
                  
                   
                     279723
                  
                   
                     313265
                  
                   
                     346825
                  
                   
                     380404
                  
                
                 
                   
                     181
                  
                   
                     30.414001
                  
                   
                     447617
                  
                   
                     481252
                  
                   
                     514905
                  
                   
                     548577
                  
                   
                     582267
                  
                   
                     615975
                  
                   
                     649703
                  
                   
                     683449
                  
                   
                     717213
                  
                
                 
                   
                     182
                  
                   
                     30.750996
                  
                   
                     784798
                  
                   
                     818618
                  
                   
                     852457
                  
                   
                     886314
                  
                   
                     920190
                  
                   
                     954084
                  
                   
                     987997
                  
                   
                     021929
                  
                   
                     055879
                  
                
                 
                   
                     183
                  
                   
                     31.089848
                  
                   
                     123835
                  
                   
                     157841
                  
                   
                     192865
                  
                   
                     225908
                  
                   
                     252970
                  
                   
                     294050
                  
                   
                     328148
                  
                   
                     362265
                  
                   
                     396401
                  
                
                 
                   
                     184
                  
                   
                     31.430556
                  
                   
                     464729
                  
                   
                     498920
                  
                   
                     533130
                  
                   
                     567359
                  
                   
                     601606
                  
                   
                     635872
                  
                   
                     670156
                  
                   
                     704459
                  
                   
                     738780
                  
                
                 
                   
                     185
                  
                   
                     31.773121
                  
                   
                     807479
                  
                   
                     841856
                  
                   
                     876252
                  
                   
                     910666
                  
                   
                     945099
                  
                   
                     979551
                  
                   
                     014021
                  
                   
                     048509
                  
                   
                     083016
                  
                
                 
                   
                     186
                  
                   
                     32.117542
                  
                   
                     152086
                  
                   
                     186649
                  
                   
                     221231
                  
                   
                     255831
                  
                   
                     290449
                  
                   
                     325508
                  
                   
                     359742
                  
                   
                     394416
                  
                   
                     429109
                  
                
                 
                   
                     187
                  
                   
                     32.463820
                  
                   
                     498550
                  
                   
                     533299
                  
                   
                     568066
                  
                   
                     602892
                  
                   
                     637656
                  
                   
                     672479
                  
                   
                     707320
                  
                   
                     742180
                  
                   
                     777058
                  
                
                 
                   
                     188
                  
                   
                     32.811955
                  
                   
                     846871
                  
                   
                     881805
                  
                   
                     916758
                  
                   
                     951729
                  
                   
                     986719
                  
                   
                     021728
                  
                   
                     056755
                  
                   
                     091800
                  
                   
                     126864
                  
                
                 
                   
                     189
                  
                   
                     33.161947
                  
                   
                     197048
                  
                   
                     232168
                  
                   
                     267307
                  
                   
                     302464
                  
                   
                     337639
                  
                   
                     372833
                  
                   
                     408046
                  
                   
                     443277
                  
                   
                     478527
                  
                
                 
                   
                     190
                  
                   
                     33.513796
                  
                   
                     549082
                  
                   
                     584388
                  
                   
                     619712
                  
                   
                     655055
                  
                   
                     690416
                  
                   
                     725796
                  
                   
                     761194
                  
                   
                     796611
                  
                   
                     832047
                  
                
                 
                   
                     191
                  
                   
                     33.867501
                  
                   
                     902973
                  
                   
                     938464
                  
                   
                     973974
                  
                   
                     009503
                  
                   
                     045050
                  
                   
                     080615
                  
                   
                     116199
                  
                   
                     151802
                  
                   
                     187423
                  
                
                 
                   
                     192
                  
                   
                     34.223063
                  
                   
                     258721
                  
                   
                     294398
                  
                   
                     330093
                  
                   
                     365807
                  
                   
                     401540
                  
                   
                     437291
                  
                   
                     473061
                  
                   
                     508849
                  
                   
                     544656
                  
                
                 
                   
                     193
                  
                   
                     34.580481
                  
                   
                     616325
                  
                   
                     652188
                  
                   
                     688069
                  
                   
                     723968
                  
                   
                     759887
                  
                   
                     795824
                  
                   
                     831779
                  
                   
                     867753
                  
                   
                     903745
                  
                
                 
                   
                     194
                  
                   
                     34.939756
                  
                   
                     975786
                  
                   
                     011834
                  
                   
                     047901
                  
                   
                     083986
                  
                   
                     120090
                  
                   
                     156213
                  
                   
                     192354
                  
                   
                     228514
                  
                   
                     264692
                  
                
                 
                   
                     195
                  
                   
                     35.300889
                  
                   
                     337104
                  
                   
                     373338
                  
                   
                     409590
                  
                   
                     445861
                  
                   
                     482151
                  
                   
                     518459
                  
                   
                     554786
                  
                   
                     591131
                  
                   
                     627495
                  
                
                 
                   
                     196
                  
                   
                     35.663877
                  
                   
                     700278
                  
                   
                     736698
                  
                   
                     773136
                  
                   
                     809593
                  
                   
                     846068
                  
                   
                     882562
                  
                   
                     919074
                  
                   
                     955605
                  
                   
                     992155
                  
                
                 
                   
                     197
                  
                   
                     36.028723
                  
                   
                     065309
                  
                   
                     101915
                  
                   
                     138538
                  
                   
                     175181
                  
                   
                     211842
                  
                   
                     248521
                  
                   
                     285219
                  
                   
                     321936
                  
                   
                     358671
                  
                
                 
                   
                     198
                  
                   
                     36.395425
                  
                   
                     432197
                  
                   
                     468988
                  
                   
                     505798
                  
                   
                     542626
                  
                   
                     579472
                  
                   
                     616337
                  
                   
                     653221
                  
                   
                     690124
                  
                   
                     727044
                  
                
                 
                   
                     199
                  
                   
                     36.763984
                  
                   
                     800942
                  
                   
                     837918
                  
                   
                     874914
                  
                   
                     911927
                  
                   
                     948960
                  
                   
                     986010
                  
                   
                     023080
                  
                   
                     060168
                  
                   
                     097274
                  
                
                 
                   
                     200
                  
                   
                     37.134400
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                
              
            
             
             
               
                 
                   
                      
                  
                   
                     0
                  
                   
                     1
                  
                   
                     2
                  
                   
                     3
                  
                   
                     4
                  
                   
                     5
                  
                   
                     6
                  
                   
                     7
                  
                   
                     8
                  
                   
                     9
                  
                
                 
                   
                     01
                  
                   
                     0.002617
                  
                   
                     003167
                  
                   
                     003769
                  
                   
                     004424
                  
                   
                     005131
                  
                   
                     005890
                  
                   
                     006702
                  
                   
                     007566
                  
                   
                     008482
                  
                   
                     009450
                  
                
                 
                   
                     02
                  
                   
                     0.010471
                  
                   
                     011545
                  
                   
                     012671
                  
                   
                     013849
                  
                   
                     015079
                  
                   
                     016362
                  
                   
                     017697
                  
                   
                     019085
                  
                   
                     020525
                  
                   
                     022017
                  
                
                 
                   
                     03
                  
                   
                     0.023561
                  
                   
                     025158
                  
                   
                     026808
                  
                   
                     028509
                  
                   
                     030264
                  
                   
                     032070
                  
                   
                     033929
                  
                   
                     035840
                  
                   
                     037803
                  
                   
                     039819
                  
                
                 
                   
                     04
                  
                   
                     0.041887
                  
                   
                     044008
                  
                   
                     046181
                  
                   
                     048406
                  
                   
                     050684
                  
                   
                     053014
                  
                   
                     055396
                  
                   
                     057831
                  
                   
                     060318
                  
                   
                     062858
                  
                
                 
                   
                     05
                  
                   
                     0.065449
                  
                   
                     068093
                  
                   
                     070790
                  
                   
                     073539
                  
                   
                     076340
                  
                   
                     079194
                  
                   
                     082100
                  
                   
                     085058
                  
                   
                     088069
                  
                   
                     091132
                  
                
                 
                   
                     06
                  
                   
                     0.094247
                  
                   
                     097415
                  
                   
                     100635
                  
                   
                     103908
                  
                   
                     107232
                  
                   
                     110610
                  
                   
                     114039
                  
                   
                     117521
                  
                   
                     121055
                  
                   
                     124642
                  
                
                 
                   
                     07
                  
                   
                     0.128281
                  
                   
                     131973
                  
                   
                     135716
                  
                   
                     139512
                  
                   
                     143361
                  
                   
                     147262
                  
                   
                     151215
                  
                   
                     155220
                  
                   
                     159278
                  
                   
                     163388
                  
                
                 
                   
                     08
                  
                   
                     0.167551
                  
                   
                     171766
                  
                   
                     176033
                  
                   
                     180353
                  
                   
                     184725
                  
                   
                     189149
                  
                   
                     193626
                  
                   
                     198155
                  
                   
                     202737
                  
                   
                     207371
                  
                
                 
                   
                     09
                  
                   
                     0.212057
                  
                   
                     216796
                  
                   
                     221586
                  
                   
                     226430
                  
                   
                     231325
                  
                   
                     236273
                  
                   
                     241274
                  
                   
                     246326
                  
                   
                     251432
                  
                   
                     256589
                  
                
                 
                   
                     1.0
                  
                   
                     0.261799
                  
                   
                     267061
                  
                   
                     272376
                  
                   
                     277742
                  
                   
                     283162
                  
                   
                     288633
                  
                   
                     294157
                  
                   
                     299734
                  
                   
                     305362
                  
                   
                     311043
                  
                
                 
                   
                     1.1
                  
                   
                     0.316777
                  
                   
                     322563
                  
                   
                     328401
                  
                   
                     334291
                  
                   
                     340234
                  
                   
                     346229
                  
                   
                     352277
                  
                   
                     358377
                  
                   
                     364529
                  
                   
                     370734
                  
                
                 
                   
                     1.2
                  
                   
                     0.376991
                  
                   
                     383300
                  
                   
                     389662
                  
                   
                     396076
                  
                   
                     402542
                  
                   
                     409061
                  
                   
                     415632
                  
                   
                     422256
                  
                   
                     482932
                  
                   
                     435660
                  
                
                 
                   
                     1.3
                  
                   
                     0.442440
                  
                   
                     449273
                  
                   
                     456159
                  
                   
                     463096
                  
                   
                     470086
                  
                   
                     477129
                  
                   
                     484224
                  
                   
                     491371
                  
                   
                     498570
                  
                   
                     505822
                  
                
                 
                   
                     1.4
                  
                   
                     0.513126
                  
                   
                     520483
                  
                   
                     527892
                  
                   
                     535353
                  
                   
                     542867
                  
                   
                     550433
                  
                   
                     558051
                  
                   
                     565722
                  
                   
                     573445
                  
                   
                     581220
                  
                
                 
                   
                     1.5
                  
                   
                     0.589048
                  
                   
                     596928
                  
                   
                     604861
                  
                   
                     612846
                  
                   
                     620883
                  
                   
                     628973
                  
                   
                     637114
                  
                   
                     645309
                  
                   
                     653555
                  
                   
                     661855
                  
                
                 
                   
                     1.6
                  
                   
                     0.670206
                  
                   
                     678610
                  
                   
                     687066
                  
                   
                     695574
                  
                   
                     704135
                  
                   
                     712748
                  
                   
                     721414
                  
                   
                     730132
                  
                   
                     738902
                  
                   
                     747725
                  
                
                 
                   
                     1.7
                  
                   
                     0.756600
                  
                   
                     765527
                  
                   
                     774507
                  
                   
                     783539
                  
                   
                     792623
                  
                   
                     801760
                  
                   
                     810949
                  
                   
                     820191
                  
                   
                     829485
                  
                   
                     838831
                  
                
                 
                   
                     1.8
                  
                   
                     0.848230
                  
                   
                     857680
                  
                   
                     867184
                  
                   
                     876739
                  
                   
                     886348
                  
                   
                     896008
                  
                   
                     905721
                  
                   
                     915486
                  
                   
                     925303
                  
                   
                     935173
                  
                
                 
                   
                     1.9
                  
                   
                     0.945097
                  
                   
                     955070
                  
                   
                     965097
                  
                   
                     975176
                  
                   
                     985308
                  
                   
                     995492
                  
                   
                     005728
                  
                   
                     016017
                  
                   
                     026358
                  
                   
                     036751
                  
                
                 
                   
                     2.0
                  
                   
                     1.047197
                  
                   
                     057695
                  
                   
                     068246
                  
                   
                     078849
                  
                   
                     089504
                  
                   
                     100211
                  
                   
                     110971
                  
                   
                     121784
                  
                   
                     132648
                  
                   
                     143565
                  
                
                 
                   
                     2.1
                  
                   
                     1.154535
                  
                   
                     165557
                  
                   
                     176631
                  
                   
                     187757
                  
                   
                     198936
                  
                   
                     210167
                  
                   
                     221451
                  
                   
                     232787
                  
                   
                     244175
                  
                   
                     255616
                  
                
                 
                   
                     2.2
                  
                   
                     1.267109
                  
                   
                     278654
                  
                   
                     290252
                  
                   
                     301902
                  
                   
                     313604
                  
                   
                     325359
                  
                   
                     337166
                  
                   
                     349026
                  
                   
                     360937
                  
                   
                     372902
                  
                
                 
                   
                     2.3
                  
                   
                     1.384918
                  
                   
                     396987
                  
                   
                     409109
                  
                   
                     421282
                  
                   
                     433508
                  
                   
                     445787
                  
                   
                     458117
                  
                   
                     470500
                  
                   
                     482936
                  
                   
                     495424
                  
                
                 
                   
                     2.4
                  
                   
                     1.507964
                  
                   
                     520557
                  
                   
                     533201
                  
                   
                     545899
                  
                   
                     558648
                  
                   
                     571450
                  
                   
                     584305
                  
                   
                     597211
                  
                   
                     610170
                  
                   
                     623182
                  
                
                 
                   
                     2.5
                  
                   
                     1.636246
                  
                   
                     649362
                  
                   
                     662530
                  
                   
                     675751
                  
                   
                     689024
                  
                   
                     702350
                  
                   
                     715728
                  
                   
                     729158
                  
                   
                     742641
                  
                   
                     756176
                  
                
                 
                   
                     2.6
                  
                   
                     1.769763
                  
                   
                     783403
                  
                   
                     797095
                  
                   
                     810840
                  
                   
                     824637
                  
                   
                     838486
                  
                   
                     852387
                  
                   
                     866341
                  
                   
                     880347
                  
                   
                     894406
                  
                
                 
                   
                     2.7
                  
                   
                     1.908517
                  
                   
                     922680
                  
                   
                     036896
                  
                   
                     951164
                  
                   
                     965485
                  
                   
                     979857
                  
                   
                     994283
                  
                   
                     008760
                  
                   
                     023290
                  
                   
                     037872
                  
                
                 
                   
                     2.8
                  
                   
                     2.052507
                  
                   
                     067194
                  
                   
                     081933
                  
                   
                     096725
                  
                   
                     111569
                  
                   
                     126465
                  
                   
                     141414
                  
                   
                     156415
                  
                   
                     171468
                  
                   
                     186574
                  
                
                 
                   
                     2.9
                  
                   
                     2.201732
                  
                   
                     216943
                  
                   
                     232206
                  
                   
                     247521
                  
                   
                     262889
                  
                   
                     278309
                  
                   
                     293781
                  
                   
                     309306
                  
                   
                     324883
                  
                   
                     340512
                  
                
                 
                   
                     3.0
                  
                   
                     2.356194
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                
              
            
             
             
               
                 
                   
                      
                  
                   
                     0
                  
                   
                     1
                  
                   
                     2
                  
                   
                     3
                  
                   
                     4
                  
                   
                     5
                  
                   
                     6
                  
                   
                     7
                  
                   
                     8
                  
                   
                     9
                  
                
                 
                   
                     10
                  
                   
                     0.314159
                  
                   
                     345575
                  
                   
                     376991
                  
                   
                     408407
                  
                   
                     439822
                  
                   
                     471238
                  
                   
                     502654
                  
                   
                     534070
                  
                   
                     565486
                  
                   
                     596902
                  
                
                 
                   
                     20
                  
                   
                     0.628318
                  
                   
                     659734
                  
                   
                     691150
                  
                   
                     722566
                  
                   
                     753982
                  
                   
                     785398
                  
                   
                     816814
                  
                   
                     848230
                  
                   
                     879645
                  
                   
                     911061
                  
                
                 
                   
                     30
                  
                   
                     0.942477
                  
                   
                     974893
                  
                   
                     006309
                  
                   
                     037725
                  
                   
                     069148
                  
                   
                     100557
                  
                   
                     131973
                  
                   
                     162389
                  
                   
                     193805
                  
                   
                     225221
                  
                
                 
                   
                     40
                  
                   
                     1.256637
                  
                   
                     288052
                  
                   
                     319468
                  
                   
                     350884
                  
                   
                     382300
                  
                   
                     413716
                  
                   
                     445132
                  
                   
                     476548
                  
                   
                     507964
                  
                   
                     539380
                  
                
                 
                   
                     50
                  
                   
                     1.570796
                  
                   
                     602212
                  
                   
                     633628
                  
                   
                     665044
                  
                   
                     696460
                  
                   
                     727875
                  
                   
                     759291
                  
                   
                     790707
                  
                   
                     822123
                  
                   
                     853539
                  
                
                 
                   
                     60
                  
                   
                     1.884955
                  
                   
                     916371
                  
                   
                     947787
                  
                   
                     979203
                  
                   
                     010619
                  
                   
                     042035
                  
                   
                     073451
                  
                   
                     104867
                  
                   
                     136283
                  
                   
                     167698
                  
                
                 
                   
                     70
                  
                   
                     2.199114
                  
                   
                     230530
                  
                   
                     261946
                  
                   
                     293362
                  
                   
                     324778
                  
                   
                     356194
                  
                   
                     387610
                  
                   
                     419026
                  
                   
                     450442
                  
                   
                     481858
                  
                
                 
                   
                     80
                  
                   
                     2.513274
                  
                   
                     544690
                  
                   
                     576105
                  
                   
                     607521
                  
                   
                     638937
                  
                   
                     670353
                  
                   
                     701769
                  
                   
                     733185
                  
                   
                     764601
                  
                   
                     796017
                  
                
                 
                   
                     90
                  
                   
                     2.827433
                  
                   
                     858849
                  
                   
                     890265
                  
                   
                     921681
                  
                   
                     953097
                  
                   
                     984513
                  
                   
                     015928
                  
                   
                     047344
                  
                   
                     078760
                  
                   
                     110176
                  
                
                 
                   
                     1.00
                  
                   
                     3.141592
                  
                   
                     173008
                  
                   
                     204424
                  
                   
                     235840
                  
                   
                     267256
                  
                   
                     298672
                  
                   
                     330088
                  
                   
                     361504
                  
                   
                     392920
                  
                   
                     424335
                  
                
                 
                   
                     10
                  
                   
                     3.455751
                  
                   
                     487167
                  
                   
                     518583
                  
                   
                     549999
                  
                   
                     581415
                  
                   
                     613831
                  
                   
                     644247
                  
                   
                     675663
                  
                   
                     707079
                  
                   
                     738495
                  
                
                 
                   
                     20
                  
                   
                     3.769911
                  
                   
                     801327
                  
                   
                     832743
                  
                   
                     864158
                  
                   
                     895574
                  
                   
                     926990
                  
                   
                     958406
                  
                   
                     989822
                  
                   
                     021238
                  
                   
                     052654
                  
                
                 
                   
                     30
                  
                   
                     4.084070
                  
                   
                     115486
                  
                   
                     146902
                  
                   
                     178318
                  
                   
                     209734
                  
                   
                     241150
                  
                   
                     272566
                  
                   
                     303981
                  
                   
                     335397
                  
                   
                     366813
                  
                
                 
                   
                     40
                  
                   
                     4.398229
                  
                   
                     429645
                  
                   
                     461061
                  
                   
                     492477
                  
                   
                     523893
                  
                   
                     555309
                  
                   
                     586725
                  
                   
                     618141
                  
                   
                     649557
                  
                   
                     680973
                  
                
                 
                   
                     50
                  
                   
                     4.712388
                  
                   
                     743804
                  
                   
                     775220
                  
                   
                     806636
                  
                   
                     838052
                  
                   
                     869468
                  
                   
                     900884
                  
                   
                     932300
                  
                   
                     963716
                  
                   
                     995132
                  
                
                 
                   
                     60
                  
                   
                     5.026548
                  
                   
                     057964
                  
                   
                     089380
                  
                   
                     120796
                  
                   
                     152211
                  
                   
                     183627
                  
                   
                     215043
                  
                   
                     246459
                  
                   
                     277875
                  
                   
                     309291
                  
                
                 
                   
                     70
                  
                   
                     5.340707
                  
                   
                     372123
                  
                   
                     403539
                  
                   
                     434945
                  
                   
                     466371
                  
                   
                     497787
                  
                   
                     529203
                  
                   
                     560618
                  
                   
                     592034
                  
                   
                     623450
                  
                
                 
                   
                     80
                  
                   
                     5.654866
                  
                   
                     686282
                  
                   
                     717698
                  
                   
                     749144
                  
                   
                     780530
                  
                   
                     811946
                  
                   
                     843362
                  
                   
                     874778
                  
                   
                     906194
                  
                   
                     937610
                  
                
                 
                   
                     90
                  
                   
                     5.969026
                  
                   
                     000441
                  
                   
                     031857
                  
                   
                     063273
                  
                   
                     094689
                  
                   
                     126105
                  
                   
                     157521
                  
                   
                     188937
                  
                   
                     220353
                  
                   
                     251769
                  
                
                 
                   
                     2.00
                  
                   
                     6.283105
                  
                   
                     314601
                  
                   
                     346017
                  
                   
                     377433
                  
                   
                     408849
                  
                   
                     440264
                  
                   
                     471689
                  
                   
                     503096
                  
                   
                     534512
                  
                   
                     565928
                  
                
                 
                   
                     10
                  
                   
                     6.597344
                  
                   
                     628760
                  
                   
                     660176
                  
                   
                     691592
                  
                   
                     723008
                  
                   
                     754424
                  
                   
                     785840
                  
                   
                     817256
                  
                   
                     848671
                  
                   
                     880087
                  
                
                 
                   
                     20
                  
                   
                     6.911503
                  
                   
                     942919
                  
                   
                     974336
                  
                   
                     005751
                  
                   
                     037167
                  
                   
                     068583
                  
                   
                     099999
                  
                   
                     131415
                  
                   
                     162831
                  
                   
                     194247
                  
                
                 
                   
                     30
                  
                   
                     7.225663
                  
                   
                     257079
                  
                   
                     288494
                  
                   
                     319910
                  
                   
                     351326
                  
                   
                     382742
                  
                   
                     414158
                  
                   
                     445574
                  
                   
                     476990
                  
                   
                     508406
                  
                
                 
                   
                     40
                  
                   
                     7.539822
                  
                   
                     571238
                  
                   
                     602654
                  
                   
                     634070
                  
                   
                     665486
                  
                   
                     696901
                  
                   
                     728317
                  
                   
                     759733
                  
                   
                     791149
                  
                   
                     822565
                  
                
                 
                   
                     50
                  
                   
                     7.853981
                  
                   
                     885397
                  
                   
                     916813
                  
                   
                     948229
                  
                   
                     979645
                  
                   
                     011061
                  
                   
                     042477
                  
                   
                     073893
                  
                   
                     105309
                  
                   
                     136724
                  
                
                 
                   
                     60
                  
                   
                     8.168140
                  
                   
                     199556
                  
                   
                     230972
                  
                   
                     262388
                  
                   
                     293804
                  
                   
                     325220
                  
                   
                     356636
                  
                   
                     388052
                  
                   
                     419468
                  
                   
                     450884
                  
                
                 
                   
                     70
                  
                   
                     8.482300
                  
                   
                     513716
                  
                   
                     545132
                  
                   
                     576547
                  
                   
                     607963
                  
                   
                     639379
                  
                   
                     670795
                  
                   
                     702211
                  
                   
                     733627
                  
                   
                     765043
                  
                
                 
                   
                     80
                  
                   
                     8.796458
                  
                   
                     827875
                  
                   
                     859291
                  
                   
                     890707
                  
                   
                     922123
                  
                   
                     953539
                  
                   
                     984954
                  
                   
                     016370
                  
                   
                     047786
                  
                   
                     079202
                  
                
                 
                   
                     90
                  
                   
                     9.110618
                  
                   
                     142034
                  
                   
                     173450
                  
                   
                     204866
                  
                   
                     236282
                  
                   
                     267798
                  
                   
                     299114
                  
                   
                     330530
                  
                   
                     361946
                  
                   
                     393362
                  
                
                 
                   
                     3.00
                  
                   
                     9.424777
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                
              
            
             
             
               
                 
                   
                      
                  
                   
                     Natural
                  
                   
                     Artificial
                  
                
                 
                   
                     0.01
                  
                   
                     0.000002
                  
                   
                     4.423668
                  
                
                 
                   
                     .02
                  
                   
                     0.000010
                  
                   
                     5.025728
                  
                
                 
                   
                     .03
                  
                   
                     0.000023
                  
                   
                     5.377911
                  
                
                 
                   
                     .04
                  
                   
                     0.000042
                  
                   
                     5.627788
                  
                
                 
                   
                     0.05
                  
                   
                     0.000066
                  
                   
                     5.821608
                  
                
                 
                   
                     .06
                  
                   
                     0.000092
                  
                   
                     5.979971
                  
                
                 
                   
                     .07
                  
                   
                     0.000129
                  
                   
                     6.113864
                  
                
                 
                   
                     .08
                  
                   
                     0.000169
                  
                   
                     6.229848
                  
                
                 
                   
                     .09
                  
                   
                     0.000214
                  
                   
                     6.332153
                  
                
                 
                   
                     0.10
                  
                   
                     0.000265
                  
                   
                     6.423668
                  
                
                 
                   
                     .11
                  
                   
                     0.000320
                  
                   
                     6.506454
                  
                
                 
                   
                     .12
                  
                   
                     0.000382
                  
                   
                     6.582031
                  
                
                 
                   
                     .13
                  
                   
                     0.000448
                  
                   
                     6.651555
                  
                
                 
                   
                     .14
                  
                   
                     0.000519
                  
                   
                     6.715924
                  
                
                 
                   
                     0.15
                  
                   
                     0.000596
                  
                   
                     6.775851
                  
                
                 
                   
                     .16
                  
                   
                     0.000679
                  
                   
                     6.831908
                  
                
                 
                   
                     .17
                  
                   
                     0.000766
                  
                   
                     6.884566
                  
                
                 
                   
                     .18
                  
                   
                     0.000859
                  
                   
                     6.934213
                  
                
                 
                   
                     .19
                  
                   
                     0.000957
                  
                   
                     6.981176
                  
                
                 
                   
                     0.20
                  
                   
                     0.001061
                  
                   
                     7.025728
                  
                
                 
                   
                     .21
                  
                   
                     0.001169
                  
                   
                     7.068107
                  
                
                 
                   
                     .22
                  
                   
                     0.001283
                  
                   
                     7.108514
                  
                
                 
                   
                     .23
                  
                   
                     0.001403
                  
                   
                     7.147124
                  
                
                 
                   
                     .24
                  
                   
                     0.001527
                  
                   
                     7.184091
                  
                
                 
                   
                     0.25
                  
                   
                     0.001657
                  
                   
                     7.219548
                  
                
                 
                   
                     .26
                  
                   
                     0.001793
                  
                   
                     7.253615
                  
                
                 
                   
                     .27
                  
                   
                     0.001933
                  
                   
                     7.286396
                  
                
                 
                   
                     .28
                  
                   
                     0.002012
                  
                   
                     7.317984
                  
                
                 
                   
                     .29
                  
                   
                     0.002230
                  
                   
                     7.348464
                  
                
                 
                   
                     0.30
                  
                   
                     0.002353
                  
                   
                     7.377911
                  
                
                 
                   
                     .31
                  
                   
                     0.002549
                  
                   
                     7.406392
                  
                
                 
                   
                     .32
                  
                   
                     0.002716
                  
                   
                     7.433968
                  
                
                 
                   
                     .
                     3●
                  
                   
                     0.002888
                  
                   
                     7.460695
                  
                
                 
                   
                     .
                     3●
                  
                   
                     0.003066
                  
                   
                     7.486626
                  
                
                 
                   
                     0.35
                  
                   
                     0.003249
                  
                   
                     7.511804
                  
                
                 
                   
                     0.36
                  
                   
                     0.003437
                  
                   
                     7.536273
                  
                
                 
                   
                     0.37
                  
                   
                     0.003631
                  
                   
                     7.560071
                  
                
                 
                   
                     0.38
                  
                   
                     0.003830
                  
                   
                     7.583236
                  
                
                 
                   
                     0.39
                  
                   
                     0.004034
                  
                   
                     7.605798
                  
                
                 
                   
                     0.40
                  
                   
                     0.004244
                  
                   
                     7.627788
                  
                
                 
                   
                     0.41
                  
                   
                     0.004458
                  
                   
                     7.649236
                  
                
                 
                   
                     0.42
                  
                   
                     0.004679
                  
                   
                     7.670167
                  
                
                 
                   
                     0.43
                  
                   
                     0.004904
                  
                   
                     7.690605
                  
                
                 
                   
                     0.44
                  
                   
                     0.005135
                  
                   
                     7.710574
                  
                
                 
                   
                     0.45
                  
                   
                     0.005371
                  
                   
                     7.730093
                  
                
                 
                   
                     0.46
                  
                   
                     0.005612
                  
                   
                     7.749184
                  
                
                 
                   
                     0.47
                  
                   
                     0.005892
                  
                   
                     7.767864
                  
                
                 
                   
                     0.48
                  
                   
                     0.006111
                  
                   
                     7.786151
                  
                
                 
                   
                     0.49
                  
                   
                     0.006368
                  
                   
                     7.804060
                  
                
                 
                   
                     0.50
                  
                   
                     0.006631
                  
                   
                     7.821608
                  
                
                 
                   
                     0.51
                  
                   
                     0.006899
                  
                   
                     7.838809
                  
                
                 
                   
                     0.52
                  
                   
                     0.007172
                  
                   
                     7.855675
                  
                
                 
                   
                     0.53
                  
                   
                     0.007451
                  
                   
                     7.872220
                  
                
                 
                   
                     0.54
                  
                   
                     0.007734
                  
                   
                     7.888456
                  
                
                 
                   
                     0.55
                  
                   
                     0.008024
                  
                   
                     7.905394
                  
                
                 
                   
                     0.56
                  
                   
                     0.008318
                  
                   
                     7.720044
                  
                
                 
                   
                     0.57
                  
                   
                     0.008618
                  
                   
                     7.935418
                  
                
                 
                   
                     0.58
                  
                   
                     0.008923
                  
                   
                     7.950524
                  
                
                 
                   
                     0.59
                  
                   
                     0.009233
                  
                   
                     7.965372
                  
                
                 
                   
                     0.60
                  
                   
                     0.009549
                  
                   
                     7.979971
                  
                
                 
                   
                     0.61
                  
                   
                     0.009870
                  
                   
                     7.994328
                  
                
                 
                   
                     0.62
                  
                   
                     0.010196
                  
                   
                     8.008452
                  
                
                 
                   
                     0.63
                  
                   
                     0.010528
                  
                   
                     8.022358
                  
                
                 
                   
                     0.64
                  
                   
                     0.010864
                  
                   
                     8.036028
                  
                
                 
                   
                     0.65
                  
                   
                     0.011207
                  
                   
                     8.049495
                  
                
                 
                   
                     0.66
                  
                   
                     0
                     .
                     01155●
                  
                   
                     8.062756
                  
                
                 
                   
                     0.67
                  
                   
                     0.011907
                  
                   
                     8.075818
                  
                
                 
                   
                     0.68
                  
                   
                     0.012265
                  
                   
                     8.088686
                  
                
                 
                   
                     0.69
                  
                   
                     0.012628
                  
                   
                     8.101367
                  
                
                 
                   
                     0.70
                  
                   
                     0.012997
                  
                   
                     8.113864
                  
                
                 
                   
                     
                     0.71
                  
                   
                     0.013371
                  
                   
                     8.126175
                  
                
                 
                   
                     0.72
                  
                   
                     0.013750
                  
                   
                     8.138333
                  
                
                 
                   
                     0.73
                  
                   
                     0.014135
                  
                   
                     8.150314
                  
                
                 
                   
                     0.74
                  
                   
                     0.014525
                  
                   
                     8.162132
                  
                
                 
                   
                     0.75
                  
                   
                     0.014920
                  
                   
                     8.173791
                  
                
                 
                   
                     0.76
                  
                   
                     0.015321
                  
                   
                     8.185296
                  
                
                 
                   
                     0.77
                  
                   
                     0.015727
                  
                   
                     8.190991
                  
                
                 
                   
                     0.78
                  
                   
                     0.016138
                  
                   
                     8.207858
                  
                
                 
                   
                     0.79
                  
                   
                     0.016554
                  
                   
                     8.218927
                  
                
                 
                   
                     0.80
                  
                   
                     0.016976
                  
                   
                     8.229848
                  
                
                 
                   
                     0.81
                  
                   
                     0.017403
                  
                   
                     8.240638
                  
                
                 
                   
                     0.81
                  
                   
                     0.017835
                  
                   
                     8.251296
                  
                
                 
                   
                     0.83
                  
                   
                     0.018273
                  
                   
                     7.261825
                  
                
                 
                   
                     0.84
                  
                   
                     0.018716
                  
                   
                     8.272227
                  
                
                 
                   
                     0.85
                  
                   
                     0.019164
                  
                   
                     8.282506
                  
                
                 
                   
                     0.86
                  
                   
                     0.019618
                  
                   
                     8.292665
                  
                
                 
                   
                     0.87
                  
                   
                     0.020077
                  
                   
                     8.302707
                  
                
                 
                   
                     0.88
                  
                   
                     0.020541
                  
                   
                     8.312634
                  
                
                 
                   
                     0.89
                  
                   
                     0.021011
                  
                   
                     8.312448
                  
                
                 
                   
                     0.90
                  
                   
                     0.021489
                  
                   
                     8.332153
                  
                
                 
                   
                     0.91
                  
                   
                     0.021999
                  
                   
                     8.341751
                  
                
                 
                   
                     0.92
                  
                   
                     0.022451
                  
                   
                     8.351244
                  
                
                 
                   
                     0.93
                  
                   
                     0.022942
                  
                   
                     8.360634
                  
                
                 
                   
                     0.94
                  
                   
                     0.023438
                  
                   
                     8.369924
                  
                
                 
                   
                     0.95
                  
                   
                     0.023939
                  
                   
                     8.379116
                  
                
                 
                   
                     0.96
                  
                   
                     0.024446
                  
                   
                     8.388211
                  
                
                 
                   
                     0.97
                  
                   
                     0
                     .
                     02495●
                  
                   
                     8.397212
                  
                
                 
                   
                     0.98
                  
                   
                     0.025475
                  
                   
                     8.406121
                  
                
                 
                   
                     0.99
                  
                   
                     0.025997
                  
                   
                     8.414939
                  
                
                 
                   
                     1.00
                  
                   
                     0.026529
                  
                   
                     8.423668
                  
                
                 
                   
                     1.01
                  
                   
                     0.027058
                  
                   
                     8.432311
                  
                
                 
                   
                     1.02
                  
                   
                     0.027597
                  
                   
                     8.442369
                  
                
                 
                   
                     1.03
                  
                   
                     0.028141
                  
                   
                     8.449343
                  
                
                 
                   
                     1.04
                  
                   
                     0.028690
                  
                   
                     8.456735
                  
                
                 
                   
                     1.05
                  
                   
                     0
                     .
                     029●44
                  
                   
                     8.466047
                  
                
                 
                   
                     1.06
                  
                   
                     0.029804
                  
                   
                     8.474280
                  
                
                 
                   
                     1.07
                  
                   
                     0.030369
                  
                   
                     8.482437
                  
                
                 
                   
                     1.08
                  
                   
                     0.030939
                  
                   
                     8.490516
                  
                
                 
                   
                     1.09
                  
                   
                     0.031515
                  
                   
                     8.498521
                  
                
                 
                   
                     1.10
                  
                   
                     0.032096
                  
                   
                     8.506454
                  
                
                 
                   
                     1.11
                  
                   
                     0.032682
                  
                   
                     8.514314
                  
                
                 
                   
                     1.12
                  
                   
                     0.033273
                  
                   
                     8.522104
                  
                
                 
                   
                     1.13
                  
                   
                     0.033870
                  
                   
                     8.528825
                  
                
                 
                   
                     1.14
                  
                   
                     0.034472
                  
                   
                     8.537478
                  
                
                 
                   
                     1.15
                  
                   
                     0.035080
                  
                   
                     8.545064
                  
                
                 
                   
                     1.16
                  
                   
                     0.035697
                  
                   
                     8.552584
                  
                
                 
                   
                     1.17
                  
                   
                     0.036324
                  
                   
                     8.560040
                  
                
                 
                   
                     1.18
                  
                   
                     0.036934
                  
                   
                     8.567432
                  
                
                 
                   
                     1.19
                  
                   
                     0.037563
                  
                   
                     8.574762
                  
                
                 
                   
                     1.20
                  
                   
                     0.038197
                  
                   
                     8.582031
                  
                
                 
                   
                     1.21
                  
                   
                     0.038836
                  
                   
                     8.589239
                  
                
                 
                   
                     1.22
                  
                   
                     0.039481
                  
                   
                     8.596388
                  
                
                 
                   
                     1.23
                  
                   
                     0.040130
                  
                   
                     8.603471
                  
                
                 
                   
                     1.24
                  
                   
                     0.040786
                  
                   
                     8.610512
                  
                
                 
                   
                     1.25
                  
                   
                     0.041446
                  
                   
                     8
                     .
                     61●488
                  
                
                 
                   
                     1.26
                  
                   
                     0.042112
                  
                   
                     8.624410
                  
                
                 
                   
                     1.27
                  
                   
                     0.042783
                  
                   
                     8.631276
                  
                
                 
                   
                     1.28
                  
                   
                     0.043459
                  
                   
                     8.638088
                  
                
                 
                   
                     1.29
                  
                   
                     0.044141
                  
                   
                     8.644848
                  
                
                 
                   
                     1.30
                  
                   
                     0.044828
                  
                   
                     8.651555
                  
                
                 
                   
                     1.31
                  
                   
                     0.045520
                  
                   
                     8.658211
                  
                
                 
                   
                     1.31
                  
                   
                     0.046218
                  
                   
                     8.664816
                  
                
                 
                   
                     1.33
                  
                   
                     0.046921
                  
                   
                     8.671372
                  
                
                 
                   
                     1.34
                  
                   
                     0.047629
                  
                   
                     8.677878
                  
                
                 
                   
                     1.35
                  
                   
                     0.048343
                  
                   
                     8.684336
                  
                
                 
                   
                     1.36
                  
                   
                     0.049062
                  
                   
                     8.689746
                  
                
                 
                   
                     1.37
                  
                   
                     0.049786
                  
                   
                     8.697110
                  
                
                 
                   
                     1.38
                  
                   
                     0.050515
                  
                   
                     8.703427
                  
                
                 
                   
                     1.39
                  
                   
                     0.051250
                  
                   
                     8.709698
                  
                
                 
                   
                     1.40
                  
                   
                     0.051990
                  
                   
                     8
                     .
                     7●5924
                  
                
                 
                   
                     
                     1.41
                  
                   
                     0.052735
                  
                   
                     8.722107
                  
                
                 
                   
                     1.42
                  
                   
                     0.053453
                  
                   
                     8.728245
                  
                
                 
                   
                     1.43
                  
                   
                     0.054242
                  
                   
                     8.734340
                  
                
                 
                   
                     1.44
                  
                   
                     0.054007
                  
                   
                     8.740393
                  
                
                 
                   
                     1.45
                  
                   
                     0.055770
                  
                   
                     8.746404
                  
                
                 
                   
                     1.46
                  
                   
                     0.056542
                  
                   
                     8.752374
                  
                
                 
                   
                     1.47
                  
                   
                     0.057319
                  
                   
                     8.758303
                  
                
                 
                   
                     1.48
                  
                   
                     0.058102
                  
                   
                     8.764192
                  
                
                 
                   
                     1.49
                  
                   
                     0.058889
                  
                   
                     8.770071
                  
                
                 
                   
                     1.50
                  
                   
                     0.059687
                  
                   
                     8.775851
                  
                
                 
                   
                     1.51
                  
                   
                     0.060481
                  
                   
                     8.781622
                  
                
                 
                   
                     1.52
                  
                   
                     0.061285
                  
                   
                     8.793356
                  
                
                 
                   
                     1.53
                  
                   
                     0.062094
                  
                   
                     8.793051
                  
                
                 
                   
                     1.54
                  
                   
                     0.062908
                  
                   
                     8.798710
                  
                
                 
                   
                     1.55
                  
                   
                     0.063728
                  
                   
                     8.804332
                  
                
                 
                   
                     1.56
                  
                   
                     0.064556
                  
                   
                     8.809918
                  
                
                 
                   
                     1.57
                  
                   
                     0.065383
                  
                   
                     8.815468
                  
                
                 
                   
                     1.58
                  
                   
                     0.066219
                  
                   
                     8.820983
                  
                
                 
                   
                     1.59
                  
                   
                     0.067059
                  
                   
                     8.826463
                  
                
                 
                   
                     1.60
                  
                   
                     0.067906
                  
                   
                     8.831908
                  
                
                 
                   
                     1.61
                  
                   
                     0.068754
                  
                   
                     8.837320
                  
                
                 
                   
                     1.62
                  
                   
                     0.069614
                  
                   
                     8.842698
                  
                
                 
                   
                     1.63
                  
                   
                     0.070476
                  
                   
                     8.848044
                  
                
                 
                   
                     1.64
                  
                   
                     0.071343
                  
                   
                     8.853356
                  
                
                 
                   
                     1.65
                  
                   
                     0.072216
                  
                   
                     8.858636
                  
                
                 
                   
                     1.66
                  
                   
                     0.073091
                  
                   
                     8.863885
                  
                
                 
                   
                     1.67
                  
                   
                     0.073944
                  
                   
                     8.869101
                  
                
                 
                   
                     1.68
                  
                   
                     2.074533
                  
                   
                     8.874595
                  
                
                 
                   
                     1.69
                  
                   
                     0.075760
                  
                   
                     8.879442
                  
                
                 
                   
                     1.70
                  
                   
                     0.076659
                  
                   
                     8.884566
                  
                
                 
                   
                     1.71
                  
                   
                     0.077564
                  
                   
                     8.889661
                  
                
                 
                   
                     1.72
                  
                   
                     0.078440
                  
                   
                     8.894725
                  
                
                 
                   
                     1.73
                  
                   
                     0.079355
                  
                   
                     8.899761
                  
                
                 
                   
                     1.74
                  
                   
                     0.080309
                  
                   
                     8.904767
                  
                
                 
                   
                     1.75
                  
                   
                     0.081235
                  
                   
                     8.909745
                  
                
                 
                   
                     1.76
                  
                   
                     0.082166
                  
                   
                     8.914694
                  
                
                 
                   
                     1.77
                  
                   
                     0.083102
                  
                   
                     8.919615
                  
                
                 
                   
                     1.78
                  
                   
                     0.084044
                  
                   
                     8.924508
                  
                
                 
                   
                     1.79
                  
                   
                     0.084991
                  
                   
                     8.929374
                  
                
                 
                   
                     1.80
                  
                   
                     0.085943
                  
                   
                     8.934213
                  
                
                 
                   
                     1.81
                  
                   
                     0.086901
                  
                   
                     8.939026
                  
                
                 
                   
                     1.82
                  
                   
                     0.087864
                  
                   
                     8.943811
                  
                
                 
                   
                     1.83
                  
                   
                     0.088832
                  
                   
                     8.948571
                  
                
                 
                   
                     1.84
                  
                   
                     0.089805
                  
                   
                     8.953291
                  
                
                 
                   
                     1.85
                  
                   
                     0.090784
                  
                   
                     8.958012
                  
                
                 
                   
                     1.86
                  
                   
                     0.091768
                  
                   
                     8.962694
                  
                
                 
                   
                     1.87
                  
                   
                     0.092758
                  
                   
                     8.967352
                  
                
                 
                   
                     1.88
                  
                   
                     0.093752
                  
                   
                     8.971984
                  
                
                 
                   
                     1.89
                  
                   
                     0.094418
                  
                   
                     8.976592
                  
                
                 
                   
                     1.90
                  
                   
                     0.095748
                  
                   
                     8.981176
                  
                
                 
                   
                     1.91
                  
                   
                     0.096768
                  
                   
                     8.985735
                  
                
                 
                   
                     1.92
                  
                   
                     0.097784
                  
                   
                     8.990271
                  
                
                 
                   
                     1.93
                  
                   
                     0.098806
                  
                   
                     8.994783
                  
                
                 
                   
                     1.94
                  
                   
                     0.099832
                  
                   
                     8.999272
                  
                
                 
                   
                     1.95
                  
                   
                     0.100864
                  
                   
                     9.003738
                  
                
                 
                   
                     1.96
                  
                   
                     0.101901
                  
                   
                     9.008181
                  
                
                 
                   
                     1.97
                  
                   
                     0.102944
                  
                   
                     9.012601
                  
                
                 
                   
                     1.98
                  
                   
                     0.103981
                  
                   
                     9.016999
                  
                
                 
                   
                     1.99
                  
                   
                     0.105044
                  
                   
                     9.021375
                  
                
                 
                   
                     2.00
                  
                   
                     0.106103
                  
                   
                     9.025728
                  
                
                 
                   
                     2.01
                  
                   
                     0.107166
                  
                   
                     9.030061
                  
                
                 
                   
                     2.02
                  
                   
                     0.108235
                  
                   
                     9.034371
                  
                
                 
                   
                     2.03
                  
                   
                     0.109310
                  
                   
                     9.038660
                  
                
                 
                   
                     2.04
                  
                   
                     0.110389
                  
                   
                     9.042929
                  
                
                 
                   
                     2.05
                  
                   
                     0.111441
                  
                   
                     9.047176
                  
                
                 
                   
                     2.06
                  
                   
                     0.112564
                  
                   
                     9.051403
                  
                
                 
                   
                     2.07
                  
                   
                     0.113660
                  
                   
                     9.055609
                  
                
                 
                   
                     2.08
                  
                   
                     0.114427
                  
                   
                     9.059795
                  
                
                 
                   
                     2.09
                  
                   
                     0.115867
                  
                   
                     9.063961
                  
                
                 
                   
                     2.10
                  
                   
                     0.116978
                  
                   
                     9.068107
                  
                
                 
                   
                     
                     2.11
                  
                   
                     0.118095
                  
                   
                     9.072233
                  
                
                 
                   
                     2.12
                  
                   
                     0.119210
                  
                   
                     9.076340
                  
                
                 
                   
                     2.13
                  
                   
                     0.120345
                  
                   
                     9.080428
                  
                
                 
                   
                     2.14
                  
                   
                     0.121477
                  
                   
                     9.084496
                  
                
                 
                   
                     2.15
                  
                   
                     0.122614
                  
                   
                     9.088545
                  
                
                 
                   
                     2.16
                  
                   
                     0.123758
                  
                   
                     9.092576
                  
                
                 
                   
                     2.17
                  
                   
                     0.124907
                  
                   
                     9.096588
                  
                
                 
                   
                     2.18
                  
                   
                     0.126061
                  
                   
                     9.100581
                  
                
                 
                   
                     2.19
                  
                   
                     0.129220
                  
                   
                     9.104557
                  
                
                 
                   
                     2.20
                  
                   
                     0.128384
                  
                   
                     9.108514
                  
                
                 
                   
                     2.21
                  
                   
                     0.129554
                  
                   
                     9.112453
                  
                
                 
                   
                     2.22
                  
                   
                     0.130729
                  
                   
                     9.116374
                  
                
                 
                   
                     2.23
                  
                   
                     0.131910
                  
                   
                     9.120278
                  
                
                 
                   
                     2.24
                  
                   
                     0.133095
                  
                   
                     9.124164
                  
                
                 
                   
                     2.25
                  
                   
                     0.134286
                  
                   
                     9.128033
                  
                
                 
                   
                     2.26
                  
                   
                     0.135483
                  
                   
                     9.131885
                  
                
                 
                   
                     2.27
                  
                   
                     0.136684
                  
                   
                     9.135720
                  
                
                 
                   
                     2.28
                  
                   
                     0.137891
                  
                   
                     9.139538
                  
                
                 
                   
                     2.29
                  
                   
                     0.139104
                  
                   
                     9.143339
                  
                
                 
                   
                     2.30
                  
                   
                     0.140321
                  
                   
                     9.147124
                  
                
                 
                   
                     2.31
                  
                   
                     0.141544
                  
                   
                     9.150892
                  
                
                 
                   
                     2.32
                  
                   
                     0.142772
                  
                   
                     9.154644
                  
                
                 
                   
                     2.33
                  
                   
                     0.144006
                  
                   
                     9.158380
                  
                
                 
                   
                     2.34
                  
                   
                     0.145244
                  
                   
                     9.162100
                  
                
                 
                   
                     2.35
                  
                   
                     0.146488
                  
                   
                     9.165804
                  
                
                 
                   
                     2.36
                  
                   
                     0.147738
                  
                   
                     9.169492
                  
                
                 
                   
                     2.37
                  
                   
                     0.148992
                  
                   
                     9.173165
                  
                
                 
                   
                     2.38
                  
                   
                     0.150252
                  
                   
                     9.176822
                  
                
                 
                   
                     2.39
                  
                   
                     0.151518
                  
                   
                     9.180464
                  
                
                 
                   
                     2.40
                  
                   
                     0.152788
                  
                   
                     9.184091
                  
                
                 
                   
                     2.41
                  
                   
                     0.154064
                  
                   
                     9.187702
                  
                
                 
                   
                     2.42
                  
                   
                     0.155345
                  
                   
                     9.191299
                  
                
                 
                   
                     2.43
                  
                   
                     0.156632
                  
                   
                     9.194881
                  
                
                 
                   
                     2.44
                  
                   
                     0.157924
                  
                   
                     9.198448
                  
                
                 
                   
                     2.45
                  
                   
                     0.159221
                  
                   
                     9.202001
                  
                
                 
                   
                     2.46
                  
                   
                     0.160523
                  
                   
                     9.205539
                  
                
                 
                   
                     2.47
                  
                   
                     0.161831
                  
                   
                     9.209062
                  
                
                 
                   
                     2.48
                  
                   
                     0.163144
                  
                   
                     9.212571
                  
                
                 
                   
                     2.49
                  
                   
                     0.164462
                  
                   
                     9.216067
                  
                
                 
                   
                     2.50
                  
                   
                     0.165786
                  
                   
                     9.219548
                  
                
                 
                   
                     2.51
                  
                   
                     0.167115
                  
                   
                     9.222016
                  
                
                 
                   
                     2.52
                  
                   
                     0.168449
                  
                   
                     9.226469
                  
                
                 
                   
                     2.53
                  
                   
                     0.169789
                  
                   
                     9.229909
                  
                
                 
                   
                     2.54
                  
                   
                     0.171133
                  
                   
                     9.233336
                  
                
                 
                   
                     2.55
                  
                   
                     0.172484
                  
                   
                     9.236749
                  
                
                 
                   
                     2.56
                  
                   
                     0.173839
                  
                   
                     9.240148
                  
                
                 
                   
                     2.57
                  
                   
                     0.175200
                  
                   
                     9.243535
                  
                
                 
                   
                     2.58
                  
                   
                     0.176566
                  
                   
                     9.246908
                  
                
                 
                   
                     2.59
                  
                   
                     0.177937
                  
                   
                     9.250268
                  
                
                 
                   
                     2.60
                  
                   
                     0.179314
                  
                   
                     9.253615
                  
                
                 
                   
                     2.61
                  
                   
                     0.180685
                  
                   
                     9.256949
                  
                
                 
                   
                     2.62
                  
                   
                     0.182083
                  
                   
                     9.260271
                  
                
                 
                   
                     2.63
                  
                   
                     0.183476
                  
                   
                     9.263580
                  
                
                 
                   
                     2.64
                  
                   
                     0.184874
                  
                   
                     9.266876
                  
                
                 
                   
                     2.65
                  
                   
                     0.186277
                  
                   
                     9.270160
                  
                
                 
                   
                     2.66
                  
                   
                     0.187686
                  
                   
                     9.273432
                  
                
                 
                   
                     2.67
                  
                   
                     0.189099
                  
                   
                     9.276691
                  
                
                 
                   
                     2.68
                  
                   
                     0.190519
                  
                   
                     9.279938
                  
                
                 
                   
                     2.69
                  
                   
                     0.191943
                  
                   
                     9.283173
                  
                
                 
                   
                     2.70
                  
                   
                     0.193373
                  
                   
                     9.286396
                  
                
                 
                   
                     2.71
                  
                   
                     0.194808
                  
                   
                     9.289607
                  
                
                 
                   
                     2.72
                  
                   
                     0.196248
                  
                   
                     9.292806
                  
                
                 
                   
                     2.73
                  
                   
                     0.197694
                  
                   
                     9.295994
                  
                
                 
                   
                     2.74
                  
                   
                     0.199145
                  
                   
                     9.299170
                  
                
                 
                   
                     2.75
                  
                   
                     0.200601
                  
                   
                     9.302334
                  
                
                 
                   
                     2.76
                  
                   
                     0.202630
                  
                   
                     9.305486
                  
                
                 
                   
                     2.77
                  
                   
                     0.203529
                  
                   
                     9.308628
                  
                
                 
                   
                     2.78
                  
                   
                     0.205002
                  
                   
                     9.311758
                  
                
                 
                   
                     2.79
                  
                   
                     0.206479
                  
                   
                     9.314877
                  
                
                 
                   
                     2.80
                  
                   
                     0.207962
                  
                   
                     9.317984
                  
                
                 
                   
                     
                  
                   
                     Natural
                  
                   
                     Artificial
                  
                
                 
                   
                     2.81
                  
                   
                     0.209450
                  
                   
                     9.321081
                  
                
                 
                   
                     2.82
                  
                   
                     0.210943
                  
                   
                     9.324167
                  
                
                 
                   
                     2.83
                  
                   
                     0.212442
                  
                   
                     9.327241
                  
                
                 
                   
                     2.84
                  
                   
                     0.213946
                  
                   
                     9.330306
                  
                
                 
                   
                     2.85
                  
                   
                     0.215455
                  
                   
                     9.333358
                  
                
                 
                   
                     2.86
                  
                   
                     0.216970
                  
                   
                     9.336400
                  
                
                 
                   
                     2.87
                  
                   
                     0.218490
                  
                   
                     9.339442
                  
                
                 
                   
                     2.88
                  
                   
                     0.220015
                  
                   
                     9.342453
                  
                
                 
                   
                     2.89
                  
                   
                     0.221546
                  
                   
                     9.344464
                  
                
                 
                   
                     2.90
                  
                   
                     0.223082
                  
                   
                     9.348464
                  
                
                 
                   
                     2.91
                  
                   
                     0.224623
                  
                   
                     9.351454
                  
                
                 
                   
                     2.92
                  
                   
                     0.226169
                  
                   
                     9.354434
                  
                
                 
                   
                     2.93
                  
                   
                     0.227721
                  
                   
                     9.357404
                  
                
                 
                   
                     2.94
                  
                   
                     0.229278
                  
                   
                     9.360363
                  
                
                 
                   
                     2.95
                  
                   
                     0.230840
                  
                   
                     9.363312
                  
                
                 
                   
                     2.96
                  
                   
                     0.232408
                  
                   
                     9.366252
                  
                
                 
                   
                     2.97
                  
                   
                     0.233981
                  
                   
                     9.369181
                  
                
                 
                   
                     2.98
                  
                   
                     0.235559
                  
                   
                     9.372101
                  
                
                 
                   
                     2.99
                  
                   
                     0.237143
                  
                   
                     9.375011
                  
                
                 
                   
                     3.00
                  
                   
                     0.238732
                  
                   
                     9.377911
                  
                
                 
                   
                     3.01
                  
                   
                     0.240326
                  
                   
                     9.380801
                  
                
                 
                   
                     3.02
                  
                   
                     0.241926
                  
                   
                     9.383682
                  
                
                 
                   
                     3.03
                  
                   
                     0.243530
                  
                   
                     9.386554
                  
                
                 
                   
                     3.04
                  
                   
                     0.245141
                  
                   
                     9.389416
                  
                
                 
                   
                     3.05
                  
                   
                     0.246756
                  
                   
                     6.392268
                  
                
                 
                   
                     3.06
                  
                   
                     0.248377
                  
                   
                     9.395111
                  
                
                 
                   
                     3.07
                  
                   
                     0.249003
                  
                   
                     9.397945
                  
                
                 
                   
                     3.08
                  
                   
                     0.251634
                  
                   
                     9.400770
                  
                
                 
                   
                     3.09
                  
                   
                     0.253271
                  
                   
                     9.403585
                  
                
                 
                   
                     3.10
                  
                   
                     0.254713
                  
                   
                     9.406392
                  
                
                 
                   
                     3.11
                  
                   
                     0.256627
                  
                   
                     9.409189
                  
                
                 
                   
                     3.12
                  
                   
                     0.258212
                  
                   
                     9.411978
                  
                
                 
                   
                     3.13
                  
                   
                     0.259870
                  
                   
                     9.414757
                  
                
                 
                   
                     3.14
                  
                   
                     0.261534
                  
                   
                     9.417528
                  
                
                 
                   
                     3.15
                  
                   
                     0.263202
                  
                   
                     9.420290
                  
                
                 
                   
                     3.16
                  
                   
                     0.264876
                  
                   
                     9.423043
                  
                
                 
                   
                     3.17
                  
                   
                     0.266555
                  
                   
                     9.425787
                  
                
                 
                   
                     3.18
                  
                   
                     0.268239
                  
                   
                     9.428523
                  
                
                 
                   
                     3.19
                  
                   
                     0.269926
                  
                   
                     9.431250
                  
                
                 
                   
                     3.20
                  
                   
                     0.271624
                  
                   
                     9.433968
                  
                
                 
                   
                     3.21
                  
                   
                     0.273324
                  
                   
                     9.436678
                  
                
                 
                   
                     3.22
                  
                   
                     0.275030
                  
                   
                     9.439380
                  
                
                 
                   
                     3.23
                  
                   
                     0.276741
                  
                   
                     9.442073
                  
                
                 
                   
                     3.24
                  
                   
                     0.278457
                  
                   
                     9.444758
                  
                
                 
                   
                     3.25
                  
                   
                     0.280179
                  
                   
                     9.447435
                  
                
                 
                   
                     3.26
                  
                   
                     0.281905
                  
                   
                     9.450104
                  
                
                 
                   
                     3.27
                  
                   
                     0.283604
                  
                   
                     9.452764
                  
                
                 
                   
                     3.28
                  
                   
                     0.285375
                  
                   
                     9.455416
                  
                
                 
                   
                     3.29
                  
                   
                     0.287114
                  
                   
                     9.458060
                  
                
                 
                   
                     3.30
                  
                   
                     0.288866
                  
                   
                     9.460695
                  
                
                 
                   
                     3.31
                  
                   
                     0.290619
                  
                   
                     9.463324
                  
                
                 
                   
                     3.32
                  
                   
                     0.292378
                  
                   
                     9.465945
                  
                
                 
                   
                     3.33
                  
                   
                     0.294142
                  
                   
                     9.468557
                  
                
                 
                   
                     3.34
                  
                   
                     0.295911
                  
                   
                     9.471161
                  
                
                 
                   
                     3.35
                  
                   
                     0.297686
                  
                   
                     9.473758
                  
                
                 
                   
                     3.36
                  
                   
                     0.299465
                  
                   
                     9.476347
                  
                
                 
                   
                     3.37
                  
                   
                     0.301251
                  
                   
                     9.478928
                  
                
                 
                   
                     3.38
                  
                   
                     0.303041
                  
                   
                     9.481502
                  
                
                 
                   
                     3.39
                  
                   
                     0.304504
                  
                   
                     9.484068
                  
                
                 
                   
                     3.40
                  
                   
                     0.306638
                  
                   
                     9.486626
                  
                
                 
                   
                     3.41
                  
                   
                     0.308444
                  
                   
                     9.489177
                  
                
                 
                   
                     3.42
                  
                   
                     0.310256
                  
                   
                     9.491721
                  
                
                 
                   
                     3.43
                  
                   
                     0.312073
                  
                   
                     9.494257
                  
                
                 
                   
                     3.44
                  
                   
                     0.313895
                  
                   
                     9.496785
                  
                
                 
                   
                     3.45
                  
                   
                     0.315726
                  
                   
                     9.499307
                  
                
                 
                   
                     3.46
                  
                   
                     0.317556
                  
                   
                     9.501821
                  
                
                 
                   
                     3.47
                  
                   
                     0.319394
                  
                   
                     9.504327
                  
                
                 
                   
                     3.48
                  
                   
                     0.321238
                  
                   
                     9.506782
                  
                
                 
                   
                     3.49
                  
                   
                     0.323087
                  
                   
                     9.509319
                  
                
                 
                   
                     3.50
                  
                   
                     0.324941
                  
                   
                     9.511804
                  
                
                 
                   
                     
                     3.51
                  
                   
                     0.326800
                  
                   
                     9.514283
                  
                
                 
                   
                     3.52
                  
                   
                     0.328665
                  
                   
                     9.516754
                  
                
                 
                   
                     3.53
                  
                   
                     0.330502
                  
                   
                     9.519218
                  
                
                 
                   
                     3.54
                  
                   
                     0.332411
                  
                   
                     9.521675
                  
                
                 
                   
                     3.55
                  
                   
                     0.334291
                  
                   
                     9.524125
                  
                
                 
                   
                     3.56
                  
                   
                     0.336177
                  
                   
                     9.526568
                  
                
                 
                   
                     3.57
                  
                   
                     0.338068
                  
                   
                     9.528005
                  
                
                 
                   
                     3.58
                  
                   
                     0.339965
                  
                   
                     9.531434
                  
                
                 
                   
                     3.59
                  
                   
                     0.341867
                  
                   
                     9.533857
                  
                
                 
                   
                     3.60
                  
                   
                     0.343774
                  
                   
                     9.536273
                  
                
                 
                   
                     3.61
                  
                   
                     0.345687
                  
                   
                     9.538683
                  
                
                 
                   
                     3.62
                  
                   
                     0.347604
                  
                   
                     9.541086
                  
                
                 
                   
                     3.63
                  
                   
                     0.349528
                  
                   
                     9.543482
                  
                
                 
                   
                     3.64
                  
                   
                     0.351456
                  
                   
                     9.545871
                  
                
                 
                   
                     3.65
                  
                   
                     0.353390
                  
                   
                     9.547254
                  
                
                 
                   
                     3.66
                  
                   
                     0.355329
                  
                   
                     9.550631
                  
                
                 
                   
                     3.67
                  
                   
                     0.357273
                  
                   
                     9.553001
                  
                
                 
                   
                     3.68
                  
                   
                     0.359223
                  
                   
                     9.555364
                  
                
                 
                   
                     3.69
                  
                   
                     0.361178
                  
                   
                     9.557721
                  
                
                 
                   
                     3.70
                  
                   
                     0.363138
                  
                   
                     9.560071
                  
                
                 
                   
                     3.71
                  
                   
                     0.365104
                  
                   
                     9.562416
                  
                
                 
                   
                     3.72
                  
                   
                     0.367074
                  
                   
                     9.564754
                  
                
                 
                   
                     3.73
                  
                   
                     0.369051
                  
                   
                     9.567086
                  
                
                 
                   
                     3.74
                  
                   
                     0.371032
                  
                   
                     9.569412
                  
                
                 
                   
                     3.75
                  
                   
                     0.373019
                  
                   
                     9.571731
                  
                
                 
                   
                     3.76
                  
                   
                     0.375011
                  
                   
                     9.574044
                  
                
                 
                   
                     3.77
                  
                   
                     0.377008
                  
                   
                     9.576351
                  
                
                 
                   
                     3.78
                  
                   
                     0.379011
                  
                   
                     9.578652
                  
                
                 
                   
                     3.79
                  
                   
                     0.381019
                  
                   
                     9.580947
                  
                
                 
                   
                     3.80
                  
                   
                     0.383032
                  
                   
                     9.583236
                  
                
                 
                   
                     3.81
                  
                   
                     0
                     .
                     38505●
                  
                   
                     9.585518
                  
                
                 
                   
                     3.82
                  
                   
                     0.387075
                  
                   
                     9.587795
                  
                
                 
                   
                     3.83
                  
                   
                     0.389104
                  
                   
                     9.590066
                  
                
                 
                   
                     3
                     .
                     8●
                  
                   
                     0.391139
                  
                   
                     9.592331
                  
                
                 
                   
                     3.85
                  
                   
                     0.393179
                  
                   
                     9.594590
                  
                
                 
                   
                     3.86
                  
                   
                     0.395224
                  
                   
                     9.596743
                  
                
                 
                   
                     3.87
                  
                   
                     0.397274
                  
                   
                     9.599090
                  
                
                 
                   
                     3.88
                  
                   
                     0.399330
                  
                   
                     9.601332
                  
                
                 
                   
                     3.89
                  
                   
                     0.401391
                  
                   
                     9.603568
                  
                
                 
                   
                     3.90
                  
                   
                     0.403457
                  
                   
                     9.605798
                  
                
                 
                   
                     3.91
                  
                   
                     0.405529
                  
                   
                     9.608022
                  
                
                 
                   
                     3.92
                  
                   
                     0.407606
                  
                   
                     9.610241
                  
                
                 
                   
                     3.93
                  
                   
                     0.409688
                  
                   
                     9.612454
                  
                
                 
                   
                     3.94
                  
                   
                     0.411776
                  
                   
                     9.614661
                  
                
                 
                   
                     3.95
                  
                   
                     0.413869
                  
                   
                     9.616863
                  
                
                 
                   
                     3.96
                  
                   
                     0.415967
                  
                   
                     9.619059
                  
                
                 
                   
                     3.97
                  
                   
                     0.418070
                  
                   
                     9.621249
                  
                
                 
                   
                     3.98
                  
                   
                     0.420179
                  
                   
                     9.623435
                  
                
                 
                   
                     3.99
                  
                   
                     0.422293
                  
                   
                     9.625614
                  
                
                 
                   
                     4.00
                  
                   
                     0.424413
                  
                   
                     9.627788
                  
                
                 
                   
                     4.01
                  
                   
                     0.426504
                  
                   
                     9.629957
                  
                
                 
                   
                     4.02
                  
                   
                     0.428667
                  
                   
                     9.632121
                  
                
                 
                   
                     4.03
                  
                   
                     0.430803
                  
                   
                     9.634279
                  
                
                 
                   
                     4.04
                  
                   
                     0.432943
                  
                   
                     9.636431
                  
                
                 
                   
                     4.05
                  
                   
                     0.435089
                  
                   
                     9.638578
                  
                
                 
                   
                     4.06
                  
                   
                     0.437241
                  
                   
                     9.640720
                  
                
                 
                   
                     4.07
                  
                   
                     0.439397
                  
                   
                     9.642857
                  
                
                 
                   
                     4.08
                  
                   
                     0.431559
                  
                   
                     9.644989
                  
                
                 
                   
                     4.09
                  
                   
                     0.443726
                  
                   
                     9.647115
                  
                
                 
                   
                     4.10
                  
                   
                     0.445899
                  
                   
                     9.649236
                  
                
                 
                   
                     4.11
                  
                   
                     0.448076
                  
                   
                     9.651352
                  
                
                 
                   
                     4.12
                  
                   
                     0.450259
                  
                   
                     9.653463
                  
                
                 
                   
                     4.13
                  
                   
                     0.452448
                  
                   
                     9.655569
                  
                
                 
                   
                     4.14
                  
                   
                     0.454642
                  
                   
                     9.657669
                  
                
                 
                   
                     4.15
                  
                   
                     0.456840
                  
                   
                     9.659765
                  
                
                 
                   
                     4.16
                  
                   
                     0.459045
                  
                   
                     9.661855
                  
                
                 
                   
                     4.17
                  
                   
                     0.461254
                  
                   
                     9.663941
                  
                
                 
                   
                     4.18
                  
                   
                     0.463469
                  
                   
                     9.666021
                  
                
                 
                   
                     4.19
                  
                   
                     0.465690
                  
                   
                     9.668096
                  
                
                 
                   
                     4.20
                  
                   
                     0.467915
                  
                   
                     9.670167
                  
                
                 
                   
                     
                     4.21
                  
                   
                     0.470146
                  
                   
                     9.672233
                  
                
                 
                   
                     4.22
                  
                   
                     0.472382
                  
                   
                     9.674293
                  
                
                 
                   
                     4.23
                  
                   
                     0.474623
                  
                   
                     9.676349
                  
                
                 
                   
                     4.24
                  
                   
                     0.476870
                  
                   
                     9.678400
                  
                
                 
                   
                     4.25
                  
                   
                     0.479122
                  
                   
                     9.680446
                  
                
                 
                   
                     4.26
                  
                   
                     0.481380
                  
                   
                     9.682488
                  
                
                 
                   
                     4.27
                  
                   
                     0.483642
                  
                   
                     9.684524
                  
                
                 
                   
                     4.28
                  
                   
                     0.485910
                  
                   
                     9.686556
                  
                
                 
                   
                     4.29
                  
                   
                     0.488183
                  
                   
                     9.688583
                  
                
                 
                   
                     4.30
                  
                   
                     0.490462
                  
                   
                     9.690605
                  
                
                 
                   
                     4.31
                  
                   
                     0.492746
                  
                   
                     9.692623
                  
                
                 
                   
                     4.32
                  
                   
                     0.495032
                  
                   
                     9.694636
                  
                
                 
                   
                     4.33
                  
                   
                     0.497330
                  
                   
                     9.696634
                  
                
                 
                   
                     4.34
                  
                   
                     0.499629
                  
                   
                     9.698648
                  
                
                 
                   
                     4.35
                  
                   
                     0.501934
                  
                   
                     9.700647
                  
                
                 
                   
                     4.36
                  
                   
                     0.504245
                  
                   
                     9.702641
                  
                
                 
                   
                     4.37
                  
                   
                     0.506560
                  
                   
                     9.704631
                  
                
                 
                   
                     4.38
                  
                   
                     0.508882
                  
                   
                     9.706617
                  
                
                 
                   
                     4.39
                  
                   
                     0.511208
                  
                   
                     9.708597
                  
                
                 
                   
                     4.40
                  
                   
                     0.513539
                  
                   
                     9.710574
                  
                
                 
                   
                     4.41
                  
                   
                     0.515876
                  
                   
                     9.712546
                  
                
                 
                   
                     4.42
                  
                   
                     0.518219
                  
                   
                     9.714513
                  
                
                 
                   
                     4.43
                  
                   
                     0.520566
                  
                   
                     9.716476
                  
                
                 
                   
                     4.44
                  
                   
                     0.522919
                  
                   
                     9.718434
                  
                
                 
                   
                     4.45
                  
                   
                     0.527277
                  
                   
                     9.720388
                  
                
                 
                   
                     4.46
                  
                   
                     0.527641
                  
                   
                     9.722338
                  
                
                 
                   
                     4.47
                  
                   
                     0.530009
                  
                   
                     9.724283
                  
                
                 
                   
                     4.48
                  
                   
                     0.532383
                  
                   
                     9.726224
                  
                
                 
                   
                     4.49
                  
                   
                     0.534429
                  
                   
                     9.728161
                  
                
                 
                   
                     4.50
                  
                   
                     0.537147
                  
                   
                     9.730093
                  
                
                 
                   
                     4.51
                  
                   
                     0.539537
                  
                   
                     9.732021
                  
                
                 
                   
                     4.52
                  
                   
                     0.541933
                  
                   
                     9.733945
                  
                
                 
                   
                     4.53
                  
                   
                     0.544333
                  
                   
                     9.735865
                  
                
                 
                   
                     4.54
                  
                   
                     0.546739
                  
                   
                     9.737780
                  
                
                 
                   
                     4.55
                  
                   
                     0.549150
                  
                   
                     9.739691
                  
                
                 
                   
                     4.56
                  
                   
                     0.551567
                  
                   
                     9.741598
                  
                
                 
                   
                     4.57
                  
                   
                     0.553989
                  
                   
                     9.743501
                  
                
                 
                   
                     4.58
                  
                   
                     0.556416
                  
                   
                     9.745399
                  
                
                 
                   
                     4.59
                  
                   
                     0.558848
                  
                   
                     9.747294
                  
                
                 
                   
                     4.60
                  
                   
                     0.561286
                  
                   
                     9.749184
                  
                
                 
                   
                     4.61
                  
                   
                     0.563729
                  
                   
                     9.751070
                  
                
                 
                   
                     4.62
                  
                   
                     0.566177
                  
                   
                     9.752952
                  
                
                 
                   
                     4.63
                  
                   
                     0.568631
                  
                   
                     9.754830
                  
                
                 
                   
                     4.64
                  
                   
                     0.571090
                  
                   
                     9.756704
                  
                
                 
                   
                     4.65
                  
                   
                     0.573554
                  
                   
                     9.758574
                  
                
                 
                   
                     4.66
                  
                   
                     0.576024
                  
                   
                     9.760440
                  
                
                 
                   
                     4.67
                  
                   
                     0.578499
                  
                   
                     9.762302
                  
                
                 
                   
                     4.68
                  
                   
                     0.580979
                  
                   
                     9.764160
                  
                
                 
                   
                     4.69
                  
                   
                     0.583464
                  
                   
                     9.766014
                  
                
                 
                   
                     4.70
                  
                   
                     0.585955
                  
                   
                     9.767864
                  
                
                 
                   
                     4.71
                  
                   
                     0.588451
                  
                   
                     9.769710
                  
                
                 
                   
                     4.72
                  
                   
                     0.590952
                  
                   
                     9.771552
                  
                
                 
                   
                     4.73
                  
                   
                     0.593459
                  
                   
                     9.773411
                  
                
                 
                   
                     4.74
                  
                   
                     0.595971
                  
                   
                     9.775225
                  
                
                 
                   
                     4.75
                  
                   
                     0.598488
                  
                   
                     9.777056
                  
                
                 
                   
                     4.76
                  
                   
                     0.601011
                  
                   
                     9.778882
                  
                
                 
                   
                     4.77
                  
                   
                     0.603539
                  
                   
                     9.780705
                  
                
                 
                   
                     4.78
                  
                   
                     0.606072
                  
                   
                     9.782524
                  
                
                 
                   
                     4.79
                  
                   
                     0.608611
                  
                   
                     9.784339
                  
                
                 
                   
                     4.80
                  
                   
                     0.611154
                  
                   
                     9.786151
                  
                
                 
                   
                     4.81
                  
                   
                     0.613704
                  
                   
                     9.787959
                  
                
                 
                   
                     4.82
                  
                   
                     0.616258
                  
                   
                     9.789762
                  
                
                 
                   
                     4.83
                  
                   
                     0.618818
                  
                   
                     9.791563
                  
                
                 
                   
                     4.84
                  
                   
                     0.621383
                  
                   
                     9.793359
                  
                
                 
                   
                     4.85
                  
                   
                     0.623953
                  
                   
                     9.795252
                  
                
                 
                   
                     4.86
                  
                   
                     0.626529
                  
                   
                     9.796941
                  
                
                 
                   
                     4.87
                  
                   
                     0.629110
                  
                   
                     9.798726
                  
                
                 
                   
                     4.88
                  
                   
                     0.631696
                  
                   
                     9.800508
                  
                
                 
                   
                     4.89
                  
                   
                     0.634288
                  
                   
                     9.802286
                  
                
                 
                   
                     4.90
                  
                   
                     0.636885
                  
                   
                     9.804060
                  
                
                 
                   
                     
                     4.92
                  
                   
                     0.639487
                  
                   
                     9.805831
                  
                
                 
                   
                     4.92
                  
                   
                     0.642094
                  
                   
                     9.807599
                  
                
                 
                   
                     4.93
                  
                   
                     0.644707
                  
                   
                     9.809362
                  
                
                 
                   
                     4.94
                  
                   
                     0.647325
                  
                   
                     9.811122
                  
                
                 
                   
                     4.95
                  
                   
                     0.649948
                  
                   
                     9.812879
                  
                
                 
                   
                     4.96
                  
                   
                     0.652577
                  
                   
                     9.814632
                  
                
                 
                   
                     4.97
                  
                   
                     0.655211
                  
                   
                     9.815638
                  
                
                 
                   
                     4.98
                  
                   
                     0.657851
                  
                   
                     9.818127
                  
                
                 
                   
                     4.99
                  
                   
                     0.660495
                  
                   
                     9.819869
                  
                
                 
                   
                     5.00
                  
                   
                     0.663145
                  
                   
                     9.821608
                  
                
                 
                   
                     5.01
                  
                   
                     0.665800
                  
                   
                     9.823344
                  
                
                 
                   
                     5.02
                  
                   
                     0.668461
                  
                   
                     9.825076
                  
                
                 
                   
                     5.03
                  
                   
                     0.671127
                  
                   
                     9.826804
                  
                
                 
                   
                     5.04
                  
                   
                     0.673798
                  
                   
                     9.828529
                  
                
                 
                   
                     5.05
                  
                   
                     0.676474
                  
                   
                     9.830451
                  
                
                 
                   
                     5.06
                  
                   
                     0.679156
                  
                   
                     9.831979
                  
                
                 
                   
                     5.07
                  
                   
                     0.681843
                  
                   
                     9.833684
                  
                
                 
                   
                     5.08
                  
                   
                     0.684536
                  
                   
                     9.835396
                  
                
                 
                   
                     5.09
                  
                   
                     0.687267
                  
                   
                     9.837104
                  
                
                 
                   
                     5.10
                  
                   
                     0.689936
                  
                   
                     9.838809
                  
                
                 
                   
                     5.11
                  
                   
                     0.692644
                  
                   
                     9.840516
                  
                
                 
                   
                     5.12
                  
                   
                     0.695358
                  
                   
                     9.842208
                  
                
                 
                   
                     5.13
                  
                   
                     0.698077
                  
                   
                     9.843903
                  
                
                 
                   
                     5.14
                  
                   
                     0.700801
                  
                   
                     9.845595
                  
                
                 
                   
                     5.15
                  
                   
                     0.703531
                  
                   
                     9.847283
                  
                
                 
                   
                     5.16
                  
                   
                     0.706265
                  
                   
                     9.848968
                  
                
                 
                   
                     5.17
                  
                   
                     0.709006
                  
                   
                     9.850649
                  
                
                 
                   
                     5.18
                  
                   
                     0.711751
                  
                   
                     9.852328
                  
                
                 
                   
                     5.19
                  
                   
                     0
                     .
                     71450●
                  
                   
                     9.854003
                  
                
                 
                   
                     5.20
                  
                   
                     0.717258
                  
                   
                     9.855675
                  
                
                 
                   
                     5.21
                  
                   
                     0.720019
                  
                   
                     9.857344
                  
                
                 
                   
                     5.22
                  
                   
                     0.722786
                  
                   
                     9
                     :
                     859009
                  
                
                 
                   
                     5.23
                  
                   
                     0.725558
                  
                   
                     9.860672
                  
                
                 
                   
                     5.24
                  
                   
                     ●
                     .
                     728335
                  
                   
                     9.862331
                  
                
                 
                   
                     5
                     :
                     25
                  
                   
                     0.731118
                  
                   
                     9.863987
                  
                
                 
                   
                     5.26
                  
                   
                     0.733905
                  
                   
                     9.865640
                  
                
                 
                   
                     5.27
                  
                   
                     0.736699
                  
                   
                     9.867290
                  
                
                 
                   
                     5.28
                  
                   
                     0.739497
                  
                   
                     9.868936
                  
                
                 
                   
                     5.29
                  
                   
                     0.742301
                  
                   
                     9.870580
                  
                
                 
                   
                     5.30
                  
                   
                     0.745110
                  
                   
                     9.872220
                  
                
                 
                   
                     5.31
                  
                   
                     0.747924
                  
                   
                     9.873857
                  
                
                 
                   
                     5.32
                  
                   
                     0.750744
                  
                   
                     9.875492
                  
                
                 
                   
                     5.33
                  
                   
                     0.753569
                  
                   
                     9.877223
                  
                
                 
                   
                     5.34
                  
                   
                     0.756399
                  
                   
                     9.878751
                  
                
                 
                   
                     5.35
                  
                   
                     0.759235
                  
                   
                     9.880376
                  
                
                 
                   
                     5.36
                  
                   
                     0.762076
                  
                   
                     9.881998
                  
                
                 
                   
                     5.37
                  
                   
                     0.764922
                  
                   
                     9.883617
                  
                
                 
                   
                     5.38
                  
                   
                     0.767774
                  
                   
                     9.885233
                  
                
                 
                   
                     5.39
                  
                   
                     0.770630
                  
                   
                     9.886846
                  
                
                 
                   
                     5.40
                  
                   
                     0.773493
                  
                   
                     9.888456
                  
                
                 
                   
                     5.41
                  
                   
                     0.776360
                  
                   
                     9.890063
                  
                
                 
                   
                     5.42
                  
                   
                     0.779233
                  
                   
                     9.891667
                  
                
                 
                   
                     5.43
                  
                   
                     0.782111
                  
                   
                     9.892268
                  
                
                 
                   
                     5.44
                  
                   
                     0.784994
                  
                   
                     9.894866
                  
                
                 
                   
                     5.45
                  
                   
                     0
                     .
                     78788●
                  
                   
                     9.896461
                  
                
                 
                   
                     5.46
                  
                   
                     0.790777
                  
                   
                     9.898054
                  
                
                 
                   
                     5.47
                  
                   
                     0.793676
                  
                   
                     9.899643
                  
                
                 
                   
                     5.48
                  
                   
                     0.796581
                  
                   
                     9.900230
                  
                
                 
                   
                     5.49
                  
                   
                     0.799490
                  
                   
                     9.902813
                  
                
                 
                   
                     5.50
                  
                   
                     0.802406
                  
                   
                     9.905394
                  
                
                 
                   
                     5.51
                  
                   
                     0.805326
                  
                   
                     9.905972
                  
                
                 
                   
                     5.52
                  
                   
                     0.808252
                  
                   
                     9.907547
                  
                
                 
                   
                     5.53
                  
                   
                     0.811283
                  
                   
                     9.909119
                  
                
                 
                   
                     5.54
                  
                   
                     0.814129
                  
                   
                     9.910688
                  
                
                 
                   
                     5.55
                  
                   
                     0.817061
                  
                   
                     9.912254
                  
                
                 
                   
                     5.56
                  
                   
                     0.820008
                  
                   
                     9.913818
                  
                
                 
                   
                     5.57
                  
                   
                     0.822994
                  
                   
                     9.915379
                  
                
                 
                   
                     5.58
                  
                   
                     0.825918
                  
                   
                     9.916937
                  
                
                 
                   
                     5.59
                  
                   
                     0.828881
                  
                   
                     9.918492
                  
                
                 
                   
                     5.60
                  
                   
                     0.831849
                  
                   
                     9.920044
                  
                
                 
                   
                     
                     5.61
                  
                   
                     0.834823
                  
                   
                     9.921594
                  
                
                 
                   
                     5.62
                  
                   
                     0.837802
                  
                   
                     9.923141
                  
                
                 
                   
                     5.63
                  
                   
                     0.840786
                  
                   
                     9.924685
                  
                
                 
                   
                     5.64
                  
                   
                     0.843775
                  
                   
                     9.926227
                  
                
                 
                   
                     5.65
                  
                   
                     0.846770
                  
                   
                     9.927765
                  
                
                 
                   
                     5.66
                  
                   
                     0.849770
                  
                   
                     9.929301
                  
                
                 
                   
                     5.67
                  
                   
                     0.852776
                  
                   
                     9.930835
                  
                
                 
                   
                     5.68
                  
                   
                     0.855786
                  
                   
                     9.932365
                  
                
                 
                   
                     5.69
                  
                   
                     0.858802
                  
                   
                     9.933893
                  
                
                 
                   
                     5.70
                  
                   
                     0.861824
                  
                   
                     9.935418
                  
                
                 
                   
                     5.71
                  
                   
                     0.864850
                  
                   
                     9.936941
                  
                
                 
                   
                     5.72
                  
                   
                     0.867882
                  
                   
                     9.938460
                  
                
                 
                   
                     5.73
                  
                   
                     0.870919
                  
                   
                     9.939978
                  
                
                 
                   
                     5.74
                  
                   
                     0.873963
                  
                   
                     9.941492
                  
                
                 
                   
                     5.75
                  
                   
                     0.877010
                  
                   
                     9.943004
                  
                
                 
                   
                     5.76
                  
                   
                     0.880063
                  
                   
                     9.944513
                  
                
                 
                   
                     5.77
                  
                   
                     0.883121
                  
                   
                     9.946020
                  
                
                 
                   
                     5.78
                  
                   
                     0.886185
                  
                   
                     9.947524
                  
                
                 
                   
                     5.79
                  
                   
                     0.889254
                  
                   
                     9.949026
                  
                
                 
                   
                     5.80
                  
                   
                     0.892328
                  
                   
                     9.950524
                  
                
                 
                   
                     5.81
                  
                   
                     0.895408
                  
                   
                     9.952021
                  
                
                 
                   
                     5.82
                  
                   
                     0.898493
                  
                   
                     9.953514
                  
                
                 
                   
                     5.83
                  
                   
                     0.901586
                  
                   
                     9.955006
                  
                
                 
                   
                     5.84
                  
                   
                     0.904679
                  
                   
                     9.956494
                  
                
                 
                   
                     5.85
                  
                   
                     0.907779
                  
                   
                     9.957980
                  
                
                 
                   
                     5.86
                  
                   
                     0.910886
                  
                   
                     9.959464
                  
                
                 
                   
                     5.87
                  
                   
                     0.913997
                  
                   
                     9.960945
                  
                
                 
                   
                     5.88
                  
                   
                     0.917114
                  
                   
                     9.962423
                  
                
                 
                   
                     5.89
                  
                   
                     0.920236
                  
                   
                     9.963908
                  
                
                 
                   
                     5.90
                  
                   
                     0.923363
                  
                   
                     9.965372
                  
                
                 
                   
                     5.91
                  
                   
                     0.926496
                  
                   
                     9.966843
                  
                
                 
                   
                     5.92
                  
                   
                     0.929967
                  
                   
                     9.968312
                  
                
                 
                   
                     5.93
                  
                   
                     0.932777
                  
                   
                     9.969778
                  
                
                 
                   
                     5.94
                  
                   
                     0.935926
                  
                   
                     9.971241
                  
                
                 
                   
                     5.95
                  
                   
                     0.939080
                  
                   
                     9.972702
                  
                
                 
                   
                     5.96
                  
                   
                     0.942239
                  
                   
                     9.974161
                  
                
                 
                   
                     5.97
                  
                   
                     0.945404
                  
                   
                     9.975617
                  
                
                 
                   
                     5.98
                  
                   
                     0.948574
                  
                   
                     9.977071
                  
                
                 
                   
                     5.99
                  
                   
                     0.951749
                  
                   
                     9.978522
                  
                
                 
                   
                     6.00
                  
                   
                     0.954929
                  
                   
                     9.979971
                  
                
                 
                   
                     6.01
                  
                   
                     0.958115
                  
                   
                     9.981417
                  
                
                 
                   
                     6.02
                  
                   
                     0.961306
                  
                   
                     9.982861
                  
                
                 
                   
                     6.03
                  
                   
                     0.964502
                  
                   
                     9.984303
                  
                
                 
                   
                     6.04
                  
                   
                     0.967704
                  
                   
                     9.985742
                  
                
                 
                   
                     6.05
                  
                   
                     0.970911
                  
                   
                     9.987179
                  
                
                 
                   
                     6.06
                  
                   
                     0.974123
                  
                   
                     9.988614
                  
                
                 
                   
                     6.07
                  
                   
                     0.977341
                  
                   
                     9.990046
                  
                
                 
                   
                     6.08
                  
                   
                     0.980564
                  
                   
                     9.991476
                  
                
                 
                   
                     6.09
                  
                   
                     0.983792
                  
                   
                     9.992903
                  
                
                 
                   
                     6.10
                  
                   
                     0.987025
                  
                   
                     9.994328
                  
                
                 
                   
                     6.11
                  
                   
                     0.990264
                  
                   
                     9.995751
                  
                
                 
                   
                     6.12
                  
                   
                     0.993508
                  
                   
                     9.997171
                  
                
                 
                   
                     6.13
                  
                   
                     0.996758
                  
                   
                     9.998589
                  
                
                 
                   
                     6.14
                  
                   
                     1.000012
                  
                   
                     0.000005
                  
                
                 
                   
                     6.15
                  
                   
                     1.003272
                  
                   
                     0.001419
                  
                
                 
                   
                     6.16
                  
                   
                     1.006538
                  
                   
                     0.002830
                  
                
                 
                   
                     6.17
                  
                   
                     1.009808
                  
                   
                     0.004239
                  
                
                 
                   
                     6.18
                  
                   
                     1.013084
                  
                   
                     0.005645
                  
                
                 
                   
                     6.19
                  
                   
                     1.016366
                  
                   
                     0.007050
                  
                
                 
                   
                     6.20
                  
                   
                     1.019652
                  
                   
                     0.008452
                  
                
                 
                   
                     6.21
                  
                   
                     1.022944
                  
                   
                     0.009852
                  
                
                 
                   
                     6.22
                  
                   
                     1.026241
                  
                   
                     0.011249
                  
                
                 
                   
                     6.23
                  
                   
                     1.029544
                  
                   
                     0.012645
                  
                
                 
                   
                     6.24
                  
                   
                     1.032851
                  
                   
                     0.014038
                  
                
                 
                   
                     6.25
                  
                   
                     1.036164
                  
                   
                     0.015428
                  
                
                 
                   
                     6.26
                  
                   
                     1.039450
                  
                   
                     0.016817
                  
                
                 
                   
                     6.27
                  
                   
                     1.042807
                  
                   
                     0.018203
                  
                
                 
                   
                     6.28
                  
                   
                     1.046136
                  
                   
                     0.019588
                  
                
                 
                   
                     6.29
                  
                   
                     1.049470
                  
                   
                     0.020970
                  
                
                 
                   
                     6.30
                  
                   
                     1.052809
                  
                   
                     0.022350
                  
                
                 
                   
                     
                     6.31
                  
                   
                     1.056154
                  
                   
                     0.023727
                  
                
                 
                   
                     6.32
                  
                   
                     1.059505
                  
                   
                     0.025103
                  
                
                 
                   
                     6.33
                  
                   
                     1.062860
                  
                   
                     0.026476
                  
                
                 
                   
                     6.34
                  
                   
                     1.066331
                  
                   
                     0.027847
                  
                
                 
                   
                     6.35
                  
                   
                     1.069587
                  
                   
                     0.029216
                  
                
                 
                   
                     6.36
                  
                   
                     1.072958
                  
                   
                     0.030583
                  
                
                 
                   
                     6.37
                  
                   
                     1.076335
                  
                   
                     0.031947
                  
                
                 
                   
                     6.38
                  
                   
                     1.079717
                  
                   
                     0.033310
                  
                
                 
                   
                     6.39
                  
                   
                     1.083105
                  
                   
                     0.034670
                  
                
                 
                   
                     6.40
                  
                   
                     1.086497
                  
                   
                     0.036028
                  
                
                 
                   
                     6.41
                  
                   
                     1.089899
                  
                   
                     0.037384
                  
                
                 
                   
                     6.42
                  
                   
                     1.093298
                  
                   
                     0.038738
                  
                
                 
                   
                     6.43
                  
                   
                     1.096707
                  
                   
                     0.040090
                  
                
                 
                   
                     6.44
                  
                   
                     1.100121
                  
                   
                     0.041440
                  
                
                 
                   
                     6.45
                  
                   
                     1.103540
                  
                   
                     0.042788
                  
                
                 
                   
                     6.46
                  
                   
                     1.106965
                  
                   
                     0.044133
                  
                
                 
                   
                     6.47
                  
                   
                     1.110394
                  
                   
                     0.045477
                  
                
                 
                   
                     6.48
                  
                   
                     1.113829
                  
                   
                     0.046818
                  
                
                 
                   
                     6.49
                  
                   
                     1.117270
                  
                   
                     0.048158
                  
                
                 
                   
                     6.50
                  
                   
                     1.120716
                  
                   
                     0.049495
                  
                
                 
                   
                     6.51
                  
                   
                     1.124167
                  
                   
                     0.050830
                  
                
                 
                   
                     6.52
                  
                   
                     1.127623
                  
                   
                     0.052164
                  
                
                 
                   
                     6.53
                  
                   
                     1.131084
                  
                   
                     0.053495
                  
                
                 
                   
                     6.54
                  
                   
                     1.134551
                  
                   
                     0.054824
                  
                
                 
                   
                     6.55
                  
                   
                     1.138024
                  
                   
                     0.056150
                  
                
                 
                   
                     6.56
                  
                   
                     1.141501
                  
                   
                     0.057476
                  
                
                 
                   
                     6.57
                  
                   
                     1.144984
                  
                   
                     0.058799
                  
                
                 
                   
                     6.58
                  
                   
                     1.148472
                  
                   
                     0.060120
                  
                
                 
                   
                     6.59
                  
                   
                     1.152966
                  
                   
                     0.061439
                  
                
                 
                   
                     6.60
                  
                   
                     1.155464
                  
                   
                     0.062756
                  
                
                 
                   
                     6.61
                  
                   
                     1.158968
                  
                   
                     0.064071
                  
                
                 
                   
                     6.62
                  
                   
                     1.162478
                  
                   
                     0.065438
                  
                
                 
                   
                     6.63
                  
                   
                     1.165992
                  
                   
                     0.066895
                  
                
                 
                   
                     6.64
                  
                   
                     1.166951
                  
                   
                     0.068005
                  
                
                 
                   
                     6.65
                  
                   
                     1.173038
                  
                   
                     0.069312
                  
                
                 
                   
                     6.66
                  
                   
                     1.175688
                  
                   
                     0.070617
                  
                
                 
                   
                     6.67
                  
                   
                     1.180104
                  
                   
                     0.071920
                  
                
                 
                   
                     6.68
                  
                   
                     1.183645
                  
                   
                     0.073221
                  
                
                 
                   
                     6.69
                  
                   
                     1.187192
                  
                   
                     0.074521
                  
                
                 
                   
                     6.70
                  
                   
                     1.190744
                  
                   
                     0.075815
                  
                
                 
                   
                     6.71
                  
                   
                     1.194301
                  
                   
                     0.077113
                  
                
                 
                   
                     6.72
                  
                   
                     1.197863
                  
                   
                     0.078407
                  
                
                 
                   
                     6.73
                  
                   
                     1.201431
                  
                   
                     0.079699
                  
                
                 
                   
                     6.74
                  
                   
                     1.205004
                  
                   
                     0.080988
                  
                
                 
                   
                     6.75
                  
                   
                     1.208582
                  
                   
                     0.082276
                  
                
                 
                   
                     6.76
                  
                   
                     1.212166
                  
                   
                     0.083562
                  
                
                 
                   
                     6.77
                  
                   
                     1.215755
                  
                   
                     0.084846
                  
                
                 
                   
                     6.78
                  
                   
                     1.219349
                  
                   
                     0.086118
                  
                
                 
                   
                     6.79
                  
                   
                     1.222949
                  
                   
                     0.087408
                  
                
                 
                   
                     6.80
                  
                   
                     1.226554
                  
                   
                     0.088686
                  
                
                 
                   
                     6.81
                  
                   
                     1.230164
                  
                   
                     0.089963
                  
                
                 
                   
                     6.82
                  
                   
                     1.233779
                  
                   
                     0.091237
                  
                
                 
                   
                     6.83
                  
                   
                     1.237073
                  
                   
                     0.092510
                  
                
                 
                   
                     6.84
                  
                   
                     1.241026
                  
                   
                     0.093781
                  
                
                 
                   
                     6.85
                  
                   
                     1.244657
                  
                   
                     0.095049
                  
                
                 
                   
                     6.86
                  
                   
                     1.248294
                  
                   
                     0.096317
                  
                
                 
                   
                     6.87
                  
                   
                     1.252936
                  
                   
                     0.097582
                  
                
                 
                   
                     6.88
                  
                   
                     1.255587
                  
                   
                     0.098845
                  
                
                 
                   
                     6.89
                  
                   
                     1.259236
                  
                   
                     0.100107
                  
                
                 
                   
                     6.90
                  
                   
                     1.262894
                  
                   
                     0.101367
                  
                
                 
                   
                     6.91
                  
                   
                     1.266557
                  
                   
                     0.102525
                  
                
                 
                   
                     6.92
                  
                   
                     1.270226
                  
                   
                     0.103881
                  
                
                 
                   
                     6.93
                  
                   
                     1.274900
                  
                   
                     0.105135
                  
                
                 
                   
                     6.94
                  
                   
                     1.27757
                  
                   
                     0.106387
                  
                
                 
                   
                     6.95
                  
                   
                     1.281263
                  
                   
                     0.107638
                  
                
                 
                   
                     6.96
                  
                   
                     1.284953
                  
                   
                     0.108877
                  
                
                 
                   
                     6.97
                  
                   
                     1.288648
                  
                   
                     0.110134
                  
                
                 
                   
                     6.98
                  
                   
                     1.292348
                  
                   
                     0.111379
                  
                
                 
                   
                     6.99
                  
                   
                     1.296054
                  
                   
                     0.112623
                  
                
                 
                   
                     7.00
                  
                   
                     1.299765
                  
                   
                     0.113864
                  
                
                 
                   
                     
                     7.01
                  
                   
                     1.303481
                  
                   
                     0.115104
                  
                
                 
                   
                     7.02
                  
                   
                     1.307203
                  
                   
                     0.116343
                  
                
                 
                   
                     7.03
                  
                   
                     1.310930
                  
                   
                     0.117579
                  
                
                 
                   
                     7.04
                  
                   
                     1.314662
                  
                   
                     0.118814
                  
                
                 
                   
                     7.05
                  
                   
                     1.318399
                  
                   
                     0.120047
                  
                
                 
                   
                     7.06
                  
                   
                     1.322142
                  
                   
                     0.121278
                  
                
                 
                   
                     7.07
                  
                   
                     1.325890
                  
                   
                     0.122507
                  
                
                 
                   
                     7.08
                  
                   
                     1.329644
                  
                   
                     0.123735
                  
                
                 
                   
                     7.09
                  
                   
                     1.333402
                  
                   
                     0.124961
                  
                
                 
                   
                     7.10
                  
                   
                     1.337166
                  
                   
                     0.126175
                  
                
                 
                   
                     7.11
                  
                   
                     1.340936
                  
                   
                     0.127408
                  
                
                 
                   
                     7.12
                  
                   
                     1.344710
                  
                   
                     0.128628
                  
                
                 
                   
                     7.13
                  
                   
                     1.348490
                  
                   
                     0.129747
                  
                
                 
                   
                     7.14
                  
                   
                     1.352275
                  
                   
                     0.131065
                  
                
                 
                   
                     7.15
                  
                   
                     1.356066
                  
                   
                     0.132280
                  
                
                 
                   
                     7.16
                  
                   
                     1.359862
                  
                   
                     0.133494
                  
                
                 
                   
                     7.17
                  
                   
                     1.363667
                  
                   
                     0.134707
                  
                
                 
                   
                     7.18
                  
                   
                     1.367469
                  
                   
                     0.135917
                  
                
                 
                   
                     7.19
                  
                   
                     1.371281
                  
                   
                     0.137126
                  
                
                 
                   
                     7.20
                  
                   
                     1.375098
                  
                   
                     0.138333
                  
                
                 
                   
                     7.21
                  
                   
                     1.378921
                  
                   
                     0.139539
                  
                
                 
                   
                     7.22
                  
                   
                     1.382748
                  
                   
                     0.140743
                  
                
                 
                   
                     7.23
                  
                   
                     1.386581
                  
                   
                     0.141946
                  
                
                 
                   
                     7.24
                  
                   
                     1.390419
                  
                   
                     0.143146
                  
                
                 
                   
                     7.25
                  
                   
                     1.394263
                  
                   
                     0.144344
                  
                
                 
                   
                     7.26
                  
                   
                     1.398112
                  
                   
                     0.145542
                  
                
                 
                   
                     7.27
                  
                   
                     1.401966
                  
                   
                     0.146737
                  
                
                 
                   
                     7.28
                  
                   
                     1.405826
                  
                   
                     0.147931
                  
                
                 
                   
                     7.29
                  
                   
                     1.409691
                  
                   
                     0.149123
                  
                
                 
                   
                     7.30
                  
                   
                     1.413561
                  
                   
                     0.150314
                  
                
                 
                   
                     7.31
                  
                   
                     1.417436
                  
                   
                     0.151503
                  
                
                 
                   
                     7.32
                  
                   
                     1.421317
                  
                   
                     0.152691
                  
                
                 
                   
                     7.33
                  
                   
                     1.425203
                  
                   
                     0.153876
                  
                
                 
                   
                     7.34
                  
                   
                     1.429094
                  
                   
                     0.155060
                  
                
                 
                   
                     7.35
                  
                   
                     1.432991
                  
                   
                     0.156243
                  
                
                 
                   
                     7.36
                  
                   
                     1.436893
                  
                   
                     0.157424
                  
                
                 
                   
                     7.37
                  
                   
                     1.440800
                  
                   
                     0.158603
                  
                
                 
                   
                     7.38
                  
                   
                     1.444713
                  
                   
                     0.159781
                  
                
                 
                   
                     7.39
                  
                   
                     1.448630
                  
                   
                     0.160957
                  
                
                 
                   
                     7.40
                  
                   
                     1.452554
                  
                   
                     0.162132
                  
                
                 
                   
                     7.41
                  
                   
                     1.456482
                  
                   
                     0.163305
                  
                
                 
                   
                     7.42
                  
                   
                     1.460416
                  
                   
                     0.164476
                  
                
                 
                   
                     7.43
                  
                   
                     1.464355
                  
                   
                     0.165646
                  
                
                 
                   
                     7.44
                  
                   
                     1.468299
                  
                   
                     0.166814
                  
                
                 
                   
                     7.45
                  
                   
                     1.472249
                  
                   
                     0.167981
                  
                
                 
                   
                     7.46
                  
                   
                     1.476204
                  
                   
                     0.169146
                  
                
                 
                   
                     7.47
                  
                   
                     1.480164
                  
                   
                     0.170310
                  
                
                 
                   
                     7.48
                  
                   
                     1.484130
                  
                   
                     0.171472
                  
                
                 
                   
                     7.49
                  
                   
                     1.488101
                  
                   
                     0.172632
                  
                
                 
                   
                     7.50
                  
                   
                     1.492077
                  
                   
                     0.173791
                  
                
                 
                   
                     7.51
                  
                   
                     1.496059
                  
                   
                     0.174948
                  
                
                 
                   
                     7.52
                  
                   
                     1.500045
                  
                   
                     0.176104
                  
                
                 
                   
                     7.53
                  
                   
                     1.504038
                  
                   
                     0.177218
                  
                
                 
                   
                     7.54
                  
                   
                     1.508035
                  
                   
                     0.178411
                  
                
                 
                   
                     7.55
                  
                   
                     1.512038
                  
                   
                     0.179552
                  
                
                 
                   
                     7.56
                  
                   
                     1.516046
                  
                   
                     0.180712
                  
                
                 
                   
                     7.57
                  
                   
                     1.520059
                  
                   
                     0.181860
                  
                
                 
                   
                     7.58
                  
                   
                     1.524078
                  
                   
                     0.183007
                  
                
                 
                   
                     7.59
                  
                   
                     1.528102
                  
                   
                     0.184152
                  
                
                 
                   
                     7.60
                  
                   
                     1.532131
                  
                   
                     0.185296
                  
                
                 
                   
                     7
                     .
                     6●
                  
                   
                     1.536166
                  
                   
                     0.186438
                  
                
                 
                   
                     7.62
                  
                   
                     1.540260
                  
                   
                     0.187578
                  
                
                 
                   
                     7.63
                  
                   
                     1.544251
                  
                   
                     0.188717
                  
                
                 
                   
                     7.64
                  
                   
                     1.548301
                  
                   
                     0.189855
                  
                
                 
                   
                     7.65
                  
                   
                     1.552355
                  
                   
                     0.190991
                  
                
                 
                   
                     7.66
                  
                   
                     1.556418
                  
                   
                     0.192126
                  
                
                 
                   
                     7.67
                  
                   
                     1.560418
                  
                   
                     0.193259
                  
                
                 
                   
                     7.68
                  
                   
                     1.564556
                  
                   
                     0.194391
                  
                
                 
                   
                     7.69
                  
                   
                     1.568633
                  
                   
                     0.195521
                  
                
                 
                   
                     7.70
                  
                   
                     1.572716
                  
                   
                     0.196650
                  
                
                 
                   
                     
                     7.71
                  
                   
                     1.576803
                  
                   
                     0.197777
                  
                
                 
                   
                     7.72
                  
                   
                     1.580896
                  
                   
                     0.198903
                  
                
                 
                   
                     7.73
                  
                   
                     1.584994
                  
                   
                     0.200027
                  
                
                 
                   
                     7.74
                  
                   
                     1.589098
                  
                   
                     0.201150
                  
                
                 
                   
                     7.75
                  
                   
                     1.593207
                  
                   
                     0.202272
                  
                
                 
                   
                     7.78
                  
                   
                     1.597321
                  
                   
                     0.203402
                  
                
                 
                   
                     7.77
                  
                   
                     1.601440
                  
                   
                     0.204500
                  
                
                 
                   
                     7.78
                  
                   
                     1.605565
                  
                   
                     0.205628
                  
                
                 
                   
                     7.79
                  
                   
                     1.609695
                  
                   
                     0.206744
                  
                
                 
                   
                     7.80
                  
                   
                     1.613831
                  
                   
                     0.207858
                  
                
                 
                   
                     7.81
                  
                   
                     1.617971
                  
                   
                     0.208970
                  
                
                 
                   
                     7.82
                  
                   
                     1.622117
                  
                   
                     0.210082
                  
                
                 
                   
                     7.83
                  
                   
                     1.626269
                  
                   
                     0.211192
                  
                
                 
                   
                     7.84
                  
                   
                     1.630425
                  
                   
                     0.212311
                  
                
                 
                   
                     7.85
                  
                   
                     1.634587
                  
                   
                     0.213408
                  
                
                 
                   
                     7.86
                  
                   
                     1.638754
                  
                   
                     0.214514
                  
                
                 
                   
                     7.87
                  
                   
                     1.642927
                  
                   
                     0.215618
                  
                
                 
                   
                     7.88
                  
                   
                     1.647105
                  
                   
                     0.216721
                  
                
                 
                   
                     7.89
                  
                   
                     1.651288
                  
                   
                     0.217822
                  
                
                 
                   
                     7.90
                  
                   
                     1.655476
                  
                   
                     0.218923
                  
                
                 
                   
                     7.91
                  
                   
                     1.659670
                  
                   
                     0.220021
                  
                
                 
                   
                     7.92
                  
                   
                     1.663869
                  
                   
                     0.221119
                  
                
                 
                   
                     7.93
                  
                   
                     1.668073
                  
                   
                     0.222215
                  
                
                 
                   
                     7.94
                  
                   
                     1.672283
                  
                   
                     0.223309
                  
                
                 
                   
                     7.95
                  
                   
                     1.676498
                  
                   
                     0.224403
                  
                
                 
                   
                     7.96
                  
                   
                     1.680718
                  
                   
                     0.225495
                  
                
                 
                   
                     7.97
                  
                   
                     1.684944
                  
                   
                     0.226585
                  
                
                 
                   
                     7.98
                  
                   
                     1.689175
                  
                   
                     0.227674
                  
                
                 
                   
                     7.99
                  
                   
                     1.693411
                  
                   
                     0.228762
                  
                
                 
                   
                     8.00
                  
                   
                     1.697652
                  
                   
                     0.229848
                  
                
                 
                   
                     8.01
                  
                   
                     1.701899
                  
                   
                     0.230933
                  
                
                 
                   
                     8.02
                  
                   
                     1.706151
                  
                   
                     0.232017
                  
                
                 
                   
                     8.03
                  
                   
                     1.710408
                  
                   
                     0.233100
                  
                
                 
                   
                     8.04
                  
                   
                     1.714671
                  
                   
                     0
                     .
                     23418●
                  
                
                 
                   
                     8.05
                  
                   
                     1.718939
                  
                   
                     0.235260
                  
                
                 
                   
                     8.06
                  
                   
                     1.723212
                  
                   
                     0.236338
                  
                
                 
                   
                     8.07
                  
                   
                     1.727491
                  
                   
                     0.237415
                  
                
                 
                   
                     8.08
                  
                   
                     1.731775
                  
                   
                     0.238491
                  
                
                 
                   
                     8.09
                  
                   
                     1.736064
                  
                   
                     0.239565
                  
                
                 
                   
                     8.10
                  
                   
                     1.740359
                  
                   
                     0.240638
                  
                
                 
                   
                     8.11
                  
                   
                     1.744659
                  
                   
                     0.241710
                  
                
                 
                   
                     8.12
                  
                   
                     1.748964
                  
                   
                     0.242780
                  
                
                 
                   
                     8.13
                  
                   
                     1.753274
                  
                   
                     0.243850
                  
                
                 
                   
                     8.14
                  
                   
                     1.757590
                  
                   
                     0.244917
                  
                
                 
                   
                     8.15
                  
                   
                     1.761911
                  
                   
                     0.245984
                  
                
                 
                   
                     8.16
                  
                   
                     1.766237
                  
                   
                     0.247049
                  
                
                 
                   
                     8.17
                  
                   
                     1.770569
                  
                   
                     0.248113
                  
                
                 
                   
                     8.18
                  
                   
                     1.774906
                  
                   
                     0.249175
                  
                
                 
                   
                     8.19
                  
                   
                     1.779248
                  
                   
                     0.250236
                  
                
                 
                   
                     8.20
                  
                   
                     1.783596
                  
                   
                     0.251296
                  
                
                 
                   
                     8.21
                  
                   
                     1.787949
                  
                   
                     0.252355
                  
                
                 
                   
                     8.22
                  
                   
                     1.792307
                  
                   
                     0.253412
                  
                
                 
                   
                     8.23
                  
                   
                     1.796670
                  
                   
                     0.254468
                  
                
                 
                   
                     8.24
                  
                   
                     1.801039
                  
                   
                     0.255523
                  
                
                 
                   
                     8.25
                  
                   
                     1.805413
                  
                   
                     0.256576
                  
                
                 
                   
                     8.26
                  
                   
                     1.809793
                  
                   
                     0.257629
                  
                
                 
                   
                     8.27
                  
                   
                     1.814177
                  
                   
                     0.258679
                  
                
                 
                   
                     8.28
                  
                   
                     1.818568
                  
                   
                     0.259729
                  
                
                 
                   
                     8.29
                  
                   
                     1.822963
                  
                   
                     0.260777
                  
                
                 
                   
                     8.30
                  
                   
                     1.827363
                  
                   
                     0.261825
                  
                
                 
                   
                     8.31
                  
                   
                     1.831769
                  
                   
                     0.262870
                  
                
                 
                   
                     8.32
                  
                   
                     1.836181
                  
                   
                     0.263915
                  
                
                 
                   
                     8.33
                  
                   
                     1.840597
                  
                   
                     0.264958
                  
                
                 
                   
                     8.34
                  
                   
                     1.845019
                  
                   
                     0.266001
                  
                
                 
                   
                     8.35
                  
                   
                     1.849480
                  
                   
                     0.267041
                  
                
                 
                   
                     8.36
                  
                   
                     1.853879
                  
                   
                     0.268081
                  
                
                 
                   
                     8.37
                  
                   
                     2.858316
                  
                   
                     0.269119
                  
                
                 
                   
                     8.38
                  
                   
                     1.862760
                  
                   
                     0.270156
                  
                
                 
                   
                     8.39
                  
                   
                     1.867208
                  
                   
                     0.271192
                  
                
                 
                   
                     8.40
                  
                   
                     1.871662
                  
                   
                     0.272227
                  
                
                 
                   
                     
                     8.41
                  
                   
                     1.876121
                  
                   
                     0.273250
                  
                
                 
                   
                     8.42
                  
                   
                     1.880585
                  
                   
                     0.274293
                  
                
                 
                   
                     8.43
                  
                   
                     1.885054
                  
                   
                     0.275324
                  
                
                 
                   
                     8.44
                  
                   
                     1.889529
                  
                   
                     0.276353
                  
                
                 
                   
                     8.45
                  
                   
                     1.894010
                  
                   
                     0.277382
                  
                
                 
                   
                     8.46
                  
                   
                     1.898495
                  
                   
                     0.278409
                  
                
                 
                   
                     8.47
                  
                   
                     1.902886
                  
                   
                     0.279435
                  
                
                 
                   
                     8.48
                  
                   
                     1.907482
                  
                   
                     0.280450
                  
                
                 
                   
                     8.49
                  
                   
                     1.911983
                  
                   
                     0.281484
                  
                
                 
                   
                     8.50
                  
                   
                     1.916490
                  
                   
                     0.282506
                  
                
                 
                   
                     8.51
                  
                   
                     1.921002
                  
                   
                     0.283528
                  
                
                 
                   
                     8.52
                  
                   
                     1.925520
                  
                   
                     0.283748
                  
                
                 
                   
                     8.53
                  
                   
                     1.930042
                  
                   
                     0.285566
                  
                
                 
                   
                     8.54
                  
                   
                     1.934570
                  
                   
                     0.286584
                  
                
                 
                   
                     8.55
                  
                   
                     1.939104
                  
                   
                     0.287601
                  
                
                 
                   
                     8.56
                  
                   
                     1.943642
                  
                   
                     0.288616
                  
                
                 
                   
                     8.57
                  
                   
                     1.948186
                  
                   
                     0.289630
                  
                
                 
                   
                     8.58
                  
                   
                     1.952735
                  
                   
                     0.290643
                  
                
                 
                   
                     8.59
                  
                   
                     1.957290
                  
                   
                     0.291655
                  
                
                 
                   
                     8.60
                  
                   
                     1.961849
                  
                   
                     0.292665
                  
                
                 
                   
                     8.61
                  
                   
                     1.966414
                  
                   
                     0.293675
                  
                
                 
                   
                     8.62
                  
                   
                     1.970985
                  
                   
                     0.294683
                  
                
                 
                   
                     8.63
                  
                   
                     1.975561
                  
                   
                     0.295690
                  
                
                 
                   
                     8.64
                  
                   
                     1.980142
                  
                   
                     0.296696
                  
                
                 
                   
                     8.65
                  
                   
                     1.984728
                  
                   
                     0.297701
                  
                
                 
                   
                     8.66
                  
                   
                     1.989320
                  
                   
                     0.298704
                  
                
                 
                   
                     8.67
                  
                   
                     1.993916
                  
                   
                     0.299707
                  
                
                 
                   
                     8.68
                  
                   
                     1.998529
                  
                   
                     0.300708
                  
                
                 
                   
                     8.69
                  
                   
                     2.003126
                  
                   
                     0.301708
                  
                
                 
                   
                     8.70
                  
                   
                     2.007406
                  
                   
                     0.302707
                  
                
                 
                   
                     8.71
                  
                   
                     2.012357
                  
                   
                     0.303705
                  
                
                 
                   
                     8.72
                  
                   
                     2.016981
                  
                   
                     0.304701
                  
                
                 
                   
                     8.73
                  
                   
                     2.021609
                  
                   
                     0.305697
                  
                
                 
                   
                     8.74
                  
                   
                     2.026243
                  
                   
                     0.306691
                  
                
                 
                   
                     8.75
                  
                   
                     2.030883
                  
                   
                     0.307685
                  
                
                 
                   
                     8.76
                  
                   
                     2.035528
                  
                   
                     0.308677
                  
                
                 
                   
                     8.77
                  
                   
                     2.040177
                  
                   
                     0.309668
                  
                
                 
                   
                     8.78
                  
                   
                     2.044833
                  
                   
                     0.310657
                  
                
                 
                   
                     8.79
                  
                   
                     2.049493
                  
                   
                     0.311646
                  
                
                 
                   
                     8.80
                  
                   
                     2.054159
                  
                   
                     0.312634
                  
                
                 
                   
                     8.81
                  
                   
                     2.058830
                  
                   
                     0.313620
                  
                
                 
                   
                     8.82
                  
                   
                     2.063507
                  
                   
                     0.314606
                  
                
                 
                   
                     8.83
                  
                   
                     2.068189
                  
                   
                     0.315590
                  
                
                 
                   
                     8.84
                  
                   
                     2.072876
                  
                   
                     0.316573
                  
                
                 
                   
                     8.85
                  
                   
                     2.077568
                  
                   
                     5.317555
                  
                
                 
                   
                     8.86
                  
                   
                     2.082266
                  
                   
                     0.318536
                  
                
                 
                   
                     8.87
                  
                   
                     2.086969
                  
                   
                     0.319516
                  
                
                 
                   
                     8.88
                  
                   
                     2.091677
                  
                   
                     0.320494
                  
                
                 
                   
                     8.89
                  
                   
                     2.096391
                  
                   
                     0.321472
                  
                
                 
                   
                     8.90
                  
                   
                     2.101110
                  
                   
                     0.322448
                  
                
                 
                   
                     8.91
                  
                   
                     2.105834
                  
                   
                     0.323424
                  
                
                 
                   
                     8.92
                  
                   
                     2.110564
                  
                   
                     0.324498
                  
                
                 
                   
                     8.93
                  
                   
                     2.115299
                  
                   
                     0.325371
                  
                
                 
                   
                     8.94
                  
                   
                     2.120039
                  
                   
                     0.326343
                  
                
                 
                   
                     8.95
                  
                   
                     2.124784
                  
                   
                     0.327314
                  
                
                 
                   
                     8.96
                  
                   
                     2.129535
                  
                   
                     0.328284
                  
                
                 
                   
                     8.97
                  
                   
                     2.134291
                  
                   
                     0.329253
                  
                
                 
                   
                     8.98
                  
                   
                     2.139053
                  
                   
                     0.330221
                  
                
                 
                   
                     8.99
                  
                   
                     2.143819
                  
                   
                     0.331178
                  
                
                 
                   
                     9.00
                  
                   
                     2.148591
                  
                   
                     0.332153
                  
                
                 
                   
                     9.01
                  
                   
                     2.153368
                  
                   
                     2.333118
                  
                
                 
                   
                     9.02
                  
                   
                     2.158151
                  
                   
                     0.334081
                  
                
                 
                   
                     9.03
                  
                   
                     2.162939
                  
                   
                     0.335044
                  
                
                 
                   
                     9.04
                  
                   
                     2.167732
                  
                   
                     0.336005
                  
                
                 
                   
                     9.05
                  
                   
                     2.172531
                  
                   
                     0.337966
                  
                
                 
                   
                     9.06
                  
                   
                     2.177335
                  
                   
                     0.338925
                  
                
                 
                   
                     9.07
                  
                   
                     2.182144
                  
                   
                     0.338883
                  
                
                 
                   
                     9.08
                  
                   
                     2.186958
                  
                   
                     0.339840
                  
                
                 
                   
                     9.09
                  
                   
                     2.191778
                  
                   
                     0.340796
                  
                
                 
                   
                     9.10
                  
                   
                     2.196603
                  
                   
                     0.341751
                  
                
                 
                   
                     
                     9.11
                  
                   
                     2.201433
                  
                   
                     0.342705
                  
                
                 
                   
                     9.12
                  
                   
                     2.206269
                  
                   
                     0.343658
                  
                
                 
                   
                     9.13
                  
                   
                     2.211110
                  
                   
                     0.344610
                  
                
                 
                   
                     9.14
                  
                   
                     2.215956
                  
                   
                     0.345561
                  
                
                 
                   
                     9.15
                  
                   
                     2.220808
                  
                   
                     0.346511
                  
                
                 
                   
                     9.16
                  
                   
                     2.225665
                  
                   
                     0.347459
                  
                
                 
                   
                     9.17
                  
                   
                     2.230527
                  
                   
                     9.348407
                  
                
                 
                   
                     9.18
                  
                   
                     2.235394
                  
                   
                     0.349354
                  
                
                 
                   
                     9.19
                  
                   
                     2.240267
                  
                   
                     0.350299
                  
                
                 
                   
                     9.20
                  
                   
                     2.245145
                  
                   
                     0.351244
                  
                
                 
                   
                     9.21
                  
                   
                     2.250029
                  
                   
                     0.352881
                  
                
                 
                   
                     9.22
                  
                   
                     2.254917
                  
                   
                     0.353130
                  
                
                 
                   
                     9.23
                  
                   
                     2.259811
                  
                   
                     0.354072
                  
                
                 
                   
                     9.24
                  
                   
                     2.264711
                  
                   
                     0.355012
                  
                
                 
                   
                     9.25
                  
                   
                     2.269615
                  
                   
                     0.355872
                  
                
                 
                   
                     9.26
                  
                   
                     2.274525
                  
                   
                     0.356890
                  
                
                 
                   
                     9.27
                  
                   
                     2.279440
                  
                   
                     0.357828
                  
                
                 
                   
                     9.28
                  
                   
                     2.284361
                  
                   
                     0.358764
                  
                
                 
                   
                     9.29
                  
                   
                     2.289287
                  
                   
                     0.359700
                  
                
                 
                   
                     9.30
                  
                   
                     2.294218
                  
                   
                     0.360634
                  
                
                 
                   
                     9.31
                  
                   
                     2.299154
                  
                   
                     0.361568
                  
                
                 
                   
                     9.32
                  
                   
                     2.304096
                  
                   
                     0.362500
                  
                
                 
                   
                     9.33
                  
                   
                     2.309043
                  
                   
                     0.363432
                  
                
                 
                   
                     9.34
                  
                   
                     2.313996
                  
                   
                     0.364362
                  
                
                 
                   
                     9.35
                  
                   
                     2.318953
                  
                   
                     0.365292
                  
                
                 
                   
                     9.36
                  
                   
                     2.323916
                  
                   
                     0.366220
                  
                
                 
                   
                     9.37
                  
                   
                     2.328885
                  
                   
                     0.367148
                  
                
                 
                   
                     9.38
                  
                   
                     2.333858
                  
                   
                     0.368074
                  
                
                 
                   
                     9.39
                  
                   
                     2.338847
                  
                   
                     0.369000
                  
                
                 
                   
                     9.40
                  
                   
                     2.343821
                  
                   
                     0.369924
                  
                
                 
                   
                     9.41
                  
                   
                     2.348144
                  
                   
                     0.370848
                  
                
                 
                   
                     9.42
                  
                   
                     2.353806
                  
                   
                     0.371770
                  
                
                 
                   
                     9.43
                  
                   
                     2.358806
                  
                   
                     0.372692
                  
                
                 
                   
                     9.44
                  
                   
                     2.363478
                  
                   
                     0.373612
                  
                
                 
                   
                     9.45
                  
                   
                     2.368489
                  
                   
                     0.374532
                  
                
                 
                   
                     9.46
                  
                   
                     2.373838
                  
                   
                     0.375451
                  
                
                 
                   
                     9.48
                  
                   
                     2.378893
                  
                   
                     0.376368
                  
                
                 
                   
                     9.48
                  
                   
                     2.383886
                  
                   
                     0.377285
                  
                
                 
                   
                     9.49
                  
                   
                     2.388918
                  
                   
                     0.378201
                  
                
                 
                   
                     9.50
                  
                   
                     2.393955
                  
                   
                     0
                     .
                     37911●
                  
                
                 
                   
                     9.51
                  
                   
                     2.398998
                  
                   
                     0.380029
                  
                
                 
                   
                     9.52
                  
                   
                     2.404045
                  
                   
                     0.380942
                  
                
                 
                   
                     9.53
                  
                   
                     2.409099
                  
                   
                     0.381854
                  
                
                 
                   
                     9.54
                  
                   
                     2.414157
                  
                   
                     0.382765
                  
                
                 
                   
                     9.55
                  
                   
                     2.419221
                  
                   
                     0.383675
                  
                
                 
                   
                     9.56
                  
                   
                     2.424290
                  
                   
                     0.384584
                  
                
                 
                   
                     9.57
                  
                   
                     2.429364
                  
                   
                     0.385492
                  
                
                 
                   
                     9.58
                  
                   
                     2.434444
                  
                   
                     0.386399
                  
                
                 
                   
                     9.59
                  
                   
                     2.439529
                  
                   
                     0.387306
                  
                
                 
                   
                     9.60
                  
                   
                     2.444629
                  
                   
                     0.388211
                  
                
                 
                   
                     9.61
                  
                   
                     2.449715
                  
                   
                     0.389115
                  
                
                 
                   
                     9.62
                  
                   
                     2.454816
                  
                   
                     0.390019
                  
                
                 
                   
                     9.63
                  
                   
                     2.459922
                  
                   
                     0.390921
                  
                
                 
                   
                     9.64
                  
                   
                     2.465034
                  
                   
                     0.391822
                  
                
                 
                   
                     9.65
                  
                   
                     2.470150
                  
                   
                     0.392723
                  
                
                 
                   
                     9.66
                  
                   
                     2.475273
                  
                   
                     0.393623
                  
                
                 
                   
                     9.67
                  
                   
                     2.480400
                  
                   
                     0.394521
                  
                
                 
                   
                     9.68
                  
                   
                     2.485533
                  
                   
                     0.395419
                  
                
                 
                   
                     9.69
                  
                   
                     2.490671
                  
                   
                     0.396316
                  
                
                 
                   
                     9.70
                  
                   
                     2.495814
                  
                   
                     0.397212
                  
                
                 
                   
                     9.71
                  
                   
                     2.500963
                  
                   
                     0
                     .
                     39810●
                  
                
                 
                   
                     9.72
                  
                   
                     2.506117
                  
                   
                     0.399001
                  
                
                 
                   
                     9.73
                  
                   
                     2.511243
                  
                   
                     0.399894
                  
                
                 
                   
                     9.74
                  
                   
                     2.516441
                  
                   
                     0.400786
                  
                
                 
                   
                     9.75
                  
                   
                     2.521611
                  
                   
                     0
                     .
                     4●1678
                  
                
                 
                   
                     9.76
                  
                   
                     2.526786
                  
                   
                     0.402568
                  
                
                 
                   
                     9.77
                  
                   
                     2.531966
                  
                   
                     0.403458
                  
                
                 
                   
                     9.78
                  
                   
                     2.537152
                  
                   
                     0.404346
                  
                
                 
                   
                     9.79
                  
                   
                     2.542343
                  
                   
                     0.405234
                  
                
                 
                   
                     9.80
                  
                   
                     2.547540
                  
                   
                     0.406121
                  
                
                 
                   
                     
                     9.81
                  
                   
                     2.552745
                  
                   
                     0.407006
                  
                
                 
                   
                     9.82
                  
                   
                     2.557948
                  
                   
                     0.407891
                  
                
                 
                   
                     9.83
                  
                   
                     2.563164
                  
                   
                     0.408775
                  
                
                 
                   
                     9.84
                  
                   
                     2.568378
                  
                   
                     0.409659
                  
                
                 
                   
                     9.85
                  
                   
                     2.573601
                  
                   
                     0.410541
                  
                
                 
                   
                     9.86
                  
                   
                     2.578829
                  
                   
                     0.411422
                  
                
                 
                   
                     9.87
                  
                   
                     2.584063
                  
                   
                     0.412303
                  
                
                 
                   
                     9.88
                  
                   
                     2.589302
                  
                   
                     0.413182
                  
                
                 
                   
                     9.89
                  
                   
                     2.594546
                  
                   
                     0.414061
                  
                
                 
                   
                     9.90
                  
                   
                     2.599795
                  
                   
                     0.414939
                  
                
                 
                   
                     9.91
                  
                   
                     2.605050
                  
                   
                     0.415816
                  
                
                 
                   
                     9.92
                  
                   
                     2.610310
                  
                   
                     0.416692
                  
                
                 
                   
                     9.93
                  
                   
                     2.615573
                  
                   
                     0.417567
                  
                
                 
                   
                     9.94
                  
                   
                     2.620846
                  
                   
                     0.418441
                  
                
                 
                   
                     9.95
                  
                   
                     2.626122
                  
                   
                     0.419315
                  
                
                 
                   
                     9.96
                  
                   
                     2.631404
                  
                   
                     0.420187
                  
                
                 
                   
                     9.97
                  
                   
                     2.636690
                  
                   
                     0.421059
                  
                
                 
                   
                     9.98
                  
                   
                     2.641982
                  
                   
                     0.421929
                  
                
                 
                   
                     9.99
                  
                   
                     2.647279
                  
                   
                     0.422789
                  
                
                 
                   
                     10.00
                  
                   
                     2.652582
                  
                   
                     0.423668
                  
                
              
            
             
             
               A
               Table
               for
               the
               speedy
               finding
               of
               the
               Length
               or
               Circumference
               answering
               to
               any
               Arch
               in
               Degrees
               and
               Decimal
               Parts
               .
            
             
             
               A
               Table
               for
               the
               speedy
               finding
               of
               the
               Length
               or
               Circumference
               answering
               to
               any
               Arch
               ,
               in
               Degrees
               and
               Decimal
               Parts
               .
            
             
               
                 
                   
                     1
                  
                   
                     0.0174
                  
                   
                     5329
                  
                   
                     2519
                  
                
                 
                   
                     2
                  
                   
                     0.0349
                  
                   
                     0658
                  
                   
                     5038
                  
                
                 
                   
                     3
                  
                   
                     0.0523
                  
                   
                     5987
                  
                   
                     7557
                  
                
                 
                   
                     4
                  
                   
                     0.0698
                  
                   
                     1317
                  
                   
                     0076
                  
                
                 
                   
                     5
                  
                   
                     0.0872
                  
                   
                     6646
                  
                   
                     2595
                  
                
                 
                   
                     6
                  
                   
                     0.1047
                  
                   
                     1975
                  
                   
                     5114
                  
                
                 
                   
                     7
                  
                   
                     0.1221
                  
                   
                     7304
                  
                   
                     7633
                  
                
                 
                   
                     8
                  
                   
                     0.1396
                  
                   
                     2634
                  
                   
                     0152
                  
                
                 
                   
                     9
                  
                   
                     0.1570
                  
                   
                     7963
                  
                   
                     2671
                  
                
                 
                   
                     10
                  
                   
                     0.1745
                  
                   
                     3292
                  
                   
                     5190
                  
                
                 
                   
                     11
                  
                   
                     0.1919
                  
                   
                     8621
                  
                   
                     7709
                  
                
                 
                   
                     12
                  
                   
                     0.2094
                  
                   
                     3951
                  
                   
                     0228
                  
                
                 
                   
                     13
                  
                   
                     0.2268
                  
                   
                     9280
                  
                   
                     2747
                  
                
                 
                   
                     14
                  
                   
                     0.2443
                  
                   
                     4609
                  
                   
                     5266
                  
                
                 
                   
                     15
                  
                   
                     0.2617
                  
                   
                     9938
                  
                   
                     7785
                  
                
                 
                   
                     16
                  
                   
                     0.2792
                  
                   
                     5268
                  
                   
                     0304
                  
                
                 
                   
                     17
                  
                   
                     0.2967
                  
                   
                     0597
                  
                   
                     2823
                  
                
                 
                   
                     18
                  
                   
                     0.3141
                  
                   
                     5926
                  
                   
                     5342
                  
                
                 
                   
                     19
                  
                   
                     0.3316
                  
                   
                     1255
                  
                   
                     7861
                  
                
                 
                   
                     20
                  
                   
                     0.3490
                  
                   
                     6585
                  
                   
                     0380
                  
                
                 
                   
                     21
                  
                   
                     0.3665
                  
                   
                     1914
                  
                   
                     2899
                  
                
                 
                   
                     22
                  
                   
                     0.3839
                  
                   
                     7245
                  
                   
                     5418
                  
                
                 
                   
                     23
                  
                   
                     0.4014
                  
                   
                     2572
                  
                   
                     7937
                  
                
                 
                   
                     24
                  
                   
                     0.4188
                  
                   
                     7902
                  
                   
                     0456
                  
                
                 
                   
                     25
                  
                   
                     0.4363
                  
                   
                     3231
                  
                   
                     2975
                  
                
                 
                   
                     26
                  
                   
                     0.4537
                  
                   
                     8560
                  
                   
                     5495
                  
                
                 
                   
                     27
                  
                   
                     0.4712
                  
                   
                     3889
                  
                   
                     8013
                  
                
                 
                   
                     28
                  
                   
                     0.4886
                  
                   
                     8219
                  
                   
                     0532
                  
                
                 
                   
                     29
                  
                   
                     0.5061
                  
                   
                     4548
                  
                   
                     3051
                  
                
                 
                   
                     30
                  
                   
                     0.5235
                  
                   
                     4877
                  
                   
                     5570
                  
                
                 
                   
                     31
                  
                   
                     0.5410
                  
                   
                     5206
                  
                   
                     8089
                  
                
                 
                   
                     32
                  
                   
                     0.5585
                  
                   
                     0536
                  
                   
                     0608
                  
                
                 
                   
                     33
                  
                   
                     0.5759
                  
                   
                     5865
                  
                   
                     3127
                  
                
                 
                   
                     34
                  
                   
                     0.5934
                  
                   
                     1194
                  
                   
                     5646
                  
                
                 
                   
                     35
                  
                   
                     0.6108
                  
                   
                     6523
                  
                   
                     8165
                  
                
                 
                   
                     36
                  
                   
                     0.6283
                  
                   
                     1853
                  
                   
                     0684
                  
                
                 
                   
                     37
                  
                   
                     0.6457
                  
                   
                     7128
                  
                   
                     3203
                  
                
                 
                   
                     38
                  
                   
                     0.6632
                  
                   
                     2511
                  
                   
                     5722
                  
                
                 
                   
                     39
                  
                   
                     0.6806
                  
                   
                     7840
                  
                   
                     8241
                  
                
                 
                   
                     40
                  
                   
                     0.6981
                  
                   
                     3170
                  
                   
                     0760
                  
                
                 
                   
                     41
                  
                   
                     0.7155
                  
                   
                     8499
                  
                   
                     3279
                  
                
                 
                   
                     42
                  
                   
                     0.7330
                  
                   
                     3828
                  
                   
                     5798
                  
                
                 
                   
                     43
                  
                   
                     0.7504
                  
                   
                     9157
                  
                   
                     8317
                  
                
                 
                   
                     44
                  
                   
                     0.7679
                  
                   
                     4487
                  
                   
                     0836
                  
                
                 
                   
                     45
                  
                   
                     0.7853
                  
                   
                     9816
                  
                   
                     3355
                  
                
                 
                   
                     46
                  
                   
                     0.8028
                  
                   
                     3145
                  
                   
                     5874
                  
                
                 
                   
                     47
                  
                   
                     0.8203
                  
                   
                     0474
                  
                   
                     8393
                  
                
                 
                   
                     48
                  
                   
                     0.8377
                  
                   
                     5804
                  
                   
                     0912
                  
                
                 
                   
                     49
                  
                   
                     0.8552
                  
                   
                     1133
                  
                   
                     3431
                  
                
                 
                   
                     50
                  
                   
                     0.8726
                  
                   
                     6462
                  
                   
                     4950
                  
                
                 
                   
                     
                     51
                  
                   
                     0.8901
                  
                   
                     1791
                  
                   
                     8469
                  
                
                 
                   
                     52
                  
                   
                     0.9075
                  
                   
                     7121
                  
                   
                     0988
                  
                
                 
                   
                     53
                  
                   
                     0.9250
                  
                   
                     2450
                  
                   
                     3507
                  
                
                 
                   
                     54
                  
                   
                     0.9424
                  
                   
                     7779
                  
                   
                     6026
                  
                
                 
                   
                     55
                  
                   
                     0.9599
                  
                   
                     3108
                  
                   
                     8545
                  
                
                 
                   
                     56
                  
                   
                     0.9773
                  
                   
                     8438
                  
                   
                     1064
                  
                
                 
                   
                     57
                  
                   
                     0.9948
                  
                   
                     3767
                  
                   
                     3583
                  
                
                 
                   
                     58
                  
                   
                     1.0122
                  
                   
                     9096
                  
                   
                     6102
                  
                
                 
                   
                     59
                  
                   
                     1.0297
                  
                   
                     4425
                  
                   
                     8621
                  
                
                 
                   
                     60
                  
                   
                     1.0471
                  
                   
                     9755
                  
                   
                     1140
                  
                
                 
                   
                     61
                  
                   
                     1.0646
                  
                   
                     5084
                  
                   
                     3659
                  
                
                 
                   
                     62
                  
                   
                     1.0821
                  
                   
                     0413
                  
                   
                     6178
                  
                
                 
                   
                     63
                  
                   
                     1.0995
                  
                   
                     5742
                  
                   
                     8697
                  
                
                 
                   
                     64
                  
                   
                     1.1170
                  
                   
                     1072
                  
                   
                     1216
                  
                
                 
                   
                     65
                  
                   
                     1.1344
                  
                   
                     6401
                  
                   
                     3735
                  
                
                 
                   
                     66
                  
                   
                     1.1519
                  
                   
                     1730
                  
                   
                     6254
                  
                
                 
                   
                     67
                  
                   
                     1.1693
                  
                   
                     7059
                  
                   
                     8773
                  
                
                 
                   
                     68
                  
                   
                     1.1868
                  
                   
                     2389
                  
                   
                     1292
                  
                
                 
                   
                     69
                  
                   
                     1.2042
                  
                   
                     7718
                  
                   
                     3811
                  
                
                 
                   
                     70
                  
                   
                     1.2217
                  
                   
                     3047
                  
                   
                     6330
                  
                
                 
                   
                     71
                  
                   
                     1.2391
                  
                   
                     8376
                  
                   
                     8849
                  
                
                 
                   
                     72
                  
                   
                     1.2566
                  
                   
                     3706
                  
                   
                     1368
                  
                
                 
                   
                     73
                  
                   
                     1.2740
                  
                   
                     9035
                  
                   
                     3887
                  
                
                 
                   
                     74
                  
                   
                     1.2915
                  
                   
                     4364
                  
                   
                     6406
                  
                
                 
                   
                     75
                  
                   
                     1.3089
                  
                   
                     9693
                  
                   
                     8925
                  
                
                 
                   
                     76
                  
                   
                     1.3264
                  
                   
                     5023
                  
                   
                     1444
                  
                
                 
                   
                     77
                  
                   
                     1.3439
                  
                   
                     0352
                  
                   
                     3963
                  
                
                 
                   
                     78
                  
                   
                     1.3613
                  
                   
                     5681
                  
                   
                     6482
                  
                
                 
                   
                     79
                  
                   
                     1.3788
                  
                   
                     1010
                  
                   
                     9001
                  
                
                 
                   
                     80
                  
                   
                     1.3962
                  
                   
                     6340
                  
                   
                     1520
                  
                
                 
                   
                     81
                  
                   
                     1.4137
                  
                   
                     1669
                  
                   
                     4039
                  
                
                 
                   
                     82
                  
                   
                     1.4311
                  
                   
                     6998
                  
                   
                     6558
                  
                
                 
                   
                     83
                  
                   
                     1.4486
                  
                   
                     2327
                  
                   
                     9057
                  
                
                 
                   
                     84
                  
                   
                     1.4660
                  
                   
                     7657
                  
                   
                     1596
                  
                
                 
                   
                     85
                  
                   
                     1.4835
                  
                   
                     2986
                  
                   
                     4115
                  
                
                 
                   
                     86
                  
                   
                     1.5009
                  
                   
                     8315
                  
                   
                     6634
                  
                
                 
                   
                     87
                  
                   
                     2.5184
                  
                   
                     3644
                  
                   
                     9153
                  
                
                 
                   
                     88
                  
                   
                     1.5358
                  
                   
                     8974
                  
                   
                     1572
                  
                
                 
                   
                     89
                  
                   
                     1.5533
                  
                   
                     4303
                  
                   
                     4191
                  
                
                 
                   
                     90
                  
                   
                     1.5707
                  
                   
                     9632
                  
                   
                     6710
                  
                
                 
                   
                     91
                  
                   
                     1.5882
                  
                   
                     4961
                  
                   
                     9229
                  
                
                 
                   
                     92
                  
                   
                     1.6057
                  
                   
                     0291
                  
                   
                     1748
                  
                
                 
                   
                     93
                  
                   
                     1.6231
                  
                   
                     5620
                  
                   
                     4267
                  
                
                 
                   
                     94
                  
                   
                     1.6406
                  
                   
                     0949
                  
                   
                     6786
                  
                
                 
                   
                     95
                  
                   
                     1.6580
                  
                   
                     6278
                  
                   
                     9305
                  
                
                 
                   
                     96
                  
                   
                     1.6755
                  
                   
                     1608
                  
                   
                     1824
                  
                
                 
                   
                     97
                  
                   
                     1.6929
                  
                   
                     6937
                  
                   
                     4343
                  
                
                 
                   
                     98
                  
                   
                     1.7104
                  
                   
                     2266
                  
                   
                     6862
                  
                
                 
                   
                     99
                  
                   
                     1.7278
                  
                   
                     7595
                  
                   
                     9381
                  
                
                 
                   
                     100
                  
                   
                     1.7453
                  
                   
                     2925
                  
                   
                     1900
                  
                
              
            
             
             
               A
               Common
               Divisor
               for
               the
               speedy
               converting
               of
               the
               Table
               ,
               shewing
               the
               Area
               of
               the
               Segments
               of
               a
               Circle
               whose
               Diameter
               is
               2.0000
               &c.
               into
               a
               Table
               shewing
               the
               Area
               of
               the
               Segment
               of
               any
               Circle
               whose
               Area
               is
               given
               .
            
             
               
                 
                   
                     1
                  
                   
                     0031
                  
                   
                     4159
                  
                   
                     2653
                  
                
                 
                   
                     2
                  
                   
                     0062
                  
                   
                     8318
                  
                   
                     5306
                  
                
                 
                   
                     3
                  
                   
                     0094
                  
                   
                     2477
                  
                   
                     7959
                  
                
                 
                   
                     4
                  
                   
                     0125
                  
                   
                     6637
                  
                   
                     0612
                  
                
                 
                   
                     5
                  
                   
                     0157
                  
                   
                     0796
                  
                   
                     3265
                  
                
                 
                   
                     6
                  
                   
                     0188
                  
                   
                     4955
                  
                   
                     5918
                  
                
                 
                   
                     7
                  
                   
                     0219
                  
                   
                     9114
                  
                   
                     8571
                  
                
                 
                   
                     8
                  
                   
                     0251
                  
                   
                     3274
                  
                   
                     1224
                  
                
                 
                   
                     9
                  
                   
                     0282
                  
                   
                     7433
                  
                   
                     3877
                  
                
                 
                   
                     10
                  
                   
                     0314
                  
                   
                     1592
                  
                   
                     6530
                  
                
                 
                   
                     11
                  
                   
                     0345
                  
                   
                     5751
                  
                   
                     9183
                  
                
                 
                   
                     12
                  
                   
                     0376
                  
                   
                     9911
                  
                   
                     1836
                  
                
                 
                   
                     13
                  
                   
                     0408
                  
                   
                     4070
                  
                   
                     4489
                  
                
                 
                   
                     14
                  
                   
                     0439
                  
                   
                     8229
                  
                   
                     7142
                  
                
                 
                   
                     15
                  
                   
                     0471
                  
                   
                     2388
                  
                   
                     9795
                  
                
                 
                   
                     16
                  
                   
                     0502
                  
                   
                     6548
                  
                   
                     2448
                  
                
                 
                   
                     17
                  
                   
                     0534
                  
                   
                     0707
                  
                   
                     5101
                  
                
                 
                   
                     18
                  
                   
                     0565
                  
                   
                     4866
                  
                   
                     7754
                  
                
                 
                   
                     19
                  
                   
                     0596
                  
                   
                     9026
                  
                   
                     0407
                  
                
                 
                   
                     20
                  
                   
                     0628
                  
                   
                     3185
                  
                   
                     3060
                  
                
                 
                   
                     21
                  
                   
                     0659
                  
                   
                     7344
                  
                   
                     5713
                  
                
                 
                   
                     22
                  
                   
                     0691
                  
                   
                     1503
                  
                   
                     8366
                  
                
                 
                   
                     23
                  
                   
                     0722
                  
                   
                     5663
                  
                   
                     1019
                  
                
                 
                   
                     24
                  
                   
                     0753
                  
                   
                     9822
                  
                   
                     3672
                  
                
                 
                   
                     25
                  
                   
                     0785
                  
                   
                     3981
                  
                   
                     6325
                  
                
                 
                   
                     26
                  
                   
                     0816
                  
                   
                     8140
                  
                   
                     8978
                  
                
                 
                   
                     27
                  
                   
                     0848
                  
                   
                     2300
                  
                   
                     1631
                  
                
                 
                   
                     28
                  
                   
                     0889
                  
                   
                     6459
                  
                   
                     4284
                  
                
                 
                   
                     29
                  
                   
                     0911
                  
                   
                     0618
                  
                   
                     6937
                  
                
                 
                   
                     30
                  
                   
                     0942
                  
                   
                     4777
                  
                   
                     9590
                  
                
                 
                   
                     21
                  
                   
                     0973
                  
                   
                     8937
                  
                   
                     2243
                  
                
                 
                   
                     32
                  
                   
                     1005
                  
                   
                     3096
                  
                   
                     4896
                  
                
                 
                   
                     33
                  
                   
                     1036
                  
                   
                     7255
                  
                   
                     7549
                  
                
                 
                   
                     34
                  
                   
                     1068
                  
                   
                     1415
                  
                   
                     0202
                  
                
                 
                   
                     35
                  
                   
                     1099
                  
                   
                     5574
                  
                   
                     2855
                  
                
                 
                   
                     36
                  
                   
                     1130
                  
                   
                     9733
                  
                   
                     5508
                  
                
                 
                   
                     37
                  
                   
                     1162
                  
                   
                     3892
                  
                   
                     8161
                  
                
                 
                   
                     38
                  
                   
                     1193
                  
                   
                     8052
                  
                   
                     0814
                  
                
                 
                   
                     39
                  
                   
                     1225
                  
                   
                     2211
                  
                   
                     3467
                  
                
                 
                   
                     40
                  
                   
                     1256
                  
                   
                     6370
                  
                   
                     6120
                  
                
                 
                   
                     41
                  
                   
                     1288
                  
                   
                     0529
                  
                   
                     8773
                  
                
                 
                   
                     42
                  
                   
                     1319
                  
                   
                     4689
                  
                   
                     1426
                  
                
                 
                   
                     43
                  
                   
                     1350
                  
                   
                     8848
                  
                   
                     4079
                  
                
                 
                   
                     44
                  
                   
                     1382
                  
                   
                     3007
                  
                   
                     6732
                  
                
                 
                   
                     45
                  
                   
                     1413
                  
                   
                     7166
                  
                   
                     9385
                  
                
                 
                   
                     46
                  
                   
                     1445
                  
                   
                     1326
                  
                   
                     2038
                  
                
                 
                   
                     47
                  
                   
                     1476
                  
                   
                     5485
                  
                   
                     4691
                  
                
                 
                   
                     48
                  
                   
                     1507
                  
                   
                     9644
                  
                   
                     7344
                  
                
                 
                   
                     49
                  
                   
                     1539
                  
                   
                     3803
                  
                   
                     9997
                  
                
                 
                   
                     50
                  
                   
                     1570
                  
                   
                     7963
                  
                   
                     2650
                  
                
                 
                   
                     
                     51
                  
                   
                     1602
                  
                   
                     2122
                  
                   
                     5303
                  
                
                 
                   
                     52
                  
                   
                     1633
                  
                   
                     6281
                  
                   
                     7956
                  
                
                 
                   
                     53
                  
                   
                     1665
                  
                   
                     0441
                  
                   
                     0609
                  
                
                 
                   
                     54
                  
                   
                     1696
                  
                   
                     4600
                  
                   
                     3262
                  
                
                 
                   
                     55
                  
                   
                     1727
                  
                   
                     8759
                  
                   
                     5915
                  
                
                 
                   
                     56
                  
                   
                     1759
                  
                   
                     2918
                  
                   
                     6568
                  
                
                 
                   
                     57
                  
                   
                     1790
                  
                   
                     7078
                  
                   
                     1221
                  
                
                 
                   
                     58
                  
                   
                     1822
                  
                   
                     1237
                  
                   
                     3874
                  
                
                 
                   
                     59
                  
                   
                     1853
                  
                   
                     5396
                  
                   
                     6527
                  
                
                 
                   
                     60
                  
                   
                     1884
                  
                   
                     9555
                  
                   
                     9180
                  
                
                 
                   
                     61
                  
                   
                     1916
                  
                   
                     3715
                  
                   
                     1833
                  
                
                 
                   
                     62
                  
                   
                     1947
                  
                   
                     7874
                  
                   
                     4486
                  
                
                 
                   
                     63
                  
                   
                     1979
                  
                   
                     2033
                  
                   
                     7139
                  
                
                 
                   
                     64
                  
                   
                     2010
                  
                   
                     6192
                  
                   
                     9792
                  
                
                 
                   
                     65
                  
                   
                     2042
                  
                   
                     0352
                  
                   
                     2445
                  
                
                 
                   
                     66
                  
                   
                     2073
                  
                   
                     4511
                  
                   
                     5098
                  
                
                 
                   
                     67
                  
                   
                     2104
                  
                   
                     8670
                  
                   
                     7751
                  
                
                 
                   
                     68
                  
                   
                     2136
                  
                   
                     2830
                  
                   
                     0404
                  
                
                 
                   
                     69
                  
                   
                     2167
                  
                   
                     6989
                  
                   
                     3057
                  
                
                 
                   
                     70
                  
                   
                     2199
                  
                   
                     1148
                  
                   
                     5710
                  
                
                 
                   
                     71
                  
                   
                     2230
                  
                   
                     5307
                  
                   
                     8363
                  
                
                 
                   
                     72
                  
                   
                     2261
                  
                   
                     9467
                  
                   
                     1016
                  
                
                 
                   
                     53
                  
                   
                     2293
                  
                   
                     3626
                  
                   
                     3669
                  
                
                 
                   
                     74
                  
                   
                     2324
                  
                   
                     7785
                  
                   
                     6322
                  
                
                 
                   
                     75
                  
                   
                     2356
                  
                   
                     1944
                  
                   
                     8975
                  
                
                 
                   
                     76
                  
                   
                     2387
                  
                   
                     6104
                  
                   
                     1628
                  
                
                 
                   
                     77
                  
                   
                     2419
                  
                   
                     0263
                  
                   
                     4281
                  
                
                 
                   
                     78
                  
                   
                     2450
                  
                   
                     4422
                  
                   
                     6934
                  
                
                 
                   
                     79
                  
                   
                     2481
                  
                   
                     8581
                  
                   
                     9587
                  
                
                 
                   
                     80
                  
                   
                     2513
                  
                   
                     2741
                  
                   
                     2240
                  
                
                 
                   
                     81
                  
                   
                     2544
                  
                   
                     6900
                  
                   
                     4893
                  
                
                 
                   
                     82
                  
                   
                     2576
                  
                   
                     1059
                  
                   
                     7546
                  
                
                 
                   
                     83
                  
                   
                     2607
                  
                   
                     5219
                  
                   
                     0199
                  
                
                 
                   
                     84
                  
                   
                     2638
                  
                   
                     9378
                  
                   
                     2852
                  
                
                 
                   
                     85
                  
                   
                     2670
                  
                   
                     3537
                  
                   
                     5505
                  
                
                 
                   
                     86
                  
                   
                     2701
                  
                   
                     7696
                  
                   
                     8158
                  
                
                 
                   
                     87
                  
                   
                     2733
                  
                   
                     1856
                  
                   
                     0811
                  
                
                 
                   
                     88
                  
                   
                     2764
                  
                   
                     6015
                  
                   
                     3464
                  
                
                 
                   
                     89
                  
                   
                     2796
                  
                   
                     0174
                  
                   
                     6117
                  
                
                 
                   
                     90
                  
                   
                     2827
                  
                   
                     4333
                  
                   
                     8770
                  
                
                 
                   
                     91
                  
                   
                     2858
                  
                   
                     8493
                  
                   
                     1423
                  
                
                 
                   
                     92
                  
                   
                     2890
                  
                   
                     2652
                  
                   
                     4076
                  
                
                 
                   
                     93
                  
                   
                     2921
                  
                   
                     6811
                  
                   
                     6729
                  
                
                 
                   
                     94
                  
                   
                     2953
                  
                   
                     0970
                  
                   
                     9382
                  
                
                 
                   
                     95
                  
                   
                     2984
                  
                   
                     5130
                  
                   
                     2035
                  
                
                 
                   
                     96
                  
                   
                     3015
                  
                   
                     9289
                  
                   
                     4688
                  
                
                 
                   
                     97
                  
                   
                     3047
                  
                   
                     3448
                  
                   
                     7341
                  
                
                 
                   
                     98
                  
                   
                     3078
                  
                   
                     7607
                  
                   
                     9994
                  
                
                 
                   
                     99
                  
                   
                     3110
                  
                   
                     1767
                  
                   
                     2647
                  
                
                 
                   
                     100
                  
                   
                     3141
                  
                   
                     5926
                  
                   
                     5300
                  
                
              
            
             
             
               A
               Table
               shewing
               the
               Ordinates
               ,
               Arches
               and
               Areas
               of
               the
               Segments
               of
               a
               Circle
               ,
               whose
               Diameter
               is
               2000
               ,
               &c.
               to
               every
               Hundredth
               Part
               of
               the
               Radius
               .
            
             
             
               
                 
                   
                      
                  
                   
                     Ordinates
                  
                   
                     Deg.
                     &
                     Dec.
                     p.
                     
                  
                   
                     Areas
                  
                
                 
                   
                     100
                  
                   
                     10000000000
                  
                   
                     90.00000000
                  
                   
                     1.57079632
                  
                
                 
                   
                     99
                  
                   
                     9999499971
                  
                   
                     89.42704196
                  
                   
                     1.55079682
                  
                
                 
                   
                     98
                  
                   
                     9997999799
                  
                   
                     88.85400799
                  
                   
                     1.53079890
                  
                
                 
                   
                     97
                  
                   
                     9995498987
                  
                   
                     88.28987110
                  
                   
                     1.51080538
                  
                
                 
                   
                     96
                  
                   
                     99919967974
                  
                   
                     87.70756124
                  
                   
                     1.49081774
                  
                
                 
                   
                     95
                  
                   
                     9987492177
                  
                   
                     87.13402020
                  
                   
                     1.47083808
                  
                
                 
                   
                     94
                  
                   
                     9981983770
                  
                   
                     86.56018749
                  
                   
                     1.45086837
                  
                
                 
                   
                     93
                  
                   
                     9975469913
                  
                   
                     85.98601581
                  
                   
                     1.43091081
                  
                
                 
                   
                     92
                  
                   
                     9967948635
                  
                   
                     85.41143529
                  
                   
                     1.41096718
                  
                
                 
                   
                     91
                  
                   
                     9959417653
                  
                   
                     84.83639513
                  
                   
                     1.39103966
                  
                
                 
                   
                     90
                  
                   
                     9949874371
                  
                   
                     84.26083018
                  
                   
                     1.37113017
                  
                
                 
                   
                     89
                  
                   
                     9939315871
                  
                   
                     83.68468641
                  
                   
                     1.35124084
                  
                
                 
                   
                     88
                  
                   
                     9927738916
                  
                   
                     83.10789860
                  
                   
                     1.35137360
                  
                
                 
                   
                     87
                  
                   
                     9915139938
                  
                   
                     82.53040793
                  
                   
                     1.31153053
                  
                
                 
                   
                     86
                  
                   
                     9901515035
                  
                   
                     81.95215479
                  
                   
                     1.29171372
                  
                
                 
                   
                     85
                  
                   
                     9886859966
                  
                   
                     81.37307468
                  
                   
                     1.27192518
                  
                
                 
                   
                     84
                  
                   
                     9871170138
                  
                   
                     80.79310474
                  
                   
                     1.25216697
                  
                
                 
                   
                     83
                  
                   
                     9854440623
                  
                   
                     80.21218180
                  
                   
                     1.23244118
                  
                
                 
                   
                     82
                  
                   
                     9836666101
                  
                   
                     79.63024030
                  
                   
                     1.21274989
                  
                
                 
                   
                     81
                  
                   
                     9817840903
                  
                   
                     79.04721672
                  
                   
                     1.19309522
                  
                
                 
                   
                     80
                  
                   
                     9797958971
                  
                   
                     78.46304188
                  
                   
                     1.17347924
                  
                
                 
                   
                     79
                  
                   
                     9777013859
                  
                   
                     77.87762112
                  
                   
                     1.15390361
                  
                
                 
                   
                     78
                  
                   
                     9754998718
                  
                   
                     77.29096735
                  
                   
                     1.13437189
                  
                
                 
                   
                     77
                  
                   
                     9731906288
                  
                   
                     76.70292903
                  
                   
                     1.11488481
                  
                
                 
                   
                     76
                  
                   
                     9707728879
                  
                   
                     76.11243681
                  
                   
                     1.09544458
                  
                
                 
                   
                     75
                  
                   
                     9682458365
                  
                   
                     75.52248845
                  
                   
                     1.07605462
                  
                
                 
                   
                     74
                  
                   
                     9656086163
                  
                   
                     74.92996014
                  
                   
                     1.05671627
                  
                
                 
                   
                     73
                  
                   
                     9628603221
                  
                   
                     74.33573392
                  
                   
                     1.03743102
                  
                
                 
                   
                     72
                  
                   
                     9600000000
                  
                   
                     73.73979456
                  
                   
                     1.01820220
                  
                
                 
                   
                     71
                  
                   
                     9570266454
                  
                   
                     73.14202474
                  
                   
                     0.99903143
                  
                
                 
                   
                     70
                  
                   
                     9539392014
                  
                   
                     72.54239737
                  
                   
                     0.97992192
                  
                
                 
                   
                     69
                  
                   
                     950●365565
                  
                   
                     71.94076969
                  
                   
                     0.96087497
                  
                
                 
                   
                     68
                  
                   
                     9474175425
                  
                   
                     71.33707564
                  
                   
                     0.94189323
                  
                
                 
                   
                     67
                  
                   
                     9439809319
                  
                   
                     70.73122476
                  
                   
                     0.92297905
                  
                
                 
                   
                     
                     67
                  
                   
                     9439809319
                  
                   
                     70.73122476
                  
                   
                     0.92297905
                  
                
                 
                   
                     66
                  
                   
                     9404254356
                  
                   
                     70.12312662
                  
                   
                     0.90413479
                  
                
                 
                   
                     65
                  
                   
                     9367496997
                  
                   
                     69.51268522
                  
                   
                     0.88536283
                  
                
                 
                   
                     64
                  
                   
                     9329523031
                  
                   
                     68.89980401
                  
                   
                     0.86666560
                  
                
                 
                   
                     63
                  
                   
                     9290317540
                  
                   
                     68.28438326
                  
                   
                     0.84804557
                  
                
                 
                   
                     62
                  
                   
                     9249864864
                  
                   
                     67.66631784
                  
                   
                     0.82950517
                  
                
                 
                   
                     61
                  
                   
                     9208148564
                  
                   
                     67.04550117
                  
                   
                     0.81104695
                  
                
                 
                   
                     60
                  
                   
                     9165151389
                  
                   
                     66.42182324
                  
                   
                     0.79267345
                  
                
                 
                   
                     59
                  
                   
                     9120855222
                  
                   
                     65.79516567
                  
                   
                     0.77438721
                  
                
                 
                   
                     58
                  
                   
                     9075241043
                  
                   
                     65.16541298
                  
                   
                     0.75619089
                  
                
                 
                   
                     57
                  
                   
                     9028288874
                  
                   
                     64.53244020
                  
                   
                     0.73808713
                  
                
                 
                   
                     56
                  
                   
                     8979977728
                  
                   
                     63.89612058
                  
                   
                     0.72007866
                  
                
                 
                   
                     55
                  
                   
                     8930285549
                  
                   
                     63.25631645
                  
                   
                     0.70216884
                  
                
                 
                   
                     54
                  
                   
                     8879189152
                  
                   
                     62.61289754
                  
                   
                     0.68435845
                  
                
                 
                   
                     53
                  
                   
                     8826664149
                  
                   
                     61.96570387
                  
                   
                     0.66665234
                  
                
                 
                   
                     52
                  
                   
                     8772684879
                  
                   
                     61.31459838
                  
                   
                     0.64905275
                  
                
                 
                   
                     51
                  
                   
                     8717224755
                  
                   
                     60.65941181
                  
                   
                     0.63156249
                  
                
                 
                   
                     50
                  
                   
                     8660254037
                  
                   
                     60.00000000
                  
                   
                     0.61418485
                  
                
                 
                   
                     49
                  
                   
                     8601744009
                  
                   
                     59.33617061
                  
                   
                     0.59692260
                  
                
                 
                   
                     48
                  
                   
                     8541662601
                  
                   
                     58.66774875
                  
                   
                     0.57977892
                  
                
                 
                   
                     47
                  
                   
                     8479976415
                  
                   
                     57.99454553
                  
                   
                     0.56275702
                  
                
                 
                   
                     46
                  
                   
                     8416650165
                  
                   
                     57.31636147
                  
                   
                     0.54586011
                  
                
                 
                   
                     45
                  
                   
                     8351646544
                  
                   
                     56.63307065
                  
                   
                     0.52909299
                  
                
                 
                   
                     44
                  
                   
                     8284926070
                  
                   
                     55.94420256
                  
                   
                     0.51245467
                  
                
                 
                   
                     43
                  
                   
                     8216446926
                  
                   
                     55.24977433
                  
                   
                     0.49595300
                  
                
                 
                   
                     42
                  
                   
                     8146264741
                  
                   
                     54.54945742
                  
                   
                     0.47959008
                  
                
                 
                   
                     41
                  
                   
                     8074032449
                  
                   
                     53.84299205
                  
                   
                     0.46336957
                  
                
                 
                   
                     40
                  
                   
                     8000000000
                  
                   
                     53.13010237
                  
                   
                     0.44725221
                  
                
                 
                   
                     39
                  
                   
                     7924014134
                  
                   
                     52.41049708
                  
                   
                     0.43137885
                  
                
                 
                   
                     38
                  
                   
                     7846018098
                  
                   
                     51.68386597
                  
                   
                     0.41560051
                  
                
                 
                   
                     37
                  
                   
                     7765951325
                  
                   
                     50.94987748
                  
                   
                     0.39998818
                  
                
                 
                   
                     36
                  
                   
                     7683749084
                  
                   
                     50.20810657
                  
                   
                     0.38453683
                  
                
                 
                   
                     35
                  
                   
                     7599342076
                  
                   
                     49.45831012
                  
                   
                     0.36925312
                  
                
                 
                   
                     34
                  
                   
                     7512655988
                  
                   
                     48.70012721
                  
                   
                     0.35414227
                  
                
                 
                   
                     
                     34
                  
                   
                     7512655988
                  
                   
                     48.70012721
                  
                   
                     0.35414227
                  
                
                 
                   
                     33
                  
                   
                     7423610981
                  
                   
                     47.93293539
                  
                   
                     0.33920561
                  
                
                 
                   
                     32
                  
                   
                     7332121111
                  
                   
                     47.15635717
                  
                   
                     0.32444946
                  
                
                 
                   
                     31
                  
                   
                     7238093671
                  
                   
                     46.36989113
                  
                   
                     0.30987884
                  
                
                 
                   
                     30
                  
                   
                     7141428428
                  
                   
                     45.57299618
                  
                   
                     0.29549884
                  
                
                 
                   
                     29
                  
                   
                     7042016756
                  
                   
                     44.76508489
                  
                   
                     0.28131493
                  
                
                 
                   
                     28
                  
                   
                     6939740629
                  
                   
                     48.94551977
                  
                   
                     0.26733268
                  
                
                 
                   
                     27
                  
                   
                     6834471449
                  
                   
                     43.11360613
                  
                   
                     0.25355796
                  
                
                 
                   
                     26
                  
                   
                     6726068688
                  
                   
                     42.26858452
                  
                   
                     0.23999689
                  
                
                 
                   
                     25
                  
                   
                     6614378277
                  
                   
                     41.40962595
                  
                   
                     0.22665594
                  
                
                 
                   
                     24
                  
                   
                     6499230723
                  
                   
                     40.53580228
                  
                   
                     0.21354168
                  
                
                 
                   
                     23
                  
                   
                     6380438856
                  
                   
                     39.64611132
                  
                   
                     0.20066138
                  
                
                 
                   
                     22
                  
                   
                     6257795138
                  
                   
                     38.73942400
                  
                   
                     0.18802248
                  
                
                 
                   
                     21
                  
                   
                     6131068422
                  
                   
                     37.81448867
                  
                   
                     0.17563291
                  
                
                 
                   
                     20
                  
                   
                     6000000000
                  
                   
                     36.86989765
                  
                   
                     0.16350111
                  
                
                 
                   
                     19
                  
                   
                     5864298764
                  
                   
                     35.90406873
                  
                   
                     0.15163601
                  
                
                 
                   
                     18
                  
                   
                     5723635208
                  
                   
                     34.91520640
                  
                   
                     0.14004722
                  
                
                 
                   
                     17
                  
                   
                     5577633906
                  
                   
                     33.90125515
                  
                   
                     0.12874491
                  
                
                 
                   
                     16
                  
                   
                     5425863986
                  
                   
                     32.85988059
                  
                   
                     0.11774053
                  
                
                 
                   
                     15
                  
                   
                     5267826876
                  
                   
                     31.78833069
                  
                   
                     0.10704574
                  
                
                 
                   
                     14
                  
                   
                     5102940328
                  
                   
                     30.68341722
                  
                   
                     0.09667379
                  
                
                 
                   
                     13
                  
                   
                     4930517214
                  
                   
                     29.54136121
                  
                   
                     0.08663902
                  
                
                 
                   
                     12
                  
                   
                     4749736834
                  
                   
                     28.35773666
                  
                   
                     0.07695728
                  
                
                 
                   
                     11
                  
                   
                     4559605246
                  
                   
                     27.12675321
                  
                   
                     0.06764629
                  
                
                 
                   
                     10
                  
                   
                     4358898943
                  
                   
                     25.84193282
                  
                   
                     0.05872590
                  
                
                 
                   
                     09
                  
                   
                     4146082488
                  
                   
                     24.49464857
                  
                   
                     0.05021866
                  
                
                 
                   
                     08
                  
                   
                     3919183588
                  
                   
                     23.07391815
                  
                   
                     0.04215095
                  
                
                 
                   
                     07
                  
                   
                     3675595189
                  
                   
                     21.56518547
                  
                   
                     0.03455313
                  
                
                 
                   
                     06
                  
                   
                     3411744421
                  
                   
                     19.94844363
                  
                   
                     0.02746204
                  
                
                 
                   
                     05
                  
                   
                     3122498999
                  
                   
                     18.19487244
                  
                   
                     0.02092302
                  
                
                 
                   
                     04
                  
                   
                     2800000000
                  
                   
                     16
                     .
                     260204●1
                  
                   
                     0.01499411
                  
                
                 
                   
                     03
                  
                   
                     2431049156
                  
                   
                     14.06986184
                  
                   
                     0.00975364
                  
                
                 
                   
                     02
                  
                   
                     1989974874
                  
                   
                     11.47834097
                  
                   
                     0.00551730
                  
                
                 
                   
                     01
                  
                   
                     1410673597
                  
                   
                     8.10961446
                  
                   
                     0.00188278
                  
                
                 
                   
                     
                     010
                  
                   
                     1410673597
                  
                   
                     8.10961446
                  
                   
                     0.00188278
                  
                
                 
                   
                     009
                  
                   
                     1338618691
                  
                   
                     7.69281247
                  
                   
                     0.00160779
                  
                
                 
                   
                     008
                  
                   
                     1262378707
                  
                   
                     7.25224680
                  
                   
                     0.00134761
                  
                
                 
                   
                     007
                  
                   
                     1181143513
                  
                   
                     6.78328892
                  
                   
                     0.00110317
                  
                
                 
                   
                     006
                  
                   
                     1093800713
                  
                   
                     6
                     .
                     279●8064
                  
                   
                     0.00087554
                  
                
                 
                   
                     005
                  
                   
                     0998749217
                  
                   
                     5.73196797
                  
                   
                     0.00066616
                  
                
                 
                   
                     004
                  
                   
                     0893532316
                  
                   
                     5.12640010
                  
                   
                     0.00047674
                  
                
                 
                   
                     003
                  
                   
                     0774015503
                  
                   
                     4.43922228
                  
                   
                     0.00030969
                  
                
                 
                   
                     002
                  
                   
                     0632139225
                  
                   
                     3.62430750
                  
                   
                     0.00016860
                  
                
                 
                   
                     001
                  
                   
                     0447101778
                  
                   
                     2.56255874
                  
                   
                     0.00005961
                  
                
              
            
             
             
               
                 
                   
                      
                  
                   
                     1.57079632
                  
                
                 
                   
                     999
                  
                   
                     199999
                  
                
                 
                   
                      
                  
                   
                     1.56879632
                  
                
                 
                   
                     998
                  
                   
                     199999
                  
                
                 
                   
                      
                  
                   
                     1.56679632
                  
                
                 
                   
                      
                  
                   
                     199999
                  
                
                 
                   
                     997
                  
                   
                     1.56479633
                  
                
                 
                   
                      
                  
                   
                     199998
                  
                
                 
                   
                     996
                  
                   
                     1.56279634
                  
                
                 
                   
                      
                  
                   
                     199997
                  
                
                 
                   
                     995
                  
                   
                     1.56079636
                  
                
                 
                   
                      
                  
                   
                     199996
                  
                
                 
                   
                     994
                  
                   
                     1.55879639
                  
                
                 
                   
                      
                  
                   
                     199995
                  
                
                 
                   
                     993
                  
                   
                     1.55679644
                  
                
                 
                   
                      
                  
                   
                     199994
                  
                
                 
                   
                     992
                  
                   
                     1.55479649
                  
                
                 
                   
                      
                  
                   
                     199992
                  
                
                 
                   
                     991
                  
                   
                     1.55299657
                  
                
                 
                   
                      
                  
                   
                     199991
                  
                
                 
                   
                     990
                  
                   
                     1.55079666
                  
                
                 
                   
                      
                  
                   
                     199988
                  
                
                 
                   
                     989
                  
                   
                     1.54879677
                  
                
                 
                   
                      
                  
                   
                     199986
                  
                
                 
                   
                     988
                  
                   
                     1.54679690
                  
                
                 
                   
                      
                  
                   
                     199984
                  
                
                 
                   
                     987
                  
                   
                     1.54479706
                  
                
                 
                   
                      
                  
                   
                     199981
                  
                
                 
                   
                     986
                  
                   
                     1.54279724
                  
                
                 
                   
                      
                  
                   
                     199978
                  
                
                 
                   
                     985
                  
                   
                     1.54079745
                  
                
                 
                   
                      
                  
                   
                     199976
                  
                
                 
                   
                     984
                  
                   
                     1.53879769
                  
                
                 
                   
                      
                  
                   
                     199972
                  
                
                 
                   
                     983
                  
                   
                     1.53679796
                  
                
                 
                   
                     983
                  
                   
                     1.53679796
                  
                
                 
                   
                      
                  
                   
                     199969
                  
                
                 
                   
                     982
                  
                   
                     1.53479827
                  
                
                 
                   
                      
                  
                   
                     199965
                  
                
                 
                   
                     981
                  
                   
                     1.53279862
                  
                
                 
                   
                      
                  
                   
                     199962
                  
                
                 
                   
                     980
                  
                   
                     1.53079899
                  
                
                 
                   
                      
                  
                   
                     199957
                  
                
                 
                   
                     979
                  
                   
                     1.52879941
                  
                
                 
                   
                      
                  
                   
                     199953
                  
                
                 
                   
                     978
                  
                   
                     1.52679988
                  
                
                 
                   
                      
                  
                   
                     199949
                  
                
                 
                   
                     977
                  
                   
                     1.52480039
                  
                
                 
                   
                      
                  
                   
                     199944
                  
                
                 
                   
                     976
                  
                   
                     1.52280095
                  
                
                 
                   
                      
                  
                   
                     199939
                  
                
                 
                   
                     975
                  
                   
                     1.52080156
                  
                
                 
                   
                      
                  
                   
                     199934
                  
                
                 
                   
                     974
                  
                   
                     1.51880222
                  
                
                 
                   
                      
                  
                   
                     199929
                  
                
                 
                   
                     973
                  
                   
                     1.51680293
                  
                
                 
                   
                      
                  
                   
                     199924
                  
                
                 
                   
                     972
                  
                   
                     1.51480369
                  
                
                 
                   
                      
                  
                   
                     199918
                  
                
                 
                   
                     971
                  
                   
                     1.51280451
                  
                
                 
                   
                      
                  
                   
                     199912
                  
                
                 
                   
                     970
                  
                   
                     1.51080539
                  
                
                 
                   
                      
                  
                   
                     199906
                  
                
                 
                   
                     969
                  
                   
                     1.50880633
                  
                
                 
                   
                      
                  
                   
                     199909
                  
                
                 
                   
                     968
                  
                   
                     1.50680733
                  
                
                 
                   
                      
                  
                   
                     199894
                  
                
                 
                   
                     967
                  
                   
                     1.50480839
                  
                
                 
                   
                      
                  
                   
                     199887
                  
                
                 
                   
                     966
                  
                   
                     1.50280952
                  
                
                 
                   
                     
                     966
                  
                   
                     1.50280952
                  
                
                 
                   
                      
                  
                   
                     199880
                  
                
                 
                   
                     965
                  
                   
                     1.50081072
                  
                
                 
                   
                      
                  
                   
                     199873
                  
                
                 
                   
                     964
                  
                   
                     1.49881199
                  
                
                 
                   
                      
                  
                   
                     199866
                  
                
                 
                   
                     963
                  
                   
                     1.49681333
                  
                
                 
                   
                      
                  
                   
                     199859
                  
                
                 
                   
                     962
                  
                   
                     1.49481474
                  
                
                 
                   
                      
                  
                   
                     199851
                  
                
                 
                   
                     961
                  
                   
                     1.49281623
                  
                
                 
                   
                      
                  
                   
                     199843
                  
                
                 
                   
                     960
                  
                   
                     1.49081774
                  
                
                 
                   
                      
                  
                   
                     199835
                  
                
                 
                   
                     959
                  
                   
                     1.48881938
                  
                
                 
                   
                      
                  
                   
                     199827
                  
                
                 
                   
                     958
                  
                   
                     1.48682110
                  
                
                 
                   
                      
                  
                   
                     199819
                  
                
                 
                   
                     957
                  
                   
                     1.48482291
                  
                
                 
                   
                      
                  
                   
                     199810
                  
                
                 
                   
                     956
                  
                   
                     1.48282480
                  
                
                 
                   
                      
                  
                   
                     199801
                  
                
                 
                   
                     955
                  
                   
                     1.48082678
                  
                
                 
                   
                      
                  
                   
                     199792
                  
                
                 
                   
                     954
                  
                   
                     1.47882885
                  
                
                 
                   
                      
                  
                   
                     199783
                  
                
                 
                   
                     953
                  
                   
                     1.47683102
                  
                
                 
                   
                      
                  
                   
                     199774
                  
                
                 
                   
                     952
                  
                   
                     1.47483328
                  
                
                 
                   
                      
                  
                   
                     199764
                  
                
                 
                   
                     951
                  
                   
                     1.47283563
                  
                
                 
                   
                      
                  
                   
                     199754
                  
                
                 
                   
                     950
                  
                   
                     1.47083808
                  
                
                 
                   
                      
                  
                   
                     199744
                  
                
                 
                   
                     949
                  
                   
                     1.46884063
                  
                
                 
                   
                     949
                  
                   
                     1.46884063
                  
                
                 
                   
                      
                  
                   
                     199734
                  
                
                 
                   
                     948
                  
                   
                     1.46684328
                  
                
                 
                   
                      
                  
                   
                     199724
                  
                
                 
                   
                     947
                  
                   
                     1.46484604
                  
                
                 
                   
                      
                  
                   
                     199713
                  
                
                 
                   
                     946
                  
                   
                     1.46284890
                  
                
                 
                   
                      
                  
                   
                     199702
                  
                
                 
                   
                     945
                  
                   
                     1.46085187
                  
                
                 
                   
                      
                  
                   
                     199691
                  
                
                 
                   
                     944
                  
                   
                     1.45885496
                  
                
                 
                   
                      
                  
                   
                     199680
                  
                
                 
                   
                     943
                  
                   
                     1.45685815
                  
                
                 
                   
                      
                  
                   
                     199669
                  
                
                 
                   
                     942
                  
                   
                     1.45486146
                  
                
                 
                   
                      
                  
                   
                     199657
                  
                
                 
                   
                     941
                  
                   
                     1.45286489
                  
                
                 
                   
                      
                  
                   
                     199645
                  
                
                 
                   
                     940
                  
                   
                     1.45086837
                  
                
                 
                   
                      
                  
                   
                     199633
                  
                
                 
                   
                     939
                  
                   
                     1.44887204
                  
                
                 
                   
                      
                  
                   
                     199621
                  
                
                 
                   
                     938
                  
                   
                     1.44687583
                  
                
                 
                   
                      
                  
                   
                     199608
                  
                
                 
                   
                     937
                  
                   
                     1.44487975
                  
                
                 
                   
                      
                  
                   
                     199596
                  
                
                 
                   
                     936
                  
                   
                     1.44288379
                  
                
                 
                   
                      
                  
                   
                     199585
                  
                
                 
                   
                     935
                  
                   
                     1.44088794
                  
                
                 
                   
                      
                  
                   
                     199570
                  
                
                 
                   
                     934
                  
                   
                     1.43889224
                  
                
                 
                   
                      
                  
                   
                     199557
                  
                
                 
                   
                     933
                  
                   
                     1.43689667
                  
                
                 
                   
                      
                  
                   
                     199543
                  
                
                 
                   
                     932
                  
                   
                     1.43490124
                  
                
                 
                   
                     
                     932
                  
                   
                     1.43490124
                  
                
                 
                   
                      
                  
                   
                     199530
                  
                
                 
                   
                     931
                  
                   
                     1.43290594
                  
                
                 
                   
                      
                  
                   
                     199516
                  
                
                 
                   
                     930
                  
                   
                     1.43091078
                  
                
                 
                   
                      
                  
                   
                     199502
                  
                
                 
                   
                     929
                  
                   
                     1.42891578
                  
                
                 
                   
                      
                  
                   
                     199488
                  
                
                 
                   
                     928
                  
                   
                     1.42692090
                  
                
                 
                   
                      
                  
                   
                     199473
                  
                
                 
                   
                     927
                  
                   
                     1.42492617
                  
                
                 
                   
                      
                  
                   
                     199459
                  
                
                 
                   
                     926
                  
                   
                     1.42293158
                  
                
                 
                   
                      
                  
                   
                     199444
                  
                
                 
                   
                     925
                  
                   
                     1.42093714
                  
                
                 
                   
                      
                  
                   
                     199429
                  
                
                 
                   
                     924
                  
                   
                     1.41894305
                  
                
                 
                   
                      
                  
                   
                     199413
                  
                
                 
                   
                     923
                  
                   
                     1.41694892
                  
                
                 
                   
                      
                  
                   
                     199398
                  
                
                 
                   
                     922
                  
                   
                     1.41495494
                  
                
                 
                   
                      
                  
                   
                     199382
                  
                
                 
                   
                     921
                  
                   
                     1.41296112
                  
                
                 
                   
                      
                  
                   
                     199366
                  
                
                 
                   
                     920
                  
                   
                     1.41096746
                  
                
                 
                   
                      
                  
                   
                     199350
                  
                
                 
                   
                     919
                  
                   
                     1.40897396
                  
                
                 
                   
                      
                  
                   
                     199334
                  
                
                 
                   
                     918
                  
                   
                     1.40698062
                  
                
                 
                   
                      
                  
                   
                     199318
                  
                
                 
                   
                     917
                  
                   
                     1.40498744
                  
                
                 
                   
                      
                  
                   
                     199301
                  
                
                 
                   
                     916
                  
                   
                     1.40299443
                  
                
                 
                   
                      
                  
                   
                     199284
                  
                
                 
                   
                     915
                  
                   
                     1.40100159
                  
                
                 
                   
                     915
                  
                   
                     1.40100159
                  
                
                 
                   
                      
                  
                   
                     199267
                  
                
                 
                   
                     914
                  
                   
                     1.39900892
                  
                
                 
                   
                      
                  
                   
                     199250
                  
                
                 
                   
                     913
                  
                   
                     1.39701642
                  
                
                 
                   
                      
                  
                   
                     199232
                  
                
                 
                   
                     912
                  
                   
                     1.39502410
                  
                
                 
                   
                      
                  
                   
                     199215
                  
                
                 
                   
                     911
                  
                   
                     1.39303195
                  
                
                 
                   
                      
                  
                   
                     199197
                  
                
                 
                   
                     910
                  
                   
                     1.39103998
                  
                
                 
                   
                      
                  
                   
                     199178
                  
                
                 
                   
                     909
                  
                   
                     1.38904820
                  
                
                 
                   
                      
                  
                   
                     199160
                  
                
                 
                   
                     908
                  
                   
                     1.38705660
                  
                
                 
                   
                      
                  
                   
                     199142
                  
                
                 
                   
                     907
                  
                   
                     1.38506518
                  
                
                 
                   
                      
                  
                   
                     199123
                  
                
                 
                   
                     906
                  
                   
                     1.38307395
                  
                
                 
                   
                      
                  
                   
                     199104
                  
                
                 
                   
                     905
                  
                   
                     1.38108291
                  
                
                 
                   
                      
                  
                   
                     199085
                  
                
                 
                   
                     904
                  
                   
                     1.37909206
                  
                
                 
                   
                      
                  
                   
                     199066
                  
                
                 
                   
                     903
                  
                   
                     1.37710140
                  
                
                 
                   
                      
                  
                   
                     199047
                  
                
                 
                   
                     902
                  
                   
                     1.37511093
                  
                
                 
                   
                      
                  
                   
                     199027
                  
                
                 
                   
                     901
                  
                   
                     1.37312066
                  
                
                 
                   
                      
                  
                   
                     199007
                  
                
                 
                   
                     900
                  
                   
                     1.37113059
                  
                
                 
                   
                     
                     900
                  
                   
                     1.37113017
                  
                
                 
                   
                      
                  
                   
                     198987
                  
                
                 
                   
                     899
                  
                   
                     1.36914030
                  
                
                 
                   
                      
                  
                   
                     198967
                  
                
                 
                   
                     898
                  
                   
                     1.36715063
                  
                
                 
                   
                      
                  
                   
                     198946
                  
                
                 
                   
                     897
                  
                   
                     1.36516117
                  
                
                 
                   
                      
                  
                   
                     198925
                  
                
                 
                   
                     896
                  
                   
                     1.36317192
                  
                
                 
                   
                      
                  
                   
                     198904
                  
                
                 
                   
                     895
                  
                   
                     1.36118288
                  
                
                 
                   
                      
                  
                   
                     198883
                  
                
                 
                   
                     894
                  
                   
                     1.35919405
                  
                
                 
                   
                      
                  
                   
                     198861
                  
                
                 
                   
                     893
                  
                   
                     1.35720544
                  
                
                 
                   
                      
                  
                   
                     198839
                  
                
                 
                   
                     892
                  
                   
                     1.35521705
                  
                
                 
                   
                      
                  
                   
                     198818
                  
                
                 
                   
                     891
                  
                   
                     1.35322887
                  
                
                 
                   
                      
                  
                   
                     198797
                  
                
                 
                   
                     890
                  
                   
                     1.35124090
                  
                
                 
                   
                      
                  
                   
                     198775
                  
                
                 
                   
                     889
                  
                   
                     1.34925315
                  
                
                 
                   
                      
                  
                   
                     198752
                  
                
                 
                   
                     888
                  
                   
                     1.34726563
                  
                
                 
                   
                      
                  
                   
                     198729
                  
                
                 
                   
                     887
                  
                   
                     1.34527834
                  
                
                 
                   
                      
                  
                   
                     198707
                  
                
                 
                   
                     886
                  
                   
                     1.34329127
                  
                
                 
                   
                      
                  
                   
                     198684
                  
                
                 
                   
                     885
                  
                   
                     1.34130443
                  
                
                 
                   
                      
                  
                   
                     198661
                  
                
                 
                   
                     884
                  
                   
                     1.33931782
                  
                
                 
                   
                      
                  
                   
                     198638
                  
                
                 
                   
                     88●
                  
                   
                     1.33733144
                  
                
                 
                   
                     883
                  
                   
                     1.33733144
                  
                
                 
                   
                      
                  
                   
                     198619
                  
                
                 
                   
                     882
                  
                   
                     1.33534525
                  
                
                 
                   
                      
                  
                   
                     198590
                  
                
                 
                   
                     881
                  
                   
                     1.33335935
                  
                
                 
                   
                      
                  
                   
                     198566
                  
                
                 
                   
                     880
                  
                   
                     1.33137360
                  
                
                 
                   
                      
                  
                   
                     198541
                  
                
                 
                   
                     879
                  
                   
                     1.32938819
                  
                
                 
                   
                      
                  
                   
                     198517
                  
                
                 
                   
                     878
                  
                   
                     1.32740302
                  
                
                 
                   
                      
                  
                   
                     198499
                  
                
                 
                   
                     877
                  
                   
                     1.32541803
                  
                
                 
                   
                      
                  
                   
                     198480
                  
                
                 
                   
                     876
                  
                   
                     1.32343323
                  
                
                 
                   
                      
                  
                   
                     198449
                  
                
                 
                   
                     875
                  
                   
                     1.32144874
                  
                
                 
                   
                      
                  
                   
                     198418
                  
                
                 
                   
                     874
                  
                   
                     1.31946456
                  
                
                 
                   
                      
                  
                   
                     198393
                  
                
                 
                   
                     873
                  
                   
                     1.31748063
                  
                
                 
                   
                      
                  
                   
                     198367
                  
                
                 
                   
                     872
                  
                   
                     1.31549696
                  
                
                 
                   
                      
                  
                   
                     198341
                  
                
                 
                   
                     871
                  
                   
                     1.31351355
                  
                
                 
                   
                      
                  
                   
                     198315
                  
                
                 
                   
                     870
                  
                   
                     1.31153053
                  
                
                 
                   
                      
                  
                   
                     198289
                  
                
                 
                   
                     869
                  
                   
                     1.30954764
                  
                
                 
                   
                      
                  
                   
                     198262
                  
                
                 
                   
                     868
                  
                   
                     1.30756502
                  
                
                 
                   
                      
                  
                   
                     198235
                  
                
                 
                   
                     867
                  
                   
                     1.30558267
                  
                
                 
                   
                      
                  
                   
                     198209
                  
                
                 
                   
                     
                  
                   
                     198209
                  
                
                 
                   
                     866
                  
                   
                     1.30360058
                  
                
                 
                   
                      
                  
                   
                     198182
                  
                
                 
                   
                     865
                  
                   
                     1.30161876
                  
                
                 
                   
                      
                  
                   
                     198154
                  
                
                 
                   
                     864
                  
                   
                     1.29963722
                  
                
                 
                   
                      
                  
                   
                     198127
                  
                
                 
                   
                     863
                  
                   
                     1.29765595
                  
                
                 
                   
                      
                  
                   
                     198100
                  
                
                 
                   
                     862
                  
                   
                     1.29567495
                  
                
                 
                   
                      
                  
                   
                     198072
                  
                
                 
                   
                     861
                  
                   
                     1.29369423
                  
                
                 
                   
                      
                  
                   
                     198044
                  
                
                 
                   
                     860
                  
                   
                     1.29171379
                  
                
                 
                   
                      
                  
                   
                     198015
                  
                
                 
                   
                     859
                  
                   
                     1.28973357
                  
                
                 
                   
                      
                  
                   
                     197986
                  
                
                 
                   
                     858
                  
                   
                     1.28775371
                  
                
                 
                   
                      
                  
                   
                     197958
                  
                
                 
                   
                     857
                  
                   
                     1
                     .
                     2857741●
                  
                
                 
                   
                      
                  
                   
                     197929
                  
                
                 
                   
                     856
                  
                   
                     1.28379484
                  
                
                 
                   
                      
                  
                   
                     197900
                  
                
                 
                   
                     855
                  
                   
                     1.28181584
                  
                
                 
                   
                      
                  
                   
                     197871
                  
                
                 
                   
                     854
                  
                   
                     1.27983713
                  
                
                 
                   
                      
                  
                   
                     197841
                  
                
                 
                   
                     853
                  
                   
                     1.27785872
                  
                
                 
                   
                      
                  
                   
                     197811
                  
                
                 
                   
                     852
                  
                   
                     1.27588061
                  
                
                 
                   
                      
                  
                   
                     197781
                  
                
                 
                   
                     851
                  
                   
                     1.27390280
                  
                
                 
                   
                      
                  
                   
                     197751
                  
                
                 
                   
                     850
                  
                   
                     1.27192529
                  
                
                 
                   
                     850
                  
                   
                     1.27192518
                  
                
                 
                   
                      
                  
                   
                     197721
                  
                
                 
                   
                     849
                  
                   
                     1.26994797
                  
                
                 
                   
                      
                  
                   
                     197691
                  
                
                 
                   
                     848
                  
                   
                     1.26797106
                  
                
                 
                   
                      
                  
                   
                     197660
                  
                
                 
                   
                     847
                  
                   
                     1.26599446
                  
                
                 
                   
                      
                  
                   
                     197629
                  
                
                 
                   
                     846
                  
                   
                     1.26401817
                  
                
                 
                   
                      
                  
                   
                     197598
                  
                
                 
                   
                     845
                  
                   
                     1.26204219
                  
                
                 
                   
                      
                  
                   
                     197561
                  
                
                 
                   
                     844
                  
                   
                     1.26006658
                  
                
                 
                   
                      
                  
                   
                     197534
                  
                
                 
                   
                     843
                  
                   
                     1.25809124
                  
                
                 
                   
                      
                  
                   
                     197489
                  
                
                 
                   
                     842
                  
                   
                     1.25611635
                  
                
                 
                   
                      
                  
                   
                     197457
                  
                
                 
                   
                     841
                  
                   
                     1.25414178
                  
                
                 
                   
                      
                  
                   
                     197427
                  
                
                 
                   
                     840
                  
                   
                     1.25216751
                  
                
                 
                   
                      
                  
                   
                     197395
                  
                
                 
                   
                     839
                  
                   
                     1.25019356
                  
                
                 
                   
                      
                  
                   
                     197374
                  
                
                 
                   
                     838
                  
                   
                     1.24821982
                  
                
                 
                   
                      
                  
                   
                     197341
                  
                
                 
                   
                     837
                  
                   
                     1.24624641
                  
                
                 
                   
                      
                  
                   
                     197308
                  
                
                 
                   
                     836
                  
                   
                     1.24427333
                  
                
                 
                   
                      
                  
                   
                     197275
                  
                
                 
                   
                     835
                  
                   
                     1.24230058
                  
                
                 
                   
                      
                  
                   
                     197241
                  
                
                 
                   
                     834
                  
                   
                     1.24032817
                  
                
                 
                   
                      
                  
                   
                     197212
                  
                
                 
                   
                     
                  
                   
                     197272
                  
                
                 
                   
                     833
                  
                   
                     1.23835605
                  
                
                 
                   
                      
                  
                   
                     197173
                  
                
                 
                   
                     832
                  
                   
                     1.23638432
                  
                
                 
                   
                      
                  
                   
                     197139
                  
                
                 
                   
                     831
                  
                   
                     1.23441293
                  
                
                 
                   
                      
                  
                   
                     197105
                  
                
                 
                   
                     830
                  
                   
                     1.23244118
                  
                
                 
                   
                      
                  
                   
                     197072
                  
                
                 
                   
                     829
                  
                   
                     1.23047046
                  
                
                 
                   
                      
                  
                   
                     197036
                  
                
                 
                   
                     828
                  
                   
                     1.22850010
                  
                
                 
                   
                      
                  
                   
                     197001
                  
                
                 
                   
                     827
                  
                   
                     1.22653009
                  
                
                 
                   
                      
                  
                   
                     196966
                  
                
                 
                   
                     826
                  
                   
                     1.22456043
                  
                
                 
                   
                      
                  
                   
                     196930
                  
                
                 
                   
                     825
                  
                   
                     1.22259113
                  
                
                 
                   
                      
                  
                   
                     196895
                  
                
                 
                   
                     824
                  
                   
                     1.22062218
                  
                
                 
                   
                      
                  
                   
                     196861
                  
                
                 
                   
                     823
                  
                   
                     1.21865357
                  
                
                 
                   
                      
                  
                   
                     196825
                  
                
                 
                   
                     822
                  
                   
                     1.21668532
                  
                
                 
                   
                      
                  
                   
                     196787
                  
                
                 
                   
                     821
                  
                   
                     1.21471745
                  
                
                 
                   
                      
                  
                   
                     196750
                  
                
                 
                   
                     820
                  
                   
                     1.21274989
                  
                
                 
                   
                      
                  
                   
                     196714
                  
                
                 
                   
                     819
                  
                   
                     1.21078275
                  
                
                 
                   
                      
                  
                   
                     196677
                  
                
                 
                   
                     818
                  
                   
                     1.20881598
                  
                
                 
                   
                      
                  
                   
                     196640
                  
                
                 
                   
                     817
                  
                   
                     1.20684958
                  
                
                 
                   
                     817
                  
                   
                     1.20684954
                  
                
                 
                   
                      
                  
                   
                     1966●3
                  
                
                 
                   
                     816
                  
                   
                     1.20488355
                  
                
                 
                   
                      
                  
                   
                     196565
                  
                
                 
                   
                     815
                  
                   
                     1.20291790
                  
                
                 
                   
                      
                  
                   
                     196527
                  
                
                 
                   
                     814
                  
                   
                     1
                     .
                     20●95263
                  
                
                 
                   
                      
                  
                   
                     196479
                  
                
                 
                   
                     813
                  
                   
                     1.19898774
                  
                
                 
                   
                      
                  
                   
                     196451
                  
                
                 
                   
                     812
                  
                   
                     1.19702323
                  
                
                 
                   
                      
                  
                   
                     196413
                  
                
                 
                   
                     811
                  
                   
                     1.19505910
                  
                
                 
                   
                      
                  
                   
                     196375
                  
                
                 
                   
                     810
                  
                   
                     1.19309525
                  
                
                 
                   
                      
                  
                   
                     196347
                  
                
                 
                   
                     809
                  
                   
                     1.19113254
                  
                
                 
                   
                      
                  
                   
                     196298
                  
                
                 
                   
                     808
                  
                   
                     1.18916956
                  
                
                 
                   
                      
                  
                   
                     196258
                  
                
                 
                   
                     807
                  
                   
                     1.18720698
                  
                
                 
                   
                      
                  
                   
                     196219
                  
                
                 
                   
                     806
                  
                   
                     1.18524479
                  
                
                 
                   
                      
                  
                   
                     196188
                  
                
                 
                   
                     805
                  
                   
                     1.18328291
                  
                
                 
                   
                      
                  
                   
                     196148
                  
                
                 
                   
                     804
                  
                   
                     1.18132143
                  
                
                 
                   
                      
                  
                   
                     196100
                  
                
                 
                   
                     803
                  
                   
                     1.17936043
                  
                
                 
                   
                      
                  
                   
                     196060
                  
                
                 
                   
                     802
                  
                   
                     1.17739983
                  
                
                 
                   
                      
                  
                   
                     196019
                  
                
                 
                   
                     801
                  
                   
                     1.17543964
                  
                
                 
                   
                      
                  
                   
                     195978
                  
                
                 
                   
                     800
                  
                   
                     1.17347986
                  
                
                 
                   
                     
                     800
                  
                   
                     1.17347924
                  
                
                 
                   
                      
                  
                   
                     195938
                  
                
                 
                   
                     799
                  
                   
                     1.17151986
                  
                
                 
                   
                      
                  
                   
                     195897
                  
                
                 
                   
                     798
                  
                   
                     1.16956089
                  
                
                 
                   
                      
                  
                   
                     195855
                  
                
                 
                   
                     797
                  
                   
                     1.16760234
                  
                
                 
                   
                      
                  
                   
                     195814
                  
                
                 
                   
                     796
                  
                   
                     1.16564420
                  
                
                 
                   
                      
                  
                   
                     195773
                  
                
                 
                   
                     795
                  
                   
                     1.16368647
                  
                
                 
                   
                      
                  
                   
                     195731
                  
                
                 
                   
                     794
                  
                   
                     1.16172916
                  
                
                 
                   
                      
                  
                   
                     195689
                  
                
                 
                   
                     793
                  
                   
                     1.15977227
                  
                
                 
                   
                      
                  
                   
                     195646
                  
                
                 
                   
                     792
                  
                   
                     1.15781581
                  
                
                 
                   
                      
                  
                   
                     195603
                  
                
                 
                   
                     791
                  
                   
                     1.15585978
                  
                
                 
                   
                      
                  
                   
                     195561
                  
                
                 
                   
                     790
                  
                   
                     1.15390417
                  
                
                 
                   
                      
                  
                   
                     195518
                  
                
                 
                   
                     789
                  
                   
                     1.15194899
                  
                
                 
                   
                      
                  
                   
                     195472
                  
                
                 
                   
                     788
                  
                   
                     1.14999427
                  
                
                 
                   
                      
                  
                   
                     195429
                  
                
                 
                   
                     787
                  
                   
                     1.14803998
                  
                
                 
                   
                      
                  
                   
                     195388
                  
                
                 
                   
                     786
                  
                   
                     1.14608610
                  
                
                 
                   
                      
                  
                   
                     195344
                  
                
                 
                   
                     785
                  
                   
                     1.14413266
                  
                
                 
                   
                      
                  
                   
                     195300
                  
                
                 
                   
                     784
                  
                   
                     1.14217966
                  
                
                 
                   
                     784
                  
                   
                     1.14217966
                  
                
                 
                   
                      
                  
                   
                     195256
                  
                
                 
                   
                     783
                  
                   
                     1
                     .
                     14022●10
                  
                
                 
                   
                      
                  
                   
                     195211
                  
                
                 
                   
                     782
                  
                   
                     1.13827499
                  
                
                 
                   
                      
                  
                   
                     195166
                  
                
                 
                   
                     781
                  
                   
                     1.13632333
                  
                
                 
                   
                      
                  
                   
                     195122
                  
                
                 
                   
                     780
                  
                   
                     1.13437211
                  
                
                 
                   
                      
                  
                   
                     195076
                  
                
                 
                   
                     779
                  
                   
                     1.13242135
                  
                
                 
                   
                      
                  
                   
                     195031
                  
                
                 
                   
                     778
                  
                   
                     1.13047102
                  
                
                 
                   
                      
                  
                   
                     194985
                  
                
                 
                   
                     777
                  
                   
                     1.12852117
                  
                
                 
                   
                      
                  
                   
                     194939
                  
                
                 
                   
                     776
                  
                   
                     1.12657178
                  
                
                 
                   
                      
                  
                   
                     194893
                  
                
                 
                   
                     775
                  
                   
                     1.12462285
                  
                
                 
                   
                      
                  
                   
                     194847
                  
                
                 
                   
                     774
                  
                   
                     1.12267438
                  
                
                 
                   
                      
                  
                   
                     194801
                  
                
                 
                   
                     773
                  
                   
                     1.12072637
                  
                
                 
                   
                      
                  
                   
                     194755
                  
                
                 
                   
                     772
                  
                   
                     1.11877882
                  
                
                 
                   
                      
                  
                   
                     194708
                  
                
                 
                   
                     771
                  
                   
                     1.11683174
                  
                
                 
                   
                      
                  
                   
                     194661
                  
                
                 
                   
                     770
                  
                   
                     1.11488487
                  
                
                 
                   
                      
                  
                   
                     194614
                  
                
                 
                   
                     769
                  
                   
                     1.11293867
                  
                
                 
                   
                      
                  
                   
                     194566
                  
                
                 
                   
                     768
                  
                   
                     1.11099301
                  
                
                 
                   
                      
                  
                   
                     194518
                  
                
                 
                   
                     
                  
                   
                     194518
                  
                
                 
                   
                     767
                  
                   
                     1.10904783
                  
                
                 
                   
                      
                  
                   
                     194471
                  
                
                 
                   
                     766
                  
                   
                     1.10710312
                  
                
                 
                   
                      
                  
                   
                     194423
                  
                
                 
                   
                     765
                  
                   
                     1.10515889
                  
                
                 
                   
                      
                  
                   
                     194374
                  
                
                 
                   
                     764
                  
                   
                     1.10321515
                  
                
                 
                   
                      
                  
                   
                     194325
                  
                
                 
                   
                     763
                  
                   
                     1.10127190
                  
                
                 
                   
                      
                  
                   
                     194276
                  
                
                 
                   
                     762
                  
                   
                     1.09932914
                  
                
                 
                   
                      
                  
                   
                     194227
                  
                
                 
                   
                     761
                  
                   
                     1.09738687
                  
                
                 
                   
                      
                  
                   
                     194173
                  
                
                 
                   
                     760
                  
                   
                     1.09544514
                  
                
                 
                   
                      
                  
                   
                     194129
                  
                
                 
                   
                     759
                  
                   
                     1.09350385
                  
                
                 
                   
                      
                  
                   
                     194079
                  
                
                 
                   
                     758
                  
                   
                     1.09156306
                  
                
                 
                   
                      
                  
                   
                     194029
                  
                
                 
                   
                     757
                  
                   
                     1.08962277
                  
                
                 
                   
                      
                  
                   
                     193980
                  
                
                 
                   
                     756
                  
                   
                     1.08768297
                  
                
                 
                   
                      
                  
                   
                     193930
                  
                
                 
                   
                     755
                  
                   
                     1.08574367
                  
                
                 
                   
                      
                  
                   
                     193878
                  
                
                 
                   
                     754
                  
                   
                     1.08380489
                  
                
                 
                   
                      
                  
                   
                     193827
                  
                
                 
                   
                     753
                  
                   
                     1.08186662
                  
                
                 
                   
                      
                  
                   
                     193777
                  
                
                 
                   
                     752
                  
                   
                     1.07992885
                  
                
                 
                   
                      
                  
                   
                     193726
                  
                
                 
                   
                     751
                  
                   
                     1.07799159
                  
                
                 
                   
                     751
                  
                   
                     1.07799159
                  
                
                 
                   
                      
                  
                   
                     193674
                  
                
                 
                   
                     750
                  
                   
                     1.07605485
                  
                
                 
                   
                      
                  
                   
                     193622
                  
                
                 
                   
                     749
                  
                   
                     1.07411863
                  
                
                 
                   
                      
                  
                   
                     193570
                  
                
                 
                   
                     748
                  
                   
                     1.07218293
                  
                
                 
                   
                      
                  
                   
                     193518
                  
                
                 
                   
                     747
                  
                   
                     1.07024775
                  
                
                 
                   
                      
                  
                   
                     193466
                  
                
                 
                   
                     746
                  
                   
                     1.06831309
                  
                
                 
                   
                      
                  
                   
                     193414
                  
                
                 
                   
                     745
                  
                   
                     1.06637895
                  
                
                 
                   
                      
                  
                   
                     193361
                  
                
                 
                   
                     744
                  
                   
                     1.06444534
                  
                
                 
                   
                      
                  
                   
                     193308
                  
                
                 
                   
                     743
                  
                   
                     1.06251226
                  
                
                 
                   
                      
                  
                   
                     193255
                  
                
                 
                   
                     742
                  
                   
                     1.06057971
                  
                
                 
                   
                      
                  
                   
                     193201
                  
                
                 
                   
                     741
                  
                   
                     1.05864770
                  
                
                 
                   
                      
                  
                   
                     193147
                  
                
                 
                   
                     740
                  
                   
                     1.05671623
                  
                
                 
                   
                      
                  
                   
                     193093
                  
                
                 
                   
                     739
                  
                   
                     1.05478530
                  
                
                 
                   
                      
                  
                   
                     193039
                  
                
                 
                   
                     738
                  
                   
                     1.05285491
                  
                
                 
                   
                      
                  
                   
                     192985
                  
                
                 
                   
                     737
                  
                   
                     1.05092506
                  
                
                 
                   
                      
                  
                   
                     192931
                  
                
                 
                   
                     736
                  
                   
                     1.04899575
                  
                
                 
                   
                      
                  
                   
                     192876
                  
                
                 
                   
                     735
                  
                   
                     1.04706699
                  
                
                 
                   
                      
                  
                   
                     192821
                  
                
                 
                   
                     
                  
                   
                     192821
                  
                
                 
                   
                     734
                  
                   
                     1.04513878
                  
                
                 
                   
                      
                  
                   
                     192766
                  
                
                 
                   
                     733
                  
                   
                     1.04321112
                  
                
                 
                   
                      
                  
                   
                     192710
                  
                
                 
                   
                     732
                  
                   
                     1.04128402
                  
                
                 
                   
                      
                  
                   
                     192655
                  
                
                 
                   
                     731
                  
                   
                     1.03935747
                  
                
                 
                   
                      
                  
                   
                     192600
                  
                
                 
                   
                     730
                  
                   
                     1.03743147
                  
                
                 
                   
                      
                  
                   
                     192543
                  
                
                 
                   
                     729
                  
                   
                     1.03550604
                  
                
                 
                   
                      
                  
                   
                     192486
                  
                
                 
                   
                     728
                  
                   
                     1.03358118
                  
                
                 
                   
                      
                  
                   
                     192430
                  
                
                 
                   
                     727
                  
                   
                     1.03165688
                  
                
                 
                   
                      
                  
                   
                     192373
                  
                
                 
                   
                     726
                  
                   
                     1.02973115
                  
                
                 
                   
                      
                  
                   
                     192316
                  
                
                 
                   
                     725
                  
                   
                     1.02780999
                  
                
                 
                   
                      
                  
                   
                     172259
                  
                
                 
                   
                     724
                  
                   
                     1.02588740
                  
                
                 
                   
                      
                  
                   
                     192213
                  
                
                 
                   
                     723
                  
                   
                     1.02396527
                  
                
                 
                   
                      
                  
                   
                     192155
                  
                
                 
                   
                     722
                  
                   
                     1.02204372
                  
                
                 
                   
                      
                  
                   
                     192086
                  
                
                 
                   
                     721
                  
                   
                     1.02012286
                  
                
                 
                   
                      
                  
                   
                     192029
                  
                
                 
                   
                     720
                  
                   
                     1.01820221
                  
                
                 
                   
                      
                  
                   
                     191970
                  
                
                 
                   
                     719
                  
                   
                     1.01628251
                  
                
                 
                   
                      
                  
                   
                     191911
                  
                
                 
                   
                     718
                  
                   
                     1.01436340
                  
                
                 
                   
                     718
                  
                   
                     1.01436340
                  
                
                 
                   
                      
                  
                   
                     191853
                  
                
                 
                   
                     717
                  
                   
                     1.01244487
                  
                
                 
                   
                      
                  
                   
                     191794
                  
                
                 
                   
                     716
                  
                   
                     1.01052693
                  
                
                 
                   
                      
                  
                   
                     191734
                  
                
                 
                   
                     715
                  
                   
                     1.00860959
                  
                
                 
                   
                      
                  
                   
                     191674
                  
                
                 
                   
                     714
                  
                   
                     1.00669285
                  
                
                 
                   
                      
                  
                   
                     191615
                  
                
                 
                   
                     713
                  
                   
                     1.00477670
                  
                
                 
                   
                      
                  
                   
                     191556
                  
                
                 
                   
                     712
                  
                   
                     1.00286114
                  
                
                 
                   
                      
                  
                   
                     191505
                  
                
                 
                   
                     711
                  
                   
                     1.00094609
                  
                
                 
                   
                      
                  
                   
                     191444
                  
                
                 
                   
                     710
                  
                   
                     0.99903165
                  
                
                 
                   
                      
                  
                   
                     191374
                  
                
                 
                   
                     709
                  
                   
                     0.99711791
                  
                
                 
                   
                      
                  
                   
                     191313
                  
                
                 
                   
                     708
                  
                   
                     0.99520478
                  
                
                 
                   
                      
                  
                   
                     191252
                  
                
                 
                   
                     707
                  
                   
                     0.99329226
                  
                
                 
                   
                      
                  
                   
                     191191
                  
                
                 
                   
                     706
                  
                   
                     0.99138035
                  
                
                 
                   
                      
                  
                   
                     191129
                  
                
                 
                   
                     705
                  
                   
                     0.98946906
                  
                
                 
                   
                      
                  
                   
                     191067
                  
                
                 
                   
                     704
                  
                   
                     0.98755839
                  
                
                 
                   
                      
                  
                   
                     191005
                  
                
                 
                   
                     703
                  
                   
                     0.98564834
                  
                
                 
                   
                      
                  
                   
                     190943
                  
                
                 
                   
                     702
                  
                   
                     0.98273891
                  
                
                 
                   
                      
                  
                   
                     190881
                  
                
                 
                   
                     701
                  
                   
                     0.98183010
                  
                
                 
                   
                     
                  
                   
                     190818
                  
                
                 
                   
                     700
                  
                   
                     0.97992192
                  
                
                 
                   
                      
                  
                   
                     190755
                  
                
                 
                   
                     699
                  
                   
                     0.97801437
                  
                
                 
                   
                      
                  
                   
                     190692
                  
                
                 
                   
                     698
                  
                   
                     0.97610745
                  
                
                 
                   
                      
                  
                   
                     190629
                  
                
                 
                   
                     697
                  
                   
                     0.97420116
                  
                
                 
                   
                      
                  
                   
                     190566
                  
                
                 
                   
                     696
                  
                   
                     0.97229550
                  
                
                 
                   
                      
                  
                   
                     190502
                  
                
                 
                   
                     695
                  
                   
                     0.97039048
                  
                
                 
                   
                      
                  
                   
                     190438
                  
                
                 
                   
                     694
                  
                   
                     0.96848610
                  
                
                 
                   
                      
                  
                   
                     190376
                  
                
                 
                   
                     693
                  
                   
                     0.96658234
                  
                
                 
                   
                      
                  
                   
                     190304
                  
                
                 
                   
                     692
                  
                   
                     0.96467930
                  
                
                 
                   
                      
                  
                   
                     190244
                  
                
                 
                   
                     691
                  
                   
                     0.96277686
                  
                
                 
                   
                      
                  
                   
                     190179
                  
                
                 
                   
                     690
                  
                   
                     0.96087497
                  
                
                 
                   
                      
                  
                   
                     190113
                  
                
                 
                   
                     689
                  
                   
                     0.95897384
                  
                
                 
                   
                      
                  
                   
                     190048
                  
                
                 
                   
                     688
                  
                   
                     0.95707336
                  
                
                 
                   
                      
                  
                   
                     189983
                  
                
                 
                   
                     687
                  
                   
                     0.95517353
                  
                
                 
                   
                      
                  
                   
                     189917
                  
                
                 
                   
                     686
                  
                   
                     0.95327436
                  
                
                 
                   
                      
                  
                   
                     189851
                  
                
                 
                   
                     685
                  
                   
                     0.95137585
                  
                
                 
                   
                      
                  
                   
                     189784
                  
                
                 
                   
                     684
                  
                   
                     0.94947801
                  
                
                 
                   
                      
                  
                   
                     189717
                  
                
                 
                   
                      
                  
                   
                     189717
                  
                
                 
                   
                     683
                  
                   
                     0.94758084
                  
                
                 
                   
                      
                  
                   
                     189651
                  
                
                 
                   
                     682
                  
                   
                     0.94568433
                  
                
                 
                   
                      
                  
                   
                     189584
                  
                
                 
                   
                     681
                  
                   
                     0.94378848
                  
                
                 
                   
                      
                  
                   
                     189516
                  
                
                 
                   
                     680
                  
                   
                     0.94189324
                  
                
                 
                   
                      
                  
                   
                     189448
                  
                
                 
                   
                     679
                  
                   
                     0.93999876
                  
                
                 
                   
                      
                  
                   
                     189381
                  
                
                 
                   
                     678
                  
                   
                     0.93810495
                  
                
                 
                   
                      
                  
                   
                     189313
                  
                
                 
                   
                     677
                  
                   
                     0.93621182
                  
                
                 
                   
                      
                  
                   
                     189244
                  
                
                 
                   
                     676
                  
                   
                     0.93431938
                  
                
                 
                   
                      
                  
                   
                     189176
                  
                
                 
                   
                     675
                  
                   
                     0.93242762
                  
                
                 
                   
                      
                  
                   
                     189107
                  
                
                 
                   
                     674
                  
                   
                     0.93053655
                  
                
                 
                   
                      
                  
                   
                     189038
                  
                
                 
                   
                     673
                  
                   
                     0.92864617
                  
                
                 
                   
                      
                  
                   
                     188969
                  
                
                 
                   
                     672
                  
                   
                     0.92675648
                  
                
                 
                   
                      
                  
                   
                     188899
                  
                
                 
                   
                     671
                  
                   
                     0.92486749
                  
                
                 
                   
                      
                  
                   
                     188823
                  
                
                 
                   
                     670
                  
                   
                     0.92297905
                  
                
                 
                   
                      
                  
                   
                     188769
                  
                
                 
                   
                     669
                  
                   
                     0.92109136
                  
                
                 
                   
                      
                  
                   
                     188696
                  
                
                 
                   
                     668
                  
                   
                     0.91920440
                  
                
                 
                   
                      
                  
                   
                     188619
                  
                
                 
                   
                     667
                  
                   
                     0.91731821
                  
                
                 
                   
                      
                  
                   
                     188549
                  
                
                 
                   
                     
                  
                   
                     188549
                  
                
                 
                   
                     666
                  
                   
                     0.91543272
                  
                
                 
                   
                      
                  
                   
                     188478
                  
                
                 
                   
                     665
                  
                   
                     0.91354794
                  
                
                 
                   
                      
                  
                   
                     188407
                  
                
                 
                   
                     664
                  
                   
                     0.91166387
                  
                
                 
                   
                      
                  
                   
                     188336
                  
                
                 
                   
                     663
                  
                   
                     0.90978051
                  
                
                 
                   
                      
                  
                   
                     188264
                  
                
                 
                   
                     662
                  
                   
                     0.90789787
                  
                
                 
                   
                      
                  
                   
                     188192
                  
                
                 
                   
                     661
                  
                   
                     0.90601595
                  
                
                 
                   
                      
                  
                   
                     188120
                  
                
                 
                   
                     660
                  
                   
                     0.90413479
                  
                
                 
                   
                      
                  
                   
                     188048
                  
                
                 
                   
                     659
                  
                   
                     0.90225431
                  
                
                 
                   
                      
                  
                   
                     187973
                  
                
                 
                   
                     658
                  
                   
                     0.90037458
                  
                
                 
                   
                      
                  
                   
                     187900
                  
                
                 
                   
                     657
                  
                   
                     0.89849558
                  
                
                 
                   
                      
                  
                   
                     187829
                  
                
                 
                   
                     656
                  
                   
                     0.89661729
                  
                
                 
                   
                      
                  
                   
                     187757
                  
                
                 
                   
                     655
                  
                   
                     0.89473972
                  
                
                 
                   
                      
                  
                   
                     187685
                  
                
                 
                   
                     654
                  
                   
                     0.89286287
                  
                
                 
                   
                      
                  
                   
                     187610
                  
                
                 
                   
                     653
                  
                   
                     0.89098677
                  
                
                 
                   
                      
                  
                   
                     187535
                  
                
                 
                   
                     652
                  
                   
                     0.88911142
                  
                
                 
                   
                      
                  
                   
                     187461
                  
                
                 
                   
                     651
                  
                   
                     0.88723681
                  
                
                 
                   
                      
                  
                   
                     187386
                  
                
                 
                   
                     650
                  
                   
                     0.88536295
                  
                
                 
                   
                     650
                  
                   
                     0.88536284
                  
                
                 
                   
                      
                  
                   
                     187311
                  
                
                 
                   
                     649
                  
                   
                     0.88348973
                  
                
                 
                   
                      
                  
                   
                     187237
                  
                
                 
                   
                     648
                  
                   
                     0.88161736
                  
                
                 
                   
                      
                  
                   
                     187163
                  
                
                 
                   
                     647
                  
                   
                     0.87974573
                  
                
                 
                   
                      
                  
                   
                     187087
                  
                
                 
                   
                     646
                  
                   
                     0.87787486
                  
                
                 
                   
                      
                  
                   
                     187010
                  
                
                 
                   
                     645
                  
                   
                     0.87600476
                  
                
                 
                   
                      
                  
                   
                     186934
                  
                
                 
                   
                     644
                  
                   
                     0.87413542
                  
                
                 
                   
                      
                  
                   
                     186858
                  
                
                 
                   
                     643
                  
                   
                     0.87226684
                  
                
                 
                   
                      
                  
                   
                     186782
                  
                
                 
                   
                     642
                  
                   
                     0.87039902
                  
                
                 
                   
                      
                  
                   
                     186705
                  
                
                 
                   
                     641
                  
                   
                     0.86853197
                  
                
                 
                   
                      
                  
                   
                     186628
                  
                
                 
                   
                     640
                  
                   
                     0.86666560
                  
                
                 
                   
                      
                  
                   
                     186551
                  
                
                 
                   
                     639
                  
                   
                     0.86480009
                  
                
                 
                   
                      
                  
                   
                     186473
                  
                
                 
                   
                     638
                  
                   
                     0.86293536
                  
                
                 
                   
                      
                  
                   
                     186395
                  
                
                 
                   
                     637
                  
                   
                     0.86107141
                  
                
                 
                   
                      
                  
                   
                     186317
                  
                
                 
                   
                     636
                  
                   
                     0.85920824
                  
                
                 
                   
                      
                  
                   
                     186239
                  
                
                 
                   
                     635
                  
                   
                     0.85734585
                  
                
                 
                   
                      
                  
                   
                     186161
                  
                
                 
                   
                     634
                  
                   
                     0.85548424
                  
                
                 
                   
                      
                  
                   
                     186083
                  
                
                 
                   
                     633
                  
                   
                     0.85362341
                  
                
                 
                   
                     
                     633
                  
                   
                     0.85362341
                  
                
                 
                   
                      
                  
                   
                     186004
                  
                
                 
                   
                     632
                  
                   
                     0.85176337
                  
                
                 
                   
                      
                  
                   
                     185924
                  
                
                 
                   
                     631
                  
                   
                     0.84990413
                  
                
                 
                   
                      
                  
                   
                     185845
                  
                
                 
                   
                     630
                  
                   
                     0.84804557
                  
                
                 
                   
                      
                  
                   
                     185764
                  
                
                 
                   
                     629
                  
                   
                     0.84618793
                  
                
                 
                   
                      
                  
                   
                     185684
                  
                
                 
                   
                     628
                  
                   
                     0.84433109
                  
                
                 
                   
                      
                  
                   
                     185606
                  
                
                 
                   
                     627
                  
                   
                     0.84247503
                  
                
                 
                   
                      
                  
                   
                     185525
                  
                
                 
                   
                     626
                  
                   
                     0.84061978
                  
                
                 
                   
                      
                  
                   
                     185444
                  
                
                 
                   
                     625
                  
                   
                     0.83876534
                  
                
                 
                   
                      
                  
                   
                     185363
                  
                
                 
                   
                     624
                  
                   
                     0.83691171
                  
                
                 
                   
                      
                  
                   
                     185281
                  
                
                 
                   
                     623
                  
                   
                     0.83505890
                  
                
                 
                   
                      
                  
                   
                     185200
                  
                
                 
                   
                     622
                  
                   
                     0.83320690
                  
                
                 
                   
                      
                  
                   
                     185119
                  
                
                 
                   
                     621
                  
                   
                     0.83135571
                  
                
                 
                   
                      
                  
                   
                     185038
                  
                
                 
                   
                     620
                  
                   
                     0.82950517
                  
                
                 
                   
                      
                  
                   
                     184956
                  
                
                 
                   
                     619
                  
                   
                     0.82765561
                  
                
                 
                   
                      
                  
                   
                     184873
                  
                
                 
                   
                     618
                  
                   
                     0.82580688
                  
                
                 
                   
                      
                  
                   
                     184790
                  
                
                 
                   
                     617
                  
                   
                     0.82395898
                  
                
                 
                   
                      
                  
                   
                     184707
                  
                
                 
                   
                      
                  
                   
                     184707
                  
                
                 
                   
                     616
                  
                   
                     0.82211191
                  
                
                 
                   
                      
                  
                   
                     184624
                  
                
                 
                   
                     615
                  
                   
                     0.82026567
                  
                
                 
                   
                      
                  
                   
                     184540
                  
                
                 
                   
                     614
                  
                   
                     0.81842027
                  
                
                 
                   
                      
                  
                   
                     184456
                  
                
                 
                   
                     613
                  
                   
                     0.81657571
                  
                
                 
                   
                      
                  
                   
                     184372
                  
                
                 
                   
                     612
                  
                   
                     0.81473199
                  
                
                 
                   
                      
                  
                   
                     184288
                  
                
                 
                   
                     611
                  
                   
                     0.81288911
                  
                
                 
                   
                      
                  
                   
                     184204
                  
                
                 
                   
                     610
                  
                   
                     0.81104695
                  
                
                 
                   
                      
                  
                   
                     184119
                  
                
                 
                   
                     609
                  
                   
                     0.80920576
                  
                
                 
                   
                      
                  
                   
                     184035
                  
                
                 
                   
                     608
                  
                   
                     0.80736541
                  
                
                 
                   
                      
                  
                   
                     183949
                  
                
                 
                   
                     607
                  
                   
                     0.80552592
                  
                
                 
                   
                      
                  
                   
                     183865
                  
                
                 
                   
                     606
                  
                   
                     0.80368727
                  
                
                 
                   
                      
                  
                   
                     183780
                  
                
                 
                   
                     605
                  
                   
                     0.80184947
                  
                
                 
                   
                      
                  
                   
                     183693
                  
                
                 
                   
                     604
                  
                   
                     0.80001254
                  
                
                 
                   
                      
                  
                   
                     183606
                  
                
                 
                   
                     603
                  
                   
                     0.79817548
                  
                
                 
                   
                      
                  
                   
                     183519
                  
                
                 
                   
                     602
                  
                   
                     0.79634029
                  
                
                 
                   
                      
                  
                   
                     183433
                  
                
                 
                   
                     601
                  
                   
                     0.79450596
                  
                
                 
                   
                      
                  
                   
                     183346
                  
                
                 
                   
                     600
                  
                   
                     0.79267250
                  
                
                 
                   
                     
                     600
                  
                   
                     0.79267345
                  
                
                 
                   
                      
                  
                   
                     183258
                  
                
                 
                   
                     599
                  
                   
                     0.79084087
                  
                
                 
                   
                      
                  
                   
                     183170
                  
                
                 
                   
                     598
                  
                   
                     0.78900917
                  
                
                 
                   
                      
                  
                   
                     183082
                  
                
                 
                   
                     597
                  
                   
                     0.78717835
                  
                
                 
                   
                      
                  
                   
                     182994
                  
                
                 
                   
                     596
                  
                   
                     0.78534841
                  
                
                 
                   
                      
                  
                   
                     182906
                  
                
                 
                   
                     595
                  
                   
                     0.78351935
                  
                
                 
                   
                      
                  
                   
                     182818
                  
                
                 
                   
                     594
                  
                   
                     0.78169117
                  
                
                 
                   
                      
                  
                   
                     182729
                  
                
                 
                   
                     593
                  
                   
                     0.77986388
                  
                
                 
                   
                      
                  
                   
                     182640
                  
                
                 
                   
                     592
                  
                   
                     0.77803748
                  
                
                 
                   
                      
                  
                   
                     182551
                  
                
                 
                   
                     591
                  
                   
                     0.77621197
                  
                
                 
                   
                      
                  
                   
                     182461
                  
                
                 
                   
                     590
                  
                   
                     0.77438736
                  
                
                 
                   
                      
                  
                   
                     182371
                  
                
                 
                   
                     589
                  
                   
                     0.77256365
                  
                
                 
                   
                      
                  
                   
                     182281
                  
                
                 
                   
                     588
                  
                   
                     0.77074084
                  
                
                 
                   
                      
                  
                   
                     182191
                  
                
                 
                   
                     587
                  
                   
                     0.76891893
                  
                
                 
                   
                      
                  
                   
                     182100
                  
                
                 
                   
                     586
                  
                   
                     0.76709793
                  
                
                 
                   
                      
                  
                   
                     182009
                  
                
                 
                   
                     585
                  
                   
                     0.76527784
                  
                
                 
                   
                      
                  
                   
                     181918
                  
                
                 
                   
                     584
                  
                   
                     0.76345866
                  
                
                 
                   
                      
                  
                   
                     131826
                  
                
                 
                   
                     583
                  
                   
                     0.76164040
                  
                
                 
                   
                      
                  
                   
                     181734
                  
                
                 
                   
                     582
                  
                   
                     0.75982306
                  
                
                 
                   
                      
                  
                   
                     181639
                  
                
                 
                   
                     581
                  
                   
                     0.75800667
                  
                
                 
                   
                      
                  
                   
                     181543
                  
                
                 
                   
                     580
                  
                   
                     0.75619124
                  
                
                 
                   
                      
                  
                   
                     181458
                  
                
                 
                   
                     579
                  
                   
                     0.75437670
                  
                
                 
                   
                      
                  
                   
                     181365
                  
                
                 
                   
                     578
                  
                   
                     0.75256305
                  
                
                 
                   
                      
                  
                   
                     181271
                  
                
                 
                   
                     577
                  
                   
                     0.75075934
                  
                
                 
                   
                      
                  
                   
                     181178
                  
                
                 
                   
                     576
                  
                   
                     0.74893856
                  
                
                 
                   
                      
                  
                   
                     181085
                  
                
                 
                   
                     575
                  
                   
                     0.74712771
                  
                
                 
                   
                      
                  
                   
                     180991
                  
                
                 
                   
                     574
                  
                   
                     0.74531780
                  
                
                 
                   
                      
                  
                   
                     180897
                  
                
                 
                   
                     573
                  
                   
                     0.74350883
                  
                
                 
                   
                      
                  
                   
                     180802
                  
                
                 
                   
                     572
                  
                   
                     0.74170081
                  
                
                 
                   
                      
                  
                   
                     180707
                  
                
                 
                   
                     571
                  
                   
                     0.73989374
                  
                
                 
                   
                      
                  
                   
                     180611
                  
                
                 
                   
                     570
                  
                   
                     0.73708713
                  
                
                 
                   
                      
                  
                   
                     180516
                  
                
                 
                   
                     569
                  
                   
                     0.73628197
                  
                
                 
                   
                      
                  
                   
                     180422
                  
                
                 
                   
                     568
                  
                   
                     0.73447775
                  
                
                 
                   
                      
                  
                   
                     180326
                  
                
                 
                   
                     567
                  
                   
                     0.73267449
                  
                
                 
                   
                      
                  
                   
                     180230
                  
                
                 
                   
                     
                  
                   
                     180230
                  
                
                 
                   
                     566
                  
                   
                     0.73087219
                  
                
                 
                   
                      
                  
                   
                     180134
                  
                
                 
                   
                     565
                  
                   
                     0.72907085
                  
                
                 
                   
                      
                  
                   
                     180037
                  
                
                 
                   
                     564
                  
                   
                     0.72727048
                  
                
                 
                   
                      
                  
                   
                     179940
                  
                
                 
                   
                     563
                  
                   
                     0.72547108
                  
                
                 
                   
                      
                  
                   
                     279843
                  
                
                 
                   
                     562
                  
                   
                     0.72367265
                  
                
                 
                   
                      
                  
                   
                     179745
                  
                
                 
                   
                     561
                  
                   
                     0.72187520
                  
                
                 
                   
                      
                  
                   
                     179647
                  
                
                 
                   
                     560
                  
                   
                     0.72007866
                  
                
                 
                   
                      
                  
                   
                     179548
                  
                
                 
                   
                     559
                  
                   
                     0.71828318
                  
                
                 
                   
                      
                  
                   
                     179450
                  
                
                 
                   
                     558
                  
                   
                     0.71648868
                  
                
                 
                   
                      
                  
                   
                     179353
                  
                
                 
                   
                     557
                  
                   
                     0.71469515
                  
                
                 
                   
                      
                  
                   
                     179254
                  
                
                 
                   
                     556
                  
                   
                     0.71290261
                  
                
                 
                   
                      
                  
                   
                     179155
                  
                
                 
                   
                     555
                  
                   
                     0.71111106
                  
                
                 
                   
                      
                  
                   
                     179056
                  
                
                 
                   
                     554
                  
                   
                     0.70932050
                  
                
                 
                   
                      
                  
                   
                     178956
                  
                
                 
                   
                     553
                  
                   
                     0.70753094
                  
                
                 
                   
                      
                  
                   
                     178856
                  
                
                 
                   
                     552
                  
                   
                     0.70574238
                  
                
                 
                   
                      
                  
                   
                     178755
                  
                
                 
                   
                     551
                  
                   
                     0.70395483
                  
                
                 
                   
                      
                  
                   
                     178654
                  
                
                 
                   
                     550
                  
                   
                     0.70216829
                  
                
                 
                   
                     550
                  
                   
                     0.70216834
                  
                
                 
                   
                      
                  
                   
                     178553
                  
                
                 
                   
                     549
                  
                   
                     0.70038281
                  
                
                 
                   
                      
                  
                   
                     178452
                  
                
                 
                   
                     548
                  
                   
                     0.69859829
                  
                
                 
                   
                      
                  
                   
                     178352
                  
                
                 
                   
                     547
                  
                   
                     0.69681477
                  
                
                 
                   
                      
                  
                   
                     178250
                  
                
                 
                   
                     546
                  
                   
                     0.69503227
                  
                
                 
                   
                      
                  
                   
                     178149
                  
                
                 
                   
                     545
                  
                   
                     0.69325078
                  
                
                 
                   
                      
                  
                   
                     178048
                  
                
                 
                   
                     544
                  
                   
                     0.69147030
                  
                
                 
                   
                      
                  
                   
                     177943
                  
                
                 
                   
                     543
                  
                   
                     0.68969087
                  
                
                 
                   
                      
                  
                   
                     177841
                  
                
                 
                   
                     542
                  
                   
                     0.68791246
                  
                
                 
                   
                      
                  
                   
                     177738
                  
                
                 
                   
                     541
                  
                   
                     0.68613508
                  
                
                 
                   
                      
                  
                   
                     177634
                  
                
                 
                   
                     540
                  
                   
                     0.68435845
                  
                
                 
                   
                      
                  
                   
                     177528
                  
                
                 
                   
                     539
                  
                   
                     0.68258317
                  
                
                 
                   
                      
                  
                   
                     177423
                  
                
                 
                   
                     538
                  
                   
                     0.68080894
                  
                
                 
                   
                      
                  
                   
                     177318
                  
                
                 
                   
                     537
                  
                   
                     0.67903576
                  
                
                 
                   
                      
                  
                   
                     177218
                  
                
                 
                   
                     536
                  
                   
                     0.67726358
                  
                
                 
                   
                      
                  
                   
                     177114
                  
                
                 
                   
                     535
                  
                   
                     0.67549244
                  
                
                 
                   
                      
                  
                   
                     177009
                  
                
                 
                   
                     534
                  
                   
                     0.67372235
                  
                
                 
                   
                      
                  
                   
                     176903
                  
                
                 
                   
                     
                     533
                  
                   
                     0.67195332
                  
                
                 
                   
                      
                  
                   
                     176799
                  
                
                 
                   
                     532
                  
                   
                     0.67018533
                  
                
                 
                   
                      
                  
                   
                     176693
                  
                
                 
                   
                     531
                  
                   
                     0.66841840
                  
                
                 
                   
                      
                  
                   
                     176585
                  
                
                 
                   
                     530
                  
                   
                     0.66665234
                  
                
                 
                   
                      
                  
                   
                     176479
                  
                
                 
                   
                     529
                  
                   
                     0.66488755
                  
                
                 
                   
                      
                  
                   
                     176372
                  
                
                 
                   
                     528
                  
                   
                     0.66312383
                  
                
                 
                   
                      
                  
                   
                     176265
                  
                
                 
                   
                     527
                  
                   
                     0.66136118
                  
                
                 
                   
                      
                  
                   
                     176158
                  
                
                 
                   
                     526
                  
                   
                     0.65959960
                  
                
                 
                   
                      
                  
                   
                     176050
                  
                
                 
                   
                     525
                  
                   
                     0.65783910
                  
                
                 
                   
                      
                  
                   
                     175942
                  
                
                 
                   
                     524
                  
                   
                     0.65607968
                  
                
                 
                   
                      
                  
                   
                     175834
                  
                
                 
                   
                     523
                  
                   
                     0.65432134
                  
                
                 
                   
                      
                  
                   
                     175725
                  
                
                 
                   
                     522
                  
                   
                     0.65256409
                  
                
                 
                   
                      
                  
                   
                     175622
                  
                
                 
                   
                     521
                  
                   
                     0.65080787
                  
                
                 
                   
                      
                  
                   
                     175512
                  
                
                 
                   
                     520
                  
                   
                     0.64905275
                  
                
                 
                   
                      
                  
                   
                     175398
                  
                
                 
                   
                     519
                  
                   
                     0.64729877
                  
                
                 
                   
                      
                  
                   
                     175289
                  
                
                 
                   
                     518
                  
                   
                     0.64554588
                  
                
                 
                   
                      
                  
                   
                     175179
                  
                
                 
                   
                     517
                  
                   
                     0.64379409
                  
                
                 
                   
                      
                  
                   
                     175068
                  
                
                 
                   
                      
                  
                   
                     175068
                  
                
                 
                   
                     516
                  
                   
                     0.64204341
                  
                
                 
                   
                      
                  
                   
                     174957
                  
                
                 
                   
                     515
                  
                   
                     0.64029384
                  
                
                 
                   
                      
                  
                   
                     174846
                  
                
                 
                   
                     514
                  
                   
                     0.63854538
                  
                
                 
                   
                      
                  
                   
                     174735
                  
                
                 
                   
                     513
                  
                   
                     0.63679803
                  
                
                 
                   
                      
                  
                   
                     174624
                  
                
                 
                   
                     512
                  
                   
                     0.63505179
                  
                
                 
                   
                      
                  
                   
                     174512
                  
                
                 
                   
                     511
                  
                   
                     0.63330667
                  
                
                 
                   
                      
                  
                   
                     174400
                  
                
                 
                   
                     510
                  
                   
                     0.63156249
                  
                
                 
                   
                      
                  
                   
                     174287
                  
                
                 
                   
                     509
                  
                   
                     0.62981962
                  
                
                 
                   
                      
                  
                   
                     174174
                  
                
                 
                   
                     508
                  
                   
                     0.62807788
                  
                
                 
                   
                      
                  
                   
                     174062
                  
                
                 
                   
                     507
                  
                   
                     0.62633726
                  
                
                 
                   
                      
                  
                   
                     173948
                  
                
                 
                   
                     506
                  
                   
                     0.62459778
                  
                
                 
                   
                      
                  
                   
                     173835
                  
                
                 
                   
                     505
                  
                   
                     0.62285943
                  
                
                 
                   
                      
                  
                   
                     173721
                  
                
                 
                   
                     504
                  
                   
                     0.62112222
                  
                
                 
                   
                      
                  
                   
                     173607
                  
                
                 
                   
                     503
                  
                   
                     0.61938615
                  
                
                 
                   
                      
                  
                   
                     173492
                  
                
                 
                   
                     502
                  
                   
                     0.61765123
                  
                
                 
                   
                      
                  
                   
                     173377
                  
                
                 
                   
                     501
                  
                   
                     0.61591746
                  
                
                 
                   
                      
                  
                   
                     173262
                  
                
                 
                   
                     500
                  
                   
                     0.61418484
                  
                
                 
                   
                     
                     500
                  
                   
                     0.61418485
                  
                
                 
                   
                      
                  
                   
                     173147
                  
                
                 
                   
                     499
                  
                   
                     0.61245338
                  
                
                 
                   
                      
                  
                   
                     173031
                  
                
                 
                   
                     498
                  
                   
                     0.61072307
                  
                
                 
                   
                      
                  
                   
                     172914
                  
                
                 
                   
                     497
                  
                   
                     0.60899393
                  
                
                 
                   
                      
                  
                   
                     172798
                  
                
                 
                   
                     496
                  
                   
                     0.60726595
                  
                
                 
                   
                      
                  
                   
                     172681
                  
                
                 
                   
                     495
                  
                   
                     0.60553914
                  
                
                 
                   
                      
                  
                   
                     172564
                  
                
                 
                   
                     494
                  
                   
                     0.60381350
                  
                
                 
                   
                      
                  
                   
                     172447
                  
                
                 
                   
                     493
                  
                   
                     0.60208903
                  
                
                 
                   
                      
                  
                   
                     172329
                  
                
                 
                   
                     492
                  
                   
                     0.60036574
                  
                
                 
                   
                      
                  
                   
                     172211
                  
                
                 
                   
                     491
                  
                   
                     0.59864363
                  
                
                 
                   
                      
                  
                   
                     172093
                  
                
                 
                   
                     490
                  
                   
                     0.59692260
                  
                
                 
                   
                      
                  
                   
                     171975
                  
                
                 
                   
                     489
                  
                   
                     0.59520285
                  
                
                 
                   
                      
                  
                   
                     171856
                  
                
                 
                   
                     488
                  
                   
                     0.59348429
                  
                
                 
                   
                      
                  
                   
                     171736
                  
                
                 
                   
                     487
                  
                   
                     0.59176693
                  
                
                 
                   
                      
                  
                   
                     171617
                  
                
                 
                   
                     486
                  
                   
                     0.59005076
                  
                
                 
                   
                      
                  
                   
                     171498
                  
                
                 
                   
                     485
                  
                   
                     0.58833578
                  
                
                 
                   
                      
                  
                   
                     171377
                  
                
                 
                   
                     484
                  
                   
                     0.58662201
                  
                
                 
                   
                      
                  
                   
                     171256
                  
                
                 
                   
                     483
                  
                   
                     0.58490948
                  
                
                 
                   
                      
                  
                   
                     171136
                  
                
                 
                   
                     482
                  
                   
                     0.58319809
                  
                
                 
                   
                      
                  
                   
                     171015
                  
                
                 
                   
                     481
                  
                   
                     0.58148794
                  
                
                 
                   
                      
                  
                   
                     170893
                  
                
                 
                   
                     480
                  
                   
                     0.57977892
                  
                
                 
                   
                      
                  
                   
                     170771
                  
                
                 
                   
                     479
                  
                   
                     0.57807121
                  
                
                 
                   
                      
                  
                   
                     170649
                  
                
                 
                   
                     478
                  
                   
                     0.57636472
                  
                
                 
                   
                      
                  
                   
                     170527
                  
                
                 
                   
                     477
                  
                   
                     0.57465945
                  
                
                 
                   
                      
                  
                   
                     170406
                  
                
                 
                   
                     476
                  
                   
                     0.57295539
                  
                
                 
                   
                      
                  
                   
                     170281
                  
                
                 
                   
                     475
                  
                   
                     0.57125258
                  
                
                 
                   
                      
                  
                   
                     170158
                  
                
                 
                   
                     474
                  
                   
                     0.56955100
                  
                
                 
                   
                      
                  
                   
                     170034
                  
                
                 
                   
                     473
                  
                   
                     0.56785066
                  
                
                 
                   
                      
                  
                   
                     169910
                  
                
                 
                   
                     472
                  
                   
                     0.56615156
                  
                
                 
                   
                      
                  
                   
                     169786
                  
                
                 
                   
                     471
                  
                   
                     0.56445370
                  
                
                 
                   
                      
                  
                   
                     169661
                  
                
                 
                   
                     470
                  
                   
                     0.56275702
                  
                
                 
                   
                      
                  
                   
                     169536
                  
                
                 
                   
                     469
                  
                   
                     0.56106166
                  
                
                 
                   
                      
                  
                   
                     169411
                  
                
                 
                   
                     468
                  
                   
                     0.55936755
                  
                
                 
                   
                      
                  
                   
                     169285
                  
                
                 
                   
                     467
                  
                   
                     0.55767470
                  
                
                 
                   
                      
                  
                   
                     169159
                  
                
                 
                   
                     
                  
                   
                     169159
                  
                
                 
                   
                     466
                  
                   
                     0.55598311
                  
                
                 
                   
                      
                  
                   
                     169035
                  
                
                 
                   
                     465
                  
                   
                     0.55429278
                  
                
                 
                   
                      
                  
                   
                     168901
                  
                
                 
                   
                     464
                  
                   
                     0.55260377
                  
                
                 
                   
                      
                  
                   
                     168779
                  
                
                 
                   
                     463
                  
                   
                     0.55091598
                  
                
                 
                   
                      
                  
                   
                     168652
                  
                
                 
                   
                     462
                  
                   
                     0.54922946
                  
                
                 
                   
                      
                  
                   
                     168524
                  
                
                 
                   
                     461
                  
                   
                     0.54754422
                  
                
                 
                   
                      
                  
                   
                     168397
                  
                
                 
                   
                     460
                  
                   
                     0.54586011
                  
                
                 
                   
                      
                  
                   
                     168268
                  
                
                 
                   
                     459
                  
                   
                     0.54417743
                  
                
                 
                   
                      
                  
                   
                     168139
                  
                
                 
                   
                     458
                  
                   
                     0.54249604
                  
                
                 
                   
                      
                  
                   
                     168010
                  
                
                 
                   
                     457
                  
                   
                     0.54081594
                  
                
                 
                   
                      
                  
                   
                     167881
                  
                
                 
                   
                     456
                  
                   
                     0.53913713
                  
                
                 
                   
                      
                  
                   
                     167751
                  
                
                 
                   
                     455
                  
                   
                     0.53745962
                  
                
                 
                   
                      
                  
                   
                     167621
                  
                
                 
                   
                     454
                  
                   
                     0.53578341
                  
                
                 
                   
                      
                  
                   
                     167491
                  
                
                 
                   
                     453
                  
                   
                     0.53410850
                  
                
                 
                   
                      
                  
                   
                     167360
                  
                
                 
                   
                     452
                  
                   
                     0.53243490
                  
                
                 
                   
                      
                  
                   
                     167229
                  
                
                 
                   
                     451
                  
                   
                     0.53076261
                  
                
                 
                   
                      
                  
                   
                     167098
                  
                
                 
                   
                     450
                  
                   
                     0.52909163
                  
                
                 
                   
                     450
                  
                   
                     0.52909299
                  
                
                 
                   
                      
                  
                   
                     166966
                  
                
                 
                   
                     449
                  
                   
                     0
                     .
                     527423●3
                  
                
                 
                   
                      
                  
                   
                     166834
                  
                
                 
                   
                     448
                  
                   
                     0.52575499
                  
                
                 
                   
                      
                  
                   
                     166702
                  
                
                 
                   
                     447
                  
                   
                     0.52408797
                  
                
                 
                   
                      
                  
                   
                     166570
                  
                
                 
                   
                     446
                  
                   
                     0.52242227
                  
                
                 
                   
                      
                  
                   
                     166437
                  
                
                 
                   
                     445
                  
                   
                     0.52075790
                  
                
                 
                   
                      
                  
                   
                     166302
                  
                
                 
                   
                     444
                  
                   
                     0.51909488
                  
                
                 
                   
                      
                  
                   
                     166168
                  
                
                 
                   
                     443
                  
                   
                     0.51743320
                  
                
                 
                   
                      
                  
                   
                     166035
                  
                
                 
                   
                     442
                  
                   
                     0.51577285
                  
                
                 
                   
                      
                  
                   
                     165900
                  
                
                 
                   
                     441
                  
                   
                     0.51411385
                  
                
                 
                   
                      
                  
                   
                     165765
                  
                
                 
                   
                     440
                  
                   
                     0.51245467
                  
                
                 
                   
                      
                  
                   
                     165634
                  
                
                 
                   
                     439
                  
                   
                     0.51079833
                  
                
                 
                   
                      
                  
                   
                     165494
                  
                
                 
                   
                     438
                  
                   
                     0.50914339
                  
                
                 
                   
                      
                  
                   
                     165358
                  
                
                 
                   
                     437
                  
                   
                     0.50748981
                  
                
                 
                   
                      
                  
                   
                     165222
                  
                
                 
                   
                     436
                  
                   
                     0.50583759
                  
                
                 
                   
                      
                  
                   
                     16508●
                  
                
                 
                   
                     435
                  
                   
                     0.50418673
                  
                
                 
                   
                      
                  
                   
                     164949
                  
                
                 
                   
                     434
                  
                   
                     0.50253724
                  
                
                 
                   
                      
                  
                   
                     164811
                  
                
                 
                   
                     
                     433
                  
                   
                     0.50088913
                  
                
                 
                   
                      
                  
                   
                     164673
                  
                
                 
                   
                     432
                  
                   
                     0.49924240
                  
                
                 
                   
                      
                  
                   
                     164535
                  
                
                 
                   
                     431
                  
                   
                     0.49759705
                  
                
                 
                   
                      
                  
                   
                     164397
                  
                
                 
                   
                     430
                  
                   
                     0.49595308
                  
                
                 
                   
                      
                  
                   
                     164259
                  
                
                 
                   
                     429
                  
                   
                     0.49431049
                  
                
                 
                   
                      
                  
                   
                     164120
                  
                
                 
                   
                     428
                  
                   
                     0.49266929
                  
                
                 
                   
                      
                  
                   
                     163980
                  
                
                 
                   
                     427
                  
                   
                     0.49102949
                  
                
                 
                   
                      
                  
                   
                     163835
                  
                
                 
                   
                     426
                  
                   
                     0.48939114
                  
                
                 
                   
                      
                  
                   
                     163700
                  
                
                 
                   
                     425
                  
                   
                     0.48775414
                  
                
                 
                   
                      
                  
                   
                     163560
                  
                
                 
                   
                     424
                  
                   
                     0.48611854
                  
                
                 
                   
                      
                  
                   
                     163419
                  
                
                 
                   
                     423
                  
                   
                     0.48448435
                  
                
                 
                   
                      
                  
                   
                     163277
                  
                
                 
                   
                     422
                  
                   
                     0.48285158
                  
                
                 
                   
                      
                  
                   
                     163135
                  
                
                 
                   
                     421
                  
                   
                     0.48122023
                  
                
                 
                   
                      
                  
                   
                     162998
                  
                
                 
                   
                     420
                  
                   
                     0.47959025
                  
                
                 
                   
                      
                  
                   
                     162843
                  
                
                 
                   
                     419
                  
                   
                     0.47796165
                  
                
                 
                   
                      
                  
                   
                     162708
                  
                
                 
                   
                     418
                  
                   
                     0.47633457
                  
                
                 
                   
                      
                  
                   
                     162565
                  
                
                 
                   
                     417
                  
                   
                     0.47470892
                  
                
                 
                   
                      
                  
                   
                     162422
                  
                
                 
                   
                      
                  
                   
                     162422
                  
                
                 
                   
                     416
                  
                   
                     0.47308470
                  
                
                 
                   
                      
                  
                   
                     162278
                  
                
                 
                   
                     415
                  
                   
                     0.47146192
                  
                
                 
                   
                      
                  
                   
                     162134
                  
                
                 
                   
                     414
                  
                   
                     0.46984058
                  
                
                 
                   
                      
                  
                   
                     161989
                  
                
                 
                   
                     413
                  
                   
                     0.46822069
                  
                
                 
                   
                      
                  
                   
                     161844
                  
                
                 
                   
                     412
                  
                   
                     0.46660225
                  
                
                 
                   
                      
                  
                   
                     161699
                  
                
                 
                   
                     411
                  
                   
                     0.46498526
                  
                
                 
                   
                      
                  
                   
                     161570
                  
                
                 
                   
                     410
                  
                   
                     0.46336957
                  
                
                 
                   
                      
                  
                   
                     161410
                  
                
                 
                   
                     409
                  
                   
                     0.46175547
                  
                
                 
                   
                      
                  
                   
                     161260
                  
                
                 
                   
                     408
                  
                   
                     0.46014287
                  
                
                 
                   
                      
                  
                   
                     161113
                  
                
                 
                   
                     407
                  
                   
                     0.45853174
                  
                
                 
                   
                      
                  
                   
                     160966
                  
                
                 
                   
                     406
                  
                   
                     0.45692208
                  
                
                 
                   
                      
                  
                   
                     160818
                  
                
                 
                   
                     405
                  
                   
                     0.45531390
                  
                
                 
                   
                      
                  
                   
                     160670
                  
                
                 
                   
                     404
                  
                   
                     0.45370720
                  
                
                 
                   
                      
                  
                   
                     160522
                  
                
                 
                   
                     403
                  
                   
                     0.45210198
                  
                
                 
                   
                      
                  
                   
                     160373
                  
                
                 
                   
                     402
                  
                   
                     0.45049825
                  
                
                 
                   
                      
                  
                   
                     160223
                  
                
                 
                   
                     401
                  
                   
                     0.44889602
                  
                
                 
                   
                      
                  
                   
                     160073
                  
                
                 
                   
                     400
                  
                   
                     0.44729529
                  
                
                 
                   
                     
                     400
                  
                   
                     0.44729522
                  
                
                 
                   
                      
                  
                   
                     159923
                  
                
                 
                   
                     399
                  
                   
                     0.44569599
                  
                
                 
                   
                      
                  
                   
                     159773
                  
                
                 
                   
                     398
                  
                   
                     0.44409826
                  
                
                 
                   
                      
                  
                   
                     159623
                  
                
                 
                   
                     397
                  
                   
                     0.44250203
                  
                
                 
                   
                      
                  
                   
                     159472
                  
                
                 
                   
                     396
                  
                   
                     0.44090731
                  
                
                 
                   
                      
                  
                   
                     159320
                  
                
                 
                   
                     395
                  
                   
                     0.43931411
                  
                
                 
                   
                      
                  
                   
                     159168
                  
                
                 
                   
                     394
                  
                   
                     0.43772243
                  
                
                 
                   
                      
                  
                   
                     159016
                  
                
                 
                   
                     393
                  
                   
                     0.43613227
                  
                
                 
                   
                      
                  
                   
                     158863
                  
                
                 
                   
                     392
                  
                   
                     0.43454364
                  
                
                 
                   
                      
                  
                   
                     158710
                  
                
                 
                   
                     391
                  
                   
                     0.43295654
                  
                
                 
                   
                      
                  
                   
                     158557
                  
                
                 
                   
                     390
                  
                   
                     0.43137086
                  
                
                 
                   
                      
                  
                   
                     158403
                  
                
                 
                   
                     389
                  
                   
                     0.42978683
                  
                
                 
                   
                      
                  
                   
                     158248
                  
                
                 
                   
                     388
                  
                   
                     0.42820435
                  
                
                 
                   
                      
                  
                   
                     158093
                  
                
                 
                   
                     387
                  
                   
                     0.42662342
                  
                
                 
                   
                      
                  
                   
                     157938
                  
                
                 
                   
                     386
                  
                   
                     0.42504404
                  
                
                 
                   
                      
                  
                   
                     157782
                  
                
                 
                   
                     385
                  
                   
                     0
                     ,
                     42346622
                  
                
                 
                   
                      
                  
                   
                     157626
                  
                
                 
                   
                     384
                  
                   
                     0.42188996
                  
                
                 
                   
                      
                  
                   
                     157470
                  
                
                 
                   
                     383
                  
                   
                     0.42031526
                  
                
                 
                   
                      
                  
                   
                     157313
                  
                
                 
                   
                     382
                  
                   
                     0.41874213
                  
                
                 
                   
                      
                  
                   
                     157156
                  
                
                 
                   
                     381
                  
                   
                     0.41717057
                  
                
                 
                   
                      
                  
                   
                     156999
                  
                
                 
                   
                     380
                  
                   
                     0.41560058
                  
                
                 
                   
                      
                  
                   
                     156841
                  
                
                 
                   
                     379
                  
                   
                     0.41403217
                  
                
                 
                   
                      
                  
                   
                     156682
                  
                
                 
                   
                     378
                  
                   
                     0.41246535
                  
                
                 
                   
                      
                  
                   
                     156522
                  
                
                 
                   
                     377
                  
                   
                     0.41090013
                  
                
                 
                   
                      
                  
                   
                     156363
                  
                
                 
                   
                     376
                  
                   
                     0.40933650
                  
                
                 
                   
                      
                  
                   
                     156204
                  
                
                 
                   
                     375
                  
                   
                     0.40777446
                  
                
                 
                   
                      
                  
                   
                     156044
                  
                
                 
                   
                     374
                  
                   
                     0.40621402
                  
                
                 
                   
                      
                  
                   
                     155883
                  
                
                 
                   
                     373
                  
                   
                     0.40465519
                  
                
                 
                   
                      
                  
                   
                     155722
                  
                
                 
                   
                     372
                  
                   
                     0.40309797
                  
                
                 
                   
                      
                  
                   
                     155561
                  
                
                 
                   
                     371
                  
                   
                     0.40154236
                  
                
                 
                   
                      
                  
                   
                     155399
                  
                
                 
                   
                     370
                  
                   
                     0.39998818
                  
                
                 
                   
                      
                  
                   
                     155238
                  
                
                 
                   
                     369
                  
                   
                     0.39843580
                  
                
                 
                   
                      
                  
                   
                     155025
                  
                
                 
                   
                     368
                  
                   
                     0.39688555
                  
                
                 
                   
                      
                  
                   
                     154911
                  
                
                 
                   
                     367
                  
                   
                     0.39533644
                  
                
                 
                   
                      
                  
                   
                     154788
                  
                
                 
                   
                     
                  
                   
                     154788
                  
                
                 
                   
                     366
                  
                   
                     0.39378896
                  
                
                 
                   
                      
                  
                   
                     154584
                  
                
                 
                   
                     365
                  
                   
                     0.39224312
                  
                
                 
                   
                      
                  
                   
                     154419
                  
                
                 
                   
                     364
                  
                   
                     0.39069893
                  
                
                 
                   
                      
                  
                   
                     154254
                  
                
                 
                   
                     363
                  
                   
                     0.38915639
                  
                
                 
                   
                      
                  
                   
                     154089
                  
                
                 
                   
                     362
                  
                   
                     0.38761550
                  
                
                 
                   
                      
                  
                   
                     153923
                  
                
                 
                   
                     361
                  
                   
                     0.38607627
                  
                
                 
                   
                      
                  
                   
                     153757
                  
                
                 
                   
                     360
                  
                   
                     0.38453683
                  
                
                 
                   
                      
                  
                   
                     153591
                  
                
                 
                   
                     359
                  
                   
                     0.38300092
                  
                
                 
                   
                      
                  
                   
                     153424
                  
                
                 
                   
                     358
                  
                   
                     0.38146668
                  
                
                 
                   
                      
                  
                   
                     153256
                  
                
                 
                   
                     357
                  
                   
                     0.37993412
                  
                
                 
                   
                      
                  
                   
                     153088
                  
                
                 
                   
                     356
                  
                   
                     0.37840324
                  
                
                 
                   
                      
                  
                   
                     152920
                  
                
                 
                   
                     355
                  
                   
                     0.37687404
                  
                
                 
                   
                      
                  
                   
                     152751
                  
                
                 
                   
                     354
                  
                   
                     0.37534653
                  
                
                 
                   
                      
                  
                   
                     152582
                  
                
                 
                   
                     353
                  
                   
                     0.37382071
                  
                
                 
                   
                      
                  
                   
                     152443
                  
                
                 
                   
                     352
                  
                   
                     0.37229658
                  
                
                 
                   
                      
                  
                   
                     152242
                  
                
                 
                   
                     351
                  
                   
                     0.37077416
                  
                
                 
                   
                      
                  
                   
                     152075
                  
                
                 
                   
                     350
                  
                   
                     0.36925315
                  
                
                 
                   
                     350
                  
                   
                     0.36925312
                  
                
                 
                   
                      
                  
                   
                     151905
                  
                
                 
                   
                     349
                  
                   
                     0.36773407
                  
                
                 
                   
                      
                  
                   
                     151728
                  
                
                 
                   
                     348
                  
                   
                     0.36621679
                  
                
                 
                   
                      
                  
                   
                     151556
                  
                
                 
                   
                     347
                  
                   
                     0.36470123
                  
                
                 
                   
                      
                  
                   
                     151384
                  
                
                 
                   
                     346
                  
                   
                     0.36318739
                  
                
                 
                   
                      
                  
                   
                     151211
                  
                
                 
                   
                     345
                  
                   
                     0.36167528
                  
                
                 
                   
                      
                  
                   
                     151038
                  
                
                 
                   
                     344
                  
                   
                     0.36016490
                  
                
                 
                   
                      
                  
                   
                     150865
                  
                
                 
                   
                     343
                  
                   
                     0.35865625
                  
                
                 
                   
                      
                  
                   
                     150690
                  
                
                 
                   
                     342
                  
                   
                     0.35714935
                  
                
                 
                   
                      
                  
                   
                     150515
                  
                
                 
                   
                     341
                  
                   
                     0.35564420
                  
                
                 
                   
                      
                  
                   
                     150340
                  
                
                 
                   
                     340
                  
                   
                     0.35414227
                  
                
                 
                   
                      
                  
                   
                     150164
                  
                
                 
                   
                     339
                  
                   
                     0.35264063
                  
                
                 
                   
                      
                  
                   
                     149988
                  
                
                 
                   
                     338
                  
                   
                     0.35114075
                  
                
                 
                   
                      
                  
                   
                     149811
                  
                
                 
                   
                     337
                  
                   
                     0.34964264
                  
                
                 
                   
                      
                  
                   
                     149634
                  
                
                 
                   
                     336
                  
                   
                     0.34814630
                  
                
                 
                   
                      
                  
                   
                     149457
                  
                
                 
                   
                     335
                  
                   
                     0.34665173
                  
                
                 
                   
                      
                  
                   
                     149279
                  
                
                 
                   
                     334
                  
                   
                     0.34515894
                  
                
                 
                   
                      
                  
                   
                     149100
                  
                
                 
                   
                     
                     333
                  
                   
                     0.34366794
                  
                
                 
                   
                      
                  
                   
                     148921
                  
                
                 
                   
                     332
                  
                   
                     0.34217873
                  
                
                 
                   
                      
                  
                   
                     148742
                  
                
                 
                   
                     331
                  
                   
                     0.34069131
                  
                
                 
                   
                      
                  
                   
                     148562
                  
                
                 
                   
                     330
                  
                   
                     0.33920561
                  
                
                 
                   
                      
                  
                   
                     148381
                  
                
                 
                   
                     329
                  
                   
                     0.33772180
                  
                
                 
                   
                      
                  
                   
                     148200
                  
                
                 
                   
                     328
                  
                   
                     0.33623980
                  
                
                 
                   
                      
                  
                   
                     148024
                  
                
                 
                   
                     327
                  
                   
                     0.33475956
                  
                
                 
                   
                      
                  
                   
                     147842
                  
                
                 
                   
                     326
                  
                   
                     0.33328114
                  
                
                 
                   
                      
                  
                   
                     147663
                  
                
                 
                   
                     325
                  
                   
                     0.33180451
                  
                
                 
                   
                      
                  
                   
                     147480
                  
                
                 
                   
                     324
                  
                   
                     0.33032971
                  
                
                 
                   
                      
                  
                   
                     147288
                  
                
                 
                   
                     323
                  
                   
                     0.32885683
                  
                
                 
                   
                      
                  
                   
                     147104
                  
                
                 
                   
                     322
                  
                   
                     0.32738579
                  
                
                 
                   
                      
                  
                   
                     146919
                  
                
                 
                   
                     321
                  
                   
                     0.32591660
                  
                
                 
                   
                      
                  
                   
                     146735
                  
                
                 
                   
                     320
                  
                   
                     2.32444946
                  
                
                 
                   
                      
                  
                   
                     146550
                  
                
                 
                   
                     319
                  
                   
                     0.32298396
                  
                
                 
                   
                      
                  
                   
                     146362
                  
                
                 
                   
                     318
                  
                   
                     0.32152034
                  
                
                 
                   
                      
                  
                   
                     146175
                  
                
                 
                   
                     317
                  
                   
                     0.32005859
                  
                
                 
                   
                      
                  
                   
                     145990
                  
                
                 
                   
                      
                  
                   
                     145990
                  
                
                 
                   
                     316
                  
                   
                     0.31859869
                  
                
                 
                   
                      
                  
                   
                     145803
                  
                
                 
                   
                     315
                  
                   
                     0.31714066
                  
                
                 
                   
                      
                  
                   
                     145614
                  
                
                 
                   
                     314
                  
                   
                     0.31568452
                  
                
                 
                   
                      
                  
                   
                     145425
                  
                
                 
                   
                     313
                  
                   
                     0.31423027
                  
                
                 
                   
                      
                  
                   
                     145236
                  
                
                 
                   
                     312
                  
                   
                     0.31277791
                  
                
                 
                   
                      
                  
                   
                     145047
                  
                
                 
                   
                     311
                  
                   
                     0.31132744
                  
                
                 
                   
                      
                  
                   
                     144856
                  
                
                 
                   
                     310
                  
                   
                     0.30987884
                  
                
                 
                   
                      
                  
                   
                     144665
                  
                
                 
                   
                     309
                  
                   
                     2.30843219
                  
                
                 
                   
                      
                  
                   
                     144474
                  
                
                 
                   
                     308
                  
                   
                     0.30698745
                  
                
                 
                   
                      
                  
                   
                     144282
                  
                
                 
                   
                     307
                  
                   
                     0.30554463
                  
                
                 
                   
                      
                  
                   
                     144090
                  
                
                 
                   
                     306
                  
                   
                     0.30410373
                  
                
                 
                   
                      
                  
                   
                     143897
                  
                
                 
                   
                     303
                  
                   
                     0.30266476
                  
                
                 
                   
                      
                  
                   
                     143703
                  
                
                 
                   
                     304
                  
                   
                     0.30122773
                  
                
                 
                   
                      
                  
                   
                     143508
                  
                
                 
                   
                     303
                  
                   
                     0.29978265
                  
                
                 
                   
                      
                  
                   
                     143315
                  
                
                 
                   
                     302
                  
                   
                     0.29835950
                  
                
                 
                   
                      
                  
                   
                     143120
                  
                
                 
                   
                     301
                  
                   
                     0.29692830
                  
                
                 
                   
                      
                  
                   
                     142926
                  
                
                 
                   
                     300
                  
                   
                     0.29549904
                  
                
                 
                   
                     
                     300
                  
                   
                     0.29549884
                  
                
                 
                   
                      
                  
                   
                     142730
                  
                
                 
                   
                     299
                  
                   
                     0.29407154
                  
                
                 
                   
                      
                  
                   
                     142533
                  
                
                 
                   
                     298
                  
                   
                     0.29264621
                  
                
                 
                   
                      
                  
                   
                     142335
                  
                
                 
                   
                     297
                  
                   
                     0.29122286
                  
                
                 
                   
                      
                  
                   
                     142137
                  
                
                 
                   
                     296
                  
                   
                     0.28980149
                  
                
                 
                   
                      
                  
                   
                     141939
                  
                
                 
                   
                     295
                  
                   
                     0.28838210
                  
                
                 
                   
                      
                  
                   
                     141741
                  
                
                 
                   
                     294
                  
                   
                     0.28696469
                  
                
                 
                   
                      
                  
                   
                     141460
                  
                
                 
                   
                     293
                  
                   
                     0.28555009
                  
                
                 
                   
                      
                  
                   
                     141260
                  
                
                 
                   
                     292
                  
                   
                     0.28413749
                  
                
                 
                   
                      
                  
                   
                     141191
                  
                
                 
                   
                     291
                  
                   
                     0.28272558
                  
                
                 
                   
                      
                  
                   
                     140990
                  
                
                 
                   
                     290
                  
                   
                     0.28131493
                  
                
                 
                   
                      
                  
                   
                     140730
                  
                
                 
                   
                     289
                  
                   
                     0.27990763
                  
                
                 
                   
                      
                  
                   
                     140527
                  
                
                 
                   
                     288
                  
                   
                     0.27850236
                  
                
                 
                   
                      
                  
                   
                     140331
                  
                
                 
                   
                     287
                  
                   
                     0.27709905
                  
                
                 
                   
                      
                  
                   
                     140124
                  
                
                 
                   
                     286
                  
                   
                     0.27569781
                  
                
                 
                   
                      
                  
                   
                     139920
                  
                
                 
                   
                     285
                  
                   
                     0.27429861
                  
                
                 
                   
                      
                  
                   
                     139720
                  
                
                 
                   
                     284
                  
                   
                     0.27290141
                  
                
                 
                   
                      
                  
                   
                     139517
                  
                
                 
                   
                     283
                  
                   
                     0.27150624
                  
                
                 
                   
                      
                  
                   
                     139311
                  
                
                 
                   
                     282
                  
                   
                     0.27011313
                  
                
                 
                   
                      
                  
                   
                     139105
                  
                
                 
                   
                     281
                  
                   
                     0.26872208
                  
                
                 
                   
                      
                  
                   
                     138898
                  
                
                 
                   
                     280
                  
                   
                     0.26733268
                  
                
                 
                   
                      
                  
                   
                     138690
                  
                
                 
                   
                     279
                  
                   
                     0.26594578
                  
                
                 
                   
                      
                  
                   
                     138482
                  
                
                 
                   
                     278
                  
                   
                     0.26456096
                  
                
                 
                   
                      
                  
                   
                     138273
                  
                
                 
                   
                     277
                  
                   
                     0.26317823
                  
                
                 
                   
                      
                  
                   
                     138063
                  
                
                 
                   
                     276
                  
                   
                     0.26179760
                  
                
                 
                   
                      
                  
                   
                     137853
                  
                
                 
                   
                     275
                  
                   
                     0.26041907
                  
                
                 
                   
                      
                  
                   
                     137643
                  
                
                 
                   
                     274
                  
                   
                     0.25904264
                  
                
                 
                   
                      
                  
                   
                     137432
                  
                
                 
                   
                     273
                  
                   
                     0.25766832
                  
                
                 
                   
                      
                  
                   
                     137220
                  
                
                 
                   
                     272
                  
                   
                     0.25629612
                  
                
                 
                   
                      
                  
                   
                     137008
                  
                
                 
                   
                     271
                  
                   
                     0.25492604
                  
                
                 
                   
                      
                  
                   
                     136795
                  
                
                 
                   
                     270
                  
                   
                     0.25355796
                  
                
                 
                   
                      
                  
                   
                     136583
                  
                
                 
                   
                     269
                  
                   
                     0.25219213
                  
                
                 
                   
                      
                  
                   
                     136370
                  
                
                 
                   
                     268
                  
                   
                     0.25082843
                  
                
                 
                   
                      
                  
                   
                     136153
                  
                
                 
                   
                     267
                  
                   
                     0.24946690
                  
                
                 
                   
                      
                  
                   
                     135936
                  
                
                 
                   
                     
                  
                   
                     135936
                  
                
                 
                   
                     266
                  
                   
                     0.24810754
                  
                
                 
                   
                      
                  
                   
                     135720
                  
                
                 
                   
                     265
                  
                   
                     0.24675034
                  
                
                 
                   
                      
                  
                   
                     135504
                  
                
                 
                   
                     264
                  
                   
                     0.24539530
                  
                
                 
                   
                      
                  
                   
                     135287
                  
                
                 
                   
                     263
                  
                   
                     0.24404243
                  
                
                 
                   
                      
                  
                   
                     135069
                  
                
                 
                   
                     262
                  
                   
                     0.24269174
                  
                
                 
                   
                      
                  
                   
                     134850
                  
                
                 
                   
                     261
                  
                   
                     0.24134324
                  
                
                 
                   
                      
                  
                   
                     134553
                  
                
                 
                   
                     260
                  
                   
                     0.23999689
                  
                
                 
                   
                      
                  
                   
                     134333
                  
                
                 
                   
                     259
                  
                   
                     0.23865356
                  
                
                 
                   
                      
                  
                   
                     134189
                  
                
                 
                   
                     258
                  
                   
                     0.23731165
                  
                
                 
                   
                      
                  
                   
                     133968
                  
                
                 
                   
                     257
                  
                   
                     0.23597197
                  
                
                 
                   
                      
                  
                   
                     133746
                  
                
                 
                   
                     256
                  
                   
                     0.23463451
                  
                
                 
                   
                      
                  
                   
                     133523
                  
                
                 
                   
                     255
                  
                   
                     0.23329928
                  
                
                 
                   
                      
                  
                   
                     133300
                  
                
                 
                   
                     254
                  
                   
                     0.23196628
                  
                
                 
                   
                      
                  
                   
                     133076
                  
                
                 
                   
                     253
                  
                   
                     0.23063552
                  
                
                 
                   
                      
                  
                   
                     132801
                  
                
                 
                   
                     252
                  
                   
                     0.22930751
                  
                
                 
                   
                      
                  
                   
                     132575
                  
                
                 
                   
                     251
                  
                   
                     0.22798176
                  
                
                 
                   
                      
                  
                   
                     132399
                  
                
                 
                   
                     250
                  
                   
                     0.22665777
                  
                
                 
                   
                     250
                  
                   
                     0.22665594
                  
                
                 
                   
                      
                  
                   
                     132173
                  
                
                 
                   
                     249
                  
                   
                     0.22533421
                  
                
                 
                   
                      
                  
                   
                     131946
                  
                
                 
                   
                     248
                  
                   
                     0.22401475
                  
                
                 
                   
                      
                  
                   
                     131718
                  
                
                 
                   
                     247
                  
                   
                     0.22269757
                  
                
                 
                   
                      
                  
                   
                     131488
                  
                
                 
                   
                     246
                  
                   
                     0.22138269
                  
                
                 
                   
                      
                  
                   
                     131259
                  
                
                 
                   
                     245
                  
                   
                     0.22007010
                  
                
                 
                   
                      
                  
                   
                     131029
                  
                
                 
                   
                     244
                  
                   
                     0.21875981
                  
                
                 
                   
                      
                  
                   
                     130799
                  
                
                 
                   
                     243
                  
                   
                     0.21745182
                  
                
                 
                   
                      
                  
                   
                     130567
                  
                
                 
                   
                     242
                  
                   
                     0.21614615
                  
                
                 
                   
                      
                  
                   
                     130334
                  
                
                 
                   
                     241
                  
                   
                     0
                     21484281
                  
                
                 
                   
                      
                  
                   
                     130101
                  
                
                 
                   
                     240
                  
                   
                     0.21354168
                  
                
                 
                   
                      
                  
                   
                     129867
                  
                
                 
                   
                     239
                  
                   
                     0.21224301
                  
                
                 
                   
                      
                  
                   
                     129632
                  
                
                 
                   
                     238
                  
                   
                     0.21094669
                  
                
                 
                   
                      
                  
                   
                     129396
                  
                
                 
                   
                     237
                  
                   
                     0.20965273
                  
                
                 
                   
                      
                  
                   
                     129160
                  
                
                 
                   
                     236
                  
                   
                     0.20836113
                  
                
                 
                   
                      
                  
                   
                     128924
                  
                
                 
                   
                     235
                  
                   
                     0.20707189
                  
                
                 
                   
                      
                  
                   
                     128688
                  
                
                 
                   
                     234
                  
                   
                     0.20578501
                  
                
                 
                   
                      
                  
                   
                     128449
                  
                
                 
                   
                     
                     233
                  
                   
                     0.20450052
                  
                
                 
                   
                      
                  
                   
                     128208
                  
                
                 
                   
                     232
                  
                   
                     0.20321844
                  
                
                 
                   
                      
                  
                   
                     123968
                  
                
                 
                   
                     231
                  
                   
                     0.20193876
                  
                
                 
                   
                      
                  
                   
                     127729
                  
                
                 
                   
                     230
                  
                   
                     0.20066138
                  
                
                 
                   
                      
                  
                   
                     127488
                  
                
                 
                   
                     229
                  
                   
                     0.19938650
                  
                
                 
                   
                      
                  
                   
                     127245
                  
                
                 
                   
                     228
                  
                   
                     0.19811405
                  
                
                 
                   
                      
                  
                   
                     127002
                  
                
                 
                   
                     227
                  
                   
                     0.19684403
                  
                
                 
                   
                      
                  
                   
                     126758
                  
                
                 
                   
                     226
                  
                   
                     0.19557645
                  
                
                 
                   
                      
                  
                   
                     126514
                  
                
                 
                   
                     225
                  
                   
                     0.19431131
                  
                
                 
                   
                      
                  
                   
                     126269
                  
                
                 
                   
                     224
                  
                   
                     0.19304862
                  
                
                 
                   
                      
                  
                   
                     126023
                  
                
                 
                   
                     223
                  
                   
                     0.19178839
                  
                
                 
                   
                      
                  
                   
                     125776
                  
                
                 
                   
                     222
                  
                   
                     0.19053063
                  
                
                 
                   
                      
                  
                   
                     125528
                  
                
                 
                   
                     221
                  
                   
                     0.18927535
                  
                
                 
                   
                      
                  
                   
                     125279
                  
                
                 
                   
                     220
                  
                   
                     0.18802248
                  
                
                 
                   
                      
                  
                   
                     125027
                  
                
                 
                   
                     219
                  
                   
                     0.18677221
                  
                
                 
                   
                      
                  
                   
                     124777
                  
                
                 
                   
                     218
                  
                   
                     0.18552444
                  
                
                 
                   
                      
                  
                   
                     124529
                  
                
                 
                   
                     217
                  
                   
                     0.18427915
                  
                
                 
                   
                      
                  
                   
                     124278
                  
                
                 
                   
                      
                  
                   
                     124278
                  
                
                 
                   
                     216
                  
                   
                     0.18303637
                  
                
                 
                   
                      
                  
                   
                     124025
                  
                
                 
                   
                     215
                  
                   
                     0.18179612
                  
                
                 
                   
                      
                  
                   
                     123771
                  
                
                 
                   
                     214
                  
                   
                     0.18055841
                  
                
                 
                   
                      
                  
                   
                     123517
                  
                
                 
                   
                     213
                  
                   
                     0.17932324
                  
                
                 
                   
                      
                  
                   
                     123262
                  
                
                 
                   
                     212
                  
                   
                     0.17809062
                  
                
                 
                   
                      
                  
                   
                     123006
                  
                
                 
                   
                     211
                  
                   
                     0.17686056
                  
                
                 
                   
                      
                  
                   
                     122749
                  
                
                 
                   
                     210
                  
                   
                     0.17563291
                  
                
                 
                   
                      
                  
                   
                     122490
                  
                
                 
                   
                     209
                  
                   
                     0.17440801
                  
                
                 
                   
                      
                  
                   
                     122232
                  
                
                 
                   
                     208
                  
                   
                     0.17318569
                  
                
                 
                   
                      
                  
                   
                     122974
                  
                
                 
                   
                     207
                  
                   
                     0.17196595
                  
                
                 
                   
                      
                  
                   
                     121713
                  
                
                 
                   
                     206
                  
                   
                     0.17074882
                  
                
                 
                   
                      
                  
                   
                     121451
                  
                
                 
                   
                     205
                  
                   
                     0.16953431
                  
                
                 
                   
                      
                  
                   
                     121189
                  
                
                 
                   
                     204
                  
                   
                     0.16832242
                  
                
                 
                   
                      
                  
                   
                     120926
                  
                
                 
                   
                     203
                  
                   
                     0.16711316
                  
                
                 
                   
                      
                  
                   
                     120663
                  
                
                 
                   
                     202
                  
                   
                     0.16590653
                  
                
                 
                   
                      
                  
                   
                     120399
                  
                
                 
                   
                     201
                  
                   
                     0.16470254
                  
                
                 
                   
                      
                  
                   
                     120133
                  
                
                 
                   
                     200
                  
                   
                     0.16350121
                  
                
                 
                   
                     
                     200
                  
                   
                     0.16350111
                  
                
                 
                   
                      
                  
                   
                     119866
                  
                
                 
                   
                     199
                  
                   
                     0.16230245
                  
                
                 
                   
                      
                  
                   
                     119598
                  
                
                 
                   
                     198
                  
                   
                     0.16110647
                  
                
                 
                   
                      
                  
                   
                     119329
                  
                
                 
                   
                     197
                  
                   
                     0.15991318
                  
                
                 
                   
                      
                  
                   
                     119959
                  
                
                 
                   
                     196
                  
                   
                     0.15872259
                  
                
                 
                   
                      
                  
                   
                     118789
                  
                
                 
                   
                     195
                  
                   
                     0.15753470
                  
                
                 
                   
                      
                  
                   
                     118518
                  
                
                 
                   
                     194
                  
                   
                     0.15634952
                  
                
                 
                   
                      
                  
                   
                     118246
                  
                
                 
                   
                     193
                  
                   
                     0.15516706
                  
                
                 
                   
                      
                  
                   
                     117972
                  
                
                 
                   
                     192
                  
                   
                     0.15398733
                  
                
                 
                   
                      
                  
                   
                     117698
                  
                
                 
                   
                     191
                  
                   
                     0.15281035
                  
                
                 
                   
                      
                  
                   
                     117422
                  
                
                 
                   
                     190
                  
                   
                     0.15163596
                  
                
                 
                   
                      
                  
                   
                     117146
                  
                
                 
                   
                     189
                  
                   
                     0.15046450
                  
                
                 
                   
                      
                  
                   
                     116869
                  
                
                 
                   
                     188
                  
                   
                     0.14929581
                  
                
                 
                   
                      
                  
                   
                     116591
                  
                
                 
                   
                     187
                  
                   
                     0.14812990
                  
                
                 
                   
                      
                  
                   
                     116312
                  
                
                 
                   
                     186
                  
                   
                     0.14696678
                  
                
                 
                   
                      
                  
                   
                     116032
                  
                
                 
                   
                     185
                  
                   
                     0.14580646
                  
                
                 
                   
                      
                  
                   
                     115751
                  
                
                 
                   
                     184
                  
                   
                     0.14464895
                  
                
                 
                   
                      
                  
                   
                     115468
                  
                
                 
                   
                     183
                  
                   
                     0.14349427
                  
                
                 
                   
                      
                  
                   
                     115084
                  
                
                 
                   
                     182
                  
                   
                     0.14234243
                  
                
                 
                   
                      
                  
                   
                     114900
                  
                
                 
                   
                     181
                  
                   
                     0.14119343
                  
                
                 
                   
                      
                  
                   
                     114615
                  
                
                 
                   
                     180
                  
                   
                     0.14004728
                  
                
                 
                   
                      
                  
                   
                     114328
                  
                
                 
                   
                     179
                  
                   
                     0.13890400
                  
                
                 
                   
                      
                  
                   
                     114040
                  
                
                 
                   
                     178
                  
                   
                     0.13776354
                  
                
                 
                   
                      
                  
                   
                     113752
                  
                
                 
                   
                     177
                  
                   
                     0.13612602
                  
                
                 
                   
                      
                  
                   
                     163462
                  
                
                 
                   
                     176
                  
                   
                     0.13549140
                  
                
                 
                   
                      
                  
                   
                     113164
                  
                
                 
                   
                     175
                  
                   
                     0.13435926
                  
                
                 
                   
                      
                  
                   
                     112873
                  
                
                 
                   
                     174
                  
                   
                     0.13323103
                  
                
                 
                   
                      
                  
                   
                     112587
                  
                
                 
                   
                     173
                  
                   
                     0.13210516
                  
                
                 
                   
                      
                  
                   
                     112292
                  
                
                 
                   
                     172
                  
                   
                     0.13098224
                  
                
                 
                   
                      
                  
                   
                     111996
                  
                
                 
                   
                     171
                  
                   
                     0.12986228
                  
                
                 
                   
                      
                  
                   
                     111700
                  
                
                 
                   
                     170
                  
                   
                     0.12874498
                  
                
                 
                   
                      
                  
                   
                     111403
                  
                
                 
                   
                     169
                  
                   
                     0.21763088
                  
                
                 
                   
                      
                  
                   
                     111105
                  
                
                 
                   
                     168
                  
                   
                     0.12651983
                  
                
                 
                   
                      
                  
                   
                     110805
                  
                
                 
                   
                     167
                  
                   
                     0.12541178
                  
                
                 
                   
                      
                  
                   
                     110503
                  
                
                 
                   
                     
                  
                   
                     110503
                  
                
                 
                   
                     166
                  
                   
                     0.12430675
                  
                
                 
                   
                      
                  
                   
                     110200
                  
                
                 
                   
                     165
                  
                   
                     0.12320475
                  
                
                 
                   
                      
                  
                   
                     109896
                  
                
                 
                   
                     164
                  
                   
                     0.12210579
                  
                
                 
                   
                      
                  
                   
                     109592
                  
                
                 
                   
                     163
                  
                   
                     0.12100987
                  
                
                 
                   
                      
                  
                   
                     109287
                  
                
                 
                   
                     162
                  
                   
                     0.11991700
                  
                
                 
                   
                      
                  
                   
                     108980
                  
                
                 
                   
                     161
                  
                   
                     0.11882720
                  
                
                 
                   
                      
                  
                   
                     108671
                  
                
                 
                   
                     160
                  
                   
                     0.11774053
                  
                
                 
                   
                      
                  
                   
                     108361
                  
                
                 
                   
                     159
                  
                   
                     0.11665692
                  
                
                 
                   
                      
                  
                   
                     108047
                  
                
                 
                   
                     158
                  
                   
                     0.11557645
                  
                
                 
                   
                      
                  
                   
                     107735
                  
                
                 
                   
                     157
                  
                   
                     0.11449910
                  
                
                 
                   
                      
                  
                   
                     107425
                  
                
                 
                   
                     156
                  
                   
                     0.11342485
                  
                
                 
                   
                      
                  
                   
                     107110
                  
                
                 
                   
                     155
                  
                   
                     0.11235375
                  
                
                 
                   
                      
                  
                   
                     106794
                  
                
                 
                   
                     154
                  
                   
                     0.11128581
                  
                
                 
                   
                      
                  
                   
                     106478
                  
                
                 
                   
                     153
                  
                   
                     0.11022103
                  
                
                 
                   
                      
                  
                   
                     106159
                  
                
                 
                   
                     152
                  
                   
                     0.10915944
                  
                
                 
                   
                      
                  
                   
                     105838
                  
                
                 
                   
                     151
                  
                   
                     0.10810106
                  
                
                 
                   
                      
                  
                   
                     105517
                  
                
                 
                   
                     150
                  
                   
                     0.10704589
                  
                
                 
                   
                     150
                  
                   
                     0.10704589
                  
                
                 
                   
                      
                  
                   
                     105194
                  
                
                 
                   
                     149
                  
                   
                     0.10599395
                  
                
                 
                   
                      
                  
                   
                     104870
                  
                
                 
                   
                     148
                  
                   
                     0.10494525
                  
                
                 
                   
                      
                  
                   
                     104545
                  
                
                 
                   
                     147
                  
                   
                     0.10389980
                  
                
                 
                   
                      
                  
                   
                     104218
                  
                
                 
                   
                     146
                  
                   
                     0.10285762
                  
                
                 
                   
                      
                  
                   
                     105889
                  
                
                 
                   
                     145
                  
                   
                     0.10181873
                  
                
                 
                   
                      
                  
                   
                     103560
                  
                
                 
                   
                     144
                  
                   
                     0.10078313
                  
                
                 
                   
                      
                  
                   
                     103229
                  
                
                 
                   
                     143
                  
                   
                     0.09975084
                  
                
                 
                   
                      
                  
                   
                     102895
                  
                
                 
                   
                     142
                  
                   
                     0.09872199
                  
                
                 
                   
                      
                  
                   
                     102561
                  
                
                 
                   
                     141
                  
                   
                     0.09769638
                  
                
                 
                   
                      
                  
                   
                     102213
                  
                
                 
                   
                     140
                  
                   
                     0.09667379
                  
                
                 
                   
                      
                  
                   
                     101876
                  
                
                 
                   
                     139
                  
                   
                     0.09565503
                  
                
                 
                   
                      
                  
                   
                     101550
                  
                
                 
                   
                     138
                  
                   
                     0.09463953
                  
                
                 
                   
                      
                  
                   
                     101210
                  
                
                 
                   
                     137
                  
                   
                     0.09362743
                  
                
                 
                   
                      
                  
                   
                     100869
                  
                
                 
                   
                     136
                  
                   
                     0.09261874
                  
                
                 
                   
                      
                  
                   
                     100526
                  
                
                 
                   
                     135
                  
                   
                     0.09161348
                  
                
                 
                   
                      
                  
                   
                     100181
                  
                
                 
                   
                     134
                  
                   
                     0.09061167
                  
                
                 
                   
                      
                  
                   
                     99834
                  
                
                 
                   
                     
                     133
                  
                   
                     0.08961333
                  
                
                 
                   
                      
                  
                   
                     99461
                  
                
                 
                   
                     132
                  
                   
                     0.08861872
                  
                
                 
                   
                      
                  
                   
                     99112
                  
                
                 
                   
                     131
                  
                   
                     0.08762760
                  
                
                 
                   
                      
                  
                   
                     98786
                  
                
                 
                   
                     130
                  
                   
                     0.08663902
                  
                
                 
                   
                      
                  
                   
                     98433
                  
                
                 
                   
                     129
                  
                   
                     0.08565469
                  
                
                 
                   
                      
                  
                   
                     98078
                  
                
                 
                   
                     128
                  
                   
                     0.08467391
                  
                
                 
                   
                      
                  
                   
                     97722
                  
                
                 
                   
                     127
                  
                   
                     0.08369669
                  
                
                 
                   
                      
                  
                   
                     97364
                  
                
                 
                   
                     126
                  
                   
                     0.08272305
                  
                
                 
                   
                      
                  
                   
                     97004
                  
                
                 
                   
                     125
                  
                   
                     0.08175301
                  
                
                 
                   
                      
                  
                   
                     96643
                  
                
                 
                   
                     124
                  
                   
                     0.08078658
                  
                
                 
                   
                      
                  
                   
                     96280
                  
                
                 
                   
                     123
                  
                   
                     0.07982378
                  
                
                 
                   
                      
                  
                   
                     95915
                  
                
                 
                   
                     122
                  
                   
                     0.07886463
                  
                
                 
                   
                      
                  
                   
                     95548
                  
                
                 
                   
                     121
                  
                   
                     0.07790915
                  
                
                 
                   
                      
                  
                   
                     95179
                  
                
                 
                   
                     120
                  
                   
                     0.07695736
                  
                
                 
                   
                      
                  
                   
                     94811
                  
                
                 
                   
                     119
                  
                   
                     0.07600925
                  
                
                 
                   
                      
                  
                   
                     94438
                  
                
                 
                   
                     118
                  
                   
                     0.07506487
                  
                
                 
                   
                      
                  
                   
                     94061
                  
                
                 
                   
                     117
                  
                   
                     0.07412426
                  
                
                 
                   
                      
                  
                   
                     93685
                  
                
                 
                   
                      
                  
                   
                     93685
                  
                
                 
                   
                     116
                  
                   
                     0.07318741
                  
                
                 
                   
                      
                  
                   
                     93307
                  
                
                 
                   
                     115
                  
                   
                     0.07225434
                  
                
                 
                   
                      
                  
                   
                     92901
                  
                
                 
                   
                     114
                  
                   
                     0.07132533
                  
                
                 
                   
                      
                  
                   
                     92524
                  
                
                 
                   
                     113
                  
                   
                     0.07040009
                  
                
                 
                   
                      
                  
                   
                     92161
                  
                
                 
                   
                     112
                  
                   
                     0.06947848
                  
                
                 
                   
                      
                  
                   
                     91774
                  
                
                 
                   
                     111
                  
                   
                     0.06856074
                  
                
                 
                   
                      
                  
                   
                     91386
                  
                
                 
                   
                     110
                  
                   
                     0.06764629
                  
                
                 
                   
                      
                  
                   
                     90944
                  
                
                 
                   
                     109
                  
                   
                     0.06673685
                  
                
                 
                   
                      
                  
                   
                     90551
                  
                
                 
                   
                     108
                  
                   
                     0.06583134
                  
                
                 
                   
                      
                  
                   
                     90208
                  
                
                 
                   
                     107
                  
                   
                     0.06492926
                  
                
                 
                   
                      
                  
                   
                     89811
                  
                
                 
                   
                     106
                  
                   
                     0.06403115
                  
                
                 
                   
                      
                  
                   
                     89412
                  
                
                 
                   
                     105
                  
                   
                     0.06313703
                  
                
                 
                   
                      
                  
                   
                     89011
                  
                
                 
                   
                     104
                  
                   
                     0.06224692
                  
                
                 
                   
                      
                  
                   
                     88608
                  
                
                 
                   
                     103
                  
                   
                     0.06136084
                  
                
                 
                   
                      
                  
                   
                     88202
                  
                
                 
                   
                     102
                  
                   
                     0.06047882
                  
                
                 
                   
                      
                  
                   
                     87793
                  
                
                 
                   
                     101
                  
                   
                     0.05960089
                  
                
                 
                   
                      
                  
                   
                     87382
                  
                
                 
                   
                     100
                  
                   
                     0.05872707
                  
                
                 
                   
                     
                     100
                  
                   
                     0.05872590
                  
                
                 
                   
                      
                  
                   
                     86969
                  
                
                 
                   
                     99
                  
                   
                     0.05785621
                  
                
                 
                   
                      
                  
                   
                     86554
                  
                
                 
                   
                     98
                  
                   
                     0.05699067
                  
                
                 
                   
                      
                  
                   
                     86137
                  
                
                 
                   
                     97
                  
                   
                     0.05612930
                  
                
                 
                   
                      
                  
                   
                     85717
                  
                
                 
                   
                     96
                  
                   
                     0.05527213
                  
                
                 
                   
                      
                  
                   
                     85293
                  
                
                 
                   
                     95
                  
                   
                     0.05441920
                  
                
                 
                   
                      
                  
                   
                     84867
                  
                
                 
                   
                     94
                  
                   
                     0.05357053
                  
                
                 
                   
                      
                  
                   
                     84440
                  
                
                 
                   
                     93
                  
                   
                     0.05272613
                  
                
                 
                   
                      
                  
                   
                     84010
                  
                
                 
                   
                     92
                  
                   
                     0.05188603
                  
                
                 
                   
                      
                  
                   
                     83666
                  
                
                 
                   
                     91
                  
                   
                     0.05104937
                  
                
                 
                   
                      
                  
                   
                     83229
                  
                
                 
                   
                     90
                  
                   
                     0.05121866
                  
                
                 
                   
                      
                  
                   
                     82700
                  
                
                 
                   
                     89
                  
                   
                     0.04939166
                  
                
                 
                   
                      
                  
                   
                     82259
                  
                
                 
                   
                     88
                  
                   
                     0.04856907
                  
                
                 
                   
                      
                  
                   
                     81814
                  
                
                 
                   
                     87
                  
                   
                     0.04775093
                  
                
                 
                   
                      
                  
                   
                     81366
                  
                
                 
                   
                     86
                  
                   
                     0.04693727
                  
                
                 
                   
                      
                  
                   
                     80916
                  
                
                 
                   
                     85
                  
                   
                     0.04612811
                  
                
                 
                   
                      
                  
                   
                     89462
                  
                
                 
                   
                     84
                  
                   
                     0.04532349
                  
                
                 
                   
                      
                  
                   
                     80005
                  
                
                 
                   
                     83
                  
                   
                     0.04452344
                  
                
                 
                   
                      
                  
                   
                     79545
                  
                
                 
                   
                     82
                  
                   
                     0.04372799
                  
                
                 
                   
                      
                  
                   
                     79083
                  
                
                 
                   
                     81
                  
                   
                     0.04293716
                  
                
                 
                   
                      
                  
                   
                     78617
                  
                
                 
                   
                     80
                  
                   
                     0.04215095
                  
                
                 
                   
                      
                  
                   
                     78147
                  
                
                 
                   
                     79
                  
                   
                     0.04136948
                  
                
                 
                   
                      
                  
                   
                     77674
                  
                
                 
                   
                     78
                  
                   
                     0.04058274
                  
                
                 
                   
                      
                  
                   
                     77197
                  
                
                 
                   
                     77
                  
                   
                     0.03982077
                  
                
                 
                   
                      
                  
                   
                     76707
                  
                
                 
                   
                     76
                  
                   
                     0.03905370
                  
                
                 
                   
                      
                  
                   
                     76224
                  
                
                 
                   
                     75
                  
                   
                     0.03829146
                  
                
                 
                   
                      
                  
                   
                     75748
                  
                
                 
                   
                     74
                  
                   
                     0.03753398
                  
                
                 
                   
                      
                  
                   
                     75250
                  
                
                 
                   
                     73
                  
                   
                     0.03678140
                  
                
                 
                   
                      
                  
                   
                     74764
                  
                
                 
                   
                     72
                  
                   
                     0.03603376
                  
                
                 
                   
                      
                  
                   
                     34265
                  
                
                 
                   
                     71
                  
                   
                     0.03529111
                  
                
                 
                   
                      
                  
                   
                     73752
                  
                
                 
                   
                     70
                  
                   
                     0.3455313
                  
                
                 
                   
                      
                  
                   
                     73246
                  
                
                 
                   
                     69
                  
                   
                     0.03382067
                  
                
                 
                   
                      
                  
                   
                     72746
                  
                
                 
                   
                     68
                  
                   
                     0.03309321
                  
                
                 
                   
                      
                  
                   
                     72232
                  
                
                 
                   
                     67
                  
                   
                     0.03237089
                  
                
                 
                   
                      
                  
                   
                     71716
                  
                
                 
                   
                     
                  
                   
                     71716
                  
                
                 
                   
                     66
                  
                   
                     0.03165373
                  
                
                 
                   
                      
                  
                   
                     71193
                  
                
                 
                   
                     65
                  
                   
                     0.03094180
                  
                
                 
                   
                      
                  
                   
                     70664
                  
                
                 
                   
                     64
                  
                   
                     0.03023516
                  
                
                 
                   
                      
                  
                   
                     70132
                  
                
                 
                   
                     63
                  
                   
                     0.02953384
                  
                
                 
                   
                      
                  
                   
                     69995
                  
                
                 
                   
                     62
                  
                   
                     0.02883789
                  
                
                 
                   
                      
                  
                   
                     69054
                  
                
                 
                   
                     61
                  
                   
                     0.02814735
                  
                
                 
                   
                      
                  
                   
                     68508
                  
                
                 
                   
                     60
                  
                   
                     0.02746204
                  
                
                 
                   
                      
                  
                   
                     67961
                  
                
                 
                   
                     59
                  
                   
                     0.02928243
                  
                
                 
                   
                      
                  
                   
                     67405
                  
                
                 
                   
                     58
                  
                   
                     0.02610838
                  
                
                 
                   
                      
                  
                   
                     66840
                  
                
                 
                   
                     57
                  
                   
                     0.02543998
                  
                
                 
                   
                      
                  
                   
                     66273
                  
                
                 
                   
                     56
                  
                   
                     0.02477725
                  
                
                 
                   
                      
                  
                   
                     65701
                  
                
                 
                   
                     55
                  
                   
                     0.02412024
                  
                
                 
                   
                      
                  
                   
                     65123
                  
                
                 
                   
                     54
                  
                   
                     0.02346901
                  
                
                 
                   
                      
                  
                   
                     64539
                  
                
                 
                   
                     53
                  
                   
                     0.02282362
                  
                
                 
                   
                      
                  
                   
                     63950
                  
                
                 
                   
                     52
                  
                   
                     0.02218412
                  
                
                 
                   
                      
                  
                   
                     63353
                  
                
                 
                   
                     51
                  
                   
                     0.02155059
                  
                
                 
                   
                      
                  
                   
                     62750
                  
                
                 
                   
                     50
                  
                   
                     0.02092309
                  
                
                 
                   
                     50
                  
                   
                     0.02092302
                  
                
                 
                   
                      
                  
                   
                     62143
                  
                
                 
                   
                     49
                  
                   
                     0.02030159
                  
                
                 
                   
                      
                  
                   
                     61528
                  
                
                 
                   
                     48
                  
                   
                     0.01968631
                  
                
                 
                   
                      
                  
                   
                     60906
                  
                
                 
                   
                     47
                  
                   
                     0.01907725
                  
                
                 
                   
                      
                  
                   
                     60277
                  
                
                 
                   
                     46
                  
                   
                     0.01847448
                  
                
                 
                   
                      
                  
                   
                     59640
                  
                
                 
                   
                     45
                  
                   
                     0.01787808
                  
                
                 
                   
                      
                  
                   
                     58996
                  
                
                 
                   
                     44
                  
                   
                     0.01728812
                  
                
                 
                   
                      
                  
                   
                     58344
                  
                
                 
                   
                     43
                  
                   
                     0.01670468
                  
                
                 
                   
                      
                  
                   
                     57683
                  
                
                 
                   
                     42
                  
                   
                     0.01612784
                  
                
                 
                   
                      
                  
                   
                     57016
                  
                
                 
                   
                     41
                  
                   
                     0.01555768
                  
                
                 
                   
                      
                  
                   
                     56340
                  
                
                 
                   
                     40
                  
                   
                     0.01499411
                  
                
                 
                   
                      
                  
                   
                     55655
                  
                
                 
                   
                     39
                  
                   
                     0.01443756
                  
                
                 
                   
                      
                  
                   
                     54960
                  
                
                 
                   
                     38
                  
                   
                     0.01388796
                  
                
                 
                   
                      
                  
                   
                     54256
                  
                
                 
                   
                     37
                  
                   
                     0.01334540
                  
                
                 
                   
                      
                  
                   
                     53540
                  
                
                 
                   
                     36
                  
                   
                     0.01281000
                  
                
                 
                   
                      
                  
                   
                     52815
                  
                
                 
                   
                     35
                  
                   
                     0.01228185
                  
                
                 
                   
                      
                  
                   
                     52079
                  
                
                 
                   
                     34
                  
                   
                     0.01176106
                  
                
                 
                   
                      
                  
                   
                     51331
                  
                
                 
                   
                     
                     33
                  
                   
                     0.01124776
                  
                
                 
                   
                      
                  
                   
                     50572
                  
                
                 
                   
                     32
                  
                   
                     0.01074204
                  
                
                 
                   
                      
                  
                   
                     49801
                  
                
                 
                   
                     31
                  
                   
                     0.01024403
                  
                
                 
                   
                      
                  
                   
                     49016
                  
                
                 
                   
                     30
                  
                   
                     0.00975364
                  
                
                 
                   
                      
                  
                   
                     48217
                  
                
                 
                   
                     29
                  
                   
                     0.00927147
                  
                
                 
                   
                      
                  
                   
                     47405
                  
                
                 
                   
                     28
                  
                   
                     0.00879742
                  
                
                 
                   
                      
                  
                   
                     46578
                  
                
                 
                   
                     27
                  
                   
                     0.00833164
                  
                
                 
                   
                      
                  
                   
                     45734
                  
                
                 
                   
                     26
                  
                   
                     0.00787430
                  
                
                 
                   
                      
                  
                   
                     44874
                  
                
                 
                   
                     25
                  
                   
                     0.00742556
                  
                
                 
                   
                      
                  
                   
                     43997
                  
                
                 
                   
                     24
                  
                   
                     0.00698559
                  
                
                 
                   
                      
                  
                   
                     43102
                  
                
                 
                   
                     23
                  
                   
                     0.00655457
                  
                
                 
                   
                      
                  
                   
                     42185
                  
                
                 
                   
                     22
                  
                   
                     0.00613272
                  
                
                 
                   
                      
                  
                   
                     41244
                  
                
                 
                   
                     21
                  
                   
                     0.00572028
                  
                
                 
                   
                      
                  
                   
                     40273
                  
                
                 
                   
                     20
                  
                   
                     0.00531730
                  
                
                 
                   
                      
                  
                   
                     39291
                  
                
                 
                   
                     19
                  
                   
                     0.00492439
                  
                
                 
                   
                      
                  
                   
                     38297
                  
                
                 
                   
                     18
                  
                   
                     0.00454142
                  
                
                 
                   
                      
                  
                   
                     37248
                  
                
                 
                   
                     17
                  
                   
                     0.00416894
                  
                
                 
                   
                      
                  
                   
                     36176
                  
                
                 
                   
                      
                  
                   
                     36176
                  
                
                 
                   
                     16
                  
                   
                     0.00380718
                  
                
                 
                   
                      
                  
                   
                     35071
                  
                
                 
                   
                     15
                  
                   
                     0.00345647
                  
                
                 
                   
                      
                  
                   
                     33929
                  
                
                 
                   
                     14
                  
                   
                     0.00311718
                  
                
                 
                   
                      
                  
                   
                     32746
                  
                
                 
                   
                     13
                  
                   
                     0.00278972
                  
                
                 
                   
                      
                  
                   
                     31517
                  
                
                 
                   
                     12
                  
                   
                     0.00247455
                  
                
                 
                   
                      
                  
                   
                     30236
                  
                
                 
                   
                     11
                  
                   
                     0.00217219
                  
                
                 
                   
                      
                  
                   
                     28897
                  
                
                 
                   
                     10
                  
                   
                     0.00188278
                  
                
                 
                   
                      
                  
                   
                     27442
                  
                
                 
                   
                     9
                  
                   
                     0.00160836
                  
                
                 
                   
                      
                  
                   
                     25959
                  
                
                 
                   
                     8
                  
                   
                     0.00134877
                  
                
                 
                   
                      
                  
                   
                     24434
                  
                
                 
                   
                     7
                  
                   
                     0.00110443
                  
                
                 
                   
                      
                  
                   
                     22749
                  
                
                 
                   
                     6
                  
                   
                     0.00087694
                  
                
                 
                   
                      
                  
                   
                     20925
                  
                
                 
                   
                     5
                  
                   
                     0.00066769
                  
                
                 
                   
                      
                  
                   
                     18922
                  
                
                 
                   
                     4
                  
                   
                     0.00047847
                  
                
                 
                   
                      
                  
                   
                     16675
                  
                
                 
                   
                     3
                  
                   
                     0.00031172
                  
                
                 
                   
                      
                  
                   
                     14061
                  
                
                 
                   
                     2
                  
                   
                     0.00017111
                  
                
                 
                   
                      
                  
                   
                     10792
                  
                
                 
                   
                     1
                  
                   
                     0.00006319
                  
                
                 
                   
                      
                  
                   
                     6319
                  
                
                 
                   
                     0
                  
                   
                     0.00000000
                  
                
              
            
          
        
      
       
         
           
             
             
               A
               TABLE
               SHEWING
               THE
               AREA
               OF
               THE
               SEGMENTS
               OF
               A
               CIRCLE
               WHOSE
               Whole
               Area
               is
               Unity
               ,
               to
               the
               ten
               Thousandth
               part
               of
               the
               Diameter
               .
            
          
        
         
           
             
             
               
                 
                   
                      
                  
                   
                     0
                  
                   
                     1
                  
                   
                     2
                  
                   
                     3
                  
                   
                     4
                  
                   
                     5
                  
                   
                     6
                  
                   
                     7
                  
                   
                     8
                  
                   
                     9
                  
                   
                      
                  
                
                 
                   
                     0
                  
                   
                     000000
                  
                   
                     000004
                  
                   
                     000007
                  
                   
                     000011
                  
                   
                     000014
                  
                   
                     000018
                  
                   
                     000025
                  
                   
                     000032
                  
                   
                     000039
                  
                   
                     000046
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     000053
                  
                   
                     000062
                  
                   
                     000071
                  
                   
                     000080
                  
                   
                     000089
                  
                   
                     000098
                  
                   
                     000108
                  
                   
                     000119
                  
                   
                     000130
                  
                   
                     000140
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     000151
                  
                   
                     000163
                  
                   
                     000175
                  
                   
                     000187
                  
                   
                     000200
                  
                   
                     000212
                  
                   
                     000225
                  
                   
                     000238
                  
                   
                     000251
                  
                   
                     000265
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     000278
                  
                   
                     000292
                  
                   
                     000307
                  
                   
                     000322
                  
                   
                     000336
                  
                   
                     000351
                  
                   
                     000366
                  
                   
                     000382
                  
                   
                     000397
                  
                   
                     000413
                  
                   
                      
                  
                
                 
                   
                     4
                  
                   
                     000428
                  
                   
                     000444
                  
                   
                     000461
                  
                   
                     000478
                  
                   
                     000494
                  
                   
                     000511
                  
                   
                     000529
                  
                   
                     000546
                  
                   
                     000564
                  
                   
                     000581
                  
                   
                      
                  
                
                 
                   
                     5
                  
                   
                     000599
                  
                   
                     000617
                  
                   
                     000636
                  
                   
                     000654
                  
                   
                     000673
                  
                   
                     000691
                  
                   
                     000710
                  
                   
                     000729
                  
                   
                     000748
                  
                   
                     000768
                  
                   
                     19
                  
                
                 
                   
                     6
                  
                   
                     000787
                  
                   
                     000807
                  
                   
                     000827
                  
                   
                     000847
                  
                   
                     000867
                  
                   
                     000887
                  
                   
                     000908
                  
                   
                     000928
                  
                   
                     000949
                  
                   
                     000970
                  
                   
                     20
                  
                
                 
                   
                     7
                  
                   
                     000991
                  
                   
                     001012
                  
                   
                     001034
                  
                   
                     001056
                  
                   
                     001077
                  
                   
                     001099
                  
                   
                     001121
                  
                   
                     001144
                  
                   
                     001166
                  
                   
                     001188
                  
                   
                     21
                  
                
                 
                   
                     8
                  
                   
                     001211
                  
                   
                     001234
                  
                   
                     001257
                  
                   
                     001280
                  
                   
                     001304
                  
                   
                     001327
                  
                   
                     001350
                  
                   
                     001374
                  
                   
                     001398
                  
                   
                     001421
                  
                   
                     23
                  
                
                 
                   
                     9
                  
                   
                     001445
                  
                   
                     001469
                  
                   
                     001494
                  
                   
                     001518
                  
                   
                     001542
                  
                   
                     001567
                  
                   
                     001592
                  
                   
                     001617
                  
                   
                     001642
                  
                   
                     001667
                  
                   
                     25
                  
                
                 
                   
                     10
                  
                   
                     001692
                  
                   
                     001717
                  
                   
                     001743
                  
                   
                     001769
                  
                   
                     001794
                  
                   
                     001820
                  
                   
                     001846
                  
                   
                     001873
                  
                   
                     001899
                  
                   
                     001925
                  
                   
                     26
                  
                
                 
                   
                     11
                  
                   
                     001952
                  
                   
                     001979
                  
                   
                     002005
                  
                   
                     002032
                  
                   
                     002059
                  
                   
                     002086
                  
                   
                     002113
                  
                   
                     002141
                  
                   
                     002168
                  
                   
                     002195
                  
                   
                     27
                  
                
                 
                   
                     12
                  
                   
                     002223
                  
                   
                     002251
                  
                   
                     002279
                  
                   
                     002307
                  
                   
                     002335
                  
                   
                     002363
                  
                   
                     002392
                  
                   
                     002420
                  
                   
                     002449
                  
                   
                     002477
                  
                   
                     28
                  
                
                 
                   
                     13
                  
                   
                     002506
                  
                   
                     002535
                  
                   
                     002564
                  
                   
                     002593
                  
                   
                     002623
                  
                   
                     002652
                  
                   
                     002681
                  
                   
                     002711
                  
                   
                     002741
                  
                   
                     002770
                  
                   
                     29
                  
                
                 
                   
                     14
                  
                   
                     002700
                  
                   
                     002830
                  
                   
                     002860
                  
                   
                     002890
                  
                   
                     002921
                  
                   
                     002951
                  
                   
                     002982
                  
                   
                     003013
                  
                   
                     003043
                  
                   
                     003074
                  
                   
                     30
                  
                
                 
                   
                     15
                  
                   
                     003105
                  
                   
                     003136
                  
                   
                     003167
                  
                   
                     003198
                  
                   
                     003229
                  
                   
                     003260
                  
                   
                     003291
                  
                   
                     003323
                  
                   
                     003355
                  
                   
                     003387
                  
                   
                     31
                  
                
                 
                   
                     16
                  
                   
                     003419
                  
                   
                     003451
                  
                   
                     003483
                  
                   
                     003515
                  
                   
                     003548
                  
                   
                     003580
                  
                   
                     003612
                  
                   
                     003645
                  
                   
                     003678
                  
                   
                     003710
                  
                   
                     32
                  
                
                 
                   
                     17
                  
                   
                     003743
                  
                   
                     003776
                  
                   
                     003809
                  
                   
                     003842
                  
                   
                     0038●6
                  
                   
                     003909
                  
                   
                     003942
                  
                   
                     003976
                  
                   
                     004009
                  
                   
                     004043
                  
                   
                     33
                  
                
                 
                   
                     18
                  
                   
                     004077
                  
                   
                     004111
                  
                   
                     004145
                  
                   
                     004179
                  
                   
                     004213
                  
                   
                     004247
                  
                   
                     004281
                  
                   
                     004316
                  
                   
                     004351
                  
                   
                     004385
                  
                   
                     34
                  
                
                 
                   
                     19
                  
                   
                     004420
                  
                   
                     004455
                  
                   
                     004490
                  
                   
                     004525
                  
                   
                     004560
                  
                   
                     004595
                  
                   
                     004630
                  
                   
                     004665
                  
                   
                     004700
                  
                   
                     004735
                  
                   
                     35
                  
                
                 
                   
                     20
                  
                   
                     004770
                  
                   
                     004806
                  
                   
                     004843
                  
                   
                     004879
                  
                   
                     004915
                  
                   
                     004952
                  
                   
                     004988
                  
                   
                     005024
                  
                   
                     005061
                  
                   
                     005097
                  
                   
                     36
                  
                
                 
                   
                     21
                  
                   
                     005133
                  
                   
                     005170
                  
                   
                     005206
                  
                   
                     005243
                  
                   
                     005280
                  
                   
                     005317
                  
                   
                     005354
                  
                   
                     005391
                  
                   
                     005428
                  
                   
                     005465
                  
                   
                     37
                  
                
                 
                   
                     22
                  
                   
                     005502
                  
                   
                     005539
                  
                   
                     005●77
                  
                   
                     005615
                  
                   
                     005652
                  
                   
                     005690
                  
                   
                     005728
                  
                   
                     005766
                  
                   
                     005804
                  
                   
                     005842
                  
                   
                     38
                  
                
                 
                   
                     23
                  
                   
                     005880
                  
                   
                     005918
                  
                   
                     005957
                  
                   
                     005995
                  
                   
                     006023
                  
                   
                     006072
                  
                   
                     006111
                  
                   
                     006150
                  
                   
                     006188
                  
                   
                     006227
                  
                   
                     39
                  
                
                 
                   
                     24
                  
                   
                     006266
                  
                   
                     0063●5
                  
                   
                     006344
                  
                   
                     006383
                  
                   
                     006423
                  
                   
                     006462
                  
                   
                     006501
                  
                   
                     006541
                  
                   
                     006581
                  
                   
                     006620
                  
                   
                     39
                  
                
                 
                   
                     25
                  
                   
                     006660
                  
                   
                     006700
                  
                   
                     006739
                  
                   
                     006779
                  
                   
                     006819
                  
                   
                     006859
                  
                   
                     006899
                  
                   
                     006940
                  
                   
                     006980
                  
                   
                     007021
                  
                   
                     40
                  
                
                 
                   
                     26
                  
                   
                     007061
                  
                   
                     007102
                  
                   
                     007142
                  
                   
                     007183
                  
                   
                     007223
                  
                   
                     007264
                  
                   
                     007305
                  
                   
                     007346
                  
                   
                     007387
                  
                   
                     007429
                  
                   
                     41
                  
                
                 
                   
                     27
                  
                   
                     007470
                  
                   
                     007511
                  
                   
                     007553
                  
                   
                     007594
                  
                   
                     007635
                  
                   
                     007677
                  
                   
                     007719
                  
                   
                     007761
                  
                   
                     007802
                  
                   
                     007844
                  
                   
                     42
                  
                
                 
                   
                     28
                  
                   
                     007886
                  
                   
                     007928
                  
                   
                     007970
                  
                   
                     008012
                  
                   
                     008055
                  
                   
                     008097
                  
                   
                     008140
                  
                   
                     008182
                  
                   
                     008225
                  
                   
                     008267
                  
                   
                     42
                  
                
                 
                   
                     29
                  
                   
                     008310
                  
                   
                     008353
                  
                   
                     008396
                  
                   
                     008439
                  
                   
                     008482
                  
                   
                     008525
                  
                   
                     008568
                  
                   
                     008611
                  
                   
                     008654
                  
                   
                     008698
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     008471
                  
                   
                     008785
                  
                   
                     008828
                  
                   
                     008872
                  
                   
                     008916
                  
                   
                     008959
                  
                   
                     009203
                  
                   
                     009047
                  
                   
                     009091
                  
                   
                     009135
                  
                   
                     44
                  
                
                 
                   
                     31
                  
                   
                     009179
                  
                   
                     009223
                  
                   
                     009267
                  
                   
                     009312
                  
                   
                     009356
                  
                   
                     009400
                  
                   
                     009445
                  
                   
                     009490
                  
                   
                     009535
                  
                   
                     009579
                  
                   
                     45
                  
                
                 
                   
                     32
                  
                   
                     009624
                  
                   
                     009669
                  
                   
                     009714
                  
                   
                     009759
                  
                   
                     009804
                  
                   
                     009849
                  
                   
                     009894
                  
                   
                     009939
                  
                   
                     009985
                  
                   
                     010030
                  
                   
                     45
                  
                
                 
                   
                     33
                  
                   
                     010075
                  
                   
                     010121
                  
                   
                     010167
                  
                   
                     010212
                  
                   
                     010258
                  
                   
                     010303
                  
                   
                     010349
                  
                   
                     010395
                  
                   
                     010441
                  
                   
                     010487
                  
                   
                     46
                  
                
                 
                   
                     
                     33
                  
                   
                     010075
                  
                   
                     010121
                  
                   
                     010167
                  
                   
                     010212
                  
                   
                     010258
                  
                   
                     010303
                  
                   
                     010349
                  
                   
                     010395
                  
                   
                     010441
                  
                   
                     010487
                  
                   
                     46
                  
                
                 
                   
                     34
                  
                   
                     010533
                  
                   
                     010580
                  
                   
                     010626
                  
                   
                     010672
                  
                   
                     010719
                  
                   
                     010765
                  
                   
                     010812
                  
                   
                     010858
                  
                   
                     010905
                  
                   
                     010952
                  
                   
                     47
                  
                
                 
                   
                     35
                  
                   
                     010999
                  
                   
                     011045
                  
                   
                     011093
                  
                   
                     011139
                  
                   
                     011186
                  
                   
                     011233
                  
                   
                     011281
                  
                   
                     011328
                  
                   
                     011375
                  
                   
                     011422
                  
                   
                     47
                  
                
                 
                   
                     36
                  
                   
                     011469
                  
                   
                     011517
                  
                   
                     011565
                  
                   
                     011612
                  
                   
                     011660
                  
                   
                     011707
                  
                   
                     011755
                  
                   
                     011803
                  
                   
                     011851
                  
                   
                     011899
                  
                   
                     47
                  
                
                 
                   
                     37
                  
                   
                     011947
                  
                   
                     011995
                  
                   
                     012043
                  
                   
                     012092
                  
                   
                     012140
                  
                   
                     012188
                  
                   
                     012237
                  
                   
                     012285
                  
                   
                     012334
                  
                   
                     012382
                  
                   
                     48
                  
                
                 
                   
                     38
                  
                   
                     012431
                  
                   
                     012479
                  
                   
                     012528
                  
                   
                     012577
                  
                   
                     012626
                  
                   
                     012675
                  
                   
                     012724
                  
                   
                     012773
                  
                   
                     012823
                  
                   
                     012872
                  
                   
                     49
                  
                
                 
                   
                     39
                  
                   
                     012921
                  
                   
                     012970
                  
                   
                     0130●0
                  
                   
                     013069
                  
                   
                     013118
                  
                   
                     013168
                  
                   
                     013218
                  
                   
                     013267
                  
                   
                     013317
                  
                   
                     013367
                  
                   
                     50
                  
                
                 
                   
                     40
                  
                   
                     013417
                  
                   
                     013467
                  
                   
                     013517
                  
                   
                     013567
                  
                   
                     013617
                  
                   
                     013667
                  
                   
                     013717
                  
                   
                     013767
                  
                   
                     013818
                  
                   
                     013868
                  
                   
                     50
                  
                
                 
                   
                     41
                  
                   
                     013919
                  
                   
                     013969
                  
                   
                     014020
                  
                   
                     014071
                  
                   
                     014121
                  
                   
                     014172
                  
                   
                     014223
                  
                   
                     014274
                  
                   
                     014325
                  
                   
                     014375
                  
                   
                     51
                  
                
                 
                   
                     42
                  
                   
                     014426
                  
                   
                     014478
                  
                   
                     014529
                  
                   
                     014580
                  
                   
                     014632
                  
                   
                     014683
                  
                   
                     014734
                  
                   
                     014786
                  
                   
                     014837
                  
                   
                     014889
                  
                   
                     51
                  
                
                 
                   
                     43
                  
                   
                     014941
                  
                   
                     014992
                  
                   
                     015044
                  
                   
                     015096
                  
                   
                     015148
                  
                   
                     015199
                  
                   
                     015252
                  
                   
                     015304
                  
                   
                     015356
                  
                   
                     015408
                  
                   
                     52
                  
                
                 
                   
                     44
                  
                   
                     015460
                  
                   
                     015512
                  
                   
                     015565
                  
                   
                     015617
                  
                   
                     015669
                  
                   
                     015721
                  
                   
                     015774
                  
                   
                     015827
                  
                   
                     015879
                  
                   
                     015932
                  
                   
                     52
                  
                
                 
                   
                     45
                  
                   
                     015985
                  
                   
                     016038
                  
                   
                     016091
                  
                   
                     016144
                  
                   
                     016197
                  
                   
                     016249
                  
                   
                     016303
                  
                   
                     016356
                  
                   
                     0164●9
                  
                   
                     016462
                  
                   
                     53
                  
                
                 
                   
                     46
                  
                   
                     016515
                  
                   
                     016569
                  
                   
                     016622
                  
                   
                     016676
                  
                   
                     016729
                  
                   
                     016783
                  
                   
                     016837
                  
                   
                     016891
                  
                   
                     016944
                  
                   
                     016998
                  
                   
                     54
                  
                
                 
                   
                     47
                  
                   
                     017052
                  
                   
                     017906
                  
                   
                     017160
                  
                   
                     017214
                  
                   
                     017268
                  
                   
                     017322
                  
                   
                     017376
                  
                   
                     017431
                  
                   
                     017485
                  
                   
                     017539
                  
                   
                     54
                  
                
                 
                   
                     48
                  
                   
                     017593
                  
                   
                     017648
                  
                   
                     017703
                  
                   
                     017757
                  
                   
                     017812
                  
                   
                     017866
                  
                   
                     017921
                  
                   
                     017976
                  
                   
                     018031
                  
                   
                     018086
                  
                   
                     55
                  
                
                 
                   
                     49
                  
                   
                     018141
                  
                   
                     018196
                  
                   
                     018251
                  
                   
                     018306
                  
                   
                     018361
                  
                   
                     018416
                  
                   
                     018471
                  
                   
                     018527
                  
                   
                     018582
                  
                   
                     018638
                  
                   
                     55
                  
                
                 
                   
                     50
                  
                   
                     018693
                  
                   
                     018749
                  
                   
                     018804
                  
                   
                     018860
                  
                   
                     018916
                  
                   
                     018971
                  
                   
                     019027
                  
                   
                     019083
                  
                   
                     019139
                  
                   
                     019195
                  
                   
                     56
                  
                
                 
                   
                     51
                  
                   
                     019251
                  
                   
                     019307
                  
                   
                     019363
                  
                   
                     019419
                  
                   
                     019475
                  
                   
                     019531
                  
                   
                     019588
                  
                   
                     019644
                  
                   
                     019701
                  
                   
                     019757
                  
                   
                     56
                  
                
                 
                   
                     52
                  
                   
                     019813
                  
                   
                     019870
                  
                   
                     019927
                  
                   
                     019984
                  
                   
                     020040
                  
                   
                     020097
                  
                   
                     020154
                  
                   
                     020211
                  
                   
                     020268
                  
                   
                     020325
                  
                   
                     57
                  
                
                 
                   
                     53
                  
                   
                     020381
                  
                   
                     020439
                  
                   
                     020496
                  
                   
                     020553
                  
                   
                     020610
                  
                   
                     020667
                  
                   
                     020725
                  
                   
                     020782
                  
                   
                     020840
                  
                   
                     020897
                  
                   
                     57
                  
                
                 
                   
                     54
                  
                   
                     020954
                  
                   
                     021012
                  
                   
                     021070
                  
                   
                     021128
                  
                   
                     021185
                  
                   
                     021243
                  
                   
                     021301
                  
                   
                     021359
                  
                   
                     021416
                  
                   
                     021474
                  
                   
                     57
                  
                
                 
                   
                     55
                  
                   
                     021532
                  
                   
                     021590
                  
                   
                     021649
                  
                   
                     021707
                  
                   
                     021765
                  
                   
                     021823
                  
                   
                     021882
                  
                   
                     021940
                  
                   
                     021999
                  
                   
                     022057
                  
                   
                     58
                  
                
                 
                   
                     56
                  
                   
                     022115
                  
                   
                     022174
                  
                   
                     022233
                  
                   
                     022292
                  
                   
                     022350
                  
                   
                     022409
                  
                   
                     022468
                  
                   
                     022527
                  
                   
                     022586
                  
                   
                     022645
                  
                   
                     59
                  
                
                 
                   
                     57
                  
                   
                     022703
                  
                   
                     022763
                  
                   
                     022822
                  
                   
                     022881
                  
                   
                     022949
                  
                   
                     022999
                  
                   
                     023058
                  
                   
                     023118
                  
                   
                     023177
                  
                   
                     023237
                  
                   
                     59
                  
                
                 
                   
                     58
                  
                   
                     023296
                  
                   
                     023356
                  
                   
                     023415
                  
                   
                     023475
                  
                   
                     023534
                  
                   
                     023594
                  
                   
                     023654
                  
                   
                     023714
                  
                   
                     023774
                  
                   
                     023834
                  
                   
                     60
                  
                
                 
                   
                     59
                  
                   
                     023894
                  
                   
                     023954
                  
                   
                     024014
                  
                   
                     024074
                  
                   
                     024134
                  
                   
                     024194
                  
                   
                     024254
                  
                   
                     024315
                  
                   
                     024375
                  
                   
                     024436
                  
                   
                     60
                  
                
                 
                   
                     60
                  
                   
                     024496
                  
                   
                     024557
                  
                   
                     024617
                  
                   
                     024678
                  
                   
                     024738
                  
                   
                     024799
                  
                   
                     024860
                  
                   
                     024921
                  
                   
                     024981
                  
                   
                     025042
                  
                   
                     60
                  
                
                 
                   
                     61
                  
                   
                     025103
                  
                   
                     025164
                  
                   
                     025225
                  
                   
                     025286
                  
                   
                     025347
                  
                   
                     025408
                  
                   
                     025470
                  
                   
                     025531
                  
                   
                     025692
                  
                   
                     025654
                  
                   
                     61
                  
                
                 
                   
                     62
                  
                   
                     025715
                  
                   
                     025776
                  
                   
                     025838
                  
                   
                     025899
                  
                   
                     025961
                  
                   
                     026022
                  
                   
                     026084
                  
                   
                     026146
                  
                   
                     026208
                  
                   
                     026270
                  
                   
                     62
                  
                
                 
                   
                     63
                  
                   
                     026331
                  
                   
                     026393
                  
                   
                     026455
                  
                   
                     026517
                  
                   
                     026579
                  
                   
                     026641
                  
                   
                     026703
                  
                   
                     026766
                  
                   
                     026828
                  
                   
                     026890
                  
                   
                     62
                  
                
                 
                   
                     64
                  
                   
                     026952
                  
                   
                     027015
                  
                   
                     027077
                  
                   
                     027140
                  
                   
                     027202
                  
                   
                     027264
                  
                   
                     027327
                  
                   
                     027390
                  
                   
                     027453
                  
                   
                     027515
                  
                   
                     63
                  
                
                 
                   
                     65
                  
                   
                     027578
                  
                   
                     027641
                  
                   
                     027704
                  
                   
                     027767
                  
                   
                     027830
                  
                   
                     027892
                  
                   
                     027956
                  
                   
                     028019
                  
                   
                     028082
                  
                   
                     028145
                  
                   
                     63
                  
                
                 
                   
                     66
                  
                   
                     028208
                  
                   
                     028271
                  
                   
                     028335
                  
                   
                     028398
                  
                   
                     028461
                  
                   
                     028524
                  
                   
                     028588
                  
                   
                     028652
                  
                   
                     028715
                  
                   
                     028779
                  
                   
                     63
                  
                
                 
                   
                     
                     67
                  
                   
                     028842
                  
                   
                     028906
                  
                   
                     028970
                  
                   
                     029034
                  
                   
                     029097
                  
                   
                     029161
                  
                   
                     029225
                  
                   
                     029289
                  
                   
                     02935●
                  
                   
                     029417
                  
                   
                     64
                  
                
                 
                   
                     68
                  
                   
                     029481
                  
                   
                     029545
                  
                   
                     029610
                  
                   
                     029674
                  
                   
                     029738
                  
                   
                     029802
                  
                   
                     029867
                  
                   
                     029931
                  
                   
                     029996
                  
                   
                     030060
                  
                   
                     65
                  
                
                 
                   
                     69
                  
                   
                     030184
                  
                   
                     030189
                  
                   
                     030253
                  
                   
                     030318
                  
                   
                     030383
                  
                   
                     030447
                  
                   
                     030512
                  
                   
                     030577
                  
                   
                     030642
                  
                   
                     030707
                  
                   
                     65
                  
                
                 
                   
                     70
                  
                   
                     030772
                  
                   
                     030837
                  
                   
                     030902
                  
                   
                     030967
                  
                   
                     031032
                  
                   
                     031097
                  
                   
                     031163
                  
                   
                     031228
                  
                   
                     031293
                  
                   
                     031359
                  
                   
                     65
                  
                
                 
                   
                     71
                  
                   
                     031424
                  
                   
                     031489
                  
                   
                     031555
                  
                   
                     031620
                  
                   
                     031686
                  
                   
                     031751
                  
                   
                     031817
                  
                   
                     031883
                  
                   
                     031949
                  
                   
                     032014
                  
                   
                     66
                  
                
                 
                   
                     72
                  
                   
                     032080
                  
                   
                     032146
                  
                   
                     032212
                  
                   
                     032278
                  
                   
                     032344
                  
                   
                     032409
                  
                   
                     032476
                  
                   
                     032542
                  
                   
                     032608
                  
                   
                     032674
                  
                   
                     66
                  
                
                 
                   
                     73
                  
                   
                     032741
                  
                   
                     032807
                  
                   
                     032873
                  
                   
                     032939
                  
                   
                     033006
                  
                   
                     033072
                  
                   
                     033139
                  
                   
                     033205
                  
                   
                     033272
                  
                   
                     033338
                  
                   
                     66
                  
                
                 
                   
                     74
                  
                   
                     033405
                  
                   
                     033472
                  
                   
                     033538
                  
                   
                     033605
                  
                   
                     033672
                  
                   
                     033738
                  
                   
                     033875
                  
                   
                     033879
                  
                   
                     033939
                  
                   
                     034006
                  
                   
                     67
                  
                
                 
                   
                     75
                  
                   
                     034073
                  
                   
                     034140
                  
                   
                     034208
                  
                   
                     034275
                  
                   
                     034342
                  
                   
                     034409
                  
                   
                     034477
                  
                   
                     034544
                  
                   
                     034612
                  
                   
                     034679
                  
                   
                     67
                  
                
                 
                   
                     76
                  
                   
                     034746
                  
                   
                     034814
                  
                   
                     034881
                  
                   
                     034949
                  
                   
                     035016
                  
                   
                     035084
                  
                   
                     035152
                  
                   
                     035219
                  
                   
                     035287
                  
                   
                     035355
                  
                   
                     68
                  
                
                 
                   
                     77
                  
                   
                     035423
                  
                   
                     035491
                  
                   
                     035559
                  
                   
                     035627
                  
                   
                     035695
                  
                   
                     035763
                  
                   
                     035831
                  
                   
                     035899
                  
                   
                     035968
                  
                   
                     036036
                  
                   
                     68
                  
                
                 
                   
                     78
                  
                   
                     036104
                  
                   
                     036172
                  
                   
                     036249
                  
                   
                     036309
                  
                   
                     036378
                  
                   
                     036446
                  
                   
                     036515
                  
                   
                     036583
                  
                   
                     036651
                  
                   
                     036720
                  
                   
                     69
                  
                
                 
                   
                     79
                  
                   
                     036789
                  
                   
                     036858
                  
                   
                     036927
                  
                   
                     036995
                  
                   
                     037064
                  
                   
                     037133
                  
                   
                     037202
                  
                   
                     037271
                  
                   
                     037339
                  
                   
                     037408
                  
                   
                     69
                  
                
                 
                   
                     80
                  
                   
                     037477
                  
                   
                     037546
                  
                   
                     037615
                  
                   
                     037684
                  
                   
                     037752
                  
                   
                     037822
                  
                   
                     037891
                  
                   
                     037961
                  
                   
                     038030
                  
                   
                     038099
                  
                   
                     69
                  
                
                 
                   
                     81
                  
                   
                     038169
                  
                   
                     038239
                  
                   
                     038308
                  
                   
                     038378
                  
                   
                     038447
                  
                   
                     038517
                  
                   
                     038587
                  
                   
                     038657
                  
                   
                     038727
                  
                   
                     038797
                  
                   
                     70
                  
                
                 
                   
                     82
                  
                   
                     038867
                  
                   
                     038937
                  
                   
                     039007
                  
                   
                     039077
                  
                   
                     039147
                  
                   
                     039217
                  
                   
                     039287
                  
                   
                     039357
                  
                   
                     039428
                  
                   
                     039498
                  
                   
                     70
                  
                
                 
                   
                     83
                  
                   
                     039568
                  
                   
                     039638
                  
                   
                     039709
                  
                   
                     039779
                  
                   
                     039849
                  
                   
                     039919
                  
                   
                     039990
                  
                   
                     040061
                  
                   
                     040131
                  
                   
                     040202
                  
                   
                     71
                  
                
                 
                   
                     84
                  
                   
                     040272
                  
                   
                     040343
                  
                   
                     040414
                  
                   
                     040485
                  
                   
                     040555
                  
                   
                     040636
                  
                   
                     040707
                  
                   
                     040778
                  
                   
                     040849
                  
                   
                     040920
                  
                   
                     71
                  
                
                 
                   
                     85
                  
                   
                     040981
                  
                   
                     041052
                  
                   
                     041123
                  
                   
                     041194
                  
                   
                     041265
                  
                   
                     041336
                  
                   
                     041407
                  
                   
                     041479
                  
                   
                     041550
                  
                   
                     041621
                  
                   
                     71
                  
                
                 
                   
                     86
                  
                   
                     041692
                  
                   
                     041764
                  
                   
                     041835
                  
                   
                     041907
                  
                   
                     041978
                  
                   
                     042050
                  
                   
                     042122
                  
                   
                     042193
                  
                   
                     042265
                  
                   
                     042336
                  
                   
                     72
                  
                
                 
                   
                     87
                  
                   
                     042408
                  
                   
                     042480
                  
                   
                     042552
                  
                   
                     042624
                  
                   
                     042696
                  
                   
                     042768
                  
                   
                     042840
                  
                   
                     042912
                  
                   
                     042984
                  
                   
                     043056
                  
                   
                     72
                  
                
                 
                   
                     88
                  
                   
                     043128
                  
                   
                     043200
                  
                   
                     043272
                  
                   
                     043345
                  
                   
                     043417
                  
                   
                     043489
                  
                   
                     043562
                  
                   
                     043634
                  
                   
                     043706
                  
                   
                     043779
                  
                   
                     73
                  
                
                 
                   
                     89
                  
                   
                     043852
                  
                   
                     043924
                  
                   
                     043697
                  
                   
                     044069
                  
                   
                     044142
                  
                   
                     044214
                  
                   
                     044287
                  
                   
                     044360
                  
                   
                     044433
                  
                   
                     044505
                  
                   
                     73
                  
                
                 
                   
                     90
                  
                   
                     044578
                  
                   
                     044651
                  
                   
                     044724
                  
                   
                     044797
                  
                   
                     044870
                  
                   
                     044943
                  
                   
                     045016
                  
                   
                     045089
                  
                   
                     045163
                  
                   
                     045236
                  
                   
                     73
                  
                
                 
                   
                     91
                  
                   
                     045309
                  
                   
                     045382
                  
                   
                     045456
                  
                   
                     045529
                  
                   
                     045603
                  
                   
                     045676
                  
                   
                     045749
                  
                   
                     045823
                  
                   
                     045896
                  
                   
                     045969
                  
                   
                     74
                  
                
                 
                   
                     92
                  
                   
                     046043
                  
                   
                     046117
                  
                   
                     046190
                  
                   
                     046264
                  
                   
                     046338
                  
                   
                     046411
                  
                   
                     046485
                  
                   
                     046559
                  
                   
                     046633
                  
                   
                     046707
                  
                   
                     74
                  
                
                 
                   
                     93
                  
                   
                     046781
                  
                   
                     046855
                  
                   
                     046929
                  
                   
                     047003
                  
                   
                     047077
                  
                   
                     047151
                  
                   
                     047●25
                  
                   
                     047299
                  
                   
                     047374
                  
                   
                     047448
                  
                   
                     74
                  
                
                 
                   
                     94
                  
                   
                     047522
                  
                   
                     047596
                  
                   
                     047671
                  
                   
                     047745
                  
                   
                     047819
                  
                   
                     047894
                  
                   
                     047969
                  
                   
                     048043
                  
                   
                     048118
                  
                   
                     048192
                  
                   
                     75
                  
                
                 
                   
                     95
                  
                   
                     048267
                  
                   
                     048342
                  
                   
                     048417
                  
                   
                     048491
                  
                   
                     048566
                  
                   
                     048641
                  
                   
                     048716
                  
                   
                     048791
                  
                   
                     048866
                  
                   
                     048941
                  
                   
                     75
                  
                
                 
                   
                     96
                  
                   
                     049015
                  
                   
                     049091
                  
                   
                     049166
                  
                   
                     049241
                  
                   
                     049316
                  
                   
                     049391
                  
                   
                     049466
                  
                   
                     049542
                  
                   
                     049617
                  
                   
                     049692
                  
                   
                     75
                  
                
                 
                   
                     97
                  
                   
                     049767
                  
                   
                     049843
                  
                   
                     049918
                  
                   
                     049994
                  
                   
                     050069
                  
                   
                     050144
                  
                   
                     050226
                  
                   
                     050296
                  
                   
                     050371
                  
                   
                     050447
                  
                   
                     75
                  
                
                 
                   
                     98
                  
                   
                     050522
                  
                   
                     050598
                  
                   
                     050674
                  
                   
                     050750
                  
                   
                     050826
                  
                   
                     050901
                  
                   
                     050977
                  
                   
                     051053
                  
                   
                     051129
                  
                   
                     051205
                  
                   
                     76
                  
                
                 
                   
                     99
                  
                   
                     051281
                  
                   
                     051358
                  
                   
                     051434
                  
                   
                     051510
                  
                   
                     051586
                  
                   
                     051662
                  
                   
                     051738
                  
                   
                     051815
                  
                   
                     051891
                  
                   
                     051968
                  
                   
                     76
                  
                
                 
                   
                     100
                  
                   
                     052044
                  
                   
                     052120
                  
                   
                     052197
                  
                   
                     052273
                  
                   
                     052350
                  
                   
                     052426
                  
                   
                     052503
                  
                   
                     052579
                  
                   
                     052656
                  
                   
                     052733
                  
                   
                     76
                  
                
                 
                   
                     
                  
                   
                     0
                  
                   
                     1
                  
                   
                     2
                  
                   
                     3
                  
                   
                     4
                  
                   
                     5
                  
                   
                     6
                  
                   
                     7
                  
                   
                     8
                  
                   
                     9
                  
                   
                     D
                  
                
                 
                   
                     100
                  
                   
                     052044
                  
                   
                     052120
                  
                   
                     052197
                  
                   
                     052273
                  
                   
                     052350
                  
                   
                     052426
                  
                   
                     052503
                  
                   
                     052579
                  
                   
                     052656
                  
                   
                     052733
                  
                   
                     076
                  
                
                 
                   
                     101
                  
                   
                     052810
                  
                   
                     052886
                  
                   
                     052963
                  
                   
                     053040
                  
                   
                     053117
                  
                   
                     053193
                  
                   
                     053271
                  
                   
                     053348
                  
                   
                     053425
                  
                   
                     053502
                  
                   
                     077
                  
                
                 
                   
                     102
                  
                   
                     053579
                  
                   
                     053656
                  
                   
                     053733
                  
                   
                     053810
                  
                   
                     053887
                  
                   
                     053964
                  
                   
                     054041
                  
                   
                     054119
                  
                   
                     054196
                  
                   
                     054273
                  
                   
                     077
                  
                
                 
                   
                     103
                  
                   
                     054351
                  
                   
                     054428
                  
                   
                     054506
                  
                   
                     054583
                  
                   
                     054661
                  
                   
                     054738
                  
                   
                     054816
                  
                   
                     054893
                  
                   
                     054973
                  
                   
                     055049
                  
                   
                     078
                  
                
                 
                   
                     104
                  
                   
                     055127
                  
                   
                     055204
                  
                   
                     055282
                  
                   
                     055360
                  
                   
                     055438
                  
                   
                     055516
                  
                   
                     055594
                  
                   
                     055672
                  
                   
                     055750
                  
                   
                     055828
                  
                   
                     078
                  
                
                 
                   
                     105
                  
                   
                     055906
                  
                   
                     055984
                  
                   
                     056062
                  
                   
                     056140
                  
                   
                     056218
                  
                   
                     056296
                  
                   
                     056374
                  
                   
                     056453
                  
                   
                     006531
                  
                   
                     056610
                  
                   
                     078
                  
                
                 
                   
                     106
                  
                   
                     056688
                  
                   
                     056766
                  
                   
                     056845
                  
                   
                     056923
                  
                   
                     057002
                  
                   
                     057080
                  
                   
                     057159
                  
                   
                     057237
                  
                   
                     057316
                  
                   
                     057395
                  
                   
                     079
                  
                
                 
                   
                     107
                  
                   
                     057474
                  
                   
                     057552
                  
                   
                     057631
                  
                   
                     057710
                  
                   
                     057789
                  
                   
                     057868
                  
                   
                     057946
                  
                   
                     058025
                  
                   
                     058104
                  
                   
                     058183
                  
                   
                     079
                  
                
                 
                   
                     108
                  
                   
                     058262
                  
                   
                     058341
                  
                   
                     058420
                  
                   
                     058499
                  
                   
                     058578
                  
                   
                     058658
                  
                   
                     058737
                  
                   
                     058816
                  
                   
                     058895
                  
                   
                     058975
                  
                   
                     079
                  
                
                 
                   
                     109
                  
                   
                     059054
                  
                   
                     059133
                  
                   
                     059213
                  
                   
                     059292
                  
                   
                     059372
                  
                   
                     059451
                  
                   
                     059531
                  
                   
                     059610
                  
                   
                     059690
                  
                   
                     059769
                  
                   
                     079
                  
                
                 
                   
                     110
                  
                   
                     059849
                  
                   
                     059929
                  
                   
                     060009
                  
                   
                     060088
                  
                   
                     060168
                  
                   
                     060248
                  
                   
                     060328
                  
                   
                     060408
                  
                   
                     060488
                  
                   
                     060560
                  
                   
                     080
                  
                
                 
                   
                     111
                  
                   
                     060648
                  
                   
                     060728
                  
                   
                     060808
                  
                   
                     060888
                  
                   
                     060968
                  
                   
                     061048
                  
                   
                     061128
                  
                   
                     061208
                  
                   
                     061289
                  
                   
                     061369
                  
                   
                     080
                  
                
                 
                   
                     112
                  
                   
                     061449
                  
                   
                     061529
                  
                   
                     061610
                  
                   
                     061690
                  
                   
                     061771
                  
                   
                     061851
                  
                   
                     061932
                  
                   
                     062012
                  
                   
                     062093
                  
                   
                     062173
                  
                   
                     080
                  
                
                 
                   
                     113
                  
                   
                     062254
                  
                   
                     062334
                  
                   
                     062415
                  
                   
                     062496
                  
                   
                     062576
                  
                   
                     062657
                  
                   
                     062738
                  
                   
                     062819
                  
                   
                     062900
                  
                   
                     062981
                  
                   
                     081
                  
                
                 
                   
                     114
                  
                   
                     063062
                  
                   
                     063143
                  
                   
                     063224
                  
                   
                     063305
                  
                   
                     063386
                  
                   
                     063467
                  
                   
                     063548
                  
                   
                     063629
                  
                   
                     063710
                  
                   
                     063791
                  
                   
                     081
                  
                
                 
                   
                     115
                  
                   
                     063873
                  
                   
                     063954
                  
                   
                     064035
                  
                   
                     064116
                  
                   
                     064198
                  
                   
                     064279
                  
                   
                     064360
                  
                   
                     064442
                  
                   
                     064523
                  
                   
                     064605
                  
                   
                     081
                  
                
                 
                   
                     116
                  
                   
                     064686
                  
                   
                     064768
                  
                   
                     064849
                  
                   
                     064931
                  
                   
                     065013
                  
                   
                     065095
                  
                   
                     065176
                  
                   
                     065258
                  
                   
                     065340
                  
                   
                     065421
                  
                   
                     082
                  
                
                 
                   
                     117
                  
                   
                     065503
                  
                   
                     065585
                  
                   
                     065667
                  
                   
                     065749
                  
                   
                     065831
                  
                   
                     065913
                  
                   
                     065995
                  
                   
                     066077
                  
                   
                     066159
                  
                   
                     066241
                  
                   
                     082
                  
                
                 
                   
                     118
                  
                   
                     066323
                  
                   
                     066405
                  
                   
                     066488
                  
                   
                     066570
                  
                   
                     066652
                  
                   
                     066735
                  
                   
                     066817
                  
                   
                     066899
                  
                   
                     066981
                  
                   
                     067064
                  
                   
                     082
                  
                
                 
                   
                     119
                  
                   
                     067146
                  
                   
                     067229
                  
                   
                     067311
                  
                   
                     067393
                  
                   
                     067476
                  
                   
                     067559
                  
                   
                     067642
                  
                   
                     067724
                  
                   
                     067807
                  
                   
                     067889
                  
                   
                     083
                  
                
                 
                   
                     120
                  
                   
                     067972
                  
                   
                     068055
                  
                   
                     068138
                  
                   
                     068221
                  
                   
                     068304
                  
                   
                     068387
                  
                   
                     068469
                  
                   
                     068552
                  
                   
                     068635
                  
                   
                     068718
                  
                   
                     083
                  
                
                 
                   
                     121
                  
                   
                     068801
                  
                   
                     068884
                  
                   
                     068967
                  
                   
                     069051
                  
                   
                     069134
                  
                   
                     069217
                  
                   
                     069300
                  
                   
                     069384
                  
                   
                     069467
                  
                   
                     069550
                  
                   
                     083
                  
                
                 
                   
                     122
                  
                   
                     069633
                  
                   
                     069717
                  
                   
                     069800
                  
                   
                     069884
                  
                   
                     069967
                  
                   
                     070051
                  
                   
                     070134
                  
                   
                     070218
                  
                   
                     070301
                  
                   
                     070385
                  
                   
                     083
                  
                
                 
                   
                     123
                  
                   
                     070468
                  
                   
                     070552
                  
                   
                     070635
                  
                   
                     070719
                  
                   
                     070803
                  
                   
                     070887
                  
                   
                     070970
                  
                   
                     071054
                  
                   
                     071138
                  
                   
                     071222
                  
                   
                     084
                  
                
                 
                   
                     124
                  
                   
                     071306
                  
                   
                     071390
                  
                   
                     071474
                  
                   
                     071558
                  
                   
                     071642
                  
                   
                     071726
                  
                   
                     071810
                  
                   
                     071895
                  
                   
                     071979
                  
                   
                     072063
                  
                   
                     084
                  
                
                 
                   
                     125
                  
                   
                     072148
                  
                   
                     072232
                  
                   
                     072316
                  
                   
                     072400
                  
                   
                     072484
                  
                   
                     072569
                  
                   
                     072653
                  
                   
                     072733
                  
                   
                     072822
                  
                   
                     072906
                  
                   
                     084
                  
                
                 
                   
                     126
                  
                   
                     072991
                  
                   
                     073075
                  
                   
                     073160
                  
                   
                     073244
                  
                   
                     073329
                  
                   
                     073414
                  
                   
                     073498
                  
                   
                     073583
                  
                   
                     073668
                  
                   
                     073752
                  
                   
                     084
                  
                
                 
                   
                     127
                  
                   
                     073837
                  
                   
                     073922
                  
                   
                     074007
                  
                   
                     074092
                  
                   
                     074177
                  
                   
                     074262
                  
                   
                     074347
                  
                   
                     074432
                  
                   
                     074517
                  
                   
                     074602
                  
                   
                     085
                  
                
                 
                   
                     128
                  
                   
                     074687
                  
                   
                     074772
                  
                   
                     074857
                  
                   
                     074942
                  
                   
                     075027
                  
                   
                     075112
                  
                   
                     075197
                  
                   
                     075283
                  
                   
                     075368
                  
                   
                     075453
                  
                   
                     085
                  
                
                 
                   
                     129
                  
                   
                     075539
                  
                   
                     075624
                  
                   
                     075709
                  
                   
                     075795
                  
                   
                     075880
                  
                   
                     075966
                  
                   
                     076051
                  
                   
                     076137
                  
                   
                     076222
                  
                   
                     076908
                  
                   
                     085
                  
                
                 
                   
                     130
                  
                   
                     076394
                  
                   
                     076479
                  
                   
                     076565
                  
                   
                     076651
                  
                   
                     076736
                  
                   
                     076822
                  
                   
                     076908
                  
                   
                     076994
                  
                   
                     077079
                  
                   
                     077165
                  
                   
                     086
                  
                
                 
                   
                     131
                  
                   
                     077251
                  
                   
                     077337
                  
                   
                     077423
                  
                   
                     077509
                  
                   
                     077595
                  
                   
                     077681
                  
                   
                     077767
                  
                   
                     077853
                  
                   
                     077939
                  
                   
                     078025
                  
                   
                     086
                  
                
                 
                   
                     132
                  
                   
                     078112
                  
                   
                     078198
                  
                   
                     078184
                  
                   
                     078370
                  
                   
                     078457
                  
                   
                     078543
                  
                   
                     078629
                  
                   
                     078716
                  
                   
                     078802
                  
                   
                     078889
                  
                   
                     086
                  
                
                 
                   
                     133
                  
                   
                     078975
                  
                   
                     079062
                  
                   
                     079148
                  
                   
                     079235
                  
                   
                     079321
                  
                   
                     079408
                  
                   
                     079494
                  
                   
                     079581
                  
                   
                     079668
                  
                   
                     079754
                  
                   
                     086
                  
                
                 
                   
                     
                     133
                  
                   
                     078975
                  
                   
                     079062
                  
                   
                     079148
                  
                   
                     079235
                  
                   
                     079321
                  
                   
                     079408
                  
                   
                     079494
                  
                   
                     079581
                  
                   
                     079668
                  
                   
                     079754
                  
                   
                     086
                  
                
                 
                   
                     134
                  
                   
                     079841
                  
                   
                     079928
                  
                   
                     080015
                  
                   
                     080101
                  
                   
                     080188
                  
                   
                     080275
                  
                   
                     080362
                  
                   
                     080449
                  
                   
                     080536
                  
                   
                     080623
                  
                   
                     087
                  
                
                 
                   
                     135
                  
                   
                     080710
                  
                   
                     080797
                  
                   
                     080885
                  
                   
                     08g972
                  
                   
                     081059
                  
                   
                     081147
                  
                   
                     081234
                  
                   
                     081321
                  
                   
                     081408
                  
                   
                     081495
                  
                   
                     087
                  
                
                 
                   
                     136
                  
                   
                     081582
                  
                   
                     081669
                  
                   
                     081756
                  
                   
                     081841
                  
                   
                     081931
                  
                   
                     032018
                  
                   
                     082106
                  
                   
                     082193
                  
                   
                     082281
                  
                   
                     082368
                  
                   
                     087
                  
                
                 
                   
                     137
                  
                   
                     082456
                  
                   
                     082543
                  
                   
                     082631
                  
                   
                     082718
                  
                   
                     082806
                  
                   
                     082894
                  
                   
                     082981
                  
                   
                     083069
                  
                   
                     083157
                  
                   
                     083245
                  
                   
                     087
                  
                
                 
                   
                     138
                  
                   
                     083333
                  
                   
                     083420
                  
                   
                     083508
                  
                   
                     083596
                  
                   
                     083684
                  
                   
                     083772
                  
                   
                     083860
                  
                   
                     083948
                  
                   
                     084036
                  
                   
                     084124
                  
                   
                     088
                  
                
                 
                   
                     139
                  
                   
                     084212
                  
                   
                     084300
                  
                   
                     084388
                  
                   
                     084477
                  
                   
                     084565
                  
                   
                     084653
                  
                   
                     084741
                  
                   
                     084830
                  
                   
                     084918
                  
                   
                     085006
                  
                   
                     088
                  
                
                 
                   
                     140
                  
                   
                     085095
                  
                   
                     085183
                  
                   
                     085271
                  
                   
                     085359
                  
                   
                     085448
                  
                   
                     085536
                  
                   
                     085625
                  
                   
                     085714
                  
                   
                     085802
                  
                   
                     085891
                  
                   
                     088
                  
                
                 
                   
                     141
                  
                   
                     085979
                  
                   
                     086068
                  
                   
                     086157
                  
                   
                     086246
                  
                   
                     086334
                  
                   
                     086423
                  
                   
                     086512
                  
                   
                     086601
                  
                   
                     086689
                  
                   
                     086778
                  
                   
                     089
                  
                
                 
                   
                     142
                  
                   
                     086867
                  
                   
                     086956
                  
                   
                     087045
                  
                   
                     087134
                  
                   
                     087223
                  
                   
                     087312
                  
                   
                     087401
                  
                   
                     087490
                  
                   
                     087579
                  
                   
                     087668
                  
                   
                     089
                  
                
                 
                   
                     143
                  
                   
                     087757
                  
                   
                     087846
                  
                   
                     087935
                  
                   
                     088025
                  
                   
                     088114
                  
                   
                     088203
                  
                   
                     088292
                  
                   
                     088383
                  
                   
                     088471
                  
                   
                     088561
                  
                   
                     089
                  
                
                 
                   
                     144
                  
                   
                     088650
                  
                   
                     088740
                  
                   
                     088829
                  
                   
                     088920
                  
                   
                     089009
                  
                   
                     089099
                  
                   
                     089188
                  
                   
                     089278
                  
                   
                     089366
                  
                   
                     089456
                  
                   
                     090
                  
                
                 
                   
                     145
                  
                   
                     089545
                  
                   
                     089635
                  
                   
                     089725
                  
                   
                     089814
                  
                   
                     089904
                  
                   
                     089994
                  
                   
                     090084
                  
                   
                     090174
                  
                   
                     090264
                  
                   
                     090354
                  
                   
                     090
                  
                
                 
                   
                     146
                  
                   
                     090444
                  
                   
                     090533
                  
                   
                     090623
                  
                   
                     090713
                  
                   
                     090803
                  
                   
                     090893
                  
                   
                     090983
                  
                   
                     091073
                  
                   
                     091163
                  
                   
                     091253
                  
                   
                     90
                  
                
                 
                   
                     147
                  
                   
                     091344
                  
                   
                     091434
                  
                   
                     091524
                  
                   
                     091614
                  
                   
                     091704
                  
                   
                     091795
                  
                   
                     091885
                  
                   
                     091975
                  
                   
                     092066
                  
                   
                     092156
                  
                   
                     90
                  
                
                 
                   
                     148
                  
                   
                     092247
                  
                   
                     092337
                  
                   
                     092427
                  
                   
                     092518
                  
                   
                     092608
                  
                   
                     092699
                  
                   
                     092790
                  
                   
                     092880
                  
                   
                     092971
                  
                   
                     093061
                  
                   
                     90
                  
                
                 
                   
                     149
                  
                   
                     093152
                  
                   
                     093243
                  
                   
                     093333
                  
                   
                     093424
                  
                   
                     0●3515
                  
                   
                     093606
                  
                   
                     093696
                  
                   
                     093787
                  
                   
                     093878
                  
                   
                     093969
                  
                   
                     91
                  
                
                 
                   
                     150
                  
                   
                     094060
                  
                   
                     094151
                  
                   
                     094242
                  
                   
                     094333
                  
                   
                     094424
                  
                   
                     094515
                  
                   
                     094606
                  
                   
                     094697
                  
                   
                     094788
                  
                   
                     094879
                  
                   
                     91
                  
                
                 
                   
                     151
                  
                   
                     094971
                  
                   
                     095062
                  
                   
                     095153
                  
                   
                     095244
                  
                   
                     095335
                  
                   
                     095427
                  
                   
                     095518
                  
                   
                     095609
                  
                   
                     095701
                  
                   
                     095792
                  
                   
                     91
                  
                
                 
                   
                     152
                  
                   
                     095884
                  
                   
                     095975
                  
                   
                     096067
                  
                   
                     096158
                  
                   
                     096249
                  
                   
                     096341
                  
                   
                     096433
                  
                   
                     096524
                  
                   
                     096616
                  
                   
                     096707
                  
                   
                     92
                  
                
                 
                   
                     153
                  
                   
                     096799
                  
                   
                     096891
                  
                   
                     096982
                  
                   
                     097074
                  
                   
                     097166
                  
                   
                     097258
                  
                   
                     097349
                  
                   
                     097441
                  
                   
                     097533
                  
                   
                     097625
                  
                   
                     92
                  
                
                 
                   
                     154
                  
                   
                     097717
                  
                   
                     097809
                  
                   
                     097901
                  
                   
                     097993
                  
                   
                     098085
                  
                   
                     098177
                  
                   
                     098269
                  
                   
                     098361
                  
                   
                     098453
                  
                   
                     098545
                  
                   
                     92
                  
                
                 
                   
                     155
                  
                   
                     098637
                  
                   
                     098729
                  
                   
                     098822
                  
                   
                     098914
                  
                   
                     099006
                  
                   
                     099098
                  
                   
                     099191
                  
                   
                     099283
                  
                   
                     099375
                  
                   
                     099468
                  
                   
                     92
                  
                
                 
                   
                     156
                  
                   
                     099569
                  
                   
                     099653
                  
                   
                     099745
                  
                   
                     099838
                  
                   
                     099830
                  
                   
                     100023
                  
                   
                     100115
                  
                   
                     100208
                  
                   
                     100300
                  
                   
                     100393
                  
                   
                     93
                  
                
                 
                   
                     157
                  
                   
                     100486
                  
                   
                     100578
                  
                   
                     100671
                  
                   
                     100763
                  
                   
                     100856
                  
                   
                     100949
                  
                   
                     101042
                  
                   
                     101135
                  
                   
                     101227
                  
                   
                     101320
                  
                   
                     93
                  
                
                 
                   
                     158
                  
                   
                     101413
                  
                   
                     101506
                  
                   
                     101599
                  
                   
                     101692
                  
                   
                     101785
                  
                   
                     101878
                  
                   
                     101971
                  
                   
                     102064
                  
                   
                     102157
                  
                   
                     101250
                  
                   
                     93
                  
                
                 
                   
                     159
                  
                   
                     102343
                  
                   
                     102436
                  
                   
                     102529
                  
                   
                     102622
                  
                   
                     102715
                  
                   
                     102809
                  
                   
                     102902
                  
                   
                     102995
                  
                   
                     103088
                  
                   
                     103182
                  
                   
                     93
                  
                
                 
                   
                     160
                  
                   
                     103275
                  
                   
                     103368
                  
                   
                     103462
                  
                   
                     103555
                  
                   
                     103649
                  
                   
                     103742
                  
                   
                     103836
                  
                   
                     103929
                  
                   
                     104023
                  
                   
                     104116
                  
                   
                     93
                  
                
                 
                   
                     161
                  
                   
                     104210
                  
                   
                     104304
                  
                   
                     104397
                  
                   
                     104491
                  
                   
                     104584
                  
                   
                     104678
                  
                   
                     104772
                  
                   
                     104866
                  
                   
                     104959
                  
                   
                     105053
                  
                   
                     94
                  
                
                 
                   
                     162
                  
                   
                     105147
                  
                   
                     105241
                  
                   
                     105335
                  
                   
                     105429
                  
                   
                     105523
                  
                   
                     105617
                  
                   
                     105711
                  
                   
                     105805
                  
                   
                     105899
                  
                   
                     105991
                  
                   
                     94
                  
                
                 
                   
                     193
                  
                   
                     106087
                  
                   
                     106181
                  
                   
                     106275
                  
                   
                     106369
                  
                   
                     106463
                  
                   
                     106557
                  
                   
                     106651
                  
                   
                     106745
                  
                   
                     106840
                  
                   
                     106934
                  
                   
                     94
                  
                
                 
                   
                     164
                  
                   
                     107028
                  
                   
                     107122
                  
                   
                     107217
                  
                   
                     107311
                  
                   
                     107406
                  
                   
                     107500
                  
                   
                     107594
                  
                   
                     107689
                  
                   
                     107783
                  
                   
                     107878
                  
                   
                     94
                  
                
                 
                   
                     165
                  
                   
                     107972
                  
                   
                     108067
                  
                   
                     108161
                  
                   
                     108256
                  
                   
                     108350
                  
                   
                     108445
                  
                   
                     108540
                  
                   
                     108634
                  
                   
                     108727
                  
                   
                     108824
                  
                   
                     95
                  
                
                 
                   
                     166
                  
                   
                     108919
                  
                   
                     109013
                  
                   
                     109108
                  
                   
                     109203
                  
                   
                     109298
                  
                   
                     109393
                  
                   
                     109488
                  
                   
                     109583
                  
                   
                     109678
                  
                   
                     109773
                  
                   
                     95
                  
                
                 
                   
                     
                     166
                  
                   
                     108919
                  
                   
                     109013
                  
                   
                     109108
                  
                   
                     109203
                  
                   
                     109298
                  
                   
                     109392
                  
                   
                     109487
                  
                   
                     109683
                  
                   
                     109677
                  
                   
                     109773
                  
                   
                     95
                  
                
                 
                   
                     167
                  
                   
                     109867
                  
                   
                     109963
                  
                   
                     110058
                  
                   
                     110153
                  
                   
                     110248
                  
                   
                     110343
                  
                   
                     110438
                  
                   
                     110533
                  
                   
                     110628
                  
                   
                     110723
                  
                   
                     95
                  
                
                 
                   
                     168
                  
                   
                     110818
                  
                   
                     110913
                  
                   
                     111009
                  
                   
                     111104
                  
                   
                     111295
                  
                   
                     111390
                  
                   
                     111485
                  
                   
                     111485
                  
                   
                     111581
                  
                   
                     111676
                  
                   
                     95
                  
                
                 
                   
                     169
                  
                   
                     111772
                  
                   
                     111867
                  
                   
                     111963
                  
                   
                     112058
                  
                   
                     112154
                  
                   
                     112249
                  
                   
                     112344
                  
                   
                     112440
                  
                   
                     112535
                  
                   
                     112631
                  
                   
                     96
                  
                
                 
                   
                     170
                  
                   
                     112726
                  
                   
                     112822
                  
                   
                     112918
                  
                   
                     113013
                  
                   
                     113109
                  
                   
                     113205
                  
                   
                     113301
                  
                   
                     113397
                  
                   
                     113492
                  
                   
                     113588
                  
                   
                     96
                  
                
                 
                   
                     171
                  
                   
                     113684
                  
                   
                     113780
                  
                   
                     113876
                  
                   
                     113972
                  
                   
                     114068
                  
                   
                     114164
                  
                   
                     114260
                  
                   
                     114356
                  
                   
                     114452
                  
                   
                     114548
                  
                   
                     96
                  
                
                 
                   
                     172
                  
                   
                     114644
                  
                   
                     114740
                  
                   
                     114836
                  
                   
                     114932
                  
                   
                     115028
                  
                   
                     115125
                  
                   
                     115221
                  
                   
                     115318
                  
                   
                     115414
                  
                   
                     115511
                  
                   
                     96
                  
                
                 
                   
                     173
                  
                   
                     115607
                  
                   
                     115703
                  
                   
                     115799
                  
                   
                     115896
                  
                   
                     115992
                  
                   
                     116088
                  
                   
                     116184
                  
                   
                     116281
                  
                   
                     116377
                  
                   
                     116473
                  
                   
                     97
                  
                
                 
                   
                     174
                  
                   
                     116570
                  
                   
                     116666
                  
                   
                     116763
                  
                   
                     116860
                  
                   
                     116956
                  
                   
                     117053
                  
                   
                     117150
                  
                   
                     117246
                  
                   
                     117343
                  
                   
                     117439
                  
                   
                     97
                  
                
                 
                   
                     175
                  
                   
                     117536
                  
                   
                     117633
                  
                   
                     117730
                  
                   
                     117827
                  
                   
                     117924
                  
                   
                     118021
                  
                   
                     118118
                  
                   
                     118215
                  
                   
                     118312
                  
                   
                     118409
                  
                   
                     97
                  
                
                 
                   
                     176
                  
                   
                     118506
                  
                   
                     118603
                  
                   
                     118700
                  
                   
                     118797
                  
                   
                     118894
                  
                   
                     118991
                  
                   
                     119088
                  
                   
                     119185
                  
                   
                     119282
                  
                   
                     119379
                  
                   
                     97
                  
                
                 
                   
                     177
                  
                   
                     119476
                  
                   
                     119574
                  
                   
                     119671
                  
                   
                     119768
                  
                   
                     119866
                  
                   
                     119963
                  
                   
                     120060
                  
                   
                     120158
                  
                   
                     120255
                  
                   
                     120352
                  
                   
                     97
                  
                
                 
                   
                     178
                  
                   
                     120449
                  
                   
                     120547
                  
                   
                     120644
                  
                   
                     120742
                  
                   
                     120839
                  
                   
                     120936
                  
                   
                     121034
                  
                   
                     121132
                  
                   
                     121229
                  
                   
                     121327
                  
                   
                     98
                  
                
                 
                   
                     179
                  
                   
                     121424
                  
                   
                     121562
                  
                   
                     121620
                  
                   
                     121717
                  
                   
                     121815
                  
                   
                     121913
                  
                   
                     122010
                  
                   
                     122108
                  
                   
                     122206
                  
                   
                     122304
                  
                   
                     98
                  
                
                 
                   
                     180
                  
                   
                     122402
                  
                   
                     122500
                  
                   
                     122597
                  
                   
                     122696
                  
                   
                     122794
                  
                   
                     122892
                  
                   
                     122990
                  
                   
                     123088
                  
                   
                     123186
                  
                   
                     123284
                  
                   
                     98
                  
                
                 
                   
                     181
                  
                   
                     123382
                  
                   
                     123480
                  
                   
                     123578
                  
                   
                     123676
                  
                   
                     123774
                  
                   
                     123872
                  
                   
                     123970
                  
                   
                     124068
                  
                   
                     124167
                  
                   
                     124265
                  
                   
                     98
                  
                
                 
                   
                     182
                  
                   
                     124363
                  
                   
                     124461
                  
                   
                     124560
                  
                   
                     124658
                  
                   
                     124756
                  
                   
                     124855
                  
                   
                     124953
                  
                   
                     125051
                  
                   
                     125150
                  
                   
                     125248
                  
                   
                     98
                  
                
                 
                   
                     183
                  
                   
                     125347
                  
                   
                     125445
                  
                   
                     125544
                  
                   
                     125642
                  
                   
                     125741
                  
                   
                     125840
                  
                   
                     125938
                  
                   
                     126037
                  
                   
                     126136
                  
                   
                     126234
                  
                   
                     98
                  
                
                 
                   
                     184
                  
                   
                     126333
                  
                   
                     126432
                  
                   
                     126530
                  
                   
                     126629
                  
                   
                     126728
                  
                   
                     126827
                  
                   
                     126925
                  
                   
                     127024
                  
                   
                     127123
                  
                   
                     127221
                  
                   
                     99
                  
                
                 
                   
                     185
                  
                   
                     127320
                  
                   
                     127419
                  
                   
                     127518
                  
                   
                     127617
                  
                   
                     127716
                  
                   
                     127815
                  
                   
                     127914
                  
                   
                     128013
                  
                   
                     128112
                  
                   
                     128211
                  
                   
                     99
                  
                
                 
                   
                     186
                  
                   
                     128310
                  
                   
                     128409
                  
                   
                     128508
                  
                   
                     128607
                  
                   
                     128706
                  
                   
                     128805
                  
                   
                     128905
                  
                   
                     129004
                  
                   
                     129103
                  
                   
                     129202
                  
                   
                     99
                  
                
                 
                   
                     187
                  
                   
                     129302
                  
                   
                     129401
                  
                   
                     129500
                  
                   
                     129600
                  
                   
                     129699
                  
                   
                     129799
                  
                   
                     129897
                  
                   
                     139997
                  
                   
                     130096
                  
                   
                     130196
                  
                   
                     99
                  
                
                 
                   
                     188
                  
                   
                     130296
                  
                   
                     130395
                  
                   
                     130495
                  
                   
                     130594
                  
                   
                     130694
                  
                   
                     130794
                  
                   
                     130893
                  
                   
                     130993
                  
                   
                     131093
                  
                   
                     131192
                  
                   
                     100
                  
                
                 
                   
                     189
                  
                   
                     131292
                  
                   
                     131392
                  
                   
                     131491
                  
                   
                     131591
                  
                   
                     131691
                  
                   
                     131791
                  
                   
                     131890
                  
                   
                     131990
                  
                   
                     132090
                  
                   
                     132190
                  
                   
                     100
                  
                
                 
                   
                     190
                  
                   
                     132290
                  
                   
                     132390
                  
                   
                     132490
                  
                   
                     132590
                  
                   
                     132690
                  
                   
                     132790
                  
                   
                     132890
                  
                   
                     132990
                  
                   
                     133090
                  
                   
                     133190
                  
                   
                     100
                  
                
                 
                   
                     191
                  
                   
                     133290
                  
                   
                     133390
                  
                   
                     133490
                  
                   
                     133590
                  
                   
                     133690
                  
                   
                     133790
                  
                   
                     133890
                  
                   
                     133990
                  
                   
                     134090
                  
                   
                     134191
                  
                   
                     100
                  
                
                 
                   
                     192
                  
                   
                     134292
                  
                   
                     134392
                  
                   
                     134492
                  
                   
                     134593
                  
                   
                     134693
                  
                   
                     134794
                  
                   
                     134894
                  
                   
                     134994
                  
                   
                     135095
                  
                   
                     135195
                  
                   
                     100
                  
                
                 
                   
                     193
                  
                   
                     135296
                  
                   
                     135396
                  
                   
                     135497
                  
                   
                     135597
                  
                   
                     135697
                  
                   
                     135798
                  
                   
                     135899
                  
                   
                     135999
                  
                   
                     136100
                  
                   
                     136201
                  
                   
                     101
                  
                
                 
                   
                     194
                  
                   
                     136302
                  
                   
                     136402
                  
                   
                     136503
                  
                   
                     136604
                  
                   
                     136704
                  
                   
                     136805
                  
                   
                     136906
                  
                   
                     137007
                  
                   
                     137108
                  
                   
                     137209
                  
                   
                     101
                  
                
                 
                   
                     195
                  
                   
                     137310
                  
                   
                     137410
                  
                   
                     137511
                  
                   
                     137612
                  
                   
                     137713
                  
                   
                     137814
                  
                   
                     137915
                  
                   
                     138016
                  
                   
                     138117
                  
                   
                     138218
                  
                   
                     101
                  
                
                 
                   
                     196
                  
                   
                     138320
                  
                   
                     138421
                  
                   
                     138522
                  
                   
                     138623
                  
                   
                     138724
                  
                   
                     138825
                  
                   
                     138926
                  
                   
                     139027
                  
                   
                     139129
                  
                   
                     139230
                  
                   
                     101
                  
                
                 
                   
                     197
                  
                   
                     139331
                  
                   
                     139432
                  
                   
                     139534
                  
                   
                     139635
                  
                   
                     139737
                  
                   
                     139838
                  
                   
                     139939
                  
                   
                     140041
                  
                   
                     140142
                  
                   
                     140244
                  
                   
                     101
                  
                
                 
                   
                     198
                  
                   
                     140345
                  
                   
                     140447
                  
                   
                     140548
                  
                   
                     140650
                  
                   
                     140751
                  
                   
                     140853
                  
                   
                     140954
                  
                   
                     141055
                  
                   
                     141157
                  
                   
                     141259
                  
                   
                     101
                  
                
                 
                   
                     199
                  
                   
                     141361
                  
                   
                     141462
                  
                   
                     141564
                  
                   
                     141665
                  
                   
                     141767
                  
                   
                     141869
                  
                   
                     141970
                  
                   
                     142072
                  
                   
                     142174
                  
                   
                     142276
                  
                   
                     102
                  
                
                 
                   
                     
                     200
                  
                   
                     142378
                  
                   
                     142480
                  
                   
                     142582
                  
                   
                     142684
                  
                   
                     142786
                  
                   
                     142888
                  
                   
                     142990
                  
                   
                     143092
                  
                   
                     143194
                  
                   
                     143296
                  
                   
                     102
                  
                
                 
                   
                     201
                  
                   
                     143398
                  
                   
                     142500
                  
                   
                     143602
                  
                   
                     143704
                  
                   
                     143806
                  
                   
                     143909
                  
                   
                     144011
                  
                   
                     144113
                  
                   
                     144215
                  
                   
                     144317
                  
                   
                     10●
                  
                
                 
                   
                     202
                  
                   
                     144419
                  
                   
                     144521
                  
                   
                     144624
                  
                   
                     144726
                  
                   
                     144828
                  
                   
                     144931
                  
                   
                     145033
                  
                   
                     145135
                  
                   
                     145238
                  
                   
                     145340
                  
                   
                     102
                  
                
                 
                   
                     203
                  
                   
                     145443
                  
                   
                     145545
                  
                   
                     145648
                  
                   
                     145750
                  
                   
                     145853
                  
                   
                     145955
                  
                   
                     146058
                  
                   
                     146160
                  
                   
                     146263
                  
                   
                     146365
                  
                   
                     102
                  
                
                 
                   
                     204
                  
                   
                     146468
                  
                   
                     146571
                  
                   
                     146673
                  
                   
                     146776
                  
                   
                     146878
                  
                   
                     146981
                  
                   
                     147084
                  
                   
                     147187
                  
                   
                     147289
                  
                   
                     147392
                  
                   
                     102
                  
                
                 
                   
                     205
                  
                   
                     147495
                  
                   
                     147598
                  
                   
                     147701
                  
                   
                     147803
                  
                   
                     147906
                  
                   
                     148009
                  
                   
                     148112
                  
                   
                     148215
                  
                   
                     148318
                  
                   
                     141421
                  
                   
                     103
                  
                
                 
                   
                     206
                  
                   
                     148524
                  
                   
                     148627
                  
                   
                     148730
                  
                   
                     148833
                  
                   
                     148936
                  
                   
                     149039
                  
                   
                     149142
                  
                   
                     149245
                  
                   
                     149348
                  
                   
                     149451
                  
                   
                     103
                  
                
                 
                   
                     207
                  
                   
                     149555
                  
                   
                     149658
                  
                   
                     149761
                  
                   
                     149864
                  
                   
                     149967
                  
                   
                     150071
                  
                   
                     150174
                  
                   
                     150277
                  
                   
                     150387
                  
                   
                     150484
                  
                   
                     103
                  
                
                 
                   
                     208
                  
                   
                     150588
                  
                   
                     150691
                  
                   
                     150794
                  
                   
                     150898
                  
                   
                     151001
                  
                   
                     151105
                  
                   
                     151208
                  
                   
                     151312
                  
                   
                     151415
                  
                   
                     151519
                  
                   
                     103
                  
                
                 
                   
                     709
                  
                   
                     151623
                  
                   
                     151726
                  
                   
                     151829
                  
                   
                     151933
                  
                   
                     151037
                  
                   
                     152141
                  
                   
                     152244
                  
                   
                     152348
                  
                   
                     152452
                  
                   
                     152555
                  
                   
                     103
                  
                
                 
                   
                     210
                  
                   
                     152659
                  
                   
                     152762
                  
                   
                     152866
                  
                   
                     152970
                  
                   
                     153074
                  
                   
                     153178
                  
                   
                     153281
                  
                   
                     153385
                  
                   
                     153489
                  
                   
                     153592
                  
                   
                     103
                  
                
                 
                   
                     211
                  
                   
                     153696
                  
                   
                     153800
                  
                   
                     153903
                  
                   
                     154009
                  
                   
                     154111
                  
                   
                     154215
                  
                   
                     154319
                  
                   
                     154423
                  
                   
                     154523
                  
                   
                     154632
                  
                   
                     103
                  
                
                 
                   
                     212
                  
                   
                     154736
                  
                   
                     154840
                  
                   
                     154944
                  
                   
                     155048
                  
                   
                     155152
                  
                   
                     155257
                  
                   
                     155361
                  
                   
                     155465
                  
                   
                     155569
                  
                   
                     155674
                  
                   
                     104
                  
                
                 
                   
                     213
                  
                   
                     155778
                  
                   
                     155882
                  
                   
                     155987
                  
                   
                     156092
                  
                   
                     156195
                  
                   
                     156300
                  
                   
                     156404
                  
                   
                     156508
                  
                   
                     156613
                  
                   
                     156717
                  
                   
                     104
                  
                
                 
                   
                     214
                  
                   
                     156822
                  
                   
                     156926
                  
                   
                     157030
                  
                   
                     157135
                  
                   
                     157239
                  
                   
                     157344
                  
                   
                     157448
                  
                   
                     157553
                  
                   
                     157657
                  
                   
                     157762
                  
                   
                     104
                  
                
                 
                   
                     215
                  
                   
                     157867
                  
                   
                     157971
                  
                   
                     158076
                  
                   
                     158180
                  
                   
                     158285
                  
                   
                     158390
                  
                   
                     158494
                  
                   
                     158599
                  
                   
                     158704
                  
                   
                     158809
                  
                   
                     105
                  
                
                 
                   
                     216
                  
                   
                     158914
                  
                   
                     159018
                  
                   
                     159123
                  
                   
                     159228
                  
                   
                     159333
                  
                   
                     159438
                  
                   
                     159453
                  
                   
                     159648
                  
                   
                     159753
                  
                   
                     159858
                  
                   
                     105
                  
                
                 
                   
                     217
                  
                   
                     159963
                  
                   
                     160068
                  
                   
                     160173
                  
                   
                     160278
                  
                   
                     160383
                  
                   
                     160488
                  
                   
                     160593
                  
                   
                     160698
                  
                   
                     160803
                  
                   
                     160908
                  
                   
                     105
                  
                
                 
                   
                     218
                  
                   
                     161013
                  
                   
                     161118
                  
                   
                     161223
                  
                   
                     161329
                  
                   
                     161434
                  
                   
                     161539
                  
                   
                     161644
                  
                   
                     161749
                  
                   
                     161855
                  
                   
                     161959
                  
                   
                     105
                  
                
                 
                   
                     219
                  
                   
                     162065
                  
                   
                     162170
                  
                   
                     162276
                  
                   
                     162387
                  
                   
                     162487
                  
                   
                     162592
                  
                   
                     162697
                  
                   
                     162803
                  
                   
                     162908
                  
                   
                     162014
                  
                   
                     105
                  
                
                 
                   
                     220
                  
                   
                     163119
                  
                   
                     163225
                  
                   
                     163330
                  
                   
                     163436
                  
                   
                     163542
                  
                   
                     163648
                  
                   
                     163753
                  
                   
                     163859
                  
                   
                     163964
                  
                   
                     164070
                  
                   
                     106
                  
                
                 
                   
                     221
                  
                   
                     164176
                  
                   
                     164281
                  
                   
                     164387
                  
                   
                     164493
                  
                   
                     164598
                  
                   
                     164704
                  
                   
                     164810
                  
                   
                     164916
                  
                   
                     165021
                  
                   
                     165127
                  
                   
                     106
                  
                
                 
                   
                     222
                  
                   
                     165233
                  
                   
                     165339
                  
                   
                     165445
                  
                   
                     165550
                  
                   
                     165656
                  
                   
                     165762
                  
                   
                     165868
                  
                   
                     165974
                  
                   
                     166080
                  
                   
                     166186
                  
                   
                     106
                  
                
                 
                   
                     223
                  
                   
                     166292
                  
                   
                     166398
                  
                   
                     166504
                  
                   
                     166610
                  
                   
                     166716
                  
                   
                     166822
                  
                   
                     166928
                  
                   
                     167034
                  
                   
                     167141
                  
                   
                     167247
                  
                   
                     106
                  
                
                 
                   
                     224
                  
                   
                     167353
                  
                   
                     167459
                  
                   
                     167565
                  
                   
                     167672
                  
                   
                     167778
                  
                   
                     167884
                  
                   
                     167990
                  
                   
                     168096
                  
                   
                     168203
                  
                   
                     168309
                  
                   
                     106
                  
                
                 
                   
                     225
                  
                   
                     168415
                  
                   
                     168521
                  
                   
                     168521
                  
                   
                     168734
                  
                   
                     168841
                  
                   
                     168947
                  
                   
                     169053
                  
                   
                     169160
                  
                   
                     169266
                  
                   
                     169373
                  
                   
                     107
                  
                
                 
                   
                     226
                  
                   
                     169479
                  
                   
                     169586
                  
                   
                     169692
                  
                   
                     169799
                  
                   
                     169905
                  
                   
                     170012
                  
                   
                     170119
                  
                   
                     170225
                  
                   
                     120332
                  
                   
                     170438
                  
                   
                     107
                  
                
                 
                   
                     227
                  
                   
                     170545
                  
                   
                     170652
                  
                   
                     170758
                  
                   
                     170865
                  
                   
                     170972
                  
                   
                     171079
                  
                   
                     171185
                  
                   
                     171292
                  
                   
                     171399
                  
                   
                     171506
                  
                   
                     107
                  
                
                 
                   
                     228
                  
                   
                     171613
                  
                   
                     171719
                  
                   
                     171826
                  
                   
                     171933
                  
                   
                     172040
                  
                   
                     172147
                  
                   
                     172254
                  
                   
                     172361
                  
                   
                     172468
                  
                   
                     172575
                  
                   
                     107
                  
                
                 
                   
                     229
                  
                   
                     172682
                  
                   
                     172789
                  
                   
                     172896
                  
                   
                     173003
                  
                   
                     173110
                  
                   
                     173217
                  
                   
                     173324
                  
                   
                     173431
                  
                   
                     173538
                  
                   
                     173645
                  
                   
                     107
                  
                
                 
                   
                     230
                  
                   
                     173753
                  
                   
                     173860
                  
                   
                     173967
                  
                   
                     174074
                  
                   
                     174181
                  
                   
                     174289
                  
                   
                     174396
                  
                   
                     174503
                  
                   
                     174610
                  
                   
                     174718
                  
                   
                     107
                  
                
                 
                   
                     231
                  
                   
                     174825
                  
                   
                     174932
                  
                   
                     175040
                  
                   
                     175147
                  
                   
                     175255
                  
                   
                     175362
                  
                   
                     175469
                  
                   
                     175577
                  
                   
                     175684
                  
                   
                     175792
                  
                   
                     107
                  
                
                 
                   
                     232
                  
                   
                     175899
                  
                   
                     176007
                  
                   
                     176114
                  
                   
                     176222
                  
                   
                     176329
                  
                   
                     176437
                  
                   
                     176554
                  
                   
                     176652
                  
                   
                     176759
                  
                   
                     176867
                  
                   
                     108
                  
                
                 
                   
                     233
                  
                   
                     176975
                  
                   
                     177082
                  
                   
                     177190
                  
                   
                     177298
                  
                   
                     177405
                  
                   
                     177513
                  
                   
                     177621
                  
                   
                     177729
                  
                   
                     177836
                  
                   
                     177944
                  
                   
                     108
                  
                
                 
                   
                     
                  
                   
                     0
                  
                   
                     1
                  
                   
                     2
                  
                   
                     3
                  
                   
                     4
                  
                   
                     5
                  
                   
                     6
                  
                   
                     7
                  
                   
                     8
                  
                   
                     9
                  
                   
                      
                  
                
                 
                   
                     233
                  
                   
                     176975
                  
                   
                     177082
                  
                   
                     177190
                  
                   
                     177298
                  
                   
                     177405
                  
                   
                     177513
                  
                   
                     177621
                  
                   
                     177729
                  
                   
                     177836
                  
                   
                     177944
                  
                   
                     108
                  
                
                 
                   
                     234
                  
                   
                     178052
                  
                   
                     178160
                  
                   
                     178268
                  
                   
                     178375
                  
                   
                     178483
                  
                   
                     178591
                  
                   
                     178699
                  
                   
                     178807
                  
                   
                     178915
                  
                   
                     179027
                  
                   
                     108
                  
                
                 
                   
                     235
                  
                   
                     179131
                  
                   
                     179239
                  
                   
                     179347
                  
                   
                     179455
                  
                   
                     179563
                  
                   
                     179672
                  
                   
                     179780
                  
                   
                     179888
                  
                   
                     179996
                  
                   
                     180104
                  
                   
                     108
                  
                
                 
                   
                     236
                  
                   
                     180212
                  
                   
                     180320
                  
                   
                     180428
                  
                   
                     180536
                  
                   
                     180644
                  
                   
                     180752
                  
                   
                     180860
                  
                   
                     180969
                  
                   
                     181077
                  
                   
                     181085
                  
                   
                     108
                  
                
                 
                   
                     237
                  
                   
                     181294
                  
                   
                     181402
                  
                   
                     181510
                  
                   
                     181618
                  
                   
                     181727
                  
                   
                     181835
                  
                   
                     181943
                  
                   
                     182052
                  
                   
                     182160
                  
                   
                     182269
                  
                   
                     108
                  
                
                 
                   
                     238
                  
                   
                     182377
                  
                   
                     182486
                  
                   
                     182594
                  
                   
                     182703
                  
                   
                     182811
                  
                   
                     182920
                  
                   
                     183028
                  
                   
                     183137
                  
                   
                     183245
                  
                   
                     183354
                  
                   
                     108
                  
                
                 
                   
                     239
                  
                   
                     183462
                  
                   
                     183571
                  
                   
                     183680
                  
                   
                     183788
                  
                   
                     183897
                  
                   
                     184006
                  
                   
                     184114
                  
                   
                     184223
                  
                   
                     184332
                  
                   
                     184440
                  
                   
                     109
                  
                
                 
                   
                     240
                  
                   
                     184549
                  
                   
                     184658
                  
                   
                     184767
                  
                   
                     184875
                  
                   
                     184984
                  
                   
                     185093
                  
                   
                     185202
                  
                   
                     185311
                  
                   
                     185419
                  
                   
                     185528
                  
                   
                     109
                  
                
                 
                   
                     241
                  
                   
                     185637
                  
                   
                     185746
                  
                   
                     185855
                  
                   
                     185964
                  
                   
                     186073
                  
                   
                     186182
                  
                   
                     186291
                  
                   
                     186400
                  
                   
                     186509
                  
                   
                     186618
                  
                   
                     109
                  
                
                 
                   
                     242
                  
                   
                     186728
                  
                   
                     186837
                  
                   
                     186946
                  
                   
                     187055
                  
                   
                     187164
                  
                   
                     187273
                  
                   
                     187382
                  
                   
                     187491
                  
                   
                     187600
                  
                   
                     187709
                  
                   
                     109
                  
                
                 
                   
                     243
                  
                   
                     187819
                  
                   
                     187928
                  
                   
                     188037
                  
                   
                     188146
                  
                   
                     188256
                  
                   
                     188365
                  
                   
                     188474
                  
                   
                     188584
                  
                   
                     188693
                  
                   
                     188802
                  
                   
                     109
                  
                
                 
                   
                     244
                  
                   
                     188911
                  
                   
                     189021
                  
                   
                     189130
                  
                   
                     189240
                  
                   
                     189349
                  
                   
                     189458
                  
                   
                     189568
                  
                   
                     189677
                  
                   
                     189787
                  
                   
                     189896
                  
                   
                     109
                  
                
                 
                   
                     245
                  
                   
                     199006
                  
                   
                     190116
                  
                   
                     190225
                  
                   
                     190335
                  
                   
                     190444
                  
                   
                     190554
                  
                   
                     190664
                  
                   
                     190773
                  
                   
                     190883
                  
                   
                     190992
                  
                   
                     110
                  
                
                 
                   
                     246
                  
                   
                     191102
                  
                   
                     191212
                  
                   
                     191322
                  
                   
                     191431
                  
                   
                     191541
                  
                   
                     191651
                  
                   
                     191761
                  
                   
                     191871
                  
                   
                     191980
                  
                   
                     192090
                  
                   
                     110
                  
                
                 
                   
                     247
                  
                   
                     192200
                  
                   
                     192310
                  
                   
                     192420
                  
                   
                     192529
                  
                   
                     192639
                  
                   
                     192749
                  
                   
                     192859
                  
                   
                     192969
                  
                   
                     193079
                  
                   
                     193189
                  
                   
                     110
                  
                
                 
                   
                     248
                  
                   
                     193298
                  
                   
                     193408
                  
                   
                     193518
                  
                   
                     193628
                  
                   
                     193738
                  
                   
                     193848
                  
                   
                     193958
                  
                   
                     194068
                  
                   
                     194178
                  
                   
                     194288
                  
                   
                     110
                  
                
                 
                   
                     249
                  
                   
                     194399
                  
                   
                     194509
                  
                   
                     194619
                  
                   
                     194729
                  
                   
                     194839
                  
                   
                     194949
                  
                   
                     195059
                  
                   
                     195169
                  
                   
                     195279
                  
                   
                     195389
                  
                   
                     110
                  
                
                 
                   
                     250
                  
                   
                     195500
                  
                   
                     195611
                  
                   
                     195721
                  
                   
                     195831
                  
                   
                     195942
                  
                   
                     196052
                  
                   
                     196163
                  
                   
                     196273
                  
                   
                     196384
                  
                   
                     196494
                  
                   
                     110
                  
                
                 
                   
                     251
                  
                   
                     196605
                  
                   
                     196715
                  
                   
                     196826
                  
                   
                     196936
                  
                   
                     197047
                  
                   
                     197157
                  
                   
                     197268
                  
                   
                     197378
                  
                   
                     197489
                  
                   
                     197599
                  
                   
                     110
                  
                
                 
                   
                     252
                  
                   
                     197710
                  
                   
                     197821
                  
                   
                     197931
                  
                   
                     198041
                  
                   
                     198152
                  
                   
                     198262
                  
                   
                     198373
                  
                   
                     198484
                  
                   
                     198594
                  
                   
                     198705
                  
                   
                     110
                  
                
                 
                   
                     253
                  
                   
                     198815
                  
                   
                     198926
                  
                   
                     199037
                  
                   
                     199148
                  
                   
                     199258
                  
                   
                     199369
                  
                   
                     199480
                  
                   
                     199591
                  
                   
                     199701
                  
                   
                     199812
                  
                   
                     111
                  
                
                 
                   
                     254
                  
                   
                     199923
                  
                   
                     200034
                  
                   
                     200145
                  
                   
                     200256
                  
                   
                     200367
                  
                   
                     200478
                  
                   
                     200●88
                  
                   
                     200699
                  
                   
                     200811
                  
                   
                     200921
                  
                   
                     111
                  
                
                 
                   
                     255
                  
                   
                     201032
                  
                   
                     201144
                  
                   
                     201255
                  
                   
                     201366
                  
                   
                     201477
                  
                   
                     201587
                  
                   
                     201699
                  
                   
                     201810
                  
                   
                     201921
                  
                   
                     202032
                  
                   
                     111
                  
                
                 
                   
                     256
                  
                   
                     202143
                  
                   
                     202254
                  
                   
                     202365
                  
                   
                     202477
                  
                   
                     202588
                  
                   
                     202699
                  
                   
                     202810
                  
                   
                     202921
                  
                   
                     203033
                  
                   
                     203144
                  
                   
                     111
                  
                
                 
                   
                     257
                  
                   
                     203255
                  
                   
                     203366
                  
                   
                     203478
                  
                   
                     203589
                  
                   
                     203700
                  
                   
                     203811
                  
                   
                     203922
                  
                   
                     204033
                  
                   
                     204145
                  
                   
                     204256
                  
                   
                     111
                  
                
                 
                   
                     258
                  
                   
                     204368
                  
                   
                     204480
                  
                   
                     204591
                  
                   
                     204703
                  
                   
                     204814
                  
                   
                     204926
                  
                   
                     205037
                  
                   
                     205149
                  
                   
                     205261
                  
                   
                     205372
                  
                   
                     111
                  
                
                 
                   
                     259
                  
                   
                     205483
                  
                   
                     205595
                  
                   
                     205707
                  
                   
                     205818
                  
                   
                     205930
                  
                   
                     206041
                  
                   
                     206153
                  
                   
                     206264
                  
                   
                     206376
                  
                   
                     206488
                  
                   
                     112
                  
                
                 
                   
                     260
                  
                   
                     206599
                  
                   
                     206711
                  
                   
                     206823
                  
                   
                     206935
                  
                   
                     207047
                  
                   
                     207158
                  
                   
                     207270
                  
                   
                     207382
                  
                   
                     207494
                  
                   
                     207606
                  
                   
                     112
                  
                
                 
                   
                     261
                  
                   
                     207717
                  
                   
                     207829
                  
                   
                     207941
                  
                   
                     208053
                  
                   
                     208165
                  
                   
                     208277
                  
                   
                     208389
                  
                   
                     208501
                  
                   
                     208613
                  
                   
                     208725
                  
                   
                     112
                  
                
                 
                   
                     262
                  
                   
                     208836
                  
                   
                     208948
                  
                   
                     209060
                  
                   
                     209172
                  
                   
                     209284
                  
                   
                     209396
                  
                   
                     209508
                  
                   
                     209620
                  
                   
                     209733
                  
                   
                     209845
                  
                   
                     112
                  
                
                 
                   
                     263
                  
                   
                     209957
                  
                   
                     210069
                  
                   
                     210181
                  
                   
                     210293
                  
                   
                     210405
                  
                   
                     210517
                  
                   
                     210630
                  
                   
                     210742
                  
                   
                     210854
                  
                   
                     210966
                  
                   
                     112
                  
                
                 
                   
                     264
                  
                   
                     211078
                  
                   
                     211191
                  
                   
                     211303
                  
                   
                     211415
                  
                   
                     211528
                  
                   
                     211640
                  
                   
                     211752
                  
                   
                     211865
                  
                   
                     211977
                  
                   
                     212089
                  
                   
                     112
                  
                
                 
                   
                     265
                  
                   
                     212202
                  
                   
                     212314
                  
                   
                     212427
                  
                   
                     212539
                  
                   
                     212651
                  
                   
                     212763
                  
                   
                     212876
                  
                   
                     212989
                  
                   
                     213101
                  
                   
                     213214
                  
                   
                     112
                  
                
                 
                   
                     266
                  
                   
                     213326
                  
                   
                     213439
                  
                   
                     213552
                  
                   
                     213665
                  
                   
                     213778
                  
                   
                     222891
                  
                   
                     214003
                  
                   
                     214115
                  
                   
                     214227
                  
                   
                     214340
                  
                   
                     113
                  
                
                 
                   
                     
                     266
                  
                   
                     213326
                  
                   
                     213439
                  
                   
                     213552
                  
                   
                     213665
                  
                   
                     2●●778
                  
                   
                     213891
                  
                   
                     214003
                  
                   
                     214115
                  
                   
                     214227
                  
                   
                     214340
                  
                   
                     112
                  
                
                 
                   
                     267
                  
                   
                     214452
                  
                   
                     214565
                  
                   
                     214677
                  
                   
                     214780
                  
                   
                     214893
                  
                   
                     214015
                  
                   
                     215128
                  
                   
                     215241
                  
                   
                     215354
                  
                   
                     215467
                  
                   
                     113
                  
                
                 
                   
                     268
                  
                   
                     215579
                  
                   
                     215692
                  
                   
                     215805
                  
                   
                     215918
                  
                   
                     216031
                  
                   
                     216143
                  
                   
                     216256
                  
                   
                     216369
                  
                   
                     216482
                  
                   
                     216595
                  
                   
                     113
                  
                
                 
                   
                     269
                  
                   
                     216708
                  
                   
                     216821
                  
                   
                     216934
                  
                   
                     217047
                  
                   
                     217160
                  
                   
                     217272
                  
                   
                     217386
                  
                   
                     217499
                  
                   
                     217612
                  
                   
                     217725
                  
                   
                     113
                  
                
                 
                   
                     270
                  
                   
                     217838
                  
                   
                     217951
                  
                   
                     218064
                  
                   
                     218177
                  
                   
                     218290
                  
                   
                     218403
                  
                   
                     218517
                  
                   
                     218630
                  
                   
                     218743
                  
                   
                     218856
                  
                   
                     113
                  
                
                 
                   
                     271
                  
                   
                     218969
                  
                   
                     219082
                  
                   
                     219195
                  
                   
                     219309
                  
                   
                     219422
                  
                   
                     219535
                  
                   
                     219648
                  
                   
                     219762
                  
                   
                     219875
                  
                   
                     219988
                  
                   
                     113
                  
                
                 
                   
                     272
                  
                   
                     220101
                  
                   
                     220215
                  
                   
                     220328
                  
                   
                     220442
                  
                   
                     220555
                  
                   
                     220668
                  
                   
                     220782
                  
                   
                     220895
                  
                   
                     221009
                  
                   
                     221122
                  
                   
                     113
                  
                
                 
                   
                     273
                  
                   
                     221235
                  
                   
                     221349
                  
                   
                     221462
                  
                   
                     221576
                  
                   
                     221689
                  
                   
                     221803
                  
                   
                     221916
                  
                   
                     222030
                  
                   
                     222143
                  
                   
                     222257
                  
                   
                     113
                  
                
                 
                   
                     274
                  
                   
                     222371
                  
                   
                     222484
                  
                   
                     222598
                  
                   
                     222711
                  
                   
                     222825
                  
                   
                     222538
                  
                   
                     223052
                  
                   
                     223166
                  
                   
                     223280
                  
                   
                     223393
                  
                   
                     114
                  
                
                 
                   
                     275
                  
                   
                     223507
                  
                   
                     223621
                  
                   
                     223734
                  
                   
                     223848
                  
                   
                     223962
                  
                   
                     224075
                  
                   
                     224189
                  
                   
                     224303
                  
                   
                     224417
                  
                   
                     224531
                  
                   
                     114
                  
                
                 
                   
                     276
                  
                   
                     224644
                  
                   
                     224754
                  
                   
                     224871
                  
                   
                     224986
                  
                   
                     225100
                  
                   
                     225214
                  
                   
                     225328
                  
                   
                     225442
                  
                   
                     225555
                  
                   
                     225670
                  
                   
                     114
                  
                
                 
                   
                     277
                  
                   
                     225784
                  
                   
                     225897
                  
                   
                     226011
                  
                   
                     226125
                  
                   
                     226239
                  
                   
                     226353
                  
                   
                     226467
                  
                   
                     226581
                  
                   
                     226695
                  
                   
                     226809
                  
                   
                     114
                  
                
                 
                   
                     278
                  
                   
                     226923
                  
                   
                     227038
                  
                   
                     227152
                  
                   
                     227266
                  
                   
                     227380
                  
                   
                     227494
                  
                   
                     227608
                  
                   
                     227723
                  
                   
                     227837
                  
                   
                     227951
                  
                   
                     114
                  
                
                 
                   
                     279
                  
                   
                     228065
                  
                   
                     228179
                  
                   
                     228294
                  
                   
                     228408
                  
                   
                     228522
                  
                   
                     228636
                  
                   
                     228751
                  
                   
                     228865
                  
                   
                     228979
                  
                   
                     229094
                  
                   
                     114
                  
                
                 
                   
                     280
                  
                   
                     229208
                  
                   
                     229322
                  
                   
                     229437
                  
                   
                     229551
                  
                   
                     229666
                  
                   
                     229780
                  
                   
                     229894
                  
                   
                     230009
                  
                   
                     230123
                  
                   
                     230238
                  
                   
                     114
                  
                
                 
                   
                     281
                  
                   
                     230352
                  
                   
                     230467
                  
                   
                     230581
                  
                   
                     230695
                  
                   
                     230810
                  
                   
                     230924
                  
                   
                     231039
                  
                   
                     231153
                  
                   
                     231268
                  
                   
                     231382
                  
                   
                     114
                  
                
                 
                   
                     282
                  
                   
                     231497
                  
                   
                     231612
                  
                   
                     231726
                  
                   
                     231841
                  
                   
                     231955
                  
                   
                     232070
                  
                   
                     232185
                  
                   
                     232299
                  
                   
                     232414
                  
                   
                     232529
                  
                   
                     115
                  
                
                 
                   
                     283
                  
                   
                     232644
                  
                   
                     232758
                  
                   
                     232873
                  
                   
                     232989
                  
                   
                     233103
                  
                   
                     233218
                  
                   
                     233332
                  
                   
                     233447
                  
                   
                     233562
                  
                   
                     233677
                  
                   
                     115
                  
                
                 
                   
                     284
                  
                   
                     233792
                  
                   
                     233906
                  
                   
                     234021
                  
                   
                     234136
                  
                   
                     234251
                  
                   
                     234366
                  
                   
                     234480
                  
                   
                     234595
                  
                   
                     234710
                  
                   
                     234825
                  
                   
                     115
                  
                
                 
                   
                     285
                  
                   
                     234946
                  
                   
                     235055
                  
                   
                     235170
                  
                   
                     235285
                  
                   
                     235400
                  
                   
                     235515
                  
                   
                     235630
                  
                   
                     235745
                  
                   
                     235860
                  
                   
                     235975
                  
                   
                     115
                  
                
                 
                   
                     286
                  
                   
                     236091
                  
                   
                     236206
                  
                   
                     236321
                  
                   
                     236436
                  
                   
                     236551
                  
                   
                     236666
                  
                   
                     236781
                  
                   
                     236896
                  
                   
                     237012
                  
                   
                     237127
                  
                   
                     115
                  
                
                 
                   
                     287
                  
                   
                     237242
                  
                   
                     237357
                  
                   
                     237472
                  
                   
                     237588
                  
                   
                     237703
                  
                   
                     237818
                  
                   
                     237933
                  
                   
                     238049
                  
                   
                     238164
                  
                   
                     238279
                  
                   
                     115
                  
                
                 
                   
                     288
                  
                   
                     238395
                  
                   
                     238510
                  
                   
                     238625
                  
                   
                     238740
                  
                   
                     238856
                  
                   
                     238971
                  
                   
                     239086
                  
                   
                     339202
                  
                   
                     239317
                  
                   
                     239433
                  
                   
                     115
                  
                
                 
                   
                     289
                  
                   
                     239548
                  
                   
                     239664
                  
                   
                     239779
                  
                   
                     239895
                  
                   
                     230010
                  
                   
                     240126
                  
                   
                     240241
                  
                   
                     240357
                  
                   
                     240472
                  
                   
                     240588
                  
                   
                     115
                  
                
                 
                   
                     290
                  
                   
                     240703
                  
                   
                     240819
                  
                   
                     240934
                  
                   
                     241050
                  
                   
                     241165
                  
                   
                     241281
                  
                   
                     241397
                  
                   
                     241522
                  
                   
                     241628
                  
                   
                     251753
                  
                   
                     116
                  
                
                 
                   
                     291
                  
                   
                     241859
                  
                   
                     241975
                  
                   
                     242090
                  
                   
                     242206
                  
                   
                     242322
                  
                   
                     242438
                  
                   
                     242553
                  
                   
                     242669
                  
                   
                     242785
                  
                   
                     242908
                  
                   
                     116
                  
                
                 
                   
                     292
                  
                   
                     243016
                  
                   
                     243132
                  
                   
                     243248
                  
                   
                     243364
                  
                   
                     243480
                  
                   
                     243595
                  
                   
                     243711
                  
                   
                     243827
                  
                   
                     243943
                  
                   
                     243059
                  
                   
                     116
                  
                
                 
                   
                     293
                  
                   
                     244175
                  
                   
                     244290
                  
                   
                     244496
                  
                   
                     244522
                  
                   
                     244638
                  
                   
                     244754
                  
                   
                     244870
                  
                   
                     244986
                  
                   
                     245102
                  
                   
                     245218
                  
                   
                     116
                  
                
                 
                   
                     294
                  
                   
                     245334
                  
                   
                     245450
                  
                   
                     245566
                  
                   
                     245682
                  
                   
                     245748
                  
                   
                     245915
                  
                   
                     246031
                  
                   
                     246147
                  
                   
                     246263
                  
                   
                     246379
                  
                   
                     116
                  
                
                 
                   
                     295
                  
                   
                     246495
                  
                   
                     246611
                  
                   
                     246727
                  
                   
                     246843
                  
                   
                     246959
                  
                   
                     247075
                  
                   
                     247192
                  
                   
                     247308
                  
                   
                     247424
                  
                   
                     247541
                  
                   
                     116
                  
                
                 
                   
                     296
                  
                   
                     247657
                  
                   
                     247773
                  
                   
                     247889
                  
                   
                     248006
                  
                   
                     248122
                  
                   
                     248238
                  
                   
                     248354
                  
                   
                     248471
                  
                   
                     248587
                  
                   
                     248704
                  
                   
                     116
                  
                
                 
                   
                     297
                  
                   
                     248820
                  
                   
                     248936
                  
                   
                     249053
                  
                   
                     249169
                  
                   
                     249285
                  
                   
                     249402
                  
                   
                     249518
                  
                   
                     249634
                  
                   
                     249751
                  
                   
                     249867
                  
                   
                     116
                  
                
                 
                   
                     298
                  
                   
                     249984
                  
                   
                     250101
                  
                   
                     250217
                  
                   
                     250334
                  
                   
                     250450
                  
                   
                     250567
                  
                   
                     250683
                  
                   
                     250799
                  
                   
                     250916
                  
                   
                     251033
                  
                   
                     117
                  
                
                 
                   
                     299
                  
                   
                     251149
                  
                   
                     251266
                  
                   
                     251382
                  
                   
                     251499
                  
                   
                     251615
                  
                   
                     251732
                  
                   
                     251849
                  
                   
                     251965
                  
                   
                     252082
                  
                   
                     252198
                  
                   
                     117
                  
                
                 
                   
                     
                     300
                  
                   
                     252315
                  
                   
                     252432
                  
                   
                     252549
                  
                   
                     252665
                  
                   
                     252782
                  
                   
                     252899
                  
                   
                     253016
                  
                   
                     253132
                  
                   
                     253249
                  
                   
                     253366
                  
                   
                     117
                  
                
                 
                   
                     301
                  
                   
                     253483
                  
                   
                     253599
                  
                   
                     253716
                  
                   
                     253833
                  
                   
                     253950
                  
                   
                     254067
                  
                   
                     254184
                  
                   
                     254301
                  
                   
                     254418
                  
                   
                     254535
                  
                   
                     117
                  
                
                 
                   
                     302
                  
                   
                     254652
                  
                   
                     254769
                  
                   
                     254886
                  
                   
                     255003
                  
                   
                     255119
                  
                   
                     255237
                  
                   
                     255353
                  
                   
                     255471
                  
                   
                     255588
                  
                   
                     255701
                  
                   
                     117
                  
                
                 
                   
                     303
                  
                   
                     255822
                  
                   
                     255939
                  
                   
                     256056
                  
                   
                     256173
                  
                   
                     256●89
                  
                   
                     256407
                  
                   
                     256524
                  
                   
                     256641
                  
                   
                     256758
                  
                   
                     256875
                  
                   
                     117
                  
                
                 
                   
                     304
                  
                   
                     256992
                  
                   
                     257109
                  
                   
                     257226
                  
                   
                     257344
                  
                   
                     257461
                  
                   
                     257573
                  
                   
                     257695
                  
                   
                     257812
                  
                   
                     257930
                  
                   
                     258047
                  
                   
                     117
                  
                
                 
                   
                     305
                  
                   
                     258164
                  
                   
                     258281
                  
                   
                     258398
                  
                   
                     258516
                  
                   
                     258633
                  
                   
                     258750
                  
                   
                     258867
                  
                   
                     258985
                  
                   
                     259102
                  
                   
                     259220
                  
                   
                     117
                  
                
                 
                   
                     306
                  
                   
                     259337
                  
                   
                     259454
                  
                   
                     259752
                  
                   
                     159689
                  
                   
                     259807
                  
                   
                     259924
                  
                   
                     259041
                  
                   
                     260159
                  
                   
                     260276
                  
                   
                     260394
                  
                   
                     117
                  
                
                 
                   
                     307
                  
                   
                     260511
                  
                   
                     260269
                  
                   
                     250746
                  
                   
                     260864
                  
                   
                     260981
                  
                   
                     261099
                  
                   
                     261216
                  
                   
                     261334
                  
                   
                     261451
                  
                   
                     261569
                  
                   
                     117
                  
                
                 
                   
                     308
                  
                   
                     261686
                  
                   
                     261803
                  
                   
                     251921
                  
                   
                     262039
                  
                   
                     262156
                  
                   
                     262274
                  
                   
                     262392
                  
                   
                     262509
                  
                   
                     262627
                  
                   
                     262744
                  
                   
                     117
                  
                
                 
                   
                     309
                  
                   
                     262862
                  
                   
                     262980
                  
                   
                     253097
                  
                   
                     263215
                  
                   
                     263332
                  
                   
                     263540
                  
                   
                     263568
                  
                   
                     263686
                  
                   
                     263804
                  
                   
                     263922
                  
                   
                     118
                  
                
                 
                   
                     310
                  
                   
                     264040
                  
                   
                     264157
                  
                   
                     264275
                  
                   
                     264393
                  
                   
                     264511
                  
                   
                     264269
                  
                   
                     264746
                  
                   
                     264864
                  
                   
                     264982
                  
                   
                     265100
                  
                   
                     118
                  
                
                 
                   
                     311
                  
                   
                     265218
                  
                   
                     265336
                  
                   
                     265454
                  
                   
                     265572
                  
                   
                     265690
                  
                   
                     265808
                  
                   
                     265925
                  
                   
                     266043
                  
                   
                     266161
                  
                   
                     266279
                  
                   
                     118
                  
                
                 
                   
                     312
                  
                   
                     266397
                  
                   
                     266515
                  
                   
                     266633
                  
                   
                     166751
                  
                   
                     266869
                  
                   
                     266987
                  
                   
                     267105
                  
                   
                     267223
                  
                   
                     267341
                  
                   
                     267459
                  
                   
                     118
                  
                
                 
                   
                     313
                  
                   
                     267578
                  
                   
                     267696
                  
                   
                     267814
                  
                   
                     267932
                  
                   
                     268050
                  
                   
                     268168
                  
                   
                     268286
                  
                   
                     268404
                  
                   
                     268522
                  
                   
                     268640
                  
                   
                     118
                  
                
                 
                   
                     314
                  
                   
                     268759
                  
                   
                     268877
                  
                   
                     268995
                  
                   
                     269113
                  
                   
                     269231
                  
                   
                     269349
                  
                   
                     269468
                  
                   
                     269586
                  
                   
                     269704
                  
                   
                     269823
                  
                   
                     118
                  
                
                 
                   
                     315
                  
                   
                     269941
                  
                   
                     270059
                  
                   
                     270177
                  
                   
                     270295
                  
                   
                     270413
                  
                   
                     270532
                  
                   
                     270650
                  
                   
                     270769
                  
                   
                     270887
                  
                   
                     271006
                  
                   
                      
                  
                
                 
                   
                     316
                  
                   
                     271124
                  
                   
                     271242
                  
                   
                     271361
                  
                   
                     271479
                  
                   
                     271598
                  
                   
                     271716
                  
                   
                     271835
                  
                   
                     271953
                  
                   
                     272072
                  
                   
                     272190
                  
                   
                      
                  
                
                 
                   
                     317
                  
                   
                     272●09
                  
                   
                     272427
                  
                   
                     272546
                  
                   
                     272664
                  
                   
                     272783
                  
                   
                     272901
                  
                   
                     273020
                  
                   
                     273138
                  
                   
                     273257
                  
                   
                     273375
                  
                   
                      
                  
                
                 
                   
                     318
                  
                   
                     273494
                  
                   
                     273612
                  
                   
                     273731
                  
                   
                     273849
                  
                   
                     ●73968
                  
                   
                     274087
                  
                   
                     274205
                  
                   
                     274324
                  
                   
                     274443
                  
                   
                     274561
                  
                   
                      
                  
                
                 
                   
                     319
                  
                   
                     274680
                  
                   
                     274799
                  
                   
                     274917
                  
                   
                     275036
                  
                   
                     275155
                  
                   
                     275274
                  
                   
                     275392
                  
                   
                     275511
                  
                   
                     275630
                  
                   
                     275749
                  
                   
                      
                  
                
                 
                   
                     320
                  
                   
                     275868
                  
                   
                     275986
                  
                   
                     276105
                  
                   
                     276224
                  
                   
                     276343
                  
                   
                     276462
                  
                   
                     276580
                  
                   
                     276699
                  
                   
                     276818
                  
                   
                     276937
                  
                   
                      
                  
                
                 
                   
                     321
                  
                   
                     277856
                  
                   
                     277175
                  
                   
                     277294
                  
                   
                     277413
                  
                   
                     277532
                  
                   
                     277651
                  
                   
                     277769
                  
                   
                     277888
                  
                   
                     278007
                  
                   
                     278126
                  
                   
                      
                  
                
                 
                   
                     322
                  
                   
                     278245
                  
                   
                     278364
                  
                   
                     278483
                  
                   
                     278602
                  
                   
                     278721
                  
                   
                     278840
                  
                   
                     278959
                  
                   
                     279078
                  
                   
                     279197
                  
                   
                     279316
                  
                   
                      
                  
                
                 
                   
                     323
                  
                   
                     279436
                  
                   
                     279555
                  
                   
                     279674
                  
                   
                     279793
                  
                   
                     27991●
                  
                   
                     280031
                  
                   
                     280150
                  
                   
                     280269
                  
                   
                     280389
                  
                   
                     280508
                  
                   
                      
                  
                
                 
                   
                     324
                  
                   
                     280627
                  
                   
                     280746
                  
                   
                     280865
                  
                   
                     280985
                  
                   
                     281104
                  
                   
                     281223
                  
                   
                     281342
                  
                   
                     281461
                  
                   
                     281581
                  
                   
                     281700
                  
                   
                      
                  
                
                 
                   
                     325
                  
                   
                     281819
                  
                   
                     281938
                  
                   
                     282058
                  
                   
                     282177
                  
                   
                     282296
                  
                   
                     282416
                  
                   
                     282535
                  
                   
                     282654
                  
                   
                     282773
                  
                   
                     282893
                  
                   
                      
                  
                
                 
                   
                     326
                  
                   
                     283012
                  
                   
                     283131
                  
                   
                     283251
                  
                   
                     283370
                  
                   
                     283490
                  
                   
                     283609
                  
                   
                     283729
                  
                   
                     283848
                  
                   
                     283968
                  
                   
                     284087
                  
                   
                      
                  
                
                 
                   
                     327
                  
                   
                     284207
                  
                   
                     284326
                  
                   
                     284446
                  
                   
                     288565
                  
                   
                     284685
                  
                   
                     284804
                  
                   
                     284924
                  
                   
                     285043
                  
                   
                     285163
                  
                   
                     285282
                  
                   
                      
                  
                
                 
                   
                     328
                  
                   
                     285402
                  
                   
                     285521
                  
                   
                     285641
                  
                   
                     285760
                  
                   
                     28●880
                  
                   
                     286000
                  
                   
                     286119
                  
                   
                     286239
                  
                   
                     286358
                  
                   
                     286478
                  
                   
                      
                  
                
                 
                   
                     329
                  
                   
                     286598
                  
                   
                     286717
                  
                   
                     286837
                  
                   
                     286956
                  
                   
                     287076
                  
                   
                     287196
                  
                   
                     287315
                  
                   
                     287435
                  
                   
                     287555
                  
                   
                     287675
                  
                   
                      
                  
                
                 
                   
                     330
                  
                   
                     287795
                  
                   
                     287915
                  
                   
                     288034
                  
                   
                     288154
                  
                   
                     288273
                  
                   
                     288393
                  
                   
                     288513
                  
                   
                     288633
                  
                   
                     288752
                  
                   
                     288872
                  
                   
                      
                  
                
                 
                   
                     331
                  
                   
                     288992
                  
                   
                     289112
                  
                   
                     289232
                  
                   
                     289352
                  
                   
                     28947●
                  
                   
                     289592
                  
                   
                     289711
                  
                   
                     289831
                  
                   
                     289951
                  
                   
                     290071
                  
                   
                      
                  
                
                 
                   
                     332
                  
                   
                     280191
                  
                   
                     290311
                  
                   
                     290431
                  
                   
                     290551
                  
                   
                     290671
                  
                   
                     290791
                  
                   
                     290911
                  
                   
                     291031
                  
                   
                     291751
                  
                   
                     291271
                  
                   
                      
                  
                
                 
                   
                     333
                  
                   
                     291●91
                  
                   
                     291511
                  
                   
                     291631
                  
                   
                     291751
                  
                   
                     291871
                  
                   
                     291991
                  
                   
                     292111
                  
                   
                     292231
                  
                   
                     292351
                  
                   
                     292471
                  
                   
                      
                  
                
                 
                   
                     
                     333
                  
                   
                     291391
                  
                   
                     291511
                  
                   
                     296331
                  
                   
                     291751
                  
                   
                     291871
                  
                   
                     291991
                  
                   
                     292111
                  
                   
                     292231
                  
                   
                     292351
                  
                   
                     292481
                  
                   
                      
                  
                
                 
                   
                     334
                  
                   
                     292592
                  
                   
                     292712
                  
                   
                     292983
                  
                   
                     292952
                  
                   
                     293072
                  
                   
                     293192
                  
                   
                     293312
                  
                   
                     293432
                  
                   
                     293552
                  
                   
                     293672
                  
                   
                      
                  
                
                 
                   
                     335
                  
                   
                     293793
                  
                   
                     293913
                  
                   
                     294033
                  
                   
                     294153
                  
                   
                     294273
                  
                   
                     294394
                  
                   
                     294514
                  
                   
                     294634
                  
                   
                     294754
                  
                   
                     294875
                  
                   
                      
                  
                
                 
                   
                     336
                  
                   
                     294995
                  
                   
                     295115
                  
                   
                     295236
                  
                   
                     295356
                  
                   
                     295476
                  
                   
                     295197
                  
                   
                     295717
                  
                   
                     295837
                  
                   
                     295957
                  
                   
                     296078
                  
                   
                      
                  
                
                 
                   
                     337
                  
                   
                     296198
                  
                   
                     296318
                  
                   
                     296779
                  
                   
                     296559
                  
                   
                     296680
                  
                   
                     296●00
                  
                   
                     296021
                  
                   
                     297041
                  
                   
                     297162
                  
                   
                     297282
                  
                   
                      
                  
                
                 
                   
                     338
                  
                   
                     297403
                  
                   
                     297523
                  
                   
                     297643
                  
                   
                     297764
                  
                   
                     297884
                  
                   
                     298005
                  
                   
                     298125
                  
                   
                     298246
                  
                   
                     298366
                  
                   
                     298487
                  
                   
                      
                  
                
                 
                   
                     339
                  
                   
                     298608
                  
                   
                     298728
                  
                   
                     298849
                  
                   
                     298969
                  
                   
                     299●90
                  
                   
                     299210
                  
                   
                     299331
                  
                   
                     299401
                  
                   
                     299572
                  
                   
                     299692
                  
                   
                      
                  
                
                 
                   
                     340
                  
                   
                     299813
                  
                   
                     299934
                  
                   
                     300054
                  
                   
                     300175
                  
                   
                     300296
                  
                   
                     300417
                  
                   
                     300537
                  
                   
                     300658
                  
                   
                     300779
                  
                   
                     300899
                  
                   
                      
                  
                
                 
                   
                     341
                  
                   
                     301020
                  
                   
                     301141
                  
                   
                     301281
                  
                   
                     301382
                  
                   
                     301503
                  
                   
                     301624
                  
                   
                     301744
                  
                   
                     301865
                  
                   
                     301986
                  
                   
                     302107
                  
                   
                      
                  
                
                 
                   
                     342
                  
                   
                     302228
                  
                   
                     302348
                  
                   
                     302469
                  
                   
                     302590
                  
                   
                     302711
                  
                   
                     302832
                  
                   
                     302952
                  
                   
                     303073
                  
                   
                     303194
                  
                   
                     303315
                  
                   
                      
                  
                
                 
                   
                     343
                  
                   
                     303436
                  
                   
                     303557
                  
                   
                     303678
                  
                   
                     303799
                  
                   
                     303920
                  
                   
                     304041
                  
                   
                     304161
                  
                   
                     304282
                  
                   
                     304043
                  
                   
                     304524
                  
                   
                      
                  
                
                 
                   
                     344
                  
                   
                     304645
                  
                   
                     304766
                  
                   
                     304887
                  
                   
                     305008
                  
                   
                     305129
                  
                   
                     305250
                  
                   
                     305371
                  
                   
                     305492
                  
                   
                     305613
                  
                   
                     305734
                  
                   
                      
                  
                
                 
                   
                     345
                  
                   
                     305856
                  
                   
                     305977
                  
                   
                     306098
                  
                   
                     306219
                  
                   
                     306340
                  
                   
                     306461
                  
                   
                     306582
                  
                   
                     306703
                  
                   
                     306824
                  
                   
                     306945
                  
                   
                      
                  
                
                 
                   
                     346
                  
                   
                     307066
                  
                   
                     307187
                  
                   
                     307308
                  
                   
                     307430
                  
                   
                     307551
                  
                   
                     307672
                  
                   
                     307192
                  
                   
                     307914
                  
                   
                     308036
                  
                   
                     308157
                  
                   
                      
                  
                
                 
                   
                     347
                  
                   
                     308278
                  
                   
                     308399
                  
                   
                     308520
                  
                   
                     308642
                  
                   
                     308763
                  
                   
                     308884
                  
                   
                     309005
                  
                   
                     309127
                  
                   
                     309248
                  
                   
                     309369
                  
                   
                      
                  
                
                 
                   
                     348
                  
                   
                     309491
                  
                   
                     309612
                  
                   
                     309733
                  
                   
                     309854
                  
                   
                     309976
                  
                   
                     310097
                  
                   
                     310219
                  
                   
                     310340
                  
                   
                     310461
                  
                   
                     310583
                  
                   
                      
                  
                
                 
                   
                     349
                  
                   
                     310704
                  
                   
                     310825
                  
                   
                     310947
                  
                   
                     311068
                  
                   
                     311●90
                  
                   
                     311311
                  
                   
                     311432
                  
                   
                     311554
                  
                   
                     311675
                  
                   
                     311797
                  
                   
                      
                  
                
                 
                   
                     350
                  
                   
                     311918
                  
                   
                     312040
                  
                   
                     312167
                  
                   
                     312283
                  
                   
                     312404
                  
                   
                     312526
                  
                   
                     312647
                  
                   
                     312769
                  
                   
                     312890
                  
                   
                     313012
                  
                   
                      
                  
                
                 
                   
                     351
                  
                   
                     313133
                  
                   
                     313255
                  
                   
                     313376
                  
                   
                     313498
                  
                   
                     313619
                  
                   
                     313741
                  
                   
                     313863
                  
                   
                     313984
                  
                   
                     314106
                  
                   
                     314227
                  
                   
                      
                  
                
                 
                   
                     352
                  
                   
                     314349
                  
                   
                     314471
                  
                   
                     314592
                  
                   
                     314714
                  
                   
                     314835
                  
                   
                     314957
                  
                   
                     315079
                  
                   
                     315200
                  
                   
                     315322
                  
                   
                     315444
                  
                   
                      
                  
                
                 
                   
                     353
                  
                   
                     315566
                  
                   
                     315687
                  
                   
                     315890
                  
                   
                     315931
                  
                   
                     316052
                  
                   
                     316174
                  
                   
                     316296
                  
                   
                     316418
                  
                   
                     316539
                  
                   
                     316661
                  
                   
                      
                  
                
                 
                   
                     354
                  
                   
                     316783
                  
                   
                     316905
                  
                   
                     312027
                  
                   
                     317148
                  
                   
                     317270
                  
                   
                     317392
                  
                   
                     317514
                  
                   
                     317636
                  
                   
                     317757
                  
                   
                     317879
                  
                   
                      
                  
                
                 
                   
                     355
                  
                   
                     318001
                  
                   
                     318123
                  
                   
                     318245
                  
                   
                     318367
                  
                   
                     318489
                  
                   
                     318611
                  
                   
                     318732
                  
                   
                     318054
                  
                   
                     318976
                  
                   
                     319098
                  
                   
                      
                  
                
                 
                   
                     356
                  
                   
                     319220
                  
                   
                     319342
                  
                   
                     319464
                  
                   
                     319586
                  
                   
                     319708
                  
                   
                     319830
                  
                   
                     319952
                  
                   
                     320074
                  
                   
                     320196
                  
                   
                     320318
                  
                   
                      
                  
                
                 
                   
                     357
                  
                   
                     320440
                  
                   
                     320562
                  
                   
                     320684
                  
                   
                     320806
                  
                   
                     320928
                  
                   
                     321050
                  
                   
                     321172
                  
                   
                     321294
                  
                   
                     321416
                  
                   
                     321538
                  
                   
                      
                  
                
                 
                   
                     358
                  
                   
                     321660
                  
                   
                     321782
                  
                   
                     321904
                  
                   
                     322026
                  
                   
                     322148
                  
                   
                     322271
                  
                   
                     322393
                  
                   
                     322515
                  
                   
                     322637
                  
                   
                     322759
                  
                   
                      
                  
                
                 
                   
                     359
                  
                   
                     322881
                  
                   
                     323003
                  
                   
                     323125
                  
                   
                     323248
                  
                   
                     323370
                  
                   
                     323492
                  
                   
                     323614
                  
                   
                     323736
                  
                   
                     323859
                  
                   
                     323981
                  
                   
                      
                  
                
                 
                   
                     360
                  
                   
                     324103
                  
                   
                     324225
                  
                   
                     324348
                  
                   
                     324470
                  
                   
                     324592
                  
                   
                     324715
                  
                   
                     324837
                  
                   
                     324959
                  
                   
                     325081
                  
                   
                     325204
                  
                   
                      
                  
                
                 
                   
                     361
                  
                   
                     325326
                  
                   
                     325448
                  
                   
                     325571
                  
                   
                     325693
                  
                   
                     325815
                  
                   
                     325938
                  
                   
                     326060
                  
                   
                     326182
                  
                   
                     326305
                  
                   
                     326427
                  
                   
                      
                  
                
                 
                   
                     362
                  
                   
                     326550
                  
                   
                     326672
                  
                   
                     326795
                  
                   
                     326917
                  
                   
                     327040
                  
                   
                     327162
                  
                   
                     327284
                  
                   
                     327406
                  
                   
                     327529
                  
                   
                     327651
                  
                   
                      
                  
                
                 
                   
                     363
                  
                   
                     327773
                  
                   
                     327896
                  
                   
                     328018
                  
                   
                     328141
                  
                   
                     328263
                  
                   
                     328386
                  
                   
                     328509
                  
                   
                     328631
                  
                   
                     328754
                  
                   
                     328876
                  
                   
                      
                  
                
                 
                   
                     364
                  
                   
                     328999
                  
                   
                     329125
                  
                   
                     329244
                  
                   
                     329366
                  
                   
                     329489
                  
                   
                     329611
                  
                   
                     329734
                  
                   
                     329856
                  
                   
                     329979
                  
                   
                     330101
                  
                   
                      
                  
                
                 
                   
                     365
                  
                   
                     330224
                  
                   
                     330346
                  
                   
                     330469
                  
                   
                     330592
                  
                   
                     330714
                  
                   
                     330837
                  
                   
                     330960
                  
                   
                     331082
                  
                   
                     331205
                  
                   
                     331327
                  
                   
                      
                  
                
                 
                   
                     366
                  
                   
                     331450
                  
                   
                     331572
                  
                   
                     331695
                  
                   
                     331818
                  
                   
                     331941
                  
                   
                     332064
                  
                   
                     332186
                  
                   
                     332309
                  
                   
                     332432
                  
                   
                     332555
                  
                   
                      
                  
                
                 
                   
                     
                     366
                  
                   
                     331450
                  
                   
                     331572
                  
                   
                     331695
                  
                   
                     331818
                  
                   
                     331941
                  
                   
                     332064
                  
                   
                     332186
                  
                   
                     332309
                  
                   
                     332432
                  
                   
                     332555
                  
                   
                      
                  
                
                 
                   
                     367
                  
                   
                     332678
                  
                   
                     332800
                  
                   
                     332923
                  
                   
                     333046
                  
                   
                     333169
                  
                   
                     333292
                  
                   
                     333414
                  
                   
                     333537
                  
                   
                     333660
                  
                   
                     333782
                  
                   
                      
                  
                
                 
                   
                     368
                  
                   
                     333905
                  
                   
                     334028
                  
                   
                     334151
                  
                   
                     334273
                  
                   
                     334396
                  
                   
                     334519
                  
                   
                     334642
                  
                   
                     334765
                  
                   
                     334888
                  
                   
                     335011
                  
                   
                      
                  
                
                 
                   
                     369
                  
                   
                     335134
                  
                   
                     335256
                  
                   
                     335379
                  
                   
                     335502
                  
                   
                     335625
                  
                   
                     335748
                  
                   
                     335871
                  
                   
                     335994
                  
                   
                     336117
                  
                   
                     336240
                  
                   
                      
                  
                
                 
                   
                     370
                  
                   
                     336313
                  
                   
                     336486
                  
                   
                     336609
                  
                   
                     336732
                  
                   
                     336855
                  
                   
                     336978
                  
                   
                     337101
                  
                   
                     337224
                  
                   
                     337347
                  
                   
                     337470
                  
                   
                      
                  
                
                 
                   
                     371
                  
                   
                     337593
                  
                   
                     337716
                  
                   
                     337839
                  
                   
                     337962
                  
                   
                     338085
                  
                   
                     338208
                  
                   
                     338331
                  
                   
                     338451
                  
                   
                     338577
                  
                   
                     338700
                  
                   
                      
                  
                
                 
                   
                     372
                  
                   
                     338823
                  
                   
                     338946
                  
                   
                     339069
                  
                   
                     339192
                  
                   
                     339315
                  
                   
                     339438
                  
                   
                     339561
                  
                   
                     339684
                  
                   
                     339807
                  
                   
                     339930
                  
                   
                      
                  
                
                 
                   
                     373
                  
                   
                     340054
                  
                   
                     340177
                  
                   
                     340300
                  
                   
                     340423
                  
                   
                     340546
                  
                   
                     340670
                  
                   
                     340793
                  
                   
                     340196
                  
                   
                     341039
                  
                   
                     341162
                  
                   
                      
                  
                
                 
                   
                     374
                  
                   
                     341286
                  
                   
                     341409
                  
                   
                     341532
                  
                   
                     341655
                  
                   
                     341779
                  
                   
                     341902
                  
                   
                     342025
                  
                   
                     342148
                  
                   
                     342271
                  
                   
                     342394
                  
                   
                      
                  
                
                 
                   
                     375
                  
                   
                     342518
                  
                   
                     342641
                  
                   
                     342764
                  
                   
                     342888
                  
                   
                     343011
                  
                   
                     343135
                  
                   
                     343258
                  
                   
                     343381
                  
                   
                     343505
                  
                   
                     343628
                  
                   
                      
                  
                
                 
                   
                     376
                  
                   
                     343752
                  
                   
                     343875
                  
                   
                     343998
                  
                   
                     344121
                  
                   
                     344245
                  
                   
                     344368
                  
                   
                     344491
                  
                   
                     344615
                  
                   
                     344738
                  
                   
                     344862
                  
                   
                      
                  
                
                 
                   
                     377
                  
                   
                     344985
                  
                   
                     345108
                  
                   
                     345233
                  
                   
                     345355
                  
                   
                     345479
                  
                   
                     345602
                  
                   
                     345726
                  
                   
                     345849
                  
                   
                     345973
                  
                   
                     346096
                  
                   
                      
                  
                
                 
                   
                     378
                  
                   
                     346220
                  
                   
                     346343
                  
                   
                     346467
                  
                   
                     346590
                  
                   
                     346714
                  
                   
                     346837
                  
                   
                     347961
                  
                   
                     347082
                  
                   
                     347208
                  
                   
                     347331
                  
                   
                      
                  
                
                 
                   
                     379
                  
                   
                     347455
                  
                   
                     347578
                  
                   
                     347702
                  
                   
                     347825
                  
                   
                     347949
                  
                   
                     348073
                  
                   
                     348916
                  
                   
                     348320
                  
                   
                     348443
                  
                   
                     348567
                  
                   
                      
                  
                
                 
                   
                     380
                  
                   
                     348691
                  
                   
                     348814
                  
                   
                     348938
                  
                   
                     349061
                  
                   
                     349185
                  
                   
                     349309
                  
                   
                     349432
                  
                   
                     349556
                  
                   
                     349679
                  
                   
                     349803
                  
                   
                      
                  
                
                 
                   
                     381
                  
                   
                     3499●7
                  
                   
                     350050
                  
                   
                     350174
                  
                   
                     350298
                  
                   
                     350421
                  
                   
                     350545
                  
                   
                     350669
                  
                   
                     350792
                  
                   
                     350916
                  
                   
                     351040
                  
                   
                      
                  
                
                 
                   
                     382
                  
                   
                     351164
                  
                   
                     351287
                  
                   
                     351411
                  
                   
                     851535
                  
                   
                     351659
                  
                   
                     351783
                  
                   
                     351806
                  
                   
                     352030
                  
                   
                     352154
                  
                   
                     352277
                  
                   
                      
                  
                
                 
                   
                     383
                  
                   
                     352401
                  
                   
                     352525
                  
                   
                     352649
                  
                   
                     352772
                  
                   
                     352896
                  
                   
                     353020
                  
                   
                     353144
                  
                   
                     353268
                  
                   
                     353392
                  
                   
                     353516
                  
                   
                      
                  
                
                 
                   
                     384
                  
                   
                     353640
                  
                   
                     353763
                  
                   
                     353887
                  
                   
                     354011
                  
                   
                     354135
                  
                   
                     354259
                  
                   
                     354382
                  
                   
                     354506
                  
                   
                     354030
                  
                   
                     354754
                  
                   
                      
                  
                
                 
                   
                     385
                  
                   
                     354878
                  
                   
                     355002
                  
                   
                     355126
                  
                   
                     355250
                  
                   
                     355374
                  
                   
                     355498
                  
                   
                     355622
                  
                   
                     355746
                  
                   
                     355870
                  
                   
                     355994
                  
                   
                      
                  
                
                 
                   
                     386
                  
                   
                     356118
                  
                   
                     356242
                  
                   
                     356366
                  
                   
                     356490
                  
                   
                     356614
                  
                   
                     356738
                  
                   
                     356862
                  
                   
                     356986
                  
                   
                     357110
                  
                   
                     357234
                  
                   
                      
                  
                
                 
                   
                     387
                  
                   
                     357358
                  
                   
                     357482
                  
                   
                     357606
                  
                   
                     357730
                  
                   
                     357854
                  
                   
                     357978
                  
                   
                     358102
                  
                   
                     358226
                  
                   
                     358350
                  
                   
                     358474
                  
                   
                      
                  
                
                 
                   
                     388
                  
                   
                     358598
                  
                   
                     358722
                  
                   
                     358846
                  
                   
                     358970
                  
                   
                     359094
                  
                   
                     359219
                  
                   
                     359343
                  
                   
                     359467
                  
                   
                     359591
                  
                   
                     359715
                  
                   
                      
                  
                
                 
                   
                     389
                  
                   
                     359840
                  
                   
                     359964
                  
                   
                     360088
                  
                   
                     360212
                  
                   
                     360336
                  
                   
                     360460
                  
                   
                     360584
                  
                   
                     360708
                  
                   
                     360832
                  
                   
                     360956
                  
                   
                      
                  
                
                 
                   
                     390
                  
                   
                     361081
                  
                   
                     361208
                  
                   
                     ●61329
                  
                   
                     361453
                  
                   
                     361578
                  
                   
                     361702
                  
                   
                     361826
                  
                   
                     361951
                  
                   
                     362075
                  
                   
                     362●99
                  
                   
                      
                  
                
                 
                   
                     391
                  
                   
                     362324
                  
                   
                     362448
                  
                   
                     362572
                  
                   
                     362698
                  
                   
                     362821
                  
                   
                     362945
                  
                   
                     363069
                  
                   
                     363194
                  
                   
                     363318
                  
                   
                     363442
                  
                   
                      
                  
                
                 
                   
                     392
                  
                   
                     363567
                  
                   
                     363191
                  
                   
                     363815
                  
                   
                     363939
                  
                   
                     364064
                  
                   
                     364188
                  
                   
                     364312
                  
                   
                     364437
                  
                   
                     364561
                  
                   
                     364686
                  
                   
                      
                  
                
                 
                   
                     393
                  
                   
                     364810
                  
                   
                     364934
                  
                   
                     365059
                  
                   
                     365183
                  
                   
                     36530●
                  
                   
                     365432
                  
                   
                     365556
                  
                   
                     315681
                  
                   
                     365805
                  
                   
                     365930
                  
                   
                      
                  
                
                 
                   
                     394
                  
                   
                     366054
                  
                   
                     366178
                  
                   
                     366303
                  
                   
                     396427
                  
                   
                     366552
                  
                   
                     366676
                  
                   
                     366808
                  
                   
                     366925
                  
                   
                     36704●
                  
                   
                     367173
                  
                   
                      
                  
                
                 
                   
                     395
                  
                   
                     367298
                  
                   
                     367422
                  
                   
                     367547
                  
                   
                     367672
                  
                   
                     367796
                  
                   
                     367921
                  
                   
                     368046
                  
                   
                     368170
                  
                   
                     368295
                  
                   
                     368419
                  
                   
                      
                  
                
                 
                   
                     396
                  
                   
                     368●44
                  
                   
                     368668
                  
                   
                     368793
                  
                   
                     369917
                  
                   
                     369042
                  
                   
                     369166
                  
                   
                     369290
                  
                   
                     369415
                  
                   
                     369539
                  
                   
                     369663
                  
                   
                      
                  
                
                 
                   
                     397
                  
                   
                     369788
                  
                   
                     369912
                  
                   
                     370037
                  
                   
                     370162
                  
                   
                     370287
                  
                   
                     370412
                  
                   
                     370537
                  
                   
                     370661
                  
                   
                     370786
                  
                   
                     370911
                  
                   
                      
                  
                
                 
                   
                     398
                  
                   
                     371036
                  
                   
                     371160
                  
                   
                     371285
                  
                   
                     371409
                  
                   
                     371534
                  
                   
                     371659
                  
                   
                     371783
                  
                   
                     376908
                  
                   
                     372033
                  
                   
                     372157
                  
                   
                      
                  
                
                 
                   
                     399
                  
                   
                     372282
                  
                   
                     372407
                  
                   
                     37253●
                  
                   
                     372656
                  
                   
                     372181
                  
                   
                     372906
                  
                   
                     373030
                  
                   
                     373155
                  
                   
                     373280
                  
                   
                     373405
                  
                   
                      
                  
                
                 
                   
                     
                     400
                  
                   
                     373530
                  
                   
                     373654
                  
                   
                     373779
                  
                   
                     373904
                  
                   
                     37●029
                  
                   
                     374154
                  
                   
                     374278
                  
                   
                     374403
                  
                   
                     374528
                  
                   
                     374655
                  
                   
                      
                  
                
                 
                   
                     401
                  
                   
                     334778
                  
                   
                     374902
                  
                   
                     375027
                  
                   
                     375152
                  
                   
                     375277
                  
                   
                     375402
                  
                   
                     375526
                  
                   
                     375651
                  
                   
                     375776
                  
                   
                     375901
                  
                   
                      
                  
                
                 
                   
                     402
                  
                   
                     376026
                  
                   
                     376150
                  
                   
                     376275
                  
                   
                     376400
                  
                   
                     376525
                  
                   
                     376650
                  
                   
                     376775
                  
                   
                     376900
                  
                   
                     377025
                  
                   
                     377150
                  
                   
                      
                  
                
                 
                   
                     403
                  
                   
                     377275
                  
                   
                     377399
                  
                   
                     377524
                  
                   
                     377649
                  
                   
                     377774
                  
                   
                     377899
                  
                   
                     378024
                  
                   
                     378149
                  
                   
                     378274
                  
                   
                     378399
                  
                   
                      
                  
                
                 
                   
                     404
                  
                   
                     378524
                  
                   
                     378649
                  
                   
                     378774
                  
                   
                     378899
                  
                   
                     379024
                  
                   
                     379149
                  
                   
                     379274
                  
                   
                     379399
                  
                   
                     379524
                  
                   
                     379649
                  
                   
                      
                  
                
                 
                   
                     405
                  
                   
                     379774
                  
                   
                     379899
                  
                   
                     380024
                  
                   
                     380149
                  
                   
                     380274
                  
                   
                     380399
                  
                   
                     380524
                  
                   
                     380649
                  
                   
                     380774
                  
                   
                     380899
                  
                   
                      
                  
                
                 
                   
                     406
                  
                   
                     381024
                  
                   
                     381149
                  
                   
                     381274
                  
                   
                     381399
                  
                   
                     381524
                  
                   
                     381649
                  
                   
                     381774
                  
                   
                     381899
                  
                   
                     382024
                  
                   
                     382149
                  
                   
                      
                  
                
                 
                   
                     407
                  
                   
                     382275
                  
                   
                     382400
                  
                   
                     382525
                  
                   
                     38265●
                  
                   
                     382775
                  
                   
                     382901
                  
                   
                     383026
                  
                   
                     383151
                  
                   
                     383276
                  
                   
                     383401
                  
                   
                      
                  
                
                 
                   
                     408
                  
                   
                     383526
                  
                   
                     385651
                  
                   
                     383776
                  
                   
                     383902
                  
                   
                     384027
                  
                   
                     384152
                  
                   
                     384277
                  
                   
                     384402
                  
                   
                     384528
                  
                   
                     384653
                  
                   
                      
                  
                
                 
                   
                     409
                  
                   
                     384778
                  
                   
                     384903
                  
                   
                     385028
                  
                   
                     385154
                  
                   
                     385279
                  
                   
                     385404
                  
                   
                     385529
                  
                   
                     385654
                  
                   
                     385779
                  
                   
                     385904
                  
                   
                      
                  
                
                 
                   
                     410
                  
                   
                     386029
                  
                   
                     386155
                  
                   
                     386280
                  
                   
                     386406
                  
                   
                     386531
                  
                   
                     386657
                  
                   
                     386782
                  
                   
                     386907
                  
                   
                     387032
                  
                   
                     387157
                  
                   
                      
                  
                
                 
                   
                     411
                  
                   
                     387283
                  
                   
                     387408
                  
                   
                     387533
                  
                   
                     387658
                  
                   
                     387784
                  
                   
                     387909
                  
                   
                     388034
                  
                   
                     388160
                  
                   
                     388285
                  
                   
                     388421
                  
                   
                      
                  
                
                 
                   
                     412
                  
                   
                     388536
                  
                   
                     388661
                  
                   
                     388787
                  
                   
                     388912
                  
                   
                     389037
                  
                   
                     389163
                  
                   
                     389288
                  
                   
                     389413
                  
                   
                     389539
                  
                   
                     389664
                  
                   
                      
                  
                
                 
                   
                     413
                  
                   
                     389790
                  
                   
                     389915
                  
                   
                     390040
                  
                   
                     390166
                  
                   
                     390291
                  
                   
                     390417
                  
                   
                     390542
                  
                   
                     390667
                  
                   
                     390793
                  
                   
                     390918
                  
                   
                      
                  
                
                 
                   
                     414
                  
                   
                     391044
                  
                   
                     391169
                  
                   
                     391294
                  
                   
                     391420
                  
                   
                     391545
                  
                   
                     391671
                  
                   
                     391796
                  
                   
                     391922
                  
                   
                     391047
                  
                   
                     392173
                  
                   
                      
                  
                
                 
                   
                     415
                  
                   
                     392298
                  
                   
                     392424
                  
                   
                     392549
                  
                   
                     392675
                  
                   
                     392800
                  
                   
                     392926
                  
                   
                     393051
                  
                   
                     393177
                  
                   
                     393302
                  
                   
                     393428
                  
                   
                      
                  
                
                 
                   
                     416
                  
                   
                     393553
                  
                   
                     393679
                  
                   
                     393804
                  
                   
                     393930
                  
                   
                     394055
                  
                   
                     394181
                  
                   
                     394306
                  
                   
                     394432
                  
                   
                     394557
                  
                   
                     394683
                  
                   
                      
                  
                
                 
                   
                     417
                  
                   
                     394809
                  
                   
                     394934
                  
                   
                     395060
                  
                   
                     395185
                  
                   
                     395311
                  
                   
                     395437
                  
                   
                     397562
                  
                   
                     395688
                  
                   
                     395813
                  
                   
                     395939
                  
                   
                      
                  
                
                 
                   
                     418
                  
                   
                     396065
                  
                   
                     396190
                  
                   
                     396316
                  
                   
                     396441
                  
                   
                     396567
                  
                   
                     396693
                  
                   
                     396818
                  
                   
                     396944
                  
                   
                     397069
                  
                   
                     397195
                  
                   
                      
                  
                
                 
                   
                     419
                  
                   
                     3973●1
                  
                   
                     397446
                  
                   
                     397572
                  
                   
                     397607
                  
                   
                     397823
                  
                   
                     397949
                  
                   
                     398074
                  
                   
                     398200
                  
                   
                     398326
                  
                   
                     398451
                  
                   
                      
                  
                
                 
                   
                     420
                  
                   
                     398577
                  
                   
                     3987●3
                  
                   
                     398828
                  
                   
                     398954
                  
                   
                     349080
                  
                   
                     399206
                  
                   
                     399331
                  
                   
                     399457
                  
                   
                     399583
                  
                   
                     399708
                  
                   
                      
                  
                
                 
                   
                     421
                  
                   
                     399834
                  
                   
                     399960
                  
                   
                     400085
                  
                   
                     400211
                  
                   
                     400337
                  
                   
                     400463
                  
                   
                     400588
                  
                   
                     400714
                  
                   
                     400840
                  
                   
                     400966
                  
                   
                      
                  
                
                 
                   
                     422
                  
                   
                     401092
                  
                   
                     401217
                  
                   
                     401343
                  
                   
                     401469
                  
                   
                     401595
                  
                   
                     401721
                  
                   
                     401846
                  
                   
                     401972
                  
                   
                     402098
                  
                   
                     40●223
                  
                   
                      
                  
                
                 
                   
                     423
                  
                   
                     402349
                  
                   
                     402475
                  
                   
                     402601
                  
                   
                     402727
                  
                   
                     402853
                  
                   
                     402979
                  
                   
                     403104
                  
                   
                     403230
                  
                   
                     403356
                  
                   
                     403482
                  
                   
                      
                  
                
                 
                   
                     424
                  
                   
                     403608
                  
                   
                     403733
                  
                   
                     403859
                  
                   
                     403985
                  
                   
                     404111
                  
                   
                     404237
                  
                   
                     404362
                  
                   
                     404488
                  
                   
                     404614
                  
                   
                     404740
                  
                   
                      
                  
                
                 
                   
                     425
                  
                   
                     404866
                  
                   
                     404992
                  
                   
                     405118
                  
                   
                     405244
                  
                   
                     405370
                  
                   
                     405496
                  
                   
                     405621
                  
                   
                     405747
                  
                   
                     405873
                  
                   
                     405999
                  
                   
                      
                  
                
                 
                   
                     426
                  
                   
                     406125
                  
                   
                     406251
                  
                   
                     406377
                  
                   
                     406503
                  
                   
                     406629
                  
                   
                     406755
                  
                   
                     406881
                  
                   
                     407007
                  
                   
                     407133
                  
                   
                     407259
                  
                   
                      
                  
                
                 
                   
                     427
                  
                   
                     407385
                  
                   
                     407511
                  
                   
                     407637
                  
                   
                     407763
                  
                   
                     407889
                  
                   
                     408015
                  
                   
                     408141
                  
                   
                     408267
                  
                   
                     408393
                  
                   
                     408519
                  
                   
                      
                  
                
                 
                   
                     428
                  
                   
                     408645
                  
                   
                     408771
                  
                   
                     408897
                  
                   
                     409023
                  
                   
                     409149
                  
                   
                     409275
                  
                   
                     409401
                  
                   
                     409527
                  
                   
                     409653
                  
                   
                     409779
                  
                   
                      
                  
                
                 
                   
                     429
                  
                   
                     409405
                  
                   
                     410031
                  
                   
                     410157
                  
                   
                     410283
                  
                   
                     401409
                  
                   
                     410535
                  
                   
                     410661
                  
                   
                     410787
                  
                   
                     410913
                  
                   
                     411039
                  
                   
                      
                  
                
                 
                   
                     430
                  
                   
                     411165
                  
                   
                     411291
                  
                   
                     411417
                  
                   
                     411543
                  
                   
                     411669
                  
                   
                     411795
                  
                   
                     411921
                  
                   
                     412047
                  
                   
                     412173
                  
                   
                     412299
                  
                   
                      
                  
                
                 
                   
                     431
                  
                   
                     412426
                  
                   
                     412552
                  
                   
                     412678
                  
                   
                     412804
                  
                   
                     412930
                  
                   
                     413056
                  
                   
                     413182
                  
                   
                     413308
                  
                   
                     413434
                  
                   
                     413560
                  
                   
                      
                  
                
                 
                   
                     432
                  
                   
                     413687
                  
                   
                     413813
                  
                   
                     413939
                  
                   
                     414065
                  
                   
                     414191
                  
                   
                     414318
                  
                   
                     414444
                  
                   
                     414570
                  
                   
                     414696
                  
                   
                     414822
                  
                   
                      
                  
                
                 
                   
                     433
                  
                   
                     414948
                  
                   
                     415074
                  
                   
                     415207
                  
                   
                     415327
                  
                   
                     415453
                  
                   
                     415579
                  
                   
                     415705
                  
                   
                     415831
                  
                   
                     415958
                  
                   
                     410084
                  
                   
                      
                  
                
                 
                   
                     
                     433
                  
                   
                     414948
                  
                   
                     415074
                  
                   
                     415200
                  
                   
                     415327
                  
                   
                     415453
                  
                   
                     415579
                  
                   
                     415705
                  
                   
                     415831
                  
                   
                     415958
                  
                   
                     416084
                  
                   
                      
                  
                
                 
                   
                     434
                  
                   
                     416210
                  
                   
                     416336
                  
                   
                     416462
                  
                   
                     416589
                  
                   
                     416715
                  
                   
                     416841
                  
                   
                     416967
                  
                   
                     417094
                  
                   
                     417220
                  
                   
                     417346
                  
                   
                      
                  
                
                 
                   
                     435
                  
                   
                     417473
                  
                   
                     417599
                  
                   
                     417725
                  
                   
                     417851
                  
                   
                     417977
                  
                   
                     418104
                  
                   
                     418230
                  
                   
                     418356
                  
                   
                     418482
                  
                   
                     418609
                  
                   
                      
                  
                
                 
                   
                     436
                  
                   
                     418735
                  
                   
                     418861
                  
                   
                     418988
                  
                   
                     419114
                  
                   
                     419240
                  
                   
                     419367
                  
                   
                     419493
                  
                   
                     419619
                  
                   
                     419745
                  
                   
                     419872
                  
                   
                      
                  
                
                 
                   
                     437
                  
                   
                     419998
                  
                   
                     420124
                  
                   
                     420251
                  
                   
                     420377
                  
                   
                     420503
                  
                   
                     420630
                  
                   
                     420756
                  
                   
                     420882
                  
                   
                     421008
                  
                   
                     421135
                  
                   
                      
                  
                
                 
                   
                     438
                  
                   
                     421261
                  
                   
                     421387
                  
                   
                     421514
                  
                   
                     421640
                  
                   
                     421767
                  
                   
                     421895
                  
                   
                     422019
                  
                   
                     422146
                  
                   
                     422272
                  
                   
                     422399
                  
                   
                      
                  
                
                 
                   
                     439
                  
                   
                     422525
                  
                   
                     422651
                  
                   
                     422778
                  
                   
                     422904
                  
                   
                     423030
                  
                   
                     423157
                  
                   
                     423283
                  
                   
                     423409
                  
                   
                     4235●6
                  
                   
                     423662
                  
                   
                      
                  
                
                 
                   
                     440
                  
                   
                     423789
                  
                   
                     423915
                  
                   
                     424041
                  
                   
                     424168
                  
                   
                     424294
                  
                   
                     424421
                  
                   
                     424547
                  
                   
                     424674
                  
                   
                     424800
                  
                   
                     424927
                  
                   
                      
                  
                
                 
                   
                     441
                  
                   
                     425053
                  
                   
                     425179
                  
                   
                     425306
                  
                   
                     425432
                  
                   
                     425559
                  
                   
                     425685
                  
                   
                     425812
                  
                   
                     425938
                  
                   
                     425065
                  
                   
                     426191
                  
                   
                      
                  
                
                 
                   
                     442
                  
                   
                     426318
                  
                   
                     426444
                  
                   
                     426570
                  
                   
                     426697
                  
                   
                     426823
                  
                   
                     426950
                  
                   
                     427076
                  
                   
                     427203
                  
                   
                     427329
                  
                   
                     427456
                  
                   
                      
                  
                
                 
                   
                     443
                  
                   
                     427582
                  
                   
                     427709
                  
                   
                     427853
                  
                   
                     427962
                  
                   
                     428088
                  
                   
                     428215
                  
                   
                     428341
                  
                   
                     428468
                  
                   
                     428594
                  
                   
                     428721
                  
                   
                      
                  
                
                 
                   
                     444
                  
                   
                     428247
                  
                   
                     428974
                  
                   
                     429100
                  
                   
                     429227
                  
                   
                     429353
                  
                   
                     429480
                  
                   
                     429607
                  
                   
                     429733
                  
                   
                     429860
                  
                   
                     429986
                  
                   
                      
                  
                
                 
                   
                     445
                  
                   
                     430113
                  
                   
                     430239
                  
                   
                     430366
                  
                   
                     430492
                  
                   
                     430619
                  
                   
                     430746
                  
                   
                     430872
                  
                   
                     430999
                  
                   
                     431125
                  
                   
                     431252
                  
                   
                      
                  
                
                 
                   
                     446
                  
                   
                     431378
                  
                   
                     431505
                  
                   
                     431631
                  
                   
                     431758
                  
                   
                     431884
                  
                   
                     432011
                  
                   
                     432138
                  
                   
                     432264
                  
                   
                     432391
                  
                   
                     432517
                  
                   
                      
                  
                
                 
                   
                     447
                  
                   
                     432644
                  
                   
                     432771
                  
                   
                     432897
                  
                   
                     433024
                  
                   
                     433050
                  
                   
                     433277
                  
                   
                     433404
                  
                   
                     433530
                  
                   
                     433657
                  
                   
                     433784
                  
                   
                      
                  
                
                 
                   
                     448
                  
                   
                     433911
                  
                   
                     434037
                  
                   
                     434164
                  
                   
                     434290
                  
                   
                     434411
                  
                   
                     43●544
                  
                   
                     434670
                  
                   
                     434797
                  
                   
                     434924
                  
                   
                     435050
                  
                   
                      
                  
                
                 
                   
                     449
                  
                   
                     435177
                  
                   
                     435304
                  
                   
                     435430
                  
                   
                     435557
                  
                   
                     435683
                  
                   
                     435810
                  
                   
                     435937
                  
                   
                     436063
                  
                   
                     436190
                  
                   
                     436317
                  
                   
                      
                  
                
                 
                   
                     450
                  
                   
                     436444
                  
                   
                     436570
                  
                   
                     436697
                  
                   
                     436824
                  
                   
                     436950
                  
                   
                     437077
                  
                   
                     437204
                  
                   
                     437330
                  
                   
                     437457
                  
                   
                     437584
                  
                   
                      
                  
                
                 
                   
                     451
                  
                   
                     437717
                  
                   
                     437837
                  
                   
                     437964
                  
                   
                     438091
                  
                   
                     438217
                  
                   
                     438344
                  
                   
                     438471
                  
                   
                     438598
                  
                   
                     438724
                  
                   
                     438851
                  
                   
                      
                  
                
                 
                   
                     452
                  
                   
                     438978
                  
                   
                     439105
                  
                   
                     439231
                  
                   
                     439358
                  
                   
                     439485
                  
                   
                     439612
                  
                   
                     439738
                  
                   
                     439865
                  
                   
                     439990
                  
                   
                     440119
                  
                   
                      
                  
                
                 
                   
                     453
                  
                   
                     440246
                  
                   
                     440372
                  
                   
                     440499
                  
                   
                     440626
                  
                   
                     440752
                  
                   
                     440879
                  
                   
                     441006
                  
                   
                     441133
                  
                   
                     441259
                  
                   
                     441386
                  
                   
                      
                  
                
                 
                   
                     454
                  
                   
                     441513
                  
                   
                     441640
                  
                   
                     441767
                  
                   
                     441893
                  
                   
                     442020
                  
                   
                     442147
                  
                   
                     442274
                  
                   
                     442400
                  
                   
                     442527
                  
                   
                     442654
                  
                   
                      
                  
                
                 
                   
                     455
                  
                   
                     442781
                  
                   
                     442907
                  
                   
                     443034
                  
                   
                     443161
                  
                   
                     443288
                  
                   
                     443415
                  
                   
                     443541
                  
                   
                     443667
                  
                   
                     443793
                  
                   
                     443929
                  
                   
                      
                  
                
                 
                   
                     456
                  
                   
                     444045
                  
                   
                     444172
                  
                   
                     444300
                  
                   
                     444428
                  
                   
                     444556
                  
                   
                     444684
                  
                   
                     444810
                  
                   
                     444937
                  
                   
                     445064
                  
                   
                     445191
                  
                   
                      
                  
                
                 
                   
                     457
                  
                   
                     445318
                  
                   
                     445444
                  
                   
                     445571
                  
                   
                     445698
                  
                   
                     445825
                  
                   
                     445952
                  
                   
                     446079
                  
                   
                     446206
                  
                   
                     446332
                  
                   
                     446459
                  
                   
                      
                  
                
                 
                   
                     458
                  
                   
                     446586
                  
                   
                     446713
                  
                   
                     446840
                  
                   
                     446967
                  
                   
                     447094
                  
                   
                     447221
                  
                   
                     447347
                  
                   
                     447474
                  
                   
                     447601
                  
                   
                     447728
                  
                   
                      
                  
                
                 
                   
                     459
                  
                   
                     447854
                  
                   
                     447982
                  
                   
                     448089
                  
                   
                     448216
                  
                   
                     448343
                  
                   
                     448490
                  
                   
                     448616
                  
                   
                     448743
                  
                   
                     448870
                  
                   
                     448997
                  
                   
                      
                  
                
                 
                   
                     460
                  
                   
                     449124
                  
                   
                     449251
                  
                   
                     449378
                  
                   
                     449505
                  
                   
                     449632
                  
                   
                     449759
                  
                   
                     449886
                  
                   
                     450013
                  
                   
                     450140
                  
                   
                     450267
                  
                   
                      
                  
                
                 
                   
                     461
                  
                   
                     450394
                  
                   
                     450520
                  
                   
                     450647
                  
                   
                     450774
                  
                   
                     450801
                  
                   
                     451028
                  
                   
                     451155
                  
                   
                     451282
                  
                   
                     451409
                  
                   
                     451536
                  
                   
                      
                  
                
                 
                   
                     462
                  
                   
                     451663
                  
                   
                     451790
                  
                   
                     451917
                  
                   
                     452044
                  
                   
                     452171
                  
                   
                     452298
                  
                   
                     452425
                  
                   
                     452552
                  
                   
                     452679
                  
                   
                     452806
                  
                   
                      
                  
                
                 
                   
                     463
                  
                   
                     452933
                  
                   
                     453060
                  
                   
                     453187
                  
                   
                     453314
                  
                   
                     453441
                  
                   
                     453568
                  
                   
                     453695
                  
                   
                     453822
                  
                   
                     453949
                  
                   
                     454076
                  
                   
                      
                  
                
                 
                   
                     464
                  
                   
                     454203
                  
                   
                     454330
                  
                   
                     454457
                  
                   
                     454584
                  
                   
                     454711
                  
                   
                     454838
                  
                   
                     454965
                  
                   
                     455092
                  
                   
                     455219
                  
                   
                     455346
                  
                   
                      
                  
                
                 
                   
                     465
                  
                   
                     455473
                  
                   
                     455600
                  
                   
                     455727
                  
                   
                     455854
                  
                   
                     455981
                  
                   
                     456108
                  
                   
                     456235
                  
                   
                     456362
                  
                   
                     456489
                  
                   
                     456616
                  
                   
                      
                  
                
                 
                   
                     466
                  
                   
                     456743
                  
                   
                     456870
                  
                   
                     456997
                  
                   
                     457124
                  
                   
                     457251
                  
                   
                     457●78
                  
                   
                     457505
                  
                   
                     457632
                  
                   
                     457759
                  
                   
                     457886
                  
                   
                      
                  
                
                 
                   
                     
                     466
                  
                   
                     456743
                  
                   
                     456870
                  
                   
                     456997
                  
                   
                     456124
                  
                   
                     457251
                  
                   
                     457378
                  
                   
                     457505
                  
                   
                     457632
                  
                   
                     457759
                  
                   
                     457386
                  
                   
                      
                  
                
                 
                   
                     467
                  
                   
                     458013
                  
                   
                     458140
                  
                   
                     458267
                  
                   
                     458394
                  
                   
                     459521
                  
                   
                     458648
                  
                   
                     458775
                  
                   
                     458902
                  
                   
                     459029
                  
                   
                     459156
                  
                   
                      
                  
                
                 
                   
                     468
                  
                   
                     459284
                  
                   
                     459411
                  
                   
                     459538
                  
                   
                     459665
                  
                   
                     459792
                  
                   
                     459919
                  
                   
                     460046
                  
                   
                     460173
                  
                   
                     460300
                  
                   
                     460427
                  
                   
                      
                  
                
                 
                   
                     469
                  
                   
                     460554
                  
                   
                     460681
                  
                   
                     460808
                  
                   
                     460935
                  
                   
                     461062
                  
                   
                     461190
                  
                   
                     461317
                  
                   
                     461444
                  
                   
                     461571
                  
                   
                     461698
                  
                   
                      
                  
                
                 
                   
                     470
                  
                   
                     461825
                  
                   
                     461952
                  
                   
                     462079
                  
                   
                     462206
                  
                   
                     462333
                  
                   
                     462461
                  
                   
                     462588
                  
                   
                     462715
                  
                   
                     462842
                  
                   
                     462969
                  
                   
                      
                  
                
                 
                   
                     471
                  
                   
                     463096
                  
                   
                     463223
                  
                   
                     463350
                  
                   
                     463477
                  
                   
                     463604
                  
                   
                     463732
                  
                   
                     463859
                  
                   
                     463986
                  
                   
                     464113
                  
                   
                     464240
                  
                   
                      
                  
                
                 
                   
                     472
                  
                   
                     464367
                  
                   
                     464494
                  
                   
                     464621
                  
                   
                     464749
                  
                   
                     464876
                  
                   
                     465003
                  
                   
                     465130
                  
                   
                     465257
                  
                   
                     465384
                  
                   
                     465511
                  
                   
                      
                  
                
                 
                   
                     473
                  
                   
                     465639
                  
                   
                     465766
                  
                   
                     465893
                  
                   
                     466020
                  
                   
                     466147
                  
                   
                     466274
                  
                   
                     466401
                  
                   
                     466528
                  
                   
                     466656
                  
                   
                     466783
                  
                   
                      
                  
                
                 
                   
                     474
                  
                   
                     466910
                  
                   
                     467037
                  
                   
                     467164
                  
                   
                     467291
                  
                   
                     467418
                  
                   
                     467546
                  
                   
                     467673
                  
                   
                     467800
                  
                   
                     467927
                  
                   
                     468054
                  
                   
                      
                  
                
                 
                   
                     475
                  
                   
                     468182
                  
                   
                     468309
                  
                   
                     468437
                  
                   
                     468563
                  
                   
                     468690
                  
                   
                     468818
                  
                   
                     468945
                  
                   
                     469072
                  
                   
                     469199
                  
                   
                     469326
                  
                   
                      
                  
                
                 
                   
                     476
                  
                   
                     469454
                  
                   
                     469581
                  
                   
                     469708
                  
                   
                     469835
                  
                   
                     469962
                  
                   
                     470089
                  
                   
                     470216
                  
                   
                     470343
                  
                   
                     470471
                  
                   
                     470598
                  
                   
                      
                  
                
                 
                   
                     477
                  
                   
                     470725
                  
                   
                     470852
                  
                   
                     470979
                  
                   
                     471107
                  
                   
                     471234
                  
                   
                     471361
                  
                   
                     471488
                  
                   
                     471615
                  
                   
                     471743
                  
                   
                     471870
                  
                   
                      
                  
                
                 
                   
                     478
                  
                   
                     471997
                  
                   
                     472124
                  
                   
                     472251
                  
                   
                     472379
                  
                   
                     472506
                  
                   
                     472633
                  
                   
                     472760
                  
                   
                     472887
                  
                   
                     473015
                  
                   
                     473142
                  
                   
                      
                  
                
                 
                   
                     479
                  
                   
                     473269
                  
                   
                     473396
                  
                   
                     473523
                  
                   
                     473651
                  
                   
                     473778
                  
                   
                     473905
                  
                   
                     474032
                  
                   
                     474160
                  
                   
                     474287
                  
                   
                     474414
                  
                   
                      
                  
                
                 
                   
                     480
                  
                   
                     474542
                  
                   
                     474669
                  
                   
                     474796
                  
                   
                     474923
                  
                   
                     475050
                  
                   
                     475178
                  
                   
                     475305
                  
                   
                     475432
                  
                   
                     475559
                  
                   
                     475686
                  
                   
                      
                  
                
                 
                   
                     481
                  
                   
                     475614
                  
                   
                     475941
                  
                   
                     476068
                  
                   
                     476195
                  
                   
                     476322
                  
                   
                     476450
                  
                   
                     476577
                  
                   
                     476704
                  
                   
                     476831
                  
                   
                     476959
                  
                   
                      
                  
                
                 
                   
                     482
                  
                   
                     477086
                  
                   
                     477213
                  
                   
                     477340
                  
                   
                     477468
                  
                   
                     477595
                  
                   
                     477722
                  
                   
                     477849
                  
                   
                     477977
                  
                   
                     478104
                  
                   
                     478231
                  
                   
                      
                  
                
                 
                   
                     483
                  
                   
                     478359
                  
                   
                     478486
                  
                   
                     478613
                  
                   
                     478740
                  
                   
                     478867
                  
                   
                     478995
                  
                   
                     479122
                  
                   
                     479249
                  
                   
                     479376
                  
                   
                     479504
                  
                   
                      
                  
                
                 
                   
                     484
                  
                   
                     479631
                  
                   
                     479758
                  
                   
                     479885
                  
                   
                     480013
                  
                   
                     480140
                  
                   
                     480267
                  
                   
                     480394
                  
                   
                     480522
                  
                   
                     480649
                  
                   
                     480776
                  
                   
                      
                  
                
                 
                   
                     485
                  
                   
                     480940
                  
                   
                     481031
                  
                   
                     481158
                  
                   
                     481285
                  
                   
                     481413
                  
                   
                     481540
                  
                   
                     481667
                  
                   
                     481794
                  
                   
                     481922
                  
                   
                     482049
                  
                   
                      
                  
                
                 
                   
                     486
                  
                   
                     482176
                  
                   
                     482303
                  
                   
                     482431
                  
                   
                     482558
                  
                   
                     482685
                  
                   
                     482813
                  
                   
                     482940
                  
                   
                     483067
                  
                   
                     483194
                  
                   
                     483322
                  
                   
                      
                  
                
                 
                   
                     487
                  
                   
                     483449
                  
                   
                     483576
                  
                   
                     483704
                  
                   
                     483831
                  
                   
                     483958
                  
                   
                     484086
                  
                   
                     484213
                  
                   
                     484340
                  
                   
                     484467
                  
                   
                     484595
                  
                   
                      
                  
                
                 
                   
                     488
                  
                   
                     484725
                  
                   
                     484849
                  
                   
                     484976
                  
                   
                     485104
                  
                   
                     485231
                  
                   
                     485359
                  
                   
                     485486
                  
                   
                     485613
                  
                   
                     485740
                  
                   
                     485867
                  
                   
                      
                  
                
                 
                   
                     489
                  
                   
                     485992
                  
                   
                     486122
                  
                   
                     486249
                  
                   
                     486376
                  
                   
                     486504
                  
                   
                     486631
                  
                   
                     486758
                  
                   
                     486886
                  
                   
                     487013
                  
                   
                     487140
                  
                   
                      
                  
                
                 
                   
                     490
                  
                   
                     487268
                  
                   
                     487395
                  
                   
                     487522
                  
                   
                     487649
                  
                   
                     487777
                  
                   
                     487904
                  
                   
                     488031
                  
                   
                     488159
                  
                   
                     488286
                  
                   
                     488413
                  
                   
                      
                  
                
                 
                   
                     491
                  
                   
                     488541
                  
                   
                     488669
                  
                   
                     488795
                  
                   
                     488922
                  
                   
                     489050
                  
                   
                     489177
                  
                   
                     489304
                  
                   
                     489432
                  
                   
                     489559
                  
                   
                     489687
                  
                   
                      
                  
                
                 
                   
                     492
                  
                   
                     489814
                  
                   
                     489931
                  
                   
                     490049
                  
                   
                     490166
                  
                   
                     490283
                  
                   
                     490401
                  
                   
                     490538
                  
                   
                     490675
                  
                   
                     490812
                  
                   
                     490950
                  
                   
                      
                  
                
                 
                   
                     493
                  
                   
                     491087
                  
                   
                     491214
                  
                   
                     491342
                  
                   
                     491469
                  
                   
                     491596
                  
                   
                     491724
                  
                   
                     491815
                  
                   
                     491978
                  
                   
                     492105
                  
                   
                     492233
                  
                   
                      
                  
                
                 
                   
                     494
                  
                   
                     492360
                  
                   
                     492487
                  
                   
                     492615
                  
                   
                     492742
                  
                   
                     492869
                  
                   
                     492997
                  
                   
                     493124
                  
                   
                     493251
                  
                   
                     493378
                  
                   
                     493505
                  
                   
                      
                  
                
                 
                   
                     495
                  
                   
                     493633
                  
                   
                     493760
                  
                   
                     493888
                  
                   
                     494015
                  
                   
                     494143
                  
                   
                     494270
                  
                   
                     494397
                  
                   
                     494525
                  
                   
                     494652
                  
                   
                     494779
                  
                   
                      
                  
                
                 
                   
                     496
                  
                   
                     494007
                  
                   
                     495034
                  
                   
                     495161
                  
                   
                     495288
                  
                   
                     495416
                  
                   
                     495543
                  
                   
                     495670
                  
                   
                     495798
                  
                   
                     495925
                  
                   
                     496052
                  
                   
                      
                  
                
                 
                   
                     497
                  
                   
                     496180
                  
                   
                     496307
                  
                   
                     496434
                  
                   
                     496561
                  
                   
                     496689
                  
                   
                     496816
                  
                   
                     496943
                  
                   
                     497071
                  
                   
                     497198
                  
                   
                     497327
                  
                   
                      
                  
                
                 
                   
                     498
                  
                   
                     497453
                  
                   
                     497580
                  
                   
                     497708
                  
                   
                     497835
                  
                   
                     497962
                  
                   
                     498090
                  
                   
                     498217
                  
                   
                     498344
                  
                   
                     498471
                  
                   
                     498599
                  
                   
                      
                  
                
                 
                   
                     499
                  
                   
                     499726
                  
                   
                     498853
                  
                   
                     498981
                  
                   
                     499108
                  
                   
                     499235
                  
                   
                     499363
                  
                   
                     499490
                  
                   
                     499616
                  
                   
                     499773
                  
                   
                     499871
                  
                   
                      
                  
                
              
            
             
               FINIS
               .
            
          
        
      
       
         
           
             
             
               COSMOGRAPHIA
               ,
               THE
               Second
               Part.
               OR
               ,
               THE
               DOCTRINE
               OF
               THE
               PRIMUM
               MOBILE
               .
            
          
        
         
           
             
             
             
             
               AN
               INTRODUCTION
               TO
               Astronomy
               .
            
             
               The
               First
               Part.
               
            
             
               
                 Of
                 the
                 Primum
                 Mobile
                 .
              
            
             
               
                 CHAP.
                 I.
                 
              
               
                 
                   Of
                   the
                   General
                   Subject
                   of
                   Astronomy
                   .
                
              
               
                 AStronomy
                 ,
                 is
                 a
                 Science
                 concerning
                 the
                 Measure
                 and
                 Motion
                 of
                 the
                 Spheres
                 and
                 Stars
                 .
              
               
                 2.
                 
                 Astronomy
                 hath
                 two
                 parts
                 ,
                 the
                 first
                 is
                 Absolute
                 ,
                 and
                 the
                 other
                 Comparative
                 .
              
               
                 3.
                 
                 The
                 Absolute
                 part
                 of
                 Astronomy
                 is
                 that
                 which
                 treateth
                 of
                 the
                 Measure
                 and
                 Motion
                 of
                 the
                 Orbs
                 and
                 Stars
                 absolutely
                 without
                 respect
                 to
                 any
                 distinction
                 of
                 Time.
                 
              
               
               
                 4.
                 
                 The
                 Comparative
                 part
                 of
                 Astronomy
                 is
                 that
                 ,
                 which
                 treateth
                 〈◊〉
                 the
                 Motion
                 of
                 the
                 Stars
                 ,
                 in
                 reference
                 to
                 some
                 certain
                 distinction
                 of
                 Time.
                 
              
               
                 5.
                 
                 The
                 Absolute
                 part
                 of
                 Astronomy
                 treateth
                 of
                 the
                 
                   Primum
                   Mobile
                
                 ,
                 or
                 Diurnal
                 Motion
                 of
                 all
                 the
                 Celestial
                 Orbs
                 or
                 Spheres
                 .
              
               
                 6.
                 
                 The
                 
                   Primum
                   Mobile
                
                 ,
                 or
                 Diurnal
                 Motion
                 of
                 the
                 Heavens
                 ,
                 is
                 that
                 Motion
                 ,
                 by
                 which
                 the
                 several
                 Spheres
                 are
                 moved
                 round
                 the
                 World
                 in
                 a
                 Day
                 〈…〉
                 from
                 East
                 towards
                 West
                 ,
                 and
                 ●o
                 forward●
                 from
                 West
                 towards
                 East
                 ,
                 and
                 so
                 continually
                 returning
                 to
                 the
                 same
                 point
                 from
                 whence
                 they
                 began
                 their
                 Motion
                 .
              
               
                 7.
                 
                 This
                 first
                 and
                 common
                 Motion
                 of
                 the
                 Heavens
                 ,
                 will
                 be
                 best
                 understood
                 ,
                 by
                 help
                 of
                 an
                 Instrument
                 called
                 a
                 Globe
                 ,
                 which
                 is
                 an
                 Artificial
                 representation
                 of
                 the
                 Heavens
                 ,
                 or
                 the
                 Earth
                 and
                 Waters
                 under
                 that
                 Form
                 and
                 Figure
                 of
                 Roundness
                 which
                 they
                 are
                 supposed
                 to
                 have
                 .
              
               
                 8.
                 
                 This
                 Representation
                 or
                 Description
                 of
                 the
                 Visible
                 World
                 is
                 by
                 Circles
                 ,
                 great
                 and
                 small
                 ,
                 some
                 of
                 which
                 are
                 expressed
                 upon
                 ,
                 and
                 others
                 are
                 framed
                 without
                 the
                 Globe
                 .
              
               
                 9.
                 
                 The
                 Circles
                 without
                 the
                 Globe
                 are
                 chiefly
                 two
                 ;
                 the
                 Meridian
                 and
                 the
                 Horizon
                 ,
                 the
                 one
                 of
                 Brass
                 ,
                 and
                 the
                 other
                 of
                 Wood
                 ▪
                 And
                 these
                 two
                 Circles
                 are
                 variable
                 or
                 mutable
                 ;
                 for
                 although
                 there
                 is
                 but
                 one
                 Horizon
                 and
                 one
                 Meridian
                 in
                 respect
                 of
                 the
                 whole
                 World
                 ,
                 or
                 in
                 respect
                 of
                 the
                 whole
                 Heaven
                 and
                 Earth
                 ,
                 yet
                 in
                 respect
                 of
                 the
                 particular
                 parts
                 of
                 Heaven
                 ,
                 or
                 rather
                 in
                 respect
                 of
                 the
                 diverse
                 Provinces
                 ,
                 Countries
                 and
                 Cities
                 on
                 the
                 Earth
                 ,
                 there
                 are
                 diverse
                 both
                 Horizons
                 and
                 Meridians
                 .
              
               
               
                 10.
                 
                 The
                 Meridian
                 then
                 is
                 a
                 great
                 Circle
                 without
                 the
                 Globe
                 ,
                 dividing
                 the
                 Globe
                 ,
                 and
                 consequently
                 the
                 Day
                 and
                 Night
                 into
                 two
                 equal
                 parts
                 ,
                 from
                 the
                 North
                 and
                 South
                 ends
                 whereof
                 a
                 strong
                 Wyre
                 of
                 Brass
                 or
                 Iron
                 is
                 drawn
                 or
                 supposed
                 to
                 be
                 drawn
                 through
                 the
                 Center
                 of
                 the
                 Globe
                 representing
                 the
                 Axis
                 of
                 the
                 Earth
                 ,
                 by
                 means
                 whereof
                 the
                 whole
                 Globe
                 turneth
                 round
                 within
                 the
                 said
                 Circle
                 ,
                 so
                 that
                 any
                 part
                 may
                 be
                 brought
                 directly
                 under
                 this
                 Brass
                 Meridian
                 at
                 pleasure
                 .
              
               
                 11.
                 
                 This
                 Brass
                 Meridian
                 is
                 divided
                 into
                 4
                 equal
                 parts
                 or
                 Quadrants
                 ,
                 and
                 each
                 of
                 them
                 are
                 subdivided
                 into
                 90
                 Degrees
                 ,
                 that
                 is
                 360
                 for
                 the
                 whole
                 Circle
                 .
                 The
                 reason
                 why
                 this
                 Circle
                 is
                 not
                 divided
                 in
                 360
                 Degrees
                 throughout
                 ,
                 but
                 still
                 stoping
                 at
                 90
                 ,
                 beginneth
                 again
                 with
                 10.
                 20.
                 30
                 
                 &c.
                 is
                 ,
                 for
                 that
                 the
                 use
                 of
                 this
                 Meridian
                 ,
                 in
                 reference
                 to
                 its
                 Division
                 in
                 Degrees
                 ,
                 requireth
                 no
                 more
                 than
                 that
                 Number
                 .
              
               
                 12.
                 
                 The
                 Horizon
                 is
                 a
                 great
                 Circle
                 without
                 the
                 Globe
                 ,
                 which
                 divides
                 the
                 upper
                 part
                 of
                 Heaven
                 from
                 the
                 lower
                 ,
                 so
                 that
                 the
                 one
                 half
                 is
                 always
                 above
                 that
                 Circle
                 ,
                 and
                 the
                 other
                 under
                 it
                 .
              
               
                 13.
                 
                 The
                 Poles
                 of
                 this
                 Circle
                 are
                 two
                 ,
                 the
                 one
                 directly
                 over
                 our
                 Heads
                 ,
                 and
                 is
                 called
                 the
                 Zenith
                 ;
                 the
                 other
                 is
                 under
                 feet
                 ,
                 and
                 is
                 called
                 the
                 Nadir
                 .
              
               
                 14.
                 
                 The
                 Horizon
                 is
                 either
                 Rational
                 or
                 Sensible
                 .
              
               
                 15.
                 
                 The
                 Rational
                 Horizon
                 is
                 that
                 ,
                 which
                 divideth
                 the
                 Heavens
                 and
                 the
                 Earth
                 into
                 two
                 equal
                 parts
                 ,
                 which
                 though
                 it
                 cannot
                 be
                 perceived
                 and
                 distinguished
                 by
                 the
                 eye
                 ,
                 yet
                 may
                 be
                 conceived
                 i●
                 our
                 minds
                 ,
                 in
                 which
                 respect
                 all
                 the
                 Stars
                 may
                 be
                 conceived
                 to
                 rise
                 and
                 set
                 as
                 in
                 our
                 view
                 .
              
               
               
                 16.
                 
                 The
                 Visible
                 Horizon
                 is
                 that
                 Circle
                 which
                 the
                 eye
                 doth
                 make
                 at
                 its
                 farthest
                 extent
                 of
                 sight
                 ,
                 when
                 the
                 body
                 in
                 any
                 particular
                 place
                 doth
                 turn
                 it self
                 round
                 .
                 Of
                 these
                 two
                 Circles
                 there
                 needeth
                 no
                 more
                 to
                 be
                 said
                 at
                 present
                 ,
                 only
                 we
                 may
                 observe
                 ,
                 that
                 it
                 was
                 ingeniously
                 devised
                 by
                 those
                 ,
                 who
                 first
                 thought
                 upon
                 it
                 ,
                 to
                 set
                 one
                 Meridian
                 and
                 one
                 Horizon
                 without
                 the
                 Globe
                 ,
                 to
                 avoid
                 the
                 confusion
                 ,
                 if
                 not
                 the
                 impossibility
                 ,
                 of
                 drawing
                 a
                 several
                 Meridian
                 and
                 a
                 several
                 Horizon
                 for
                 every
                 place
                 ,
                 which
                 must
                 have
                 been
                 done
                 if
                 this
                 or
                 the
                 like
                 device
                 had
                 not
                 been
                 thought
                 upon
                 .
              
               
                 17.
                 
                 Besides
                 these
                 two
                 great
                 Circles
                 without
                 the
                 Globe
                 ,
                 there
                 are
                 4
                 other
                 great
                 Circles
                 drawn
                 upon
                 the
                 Globe
                 it self
                 besides
                 the
                 Meridian
                 .
                 1.
                 
                 The
                 AEquator
                 or
                 Equinoctial
                 Circle
                 .
                 2.
                 
                 The
                 Zodiack
                 .
                 3.
                 
                 The
                 AEquinoctial
                 Colure
                 .
                 4.
                 
                 Solstitial
                 Colure
                 .
                 And
                 these
                 four
                 Circles
                 are
                 imm●table
                 ,
                 that
                 is
                 ,
                 in
                 whatsoever
                 part
                 of
                 the
                 World
                 you
                 are
                 ,
                 these
                 Circles
                 have
                 no
                 variation
                 ,
                 as
                 the
                 other
                 two
                 have
                 .
              
               
                 18.
                 
                 The
                 AEquator
                 is
                 a
                 great
                 Circle
                 drawn
                 upon
                 the
                 Globe
                 ,
                 in
                 the
                 middle
                 between
                 the
                 two
                 Poles
                 ▪
                 and
                 plainly
                 dividing
                 the
                 Globe
                 into
                 two
                 equal
                 parts
                 .
              
               
                 19.
                 
                 The
                 AEquator
                 is
                 the
                 measure
                 of
                 the
                 Motion
                 of
                 the
                 
                   Primum
                   Mobile
                
                 ,
                 for
                 15
                 Degrees
                 of
                 this
                 Circle
                 do
                 always
                 arise
                 in
                 an
                 hours
                 time
                 ;
                 the
                 which
                 doth
                 clearly
                 shew
                 ,
                 that
                 the
                 whole
                 Heavens
                 are
                 turned
                 round
                 by
                 equal
                 intervals
                 in
                 the
                 space
                 of
                 one
                 day
                 or
                 24
                 hours
                 .
              
               
                 20.
                 
                 In
                 this
                 Circle
                 the
                 Declinations
                 of
                 the
                 Stars
                 are
                 computed
                 from
                 the
                 mid-Heaven
                 towards
                 the
                 North
                 or
                 South
                 .
              
               
               
                 21.
                 
                 This
                 Circle
                 gives
                 denomination
                 to
                 the
                 AEquinox
                 ,
                 for
                 the
                 Sun
                 doth
                 twice
                 in
                 a
                 Year
                 and
                 no
                 more
                 cross
                 this
                 Circle
                 ,
                 to
                 wit
                 ,
                 when
                 he
                 enters
                 the
                 first
                 points
                 of
                 Aries
                 ,
                 and
                 Libra
                 ,
                 and
                 then
                 he
                 maketh
                 the
                 Days
                 and
                 the
                 Nights
                 equal
                 :
                 His
                 entrance
                 into
                 Aries
                 is
                 in
                 March
                 ,
                 and
                 is
                 called
                 the
                 Vernal
                 Equinox
                 ;
                 and
                 his
                 entrance
                 into
                 Libra
                 ,
                 is
                 in
                 September
                 ,
                 and
                 is
                 called
                 the
                 Autumnal
                 Equinox
                 .
              
               
                 22.
                 
                 And
                 from
                 one
                 certain
                 point
                 in
                 this
                 Circle
                 ,
                 the
                 Longitude
                 of
                 Places
                 upon
                 the
                 Earth
                 are
                 reckoned
                 ;
                 and
                 the
                 Latitude
                 of
                 Places
                 are
                 reckoned
                 from
                 this
                 Circle
                 towards
                 the
                 North
                 ,
                 or
                 the
                 South
                 Poles
                 .
              
               
                 23.
                 
                 The
                 Zodiack
                 is
                 a
                 great
                 Circle
                 drawn
                 upon
                 the
                 Globe
                 ,
                 cutting
                 the
                 AEquinoctial
                 Points
                 at
                 Oblique
                 Angles
                 :
                 for
                 although
                 it
                 divides
                 the
                 whole
                 World
                 into
                 two
                 equal
                 parts
                 ,
                 in
                 reference
                 to
                 its
                 own
                 Poles
                 ;
                 yet
                 in
                 reference
                 to
                 the
                 Poles
                 of
                 the
                 World
                 ,
                 it
                 hath
                 an
                 Oblique
                 Motion
                 .
              
               
                 24.
                 
                 The
                 Poles
                 of
                 this
                 Circle
                 are
                 as
                 far
                 distant
                 from
                 the
                 Poles
                 of
                 the
                 World
                 ,
                 as
                 the
                 greatest
                 Obliquity
                 thereof
                 is
                 from
                 the
                 Equinoctial
                 ,
                 that
                 is
                 23
                 Degrees
                 ,
                 and
                 31
                 Minutes
                 or
                 thereabouts
                 .
              
               
                 25.
                 
                 This
                 Circle
                 doth
                 differ
                 from
                 all
                 other
                 Circles
                 upon
                 the
                 Globe
                 in
                 this
                 :
                 other
                 Circles
                 (
                 to
                 speak
                 properly
                 )
                 have
                 Longitude
                 assigned
                 them
                 ,
                 but
                 no
                 Latitude
                 ;
                 but
                 this
                 hath
                 both
                 .
                 Whereas
                 other
                 Circles
                 are
                 in
                 reference
                 to
                 their
                 Longitude
                 or
                 Rotundity
                 only
                 divided
                 into
                 360
                 Degrees
                 ,
                 this
                 Circle
                 in
                 respect
                 of
                 its
                 Latitude
                 is
                 supposed
                 to
                 be
                 divided
                 into
                 16
                 Degrees
                 in
                 Latitude
                 .
              
               
                 26.
                 
                 The
                 Zodiack
                 then
                 in
                 respect
                 of
                 Longitude
                 is
                 commonly
                 divided
                 into
                 360
                 Degrees
                 as
                 other
                 
                 Circles
                 are
                 :
                 but
                 more
                 peculiarly
                 in
                 respect
                 of
                 its
                 self
                 it
                 is
                 divided
                 into
                 12
                 Parts
                 called
                 Signs
                 ,
                 and
                 each
                 Sign
                 into
                 30
                 Degrees
                 ,
                 and
                 12
                 times
                 30
                 do
                 make
                 360.
                 
              
               
                 27.
                 
                 
                   The
                   12
                   Signs
                   into
                   which
                   the
                   Zodiack
                   is
                   divided
                   ,
                   have
                   these
                   Names
                   and
                   Characters
                   .
                
                 Aries
                 ♈
                 .
                 Taurus
                 ♉
                 .
                 Gemini
                 ♊
                 .
                 Cancer
                 ♋
                 .
                 Leo
                 ♌
                 .
                 Virgo
                 ♍
                 .
                 Libra
                 ♎
                 .
                 Scorpio
                 ♏
                 .
                 Sagittarius
                 ♐
                 .
                 Capricornus
                 ♑
                 .
                 Aquarius
                 ♒
                 .
                 and
                 Pisces
                 ♓
                 .
              
               
                 28.
                 
                 These
                 two
                 Circles
                 of
                 the
                 Equator
                 and
                 Zodiack
                 are
                 crossed
                 by
                 two
                 other
                 great
                 Circles
                 ,
                 which
                 are
                 called
                 Colures
                 :
                 They
                 are
                 drawn
                 through
                 the
                 Poles
                 of
                 the
                 World
                 ,
                 and
                 cut
                 one
                 another
                 as
                 well
                 as
                 the
                 Equator
                 at
                 Right
                 Angles
                 .
                 One
                 of
                 them
                 passeth
                 through
                 the
                 Intersections
                 of
                 the
                 Equinoctial
                 points
                 ,
                 and
                 is
                 called
                 the
                 Equinoctial
                 Colure
                 .
                 The
                 other
                 passeth
                 through
                 the
                 points
                 of
                 the
                 greatest
                 distance
                 of
                 the
                 Zodiack
                 ,
                 from
                 the
                 Equator
                 ,
                 and
                 is
                 called
                 the
                 Solstitial
                 Colure
                 .
              
               
                 29.
                 
                 The
                 other
                 great
                 Circles
                 described
                 upon
                 the
                 Globe
                 are
                 the
                 Meridians
                 :
                 Where
                 we
                 must
                 not
                 think
                 much
                 to
                 hear
                 of
                 the
                 Meridians
                 again
                 .
                 That
                 of
                 Brass
                 without
                 the
                 Globe
                 is
                 to
                 serve
                 all
                 turns
                 ,
                 and
                 the
                 Globe
                 is
                 framed
                 to
                 apply
                 it self
                 thereto
                 .
                 The
                 Meridians
                 upon
                 the
                 Globe
                 ,
                 will
                 easily
                 be
                 perceived
                 to
                 be
                 of
                 a
                 new
                 and
                 another
                 use
                 .
              
               
                 30.
                 
                 The
                 Meridians
                 upon
                 the
                 Globe
                 are
                 either
                 the
                 great
                 or
                 the
                 less
                 :
                 Not
                 that
                 the
                 great
                 are
                 any
                 greater
                 than
                 the
                 less
                 ,
                 for
                 they
                 have
                 all
                 one
                 and
                 the
                 same
                 center
                 ,
                 and
                 equally
                 pass
                 through
                 the
                 Poles
                 of
                 the
                 Earth
                 ;
                 But
                 those
                 which
                 are
                 called
                 less
                 ,
                 are
                 of
                 less
                 use
                 than
                 that
                 ,
                 which
                 is
                 called
                 the
                 great
                 .
              
               
               
                 31.
                 
                 The
                 great
                 is
                 otherwise
                 called
                 the
                 fixt
                 and
                 first
                 Meridian
                 ,
                 to
                 which
                 the
                 less
                 are
                 second
                 ,
                 and
                 respectively
                 moveable
                 .
                 The
                 great
                 Meridian
                 is
                 as
                 it
                 were
                 the
                 Landmark
                 of
                 the
                 whole
                 Sphere
                 ,
                 from
                 whence
                 the
                 Longitude
                 of
                 the
                 Earth
                 ,
                 or
                 any
                 part
                 thereof
                 is
                 accounted
                 .
                 And
                 it
                 is
                 the
                 only
                 Circle
                 which
                 passing
                 through
                 the
                 Poles
                 is
                 graduated
                 or
                 divided
                 into
                 Degrees
                 ,
                 not
                 the
                 whole
                 Circle
                 but
                 the
                 half
                 ,
                 because
                 the
                 Longitude
                 is
                 to
                 be
                 reckoned
                 round
                 about
                 the
                 Earth
                 .
              
               
                 32.
                 
                 The
                 lesser
                 Meridians
                 are
                 those
                 black
                 lines
                 ;
                 which
                 you
                 see
                 to
                 pass
                 through
                 the
                 Poles
                 and
                 succeeding
                 the
                 great
                 at
                 10
                 and
                 10
                 Degrees
                 ,
                 as
                 in
                 most
                 Globes
                 ;
                 or
                 at
                 15
                 and
                 15
                 Degrees
                 difference
                 ,
                 as
                 in
                 some
                 .
                 Every
                 place
                 never
                 so
                 little
                 more
                 East
                 or
                 West
                 than
                 another
                 ,
                 hath
                 properly
                 a
                 several
                 Meridian
                 ,
                 yet
                 because
                 of
                 the
                 huge
                 distance
                 of
                 the
                 Earth
                 from
                 the
                 Heavens
                 ,
                 there
                 is
                 no
                 sensible
                 difference
                 between
                 the
                 Meridians
                 of
                 places
                 that
                 are
                 less
                 than
                 one
                 Degree
                 of
                 Longitude
                 asunder
                 ,
                 and
                 therefore
                 the
                 Geographers
                 as
                 well
                 as
                 the
                 Astronomers
                 allow
                 a
                 new
                 Meridian
                 to
                 every
                 Degree
                 of
                 the
                 Equator
                 ;
                 which
                 would
                 be
                 180
                 in
                 all
                 :
                 but
                 except
                 the
                 Globes
                 were
                 made
                 of
                 an
                 extream
                 and
                 an
                 unusual
                 Diameter
                 ,
                 so
                 many
                 would
                 stand
                 too
                 thick
                 for
                 the
                 Description
                 .
                 Therefore
                 most
                 commonly
                 they
                 put
                 down
                 but
                 18
                 ,
                 that
                 is
                 ,
                 at
                 10
                 Degrees
                 distance
                 from
                 one
                 another
                 ;
                 the
                 special
                 use
                 of
                 the
                 lesser
                 Meridians
                 being
                 to
                 make
                 a
                 quicker
                 dispatch
                 ,
                 in
                 the
                 account
                 of
                 the
                 Longitudes
                 .
                 Others
                 set
                 down
                 but
                 12
                 ,
                 at
                 15
                 Degrees
                 difference
                 ;
                 aiming
                 at
                 this
                 ,
                 That
                 the
                 Meridians
                 might
                 be
                 distant
                 from
                 one
                 another
                 a
                 full
                 part
                 of
                 time
                 ,
                 or
                 an
                 hour
                 :
                 for
                 seeing
                 that
                 the
                 Sun
                 is
                 carried
                 15
                 Degrees
                 of
                 the
                 Equinoctial
                 every
                 hour
                 ,
                 the
                 Meridians
                 set
                 at
                 that
                 
                 distance
                 must
                 make
                 an
                 hours
                 difference
                 in
                 the
                 rising
                 or
                 setting
                 of
                 the
                 Sun
                 in
                 those
                 places
                 which
                 differ
                 15
                 Degrees
                 in
                 Longitude
                 .
              
               
                 And
                 to
                 this
                 purpose
                 also
                 upon
                 the
                 North
                 end
                 of
                 the
                 Globe
                 ,
                 without
                 the
                 Brass
                 Meridian
                 ,
                 there
                 is
                 a
                 small
                 Circle
                 of
                 Brass
                 set
                 ,
                 and
                 divided
                 into
                 two
                 equal
                 parts
                 ,
                 and
                 each
                 of
                 them
                 into
                 twelve
                 ,
                 that
                 is
                 ,
                 twenty
                 four
                 all
                 ;
                 to
                 shew
                 the
                 hour
                 of
                 the
                 Day
                 and
                 Night
                 ,
                 in
                 any
                 place
                 where
                 the
                 Day
                 and
                 Night
                 exceed
                 not
                 24
                 hours
                 ;
                 for
                 which
                 purpose
                 it
                 hath
                 a
                 little
                 Brass
                 Pin
                 turning
                 about
                 upon
                 the
                 Pole
                 ,
                 and
                 pointing
                 to
                 the
                 several
                 hours
                 ,
                 which
                 is
                 therefore
                 the
                 
                   Index
                   Horarius
                
                 ,
                 or
                 Hour
                 Index
                 .
              
               
                 33.
                 
                 Having
                 described
                 the
                 great
                 Circles
                 framed
                 without
                 and
                 drawn
                 upon
                 the
                 Globe
                 ,
                 we
                 will
                 now
                 describe
                 the
                 lesser
                 Circles
                 also
                 ;
                 And
                 these
                 lesser
                 Circles
                 are
                 called
                 Parallels
                 ,
                 that
                 is
                 ,
                 such
                 as
                 are
                 in
                 all
                 places
                 equally
                 distant
                 from
                 the
                 Equator
                 ;
                 and
                 these
                 Circles
                 how
                 little
                 soever
                 ,
                 are
                 supposed
                 to
                 be
                 divided
                 into
                 360
                 Degrees
                 :
                 but
                 these
                 Degrees
                 are
                 not
                 so
                 large
                 as
                 in
                 the
                 great
                 Circles
                 ,
                 but
                 do
                 proportionably
                 decrease
                 according
                 to
                 the
                 Radius
                 by
                 which
                 they
                 are
                 drawn
                 .
              
               
                 34.
                 
                 These
                 lesser
                 Circles
                 are
                 either
                 the
                 Tropicks
                 or
                 the
                 Polar
                 Circles
                 .
              
               
                 35.
                 
                 The
                 Tropicks
                 are
                 two
                 small
                 Circles
                 drawn
                 upon
                 the
                 Globe
                 ,
                 one
                 beyond
                 the
                 Equator
                 towards
                 the
                 North
                 Pole
                 ,
                 and
                 the
                 other
                 towards
                 the
                 South
                 ,
                 Shewing
                 the
                 way
                 which
                 the
                 Sun
                 makes
                 in
                 his
                 Diurnal
                 Motion
                 ,
                 when
                 he
                 is
                 at
                 his
                 greatest
                 distance
                 from
                 the
                 Equator
                 either
                 North
                 or
                 South
                 .
                 These
                 Circles
                 are
                 called
                 Tropicks
                 
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                
                 ,
                 that
                 is
                 ,
                 from
                 the
                 Suns
                 returning
                 :
                 for
                 the
                 Sun
                 coming
                 to
                 these
                 Circles
                 ,
                 he
                 is
                 at
                 his
                 greatest
                 distance
                 from
                 the
                 Equator
                 ,
                 and
                 in
                 the
                 same
                 Moment
                 of
                 time
                 
                 sloping
                 as
                 it
                 were
                 his
                 course
                 ,
                 he
                 returns
                 nearer
                 and
                 nearer
                 to
                 the
                 Equator
                 again
                 .
              
               
                 36.
                 
                 These
                 Tropical
                 Circles
                 do
                 shew
                 the
                 point
                 of
                 Heaven
                 in
                 which
                 the
                 Sun
                 doth
                 make
                 either
                 the
                 longest
                 Day
                 ,
                 or
                 the
                 Shortest
                 Day
                 in
                 the
                 Year
                 ,
                 according
                 as
                 he
                 is
                 in
                 the
                 Northern
                 or
                 the
                 Southern
                 Tropick
                 :
                 And
                 are
                 drawn
                 at
                 23
                 Degrees
                 and
                 a
                 half
                 distant
                 from
                 the
                 Equator
                 .
              
               
                 37.
                 
                 The
                 Polar
                 Circles
                 are
                 two
                 lesser
                 Circles
                 drawn
                 upon
                 the
                 Globe
                 at
                 the
                 Radius
                 of
                 23
                 Degrees
                 and
                 a
                 half
                 distant
                 from
                 the
                 Poles
                 of
                 the
                 World
                 ,
                 shewing
                 thereby
                 the
                 Poles
                 of
                 the
                 Zodiack
                 ,
                 which
                 is
                 so
                 many
                 Degrees
                 distant
                 from
                 the
                 Equator
                 on
                 both
                 sides
                 thereof
                 .
              
               
                 38.
                 
                 These
                 Polar
                 Circles
                 are
                 66
                 Degrees
                 and
                 a
                 half
                 distant
                 from
                 the
                 Equator
                 ,
                 and
                 43
                 Degrees
                 distant
                 from
                 his
                 nearest
                 Tropick
                 .
                 They
                 are
                 called
                 the
                 Arctick
                 and
                 Antarctick
                 Circles
                 .
              
               
                 39.
                 
                 The
                 Arctick
                 Circle
                 is
                 that
                 which
                 is
                 described
                 about
                 the
                 Arctick
                 Pole
                 ,
                 and
                 passeth
                 almost
                 through
                 the
                 middle
                 of
                 the
                 Head
                 of
                 the
                 greater
                 Bear.
                 It
                 is
                 called
                 the
                 Arctick
                 Circle
                 
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                
                 from
                 the
                 two
                 conspicuous
                 Stars
                 towards
                 the
                 North
                 ;
                 called
                 the
                 greater
                 and
                 the
                 lesser
                 Bear.
                 
              
               
                 40.
                 
                 The
                 Antarctick
                 Circle
                 is
                 that
                 which
                 is
                 described
                 about
                 the
                 Antarctick
                 or
                 South
                 Pole.
                 It
                 is
                 so
                 called
                 
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                
                 that
                 is
                 ,
                 from
                 being
                 opposite
                 to
                 the
                 greater
                 and
                 lesser
                 Bear.
                 
              
               
                 Having
                 thus
                 described
                 the
                 Globe
                 or
                 Astronomical
                 Instrument
                 by
                 which
                 the
                 Frame
                 of
                 the
                 World
                 is
                 represented
                 to
                 our
                 view
                 ,
                 I
                 will
                 proceed
                 to
                 shew
                 the
                 use
                 for
                 which
                 it
                 is
                 intended
                 .
              
            
             
               
               
                 CHAP.
                 II.
                 
              
               
                 
                   Of
                   the
                   Distinctions
                   and
                   Affections
                   of
                   Spherical
                   Lines
                   or
                   Arches
                   .
                
              
               
                 THE
                 uses
                 of
                 the
                 Globe
                 as
                 to
                 practice
                 ,
                 are
                 either
                 such
                 as
                 concern
                 the
                 Heavens
                 or
                 the
                 Earth
                 ,
                 in
                 either
                 of
                 which
                 ,
                 if
                 we
                 should
                 descend
                 unto
                 particulars
                 ,
                 the
                 uses
                 would
                 be
                 more
                 in
                 number
                 ,
                 than
                 a
                 short
                 Treatise
                 will
                 contain
                 :
                 Seeing
                 therefore
                 that
                 all
                 Problems
                 which
                 concern
                 the
                 Globe
                 ,
                 may
                 be
                 best
                 and
                 most
                 accurately
                 resolved
                 by
                 the
                 Doctrine
                 of
                 Spherical
                 Triangles
                 ,
                 we
                 will
                 contract
                 these
                 uses
                 of
                 the
                 Globe
                 (
                 which
                 otherwise
                 might
                 prove
                 infinite
                 )
                 to
                 such
                 Problems
                 as
                 come
                 within
                 the
                 compass
                 of
                 the
                 28
                 Cases
                 of
                 Right
                 and
                 Oblique
                 angled
                 Spherical
                 Triangles
                 .
              
               
                 2.
                 
                 And
                 that
                 the
                 nature
                 of
                 Spherical
                 Triangles
                 may
                 be
                 the
                 better
                 understood
                 ,
                 and
                 by
                 which
                 of
                 the
                 28
                 Cases
                 the
                 particular
                 Problems
                 may
                 be
                 best
                 resolved
                 ,
                 I
                 will
                 set
                 down
                 some
                 General
                 Definitions
                 and
                 Affections
                 ,
                 which
                 do
                 belong
                 to
                 such
                 Lines
                 or
                 Arches
                 of
                 which
                 the
                 Triangle
                 must
                 be
                 framed
                 ,
                 with
                 the
                 Parts
                 and
                 Affections
                 of
                 those
                 Triangles
                 ,
                 and
                 how
                 the
                 things
                 given
                 and
                 required
                 in
                 them
                 ,
                 may
                 be
                 represented
                 and
                 resolved
                 upon
                 and
                 by
                 the
                 Globe
                 ,
                 as
                 also
                 how
                 they
                 may
                 be
                 represented
                 and
                 resolved
                 by
                 the
                 Projection
                 of
                 the
                 Sphere
                 ,
                 and
                 by
                 the
                 Canon
                 of
                 Triangles
                 .
              
               
                 3.
                 
                 A
                 Spherical
                 Triangle
                 then
                 is
                 a
                 Figure
                 consisting
                 of
                 three
                 Arches
                 of
                 the
                 greatest
                 Circles
                 upon
                 the
                 Superficies
                 of
                 a
                 Sphere
                 or
                 Globe
                 ,
                 every
                 one
                 being
                 less
                 than
                 a
                 semicircle
                 .
              
               
               
                 4.
                 
                 A
                 great
                 Circle
                 is
                 that
                 which
                 divideth
                 the
                 Sphere
                 or
                 Globe
                 into
                 two
                 equal
                 parts
                 ,
                 and
                 thus
                 the
                 Horizon
                 ,
                 Equator
                 ,
                 Zodiack
                 and
                 Meridians
                 before
                 described
                 are
                 all
                 of
                 them
                 great
                 Circles
                 :
                 And
                 of
                 these
                 Circles
                 or
                 any
                 other
                 ,
                 there
                 must
                 be
                 three
                 Arches
                 to
                 make
                 a
                 Triangle
                 ,
                 and
                 every
                 one
                 of
                 these
                 Arches
                 severally
                 must
                 be
                 less
                 than
                 a
                 semicircle
                 :
                 To
                 make
                 this
                 plain
                 .
              
               
                 In
                 Fig.
                 1.
                 
                 The
                 streight
                 Line
                 HAR
                 doth
                 represent
                 the
                 Horizon
                 ,
                 PR
                 the
                 height
                 of
                 the
                 Pole
                 above
                 the
                 Horizon
                 ,
                 PMS
                 a
                 Meridian
                 ,
                 and
                 these
                 three
                 Arches
                 by
                 their
                 intersecting
                 one
                 another
                 do
                 visibly
                 constitute
                 four
                 Spherical
                 Triangles
                 .
                 1.
                 
                 
                   PMR
                   .
                   2.
                   
                   PMH
                   .
                   3.
                   
                   SHM.
                   4.
                   
                   SMR
                   .
                
                 And
                 every
                 Arch
                 is
                 less
                 than
                 a
                 semicircle
                 ,
                 as
                 in
                 the
                 Triangle
                 PMR
                 ,
                 the
                 Arch
                 PR
                 is
                 less
                 than
                 the
                 Semicircle
                 PRS
                 ,
                 the
                 Arch
                 MR
                 is
                 less
                 than
                 the
                 Semicircle
                 AMR
                 ,
                 and
                 the
                 Arch
                 PM
                 is
                 less
                 than
                 the
                 Semicircle
                 PMS
                 ,
                 the
                 like
                 may
                 be
                 shewed
                 in
                 the
                 other
                 Triangles
                 .
              
               
                 5.
                 
                 Spherical
                 or
                 circular
                 Lines
                 are
                 Parallel
                 or
                 Angular
                 .
              
               
                 6.
                 
                 Parallel
                 Arches
                 or
                 Circles
                 ,
                 are
                 such
                 as
                 are
                 drawn
                 upon
                 the
                 same
                 Center
                 within
                 ,
                 without
                 ,
                 or
                 equal
                 to
                 another
                 Arch
                 or
                 Circle
                 .
                 Thus
                 in
                 
                   Fig.
                   1.
                
                 
                 The
                 Arches
                 ♋
                 
                   M
                   ♋
                
                 and
                 ♑
                 O
                 ♑
                 are
                 though
                 lesser
                 Circles
                 ,
                 parallel
                 to
                 the
                 Equinoctial
                 AE
                 
                   A
                   Q
                
                 and
                 do
                 in
                 that
                 Scheme
                 represent
                 the
                 Tropicks
                 of
                 Cancer
                 and
                 Capricorn
                 .
                 The
                 manner
                 of
                 describing
                 them
                 or
                 any
                 other
                 Parallel
                 Circle
                 is
                 thus
                 ,
                 set
                 off
                 their
                 distance
                 from
                 the
                 great
                 Circle
                 ,
                 to
                 which
                 you
                 are
                 to
                 draw
                 a
                 parallel
                 with
                 your
                 Compasses
                 ,
                 by
                 help
                 of
                 your
                 Line
                 of
                 Chords
                 ,
                 which
                 in
                 this
                 Example
                 is
                 23
                 Degrees
                 and
                 a
                 half
                 from
                 AE
                 to
                 ♋
                 ,
                 then
                 draw
                 the
                 Line
                 
                   A
                   ♋
                
                 ,
                 and
                 upon
                 the
                 point
                 ♋
                 erect
                 a
                 Perpendicular
                 ,
                 
                 where
                 that
                 Perpendicular
                 shall
                 cut
                 the
                 Axis
                 PAS
                 extended
                 ,
                 is
                 the
                 Center
                 of
                 that
                 Parallel
                 .
              
               
                 7.
                 
                 A
                 Spherical
                 Angle
                 ,
                 is
                 that
                 which
                 is
                 conteined
                 by
                 two
                 Arches
                 of
                 the
                 greatest
                 Circles
                 upon
                 the
                 Superficies
                 of
                 the
                 Globe
                 intersecting
                 one
                 another
                 :
                 Angles
                 made
                 by
                 the
                 Intersection
                 of
                 two
                 little
                 Circles
                 ,
                 or
                 of
                 a
                 little
                 Circle
                 with
                 a
                 great
                 ,
                 we
                 take
                 no
                 notice
                 of
                 in
                 the
                 Doctrine
                 of
                 Spherical
                 Triangles
                 .
              
               
                 8.
                 
                 A
                 Spherical
                 Angle
                 is
                 either
                 Right
                 or
                 Oblique
                 .
              
               
                 9.
                 
                 A
                 Spherical
                 Right
                 Angle
                 is
                 that
                 which
                 is
                 conteined
                 ,
                 by
                 two
                 Arches
                 of
                 the
                 greatest
                 Circles
                 in
                 the
                 Superficies
                 of
                 the
                 Sphere
                 cutting
                 one
                 another
                 at
                 Right
                 Angles
                 ,
                 that
                 is
                 ,
                 the
                 one
                 being
                 right
                 or
                 perpendicular
                 to
                 the
                 other
                 :
                 thus
                 the
                 Brass
                 Meridian
                 cutteth
                 the
                 Horizon
                 at
                 right
                 Angles
                 ;
                 and
                 thus
                 the
                 Meridians
                 drawn
                 upon
                 the
                 Globe
                 ,
                 as
                 well
                 as
                 the
                 Brass
                 Meridian
                 ,
                 do
                 all
                 of
                 them
                 cut
                 the
                 Equator
                 at
                 Right
                 Angles
                 .
              
               
                 10.
                 
                 An
                 Oblique
                 Spherical
                 Angle
                 ,
                 is
                 that
                 which
                 is
                 conteined
                 by
                 two
                 Arches
                 of
                 the
                 greatest
                 Circles
                 in
                 the
                 Superficies
                 of
                 the
                 Sphere
                 ,
                 not
                 being
                 right
                 or
                 perpendicular
                 to
                 one
                 another
                 .
              
               
                 11.
                 
                 An
                 Oblique
                 Spherical
                 Angle
                 is
                 Obtuse
                 ,
                 or
                 Acute
                 .
              
               
                 12.
                 
                 An
                 Obtuse
                 Spherical
                 Angle
                 ,
                 is
                 that
                 which
                 is
                 greater
                 than
                 a
                 Right
                 Angle
                 .
                 An
                 Acute
                 is
                 that
                 which
                 is
                 less
                 than
                 a
                 Right
                 Angle
                 .
              
               
                 13.
                 
                 If
                 two
                 of
                 the
                 greatest
                 Circles
                 of
                 the
                 Sphere
                 shall
                 pass
                 through
                 one
                 anothers
                 Poles
                 ,
                 those
                 two
                 great
                 Circles
                 shall
                 cut
                 one
                 another
                 at
                 Right
                 Angles
                 :
                 Thus
                 the
                 Brazen
                 Meridian
                 doth
                 intersect
                 the
                 Equinoctial
                 and
                 Horizon
                 .
              
               
               
                 14.
                 
                 If
                 two
                 of
                 the
                 greatest
                 Circles
                 of
                 the
                 Sphere
                 shall
                 intersect
                 one
                 another
                 ,
                 and
                 pass
                 through
                 each
                 others
                 Poles
                 ,
                 they
                 shall
                 intersect
                 one
                 another
                 at
                 unequal
                 or
                 Oblique
                 Angles
                 ,
                 the
                 Angle
                 upon
                 the
                 one
                 side
                 of
                 the
                 intersection
                 being
                 Obtuse
                 ,
                 or
                 more
                 than
                 a
                 Right
                 ,
                 and
                 the
                 Angle
                 upon
                 the
                 other
                 side
                 of
                 the
                 intersection
                 being
                 Acute
                 or
                 less
                 than
                 a
                 Right
                 .
                 Thus
                 in
                 Fig.
                 1.
                 
                 The
                 Arch
                 PM
                 doth
                 intersect
                 the
                 Meridian
                 and
                 Horizon
                 ,
                 but
                 not
                 in
                 the
                 Poles
                 of
                 either
                 ,
                 therefore
                 the
                 Angle
                 HPM
                 upon
                 one
                 side
                 of
                 the
                 intersection
                 of
                 that
                 Arch
                 with
                 the
                 Meridian
                 ,
                 is
                 more
                 than
                 a
                 Right
                 Angle
                 ;
                 And
                 the
                 Angle
                 MPR
                 upon
                 the
                 other
                 side
                 of
                 the
                 Intersection
                 is
                 less
                 .
                 And
                 so
                 likewise
                 the
                 Angle
                 PMH
                 upon
                 the
                 one
                 side
                 of
                 the
                 intersection
                 of
                 the
                 Arch
                 PM
                 with
                 the
                 Horizon
                 HR
                 ,
                 is
                 greater
                 than
                 a
                 right
                 Angle
                 ;
                 and
                 the
                 Angle
                 RMP
                 upon
                 the
                 other
                 side
                 of
                 the
                 Intersection
                 is
                 less
                 than
                 a
                 Right
                 .
              
               
                 15.
                 
                 A
                 Spherical
                 Angle
                 is
                 measured
                 by
                 the
                 Arch
                 of
                 a
                 great
                 Circle
                 described
                 from
                 the
                 Angular
                 point
                 between
                 the
                 sides
                 of
                 the
                 Angle
                 ,
                 those
                 sides
                 being
                 continued
                 unto
                 Quadrants
                 .
                 Thus
                 the
                 Arch
                 of
                 the
                 Equator
                 TQ
                 in
                 Fig.
                 1.
                 is
                 the
                 measure
                 of
                 the
                 Angle
                 MPR
                 ,
                 or
                 TPQ
                 ,
                 the
                 sides
                 PT
                 and
                 PQ
                 being
                 Quadrants
                 .
              
               
                 And
                 the
                 measure
                 thereof
                 in
                 the
                 Projection
                 may
                 thus
                 be
                 found
                 :
                 lay
                 a
                 Ruler
                 from
                 P
                 to
                 T
                 ,
                 and
                 it
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 V
                 ;
                 and
                 the
                 Arch
                 VQ
                 being
                 taken
                 in
                 your
                 Compasses
                 and
                 applyed
                 to
                 your
                 Line
                 of
                 Chords
                 ,
                 will
                 give
                 the
                 Quantity
                 of
                 the
                 Angle
                 propounded
                 .
              
               
                 16.
                 
                 The
                 Complement
                 of
                 a
                 Spherical
                 Arch
                 or
                 Angle
                 ,
                 is
                 so
                 much
                 as
                 it
                 wanteth
                 of
                 a
                 Quadrant
                 ,
                 if
                 the
                 Arch
                 or
                 Angle
                 given
                 be
                 less
                 than
                 a
                 Quadrant
                 ;
                 or
                 so
                 much
                 as
                 it
                 wanteth
                 of
                 a
                 Semicircle
                 ,
                 
                 if
                 it
                 be
                 more
                 than
                 a
                 Quadrant
                 .
              
               
                 17.
                 
                 An
                 Arch
                 of
                 a
                 great
                 Circle
                 cutting
                 the
                 Arch
                 of
                 another
                 great
                 Circle
                 ,
                 shall
                 intersect
                 one
                 another
                 at
                 Right
                 Angles
                 ,
                 or
                 make
                 two
                 Angles
                 ;
                 which
                 being
                 taken
                 together
                 ,
                 shall
                 be
                 equal
                 unto
                 two
                 Right
                 .
                 Thus
                 in
                 Fig.
                 1.
                 
                 The
                 Axis
                 PAS
                 or
                 Equinoctial
                 Colure
                 doth
                 cut
                 the
                 Equator
                 
                   AE
                   A
                   Q
                
                 at
                 Right
                 Angles
                 ;
                 but
                 the
                 Meridian
                 PMS
                 doth
                 cut
                 the
                 Horizon
                 HMR
                 at
                 Oblique
                 Angles
                 ,
                 making
                 the
                 Angle
                 PMR
                 less
                 than
                 a
                 Right
                 ,
                 and
                 the
                 Angle
                 SMR
                 more
                 than
                 a
                 Right
                 ,
                 and
                 both
                 together
                 equal
                 to
                 a
                 Semicircle
                 .
              
               
                 18.
                 
                 From
                 these
                 general
                 Definitions
                 proper
                 to
                 Spherical
                 Lines
                 or
                 Arches
                 ,
                 the
                 general
                 Affections
                 of
                 these
                 Arches
                 may
                 easily
                 be
                 discerned
                 ;
                 I
                 mean
                 the
                 various
                 Positions
                 of
                 the
                 Globe
                 of
                 the
                 Earth
                 ,
                 in
                 respect
                 of
                 all
                 and
                 singular
                 the
                 Inhabitants
                 thereof
                 .
              
               
                 19.
                 
                 And
                 the
                 whole
                 Body
                 of
                 the
                 Sphere
                 or
                 Globe
                 ,
                 in
                 respect
                 of
                 the
                 Horizon
                 ,
                 is
                 looked
                 upon
                 by
                 the
                 Earths
                 Inhabitants
                 ,
                 either
                 in
                 a
                 Parallel
                 ,
                 a
                 Right
                 ,
                 or
                 an
                 Oblique
                 Sphere
                 .
              
               
                 20.
                 
                 A
                 Parallel
                 Sphere
                 is
                 ,
                 when
                 one
                 of
                 the
                 Poles
                 of
                 the
                 World
                 is
                 elevated
                 above
                 the
                 Horizon
                 to
                 the
                 Zenith
                 ,
                 the
                 other
                 depressed
                 as
                 low
                 as
                 the
                 Nadir
                 ,
                 and
                 the
                 Equinoctial
                 Line
                 joyned
                 with
                 the
                 Horizon
                 .
                 They
                 which
                 there
                 inhabite
                 (
                 if
                 any
                 such
                 be
                 )
                 see
                 not
                 the
                 Sun
                 or
                 other
                 Star
                 rising
                 or
                 setting
                 ,
                 or
                 higher
                 or
                 lower
                 in
                 their
                 diurnal
                 revolution
                 .
                 And
                 seeing
                 that
                 the
                 Sun
                 traverseth
                 the
                 whole
                 Zodiack
                 in
                 a
                 Year
                 ,
                 and
                 that
                 half
                 the
                 Zodiack
                 ,
                 is
                 above
                 the
                 Horizon
                 and
                 half
                 under
                 it
                 ,
                 it
                 cometh
                 to
                 pass
                 ,
                 that
                 the
                 Sun
                 setteth
                 not
                 with
                 them
                 ,
                 for
                 the
                 space
                 of
                 six
                 Months
                 ,
                 nor
                 giveth
                 them
                 any
                 Light
                 for
                 the
                 space
                 of
                 other
                 six
                 Months
                 ,
                 and
                 so
                 
                 maketh
                 but
                 one
                 Day
                 and
                 Night
                 of
                 the
                 whole
                 Year
                 .
              
               
                 21.
                 
                 A
                 Right
                 Sphear
                 is
                 ,
                 when
                 both
                 the
                 Poles
                 of
                 the
                 World
                 do
                 lie
                 in
                 the
                 Horizon
                 ,
                 and
                 the
                 Equinoctial
                 Circle
                 is
                 at
                 his
                 greatest
                 distance
                 from
                 it
                 ,
                 passing
                 through
                 the
                 Zenith
                 of
                 the
                 place
                 .
                 And
                 in
                 this
                 position
                 of
                 the
                 Sphere
                 ,
                 all
                 the
                 Coelestiall
                 Bodies
                 ,
                 Sun
                 ,
                 Moon
                 ,
                 and
                 other
                 Planets
                 ,
                 and
                 fixed
                 Stars
                 ,
                 by
                 the
                 daily
                 turning
                 about
                 of
                 the
                 Heaven
                 ,
                 do
                 directly
                 ascend
                 above
                 ,
                 and
                 also
                 directly
                 descend
                 below
                 the
                 Horizon
                 ,
                 because
                 the
                 Motions
                 which
                 they
                 make
                 in
                 their
                 Daily
                 motion
                 do
                 cut
                 the
                 Horizon
                 Perpendicularly
                 ,
                 and
                 as
                 it
                 were
                 at
                 Right
                 Angles
                 .
                 In
                 this
                 Position
                 of
                 the
                 Sphere
                 ,
                 all
                 the
                 Stars
                 may
                 be
                 observed
                 to
                 rise
                 and
                 set
                 in
                 an
                 equal
                 space
                 of
                 time
                 ,
                 and
                 to
                 continue
                 as
                 long
                 above
                 the
                 Horizon
                 ,
                 as
                 they
                 do
                 under
                 it
                 ,
                 the
                 Day
                 and
                 Night
                 to
                 those
                 Inhabitants
                 ,
                 being
                 always
                 of
                 an
                 equal
                 length
                 .
              
               
                 22.
                 
                 An
                 Oblique
                 Sphere
                 is
                 ,
                 when
                 the
                 Axis
                 of
                 the
                 World
                 (
                 being
                 neither
                 Direct
                 nor
                 Parallel
                 to
                 the
                 Horizon
                 )
                 is
                 inclined
                 obliquely
                 towards
                 both
                 sides
                 of
                 the
                 Horizon
                 ,
                 as
                 in
                 Fig.
                 1.
                 
                 Whence
                 it
                 cometh
                 to
                 pass
                 ;
                 that
                 so
                 much
                 as
                 one
                 of
                 the
                 Poles
                 is
                 elevated
                 above
                 the
                 Horizon
                 ,
                 upon
                 the
                 one
                 side
                 ;
                 so
                 much
                 is
                 the
                 other
                 depressed
                 under
                 the
                 Horizon
                 ,
                 upon
                 the
                 other
                 side
                 .
              
               
                 And
                 in
                 this
                 Position
                 of
                 Sphere
                 ,
                 the
                 Days
                 are
                 sometimes
                 longer
                 than
                 the
                 Nights
                 ,
                 sometimes
                 shorter
                 ,
                 and
                 sometimes
                 of
                 equal
                 length
                 .
                 When
                 the
                 Sun
                 is
                 in
                 either
                 of
                 the
                 Equinoctial
                 Points
                 ,
                 the
                 Days
                 and
                 Nights
                 are
                 equal
                 ;
                 but
                 when
                 he
                 declineth
                 from
                 the
                 Equator
                 towards
                 the
                 elevated
                 Pole
                 ,
                 the
                 Days
                 are
                 observed
                 to
                 encrease
                 ;
                 and
                 when
                 he
                 declineth
                 from
                 the
                 Equator
                 towards
                 the
                 opposite
                 Pole
                 ,
                 or
                 the
                 Pole
                 
                 depressed
                 ,
                 the
                 Days
                 do
                 decrease
                 ▪
                 as
                 is
                 manifest
                 in
                 Fig.
                 1.
                 
                 For
                 when
                 the
                 Sun
                 riseth
                 at
                 M
                 ,
                 the
                 Line
                 M
                 ♋
                 above
                 the
                 Horizon
                 is
                 the
                 Semidiurnal
                 Arch
                 of
                 the
                 longest
                 day
                 .
                 When
                 he
                 riseth
                 at
                 C
                 ,
                 the
                 Arch
                 C
                 ♑
                 above
                 the
                 Horizon
                 ,
                 is
                 the
                 Semidiurnal
                 Arch
                 of
                 the
                 shortest
                 Day
                 :
                 And
                 when
                 he
                 riseth
                 at
                 A
                 ,
                 the
                 Days
                 and
                 Nights
                 are
                 of
                 equal
                 Length
                 ,
                 the
                 Semidiurnal
                 Arch
                 AAE
                 ,
                 being
                 equal
                 to
                 the
                 Seminocturnal
                 Arch
                 AQ
                 .
              
            
             
               
                 CHAP.
                 III.
                 
              
               
                 
                   Of
                   the
                   kind
                   and
                   parts
                   of
                   Spherical
                   Triangles
                   ;
                   and
                   how
                   to
                   project
                   the
                   same
                   upon
                   the
                   Plane
                   of
                   the
                   Meridian
                   .
                
              
               
                 HAving
                 shewed
                 what
                 a
                 Spherical
                 Triangle
                 is
                 ,
                 and
                 of
                 what
                 Circles
                 it
                 is
                 composed
                 ,
                 with
                 the
                 general
                 Affections
                 of
                 such
                 Lines
                 :
                 I
                 will
                 now
                 shew
                 how
                 many
                 several
                 sorts
                 of
                 Triangles
                 there
                 are
                 ,
                 of
                 what
                 Circular
                 parts
                 they
                 do
                 consist
                 ,
                 and
                 such
                 Affections
                 proper
                 to
                 them
                 as
                 will
                 render
                 the
                 so●ition
                 of
                 them
                 more
                 clear
                 and
                 certain
                 .
              
               
                 2.
                 
                 Spherical
                 Triangles
                 are
                 either
                 Right
                 or
                 Oblique
                 .
              
               
                 3.
                 
                 A
                 Right
                 Angled
                 Spherical
                 Triangle
                 ,
                 is
                 that
                 which
                 hath
                 one
                 or
                 more
                 Right
                 Angles
                 .
              
               
                 4.
                 
                 A
                 Spherical
                 Triangle
                 which
                 hath
                 three
                 Right
                 Angles
                 ,
                 hath
                 always
                 his
                 three
                 sides
                 Quadrants
                 .
                 As
                 in
                 Fig.
                 1.
                 
                 The
                 Spherical
                 Triangle
                 AZR
                 ,
                 the
                 Angles
                 
                   ZRA
                   ,
                   RAZ
                
                 and
                 AZR
                 are
                 right
                 Angles
                 ,
                 and
                 the
                 three
                 sides
                 
                   AZ
                   ,
                   ZR
                
                 and
                 AR
                 are
                 Quadrants
                 also
                 .
              
               
               
                 5.
                 
                 A
                 Triangle
                 that
                 hath
                 two
                 right
                 Angles
                 ,
                 hath
                 the
                 sides
                 opposite
                 to
                 those
                 Angles
                 Quadrants
                 ,
                 and
                 the
                 third
                 side
                 is
                 the
                 measure
                 of
                 the
                 third
                 Angle
                 .
                 As
                 in
                 Fig.
                 1.
                 
                 The
                 sides
                 of
                 the
                 Spherical
                 Triangle
                 TPQ
                 ,
                 namely
                 TP
                 and
                 PQ
                 are
                 Quadrants
                 ,
                 and
                 the
                 Angles
                 opposite
                 to
                 these
                 sides
                 ,
                 to
                 wit
                 ,
                 PTQ
                 and
                 TQP
                 are
                 Quadrants
                 also
                 ,
                 and
                 the
                 third
                 Angle
                 TQ
                 is
                 the
                 measure
                 of
                 the
                 third
                 Angle
                 TPQ
                 .
                 But
                 the
                 Right
                 Angled
                 Triangle
                 which
                 hath
                 one
                 Right
                 and
                 two
                 Acute
                 Angles
                 ,
                 is
                 that
                 which
                 cometh
                 most
                 commonly
                 to
                 be
                 resolved
                 .
              
               
                 6.
                 
                 The
                 Legs
                 of
                 a
                 right
                 Angled
                 Spherical
                 Triangle
                 are
                 of
                 the
                 same
                 Affection
                 with
                 their
                 opposite
                 Angles
                 ;
                 as
                 in
                 the
                 Triangle
                 
                   ZAR
                   Fig.
                
                 1.
                 
                 The
                 side
                 ZA
                 is
                 a
                 Quadrant
                 ,
                 and
                 the
                 Angle
                 at
                 A
                 is
                 right
                 ,
                 because
                 Z
                 is
                 the
                 Pole
                 of
                 the
                 Arch
                 AR
                 and
                 ZA
                 is
                 perpendicular
                 thereunto
                 .
                 And
                 in
                 the
                 Triangle
                 RAAE
                 the
                 side
                 RZAE
                 being
                 more
                 then
                 a
                 Quadrant
                 the
                 Angle
                 RAAE
                 is
                 more
                 then
                 a
                 Quadrant
                 also
                 ,
                 being
                 more
                 then
                 the
                 Right
                 Angle
                 RAZ
                 .
                 And
                 in
                 the
                 right
                 Angled
                 Spherical
                 Triangle
                 APR
                 the
                 side
                 PR
                 being
                 less
                 then
                 a
                 Quadrant
                 ,
                 the
                 Angle
                 PAR
                 is
                 less
                 then
                 a
                 Quadrant
                 also
                 ,
                 being
                 less
                 then
                 the
                 right
                 Angle
                 RAZ
                 .
              
               
                 7.
                 
                 An
                 Oblique
                 angled
                 Spherical
                 Triangle
                 is
                 either
                 acute
                 or
                 obtuse
                 .
              
               
                 8.
                 
                 An
                 Acute
                 angled
                 Spherical
                 Triangle
                 hath
                 all
                 his
                 Angles
                 Acute
                 ,
                 and
                 each
                 Side
                 less
                 then
                 a
                 Quadrant
                 ;
                 As
                 in
                 the
                 Triangles
                 ,
                 
                   ZFP
                   .
                   Fig.
                
                 2.
                 
                 The
                 Angles
                 at
                 Z
                 and
                 P
                 are
                 acute
                 ,
                 as
                 appeareth
                 by
                 inspection
                 ;
                 and
                 the
                 Angle
                 at
                 F
                 is
                 acute
                 also
                 because
                 the
                 Measure
                 thereof
                 
                   CD
                   =
                   EM
                
                 is
                 less
                 then
                 a
                 Quadrant
                 .
              
               
               
                 9.
                 
                 An
                 Oblique
                 Angled
                 Spherical
                 Triangle
                 hath
                 all
                 his
                 Angles
                 either
                 acute
                 or
                 obtuse
                 :
                 viz.
                 Acute
                 and
                 mixt
                 .
              
               
                 10.
                 
                 The
                 Sides
                 of
                 a
                 Spherical
                 Triangle
                 may
                 be
                 turned
                 into
                 Angles
                 ,
                 and
                 the
                 Angles
                 into
                 Sides
                 ;
                 The
                 Complement
                 of
                 the
                 greatest
                 Side
                 or
                 greatest
                 Angle
                 to
                 a
                 Semicircle
                 being
                 taken
                 in
                 each
                 conversion
                 .
                 For
                 Example
                 .
                 If
                 it
                 were
                 required
                 to
                 turn
                 the
                 Angles
                 of
                 the
                 Oblique
                 Angled
                 Spherical
                 Triangle
                 ZFP
                 into
                 sides
                 in
                 
                   Fig.
                   3.
                   
                   EAE
                
                 is
                 the
                 measure
                 of
                 the
                 Angle
                 at
                 P
                 ,
                 and
                 AD
                 in
                 the
                 Triangle
                 ADC
                 equal
                 thereunto
                 ,
                 AC
                 is
                 the
                 Complement
                 of
                 FZP
                 to
                 a
                 Semicircle
                 ,
                 and
                 KM
                 the
                 the
                 Measure
                 of
                 the
                 Angle
                 at
                 F
                 is
                 equal
                 to
                 DC
                 ,
                 and
                 so
                 the
                 Sides
                 of
                 the
                 Spherical
                 Triangle
                 ADC
                 are
                 equal
                 to
                 the
                 Angles
                 of
                 the
                 Spherical
                 Triangle
                 FZP
                 ,
                 making
                 the
                 side
                 AC
                 equal
                 to
                 the
                 Complement
                 of
                 the
                 Angle
                 Z
                 to
                 a
                 Semicircle
                 .
              
               
                 11.
                 
                 In
                 Right
                 Angled
                 Spherical
                 Triangles
                 the
                 Sides
                 intending
                 the
                 Right
                 Angle
                 we
                 call
                 the
                 Legs
                 ;
                 The
                 Side
                 subtending
                 it
                 the
                 Hypotenuse
                 .
              
               
                 12.
                 
                 In
                 every
                 Spherical
                 Triangle
                 besides
                 the
                 Area
                 or
                 space
                 contained
                 ,
                 there
                 are
                 six
                 parts
                 .
                 viz.
                 Three
                 Sides
                 and
                 three
                 Angles
                 and
                 of
                 these
                 six
                 there
                 must
                 be
                 always
                 three
                 given
                 to
                 find
                 the
                 rest
                 ,
                 but
                 in
                 right
                 Angled
                 Spherical
                 Triangles
                 there
                 are
                 but
                 five
                 of
                 the
                 six
                 parts
                 parts
                 which
                 come
                 into
                 question
                 ,
                 because
                 one
                 of
                 the
                 Angles
                 being
                 right
                 is
                 allways
                 known
                 ,
                 and
                 so
                 any
                 two
                 of
                 the
                 other
                 five
                 being
                 given
                 ,
                 the
                 three
                 remaining
                 parts
                 whether
                 Sides
                 or
                 Angles
                 ,
                 may
                 be
                 found
                 .
                 But
                 before
                 I
                 come
                 to
                 the
                 solution
                 of
                 these
                 Triangles
                 whether
                 right
                 or
                 oblique
                 ,
                 I
                 will
                 first
                 shew
                 how
                 they
                 may
                 be
                 represented
                 upon
                 the
                 Globe
                 ,
                 and
                 projected
                 upon
                 the
                 plane
                 of
                 of
                 the
                 Meridian
                 .
              
               
               
                 13.
                 
                 A
                 right
                 Angled
                 Spherical
                 Triangle
                 may
                 be
                 represented
                 upon
                 the
                 Globe
                 in
                 this
                 manner
                 :
                 Elevate
                 one
                 of
                 the
                 Poles
                 of
                 the
                 Globe
                 above
                 the
                 Horizon
                 ,
                 to
                 the
                 quantity
                 of
                 one
                 of
                 the
                 given
                 Legs
                 ,
                 so
                 shall
                 the
                 distance
                 between
                 the
                 AEquinox
                 and
                 the
                 Zenith
                 be
                 equal
                 thereunto
                 ,
                 and
                 at
                 the
                 Zenith
                 fasten
                 the
                 Quadrant
                 of
                 altitude
                 ,
                 so
                 shall
                 there
                 be
                 delineated
                 upon
                 the
                 Globe
                 the
                 right
                 Angled
                 Spherical
                 Triangle
                 AEZB
                 as
                 may
                 be
                 seen
                 in
                 Fig.
                 1.
                 
                 In
                 which
                 the
                 outward
                 Circle
                 HZR
                 doth
                 represent
                 the
                 Brass
                 Meridian
                 ,
                 AEAQ
                 the
                 Equator
                 ,
                 and
                 ZC
                 the
                 Quadrant
                 of
                 altitude
                 .
              
               
                 14.
                 
                 An
                 Oblique
                 Angled
                 Spherical
                 Triangle
                 may
                 be
                 represented
                 upon
                 the
                 Globe
                 in
                 this
                 manner
                 .
                 Number
                 one
                 of
                 the
                 given
                 sides
                 from
                 one
                 of
                 the
                 Poles
                 to
                 the
                 Zenith
                 ;
                 and
                 there
                 fasten
                 the
                 Quadrant
                 of
                 Altitude
                 ,
                 upon
                 which
                 number
                 another
                 side
                 ,
                 the
                 third
                 upon
                 the
                 great
                 Meridian
                 ,
                 from
                 the
                 Pole
                 towards
                 the
                 Equinoctial
                 ,
                 then
                 turn
                 the
                 Globe
                 till
                 the
                 Side
                 numbred
                 upon
                 the
                 Quadrant
                 of
                 Altitude
                 ,
                 and
                 the
                 Side
                 numbred
                 upon
                 the
                 great
                 Meridian
                 shall
                 intersect
                 one
                 another
                 ;
                 so
                 shall
                 there
                 be
                 delineated
                 upon
                 the
                 Globe
                 the
                 Oblique
                 Angled
                 Spherical
                 Triangle
                 ZFP
                 in
                 Fig.
                 3.
                 
                 In
                 which
                 ZP
                 is
                 numbred
                 upon
                 the
                 Brass
                 Meridian
                 from
                 S
                 the
                 Pole
                 of
                 the
                 World
                 to
                 Z
                 the
                 Zenith
                 ,
                 ZF
                 the
                 Azimuth
                 Circle
                 represents
                 the
                 Quadrant
                 of
                 Altitude
                 ,
                 and
                 PF
                 the
                 great
                 Meridian
                 upon
                 the
                 Globe
                 intersecting
                 the
                 Quadrant
                 of
                 Altitude
                 at
                 F.
                 
              
               
                 15.
                 
                 A
                 Right
                 or
                 Oblique
                 Angled
                 Spherical
                 Triangle
                 being
                 thus
                 delineated
                 upon
                 the
                 Globe
                 ,
                 there
                 needs
                 no
                 further
                 instructions
                 ,
                 as
                 to
                 the
                 measure
                 of
                 the
                 sides
                 ,
                 all
                 that
                 is
                 wanting
                 ,
                 is
                 the
                 laying
                 down
                 the
                 Angles
                 comprehended
                 by
                 those
                 sides
                 ,
                 and
                 the
                 finding
                 out
                 the
                 measure
                 of
                 these
                 Angles
                 
                 being
                 so
                 laid
                 down
                 .
                 And
                 that
                 this
                 may
                 be
                 the
                 better
                 understood
                 ,
                 I
                 will
                 first
                 shew
                 ;
                 how
                 the
                 several
                 Circles
                 upon
                 the
                 Globe
                 before
                 described
                 ,
                 may
                 be
                 projected
                 upon
                 the
                 Plane
                 of
                 the
                 Meridian
                 ,
                 and
                 the
                 several
                 useful
                 Triangles
                 that
                 are
                 described
                 by
                 such
                 Projection
                 with
                 such
                 Astronomical
                 Propositions
                 as
                 are
                 conteined
                 and
                 resolvable
                 by
                 these
                 Triangles
                 .
              
               
                 16.
                 
                 The
                 Circles
                 in
                 the
                 first
                 Figure
                 are
                 the
                 Meridian
                 ,
                 AEquator
                 ,
                 Horizon
                 ,
                 AEquinoctial
                 Colure
                 ,
                 and
                 the
                 Tropicks
                 .
                 The
                 Brass
                 Meridian
                 without
                 the
                 Globe
                 ,
                 is
                 a
                 perfect
                 Circle
                 described
                 by
                 taking
                 60
                 Degrees
                 from
                 your
                 Line
                 of
                 Chords
                 ,
                 as
                 the
                 Circle
                 HZRN
                 in
                 Fig.
                 1.
                 
                 Within
                 which
                 all
                 the
                 other
                 are
                 projected
                 .
                 The
                 Horizon
                 ,
                 AEquator
                 ,
                 AEquinoctial
                 Colure
                 ,
                 East
                 and
                 West
                 Azimuths
                 are
                 all
                 streight
                 Lines
                 .
                 Thus
                 the
                 Diameter
                 HAR
                 represents
                 the
                 Horizon
                 ,
                 AEAQ
                 the
                 Equator
                 ,
                 PAS
                 the
                 Equinoctial
                 Colure
                 and
                 ZAN
                 the
                 East
                 and
                 West
                 Azimuths
                 ,
                 in
                 the
                 drawing
                 of
                 these
                 there
                 is
                 no
                 difficulty
                 ,
                 PMS
                 is
                 a
                 Meridian
                 ,
                 and
                 ZCN
                 an
                 Azimuth
                 Circle
                 ,
                 for
                 the
                 drawing
                 of
                 which
                 there
                 are
                 three
                 points
                 given
                 and
                 the
                 Centers
                 of
                 the
                 Meridians
                 do
                 always
                 fall
                 in
                 the
                 Equinoctial
                 extended
                 if
                 need
                 be
                 ,
                 the
                 Centers
                 of
                 the
                 Azimuth
                 Circles
                 do
                 fall
                 in
                 the
                 Horizon
                 extended
                 if
                 need
                 be
                 ,
                 and
                 for
                 the
                 drawing
                 of
                 these
                 Circles
                 there
                 needs
                 no
                 further
                 direction
                 ,
                 supposing
                 the
                 middle
                 point
                 given
                 to
                 be
                 in
                 the
                 AEquator
                 or
                 Horizon
                 ,
                 but
                 yet
                 the
                 Centers
                 of
                 these
                 Circles
                 may
                 be
                 readily
                 found
                 ,
                 by
                 the
                 Lines
                 of
                 Tangents
                 or
                 Secants
                 ,
                 for
                 the
                 Tangent
                 of
                 the
                 Complement
                 of
                 AT
                 set
                 from
                 A
                 to
                 D
                 ,
                 or
                 the
                 Secant
                 of
                 the
                 Complement
                 set
                 from
                 A
                 to
                 D
                 will
                 give
                 the
                 Center
                 of
                 the
                 Meridian
                 PTS.
                 The
                 other
                 two
                 Circles
                 in
                 the
                 1.
                 
                 Fig.
                 
                 are
                 the
                 Tropicks
                 whose
                 Centers
                 are
                 thus
                 found
                 ;
                 each
                 Tropick
                 is
                 Deg.
                 23
                 ½
                 from
                 the
                 Equinoctial
                 ,
                 which
                 distance
                 being
                 set
                 upon
                 the
                 Meridian
                 from
                 AE
                 to
                 ♋
                 and
                 AE
                 to
                 ♑
                 ,
                 if
                 you
                 draw
                 a
                 Line
                 from
                 A
                 to
                 ♋
                 and
                 another
                 perpendicular
                 thereunto
                 from
                 ♋
                 it
                 will
                 cut
                 the
                 Axis
                 SAP
                 extended
                 in
                 the
                 Center
                 of
                 that
                 Tropick
                 ,
                 by
                 which
                 extent
                 of
                 the
                 compasses
                 the
                 other
                 Tropick
                 may
                 be
                 drawn
                 also
                 .
                 Or
                 thus
                 the
                 Co-tangent
                 of
                 
                   AE
                   ♋
                
                 set
                 from
                 ♋
                 to
                 the
                 Axis
                 extended
                 will
                 give
                 the
                 Center
                 as
                 before
                 ,
                 and
                 thus
                 may
                 all
                 other
                 Parallels
                 be
                 described
                 .
              
               
                 17.
                 
                 In
                 the
                 second
                 and
                 third
                 figures
                 ,
                 the
                 two
                 extream
                 points
                 given
                 in
                 the
                 Meridians
                 are
                 not
                 eqnidistant
                 from
                 the
                 third
                 ,
                 for
                 the
                 drawing
                 of
                 which
                 Circles
                 ,
                 if
                 the
                 common
                 way
                 of
                 bringing
                 three
                 points
                 into
                 a
                 Circle
                 be
                 not
                 liked
                 ;
                 you
                 may
                 do
                 thus
                 ,
                 from
                 the
                 given
                 point
                 at
                 F
                 and
                 the
                 Center
                 A
                 draw
                 the
                 Diameter
                 TAS
                 ,
                 and
                 cross
                 the
                 same
                 at
                 Right
                 Angles
                 with
                 the
                 Diameter
                 BAG
                 ,
                 a
                 Ruler
                 laid
                 from
                 G
                 to
                 F
                 will
                 cut
                 the
                 primitive
                 Circle
                 in
                 L
                 ,
                 make
                 
                   EL
                   =
                   BL
                
                 a
                 Ruler
                 laid
                 from
                 G
                 to
                 E
                 will
                 cut
                 the
                 Diameter
                 SAT
                 in
                 V
                 the
                 Center
                 of
                 the
                 Circle
                 BDG
                 .
                 Which
                 Circle
                 doth
                 cut
                 the
                 Diameter
                 HAR
                 in
                 the
                 Pole
                 of
                 ZF
                 ,
                 and
                 the
                 Diameter
                 AEAQ
                 in
                 D
                 in
                 the
                 Pole
                 of
                 PFX
                 ,
                 and
                 a
                 Ruler
                 laid
                 from
                 Z
                 to
                 C
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 Y
                 ,
                 and
                 making
                 
                   Y
                   O
                
                 equal
                 to
                 Y
                 a
                 Ruler
                 laid
                 from
                 Z
                 to
                 O
                 will
                 cut
                 the
                 Diameter
                 HAR
                 ,
                 extended
                 in
                 the
                 Center
                 of
                 the
                 Circle
                 ZF
                 .
              
               
                 18.
                 
                 Having
                 drawn
                 the
                 Circle
                 ZFI
                 ,
                 in
                 Fig.
                 13.
                 
                 The
                 Circle
                 PEX
                 ,
                 or
                 any
                 other
                 passing
                 through
                 the
                 point
                 F
                 ,
                 may
                 easily
                 be
                 described
                 .
                 Draw
                 AEQ
                 at
                 right
                 Angles
                 to
                 PX
                 ,
                 a
                 Ruler
                 laid
                 from
                 G
                 unto
                 
                   (
                   e
                
                 )
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 
                   (
                   m
                
                 )
                 make
                 
                   mn
                   =
                   Bn
                
                 ,
                 a
                 Ruler
                 laid
                 from
                 G
                 to
                 n
                 
                 shall
                 cut
                 the
                 Diameter
                 TFS
                 in
                 p
                 make
                 
                   Fq
                   =
                   Fp
                
                 so
                 shall
                 FQ
                 be
                 the
                 Radius
                 ,
                 and
                 the
                 Center
                 of
                 the
                 Circle
                 PFX
                 as
                 was
                 desired
                 .
              
               
                 19.
                 
                 The
                 preceeding
                 directions
                 are
                 sufficient
                 for
                 the
                 projecting
                 of
                 several
                 Circles
                 of
                 the
                 Globe
                 before
                 described
                 upon
                 the
                 Plane
                 of
                 the
                 Meridian
                 ,
                 and
                 the
                 parts
                 of
                 those
                 Circles
                 so
                 described
                 may
                 thus
                 be
                 measured
                 .
                 In
                 
                   Fig.
                   1.
                   
                   HZ
                   =
                   CZ
                   =
                   AZ
                   90
                
                 Degrees
                 .
                 Whence
                 it
                 followeth
                 ,
                 that
                 the
                 Quadrant
                 CZ
                 is
                 divided
                 into
                 Degrees
                 from
                 its
                 Pole
                 M
                 ,
                 by
                 the
                 Degrees
                 of
                 the
                 Quadrant
                 HZ
                 ,
                 that
                 is
                 a
                 Ruler
                 laid
                 from
                 M
                 to
                 any
                 part
                 of
                 the
                 Quadrant
                 HZ
                 will
                 cut
                 as
                 many
                 Degrees
                 in
                 CZ
                 as
                 it
                 doth
                 in
                 the
                 Quadrant
                 HZ
                 ,
                 and
                 thus
                 the
                 Arch
                 
                   CF
                   =
                   HK
                
                 the
                 Arch
                 
                   CB
                   =
                   HL
                
                 ,
                 and
                 the
                 Arch
                 
                   BF
                   =
                   LK
                
                 .
              
               
                 20.
                 
                 That
                 which
                 is
                 next
                 to
                 be
                 considered
                 is
                 the
                 projecting
                 or
                 laying
                 down
                 the
                 Angles
                 of
                 a
                 Triangle
                 ,
                 and
                 the
                 measuring
                 of
                 them
                 being
                 projected
                 ,
                 and
                 the
                 Angles
                 of
                 a
                 Triangle
                 are
                 either
                 such
                 as
                 are
                 conteined
                 between
                 two
                 right
                 Lines
                 as
                 the
                 Angle
                 A
                 in
                 the
                 Triangle
                 PAR
                 ;
                 or
                 such
                 as
                 are
                 conteined
                 by
                 a
                 streight
                 and
                 a
                 Circular
                 Line
                 ,
                 as
                 the
                 Angle
                 
                   PMR
                   .
                   Fig.
                
                 1.
                 
                 Or
                 such
                 as
                 are
                 conteined
                 by
                 two
                 circular
                 Lines
                 ,
                 as
                 the
                 Angles
                 FZP
                 or
                 ZFP
                 in
                 Fig.
                 3.
                 
                 The
                 projecting
                 or
                 measuring
                 the
                 first
                 sort
                 of
                 these
                 Angles
                 ,
                 needs
                 no
                 direction
                 .
              
               
                 21.
                 
                 To
                 project
                 an
                 Angle
                 conteined
                 by
                 a
                 streight
                 and
                 a
                 circular
                 line
                 as
                 the
                 Angle
                 AEBZ
                 in
                 Fig.
                 1.
                 
                 Do
                 thus
                 ,
                 lay
                 a
                 Ruler
                 from
                 N
                 to
                 C
                 ,
                 and
                 it
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 K
                 make
                 
                   ZX
                   =
                   HK
                
                 ,
                 a
                 Ruler
                 laid
                 from
                 N
                 to
                 X
                 will
                 cut
                 the
                 Diameter
                 HAR
                 in
                 the
                 point
                 M
                 the
                 Pole
                 of
                 the
                 Circle
                 ZCN
                 ,
                 a
                 Ruler
                 laid
                 from
                 M
                 to
                 B
                 the
                 Angular
                 point
                 propounded
                 ,
                 will
                 cut
                 the
                 primitive
                 Circle
                 in
                 I
                 ,
                 make
                 
                 
                   NY
                   =
                   HL
                
                 a
                 Ruler
                 laid
                 from
                 N
                 to
                 Y
                 will
                 cut
                 the
                 Circle
                 ZCN
                 in
                 W
                 ,
                 a
                 Ruler
                 laid
                 from
                 B
                 to
                 W
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 A
                 ,
                 make
                 AQ
                 equal
                 to
                 the
                 Angle
                 propounded
                 ,
                 and
                 draw
                 the
                 Diameter
                 BAQ
                 ,
                 then
                 is
                 the
                 Angle
                 AEBZ
                 or
                 
                   NBQ
                   =
                   NQ
                
                 as
                 was
                 required
                 .
              
               
                 22.
                 
                 If
                 the
                 Angle
                 had
                 been
                 projected
                 and
                 the
                 measure
                 required
                 ,
                 a
                 Ruler
                 laid
                 from
                 M
                 to
                 B
                 would
                 give
                 L
                 and
                 making
                 
                   NY
                   =
                   HL
                
                 a
                 Ruler
                 laid
                 from
                 M
                 to
                 Y
                 would
                 give
                 W
                 ,
                 from
                 B
                 to
                 W
                 would
                 give
                 A
                 ,
                 and
                 AQ
                 would
                 be
                 the
                 measure
                 of
                 the
                 Angle
                 propounded
                 .
              
               
                 23.
                 
                 To
                 project
                 an
                 Angle
                 conteined
                 by
                 two
                 circular
                 lines
                 ,
                 one
                 of
                 them
                 being
                 an
                 Arch
                 of
                 the
                 Primitive
                 Circle
                 ,
                 as
                 the
                 Angle
                 
                   AEZB
                   ,
                   Fig.
                
                 1.
                 
                 Do
                 thus
                 ,
                 set
                 off
                 the
                 quantity
                 of
                 the
                 Angle
                 given
                 from
                 H
                 to
                 G
                 ,
                 a
                 Ruler
                 laid
                 from
                 Z
                 to
                 G
                 will
                 cut
                 the
                 Diameter
                 HAR
                 in
                 the
                 point
                 C
                 ,
                 so
                 may
                 you
                 draw
                 the
                 Circle
                 ZCN
                 and
                 the
                 Angle
                 HZC
                 will
                 be
                 equal
                 to
                 the
                 Arch
                 
                   HG
                   =
                   HC
                
                 as
                 was
                 required
                 .
              
               
                 24.
                 
                 If
                 the
                 Angle
                 had
                 been
                 projected
                 and
                 the
                 measure
                 required
                 ,
                 a
                 Ruler
                 laid
                 from
                 Z
                 to
                 C
                 would
                 cut
                 the
                 Primitive
                 Circle
                 in
                 G
                 and
                 HG
                 would
                 be
                 the
                 measure
                 of
                 the
                 Angle
                 propounded
                 .
              
               
                 25.
                 
                 To
                 project
                 an
                 Angle
                 conteined
                 by
                 two
                 oblique
                 Arches
                 of
                 a
                 Circle
                 ,
                 as
                 the
                 Angle
                 ZFP
                 in
                 Fig.
                 3.
                 
                 You
                 must
                 first
                 find
                 the
                 Pole
                 of
                 one
                 of
                 the
                 two
                 Circles
                 conteining
                 the
                 Angle
                 propounded
                 ,
                 suppose
                 ZBI
                 ,
                 a
                 Ruler
                 laid
                 from
                 C
                 the
                 Pole
                 thereof
                 to
                 F
                 ,
                 the
                 Angular
                 point
                 propounded
                 ,
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 a
                 make
                 ab
                 equal
                 to
                 the
                 Angle
                 propounded
                 ,
                 a
                 Ruler
                 laid
                 from
                 F
                 to
                 b
                 will
                 cut
                 the
                 Diameter
                 AEAQ
                 in
                 D
                 the
                 Pole
                 of
                 the
                 Circle
                 PEX
                 ,
                 a
                 Ruler
                 laid
                 from
                 G
                 to
                 e
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 m
                 ,
                 make
                 
                   mn
                   =
                   Bm
                
                 
                 ler
                 laid
                 from
                 G
                 to
                 n
                 will
                 cut
                 the
                 Diameter
                 TAS
                 in
                 p
                 ,
                 make
                 
                   Aq
                   =
                   Ap
                
                 so
                 shall
                 Fp
                 be
                 the
                 Radius
                 and
                 the
                 Center
                 of
                 the
                 Circle
                 PFX
                 and
                 the
                 Angle
                 
                   ZFP
                   =
                   ab
                
                 ,
                 as
                 was
                 propounded
                 .
              
               
                 26.
                 
                 If
                 the
                 Angle
                 had
                 been
                 projected
                 and
                 the
                 measure
                 required
                 ;
                 through
                 the
                 point
                 F
                 draw
                 the
                 Diameter
                 TFS
                 and
                 the
                 Diameter
                 BAG
                 at
                 right
                 Angles
                 thereunto
                 ,
                 a
                 Ruler
                 laid
                 from
                 G
                 to
                 F
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 K
                 ,
                 and
                 making
                 
                   KE
                   =
                   BK
                
                 a
                 Line
                 drawn
                 from
                 G
                 to
                 E
                 will
                 cut
                 the
                 Diameter
                 TAS
                 in
                 the
                 Center
                 of
                 the
                 Circle
                 GDB
                 cutting
                 the
                 Diameter
                 HAR
                 in
                 C
                 the
                 Pole
                 of
                 the
                 Circle
                 ZBI
                 ,
                 and
                 the
                 Diameter
                 AEAQ
                 in
                 D
                 ,
                 the
                 Pole
                 of
                 the
                 Circle
                 PEX
                 and
                 a
                 Ruler
                 laid
                 from
                 F
                 to
                 C
                 and
                 D
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 a
                 and
                 b
                 the
                 measure
                 of
                 the
                 Angle
                 required
                 .
              
               
                 Or
                 a
                 Ruler
                 laid
                 from
                 F
                 to
                 K
                 and
                 M
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 Deg.
                 the
                 measure
                 of
                 the
                 Angle
                 propounded
                 as
                 before
                 .
              
               
                 Or
                 thus
                 a
                 Ruler
                 laid
                 from
                 C
                 and
                 D
                 to
                 F
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 ae
                 and
                 h
                 set
                 90
                 Degrees
                 from
                 e
                 and
                 h
                 to
                 f
                 and
                 l
                 a
                 Ruler
                 laid
                 from
                 C
                 to
                 f
                 will
                 cut
                 ZBI
                 in
                 M
                 and
                 a
                 Ruler
                 laid
                 from
                 D
                 to
                 l
                 will
                 cut
                 PEX
                 in
                 K.
                 This
                 done
                 a
                 Ruler
                 laid
                 from
                 F
                 to
                 K
                 and
                 M
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 g
                 and
                 d
                 the
                 measure
                 of
                 the
                 Angle
                 as
                 before
                 .
              
               
                 And
                 in
                 Fig.
                 2.
                 
                 The
                 quantity
                 of
                 the
                 Angle
                 ZEP
                 may
                 thus
                 be
                 found
                 .
                 A
                 Ruler
                 laid
                 from
                 C
                 the
                 Pole
                 of
                 the
                 Circle
                 ZFI
                 to
                 F
                 the
                 angular
                 point
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 a
                 ,
                 set
                 off
                 a
                 Quadrant
                 from
                 a
                 to
                 b
                 ,
                 a
                 Ruler
                 laid
                 from
                 C
                 to
                 b
                 will
                 cut
                 the
                 Circle
                 ZFI
                 in
                 the
                 point
                 M.
                 In
                 like
                 manner
                 a
                 Ruler
                 laid
                 from
                 D
                 the
                 Pole
                 of
                 the
                 Circle
                 PEX
                 ,
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 D
                 ,
                 set
                 off
                 a
                 Quadrant
                 from
                 A
                 to
                 h
                 ,
                 a
                 Ruler
                 laid
                 from
                 D
                 to
                 P
                 will
                 
                 cut
                 the
                 Circle
                 PFX
                 in
                 K
                 :
                 Lastly
                 a
                 Ruler
                 laid
                 from
                 F
                 to
                 K
                 ,
                 and
                 M
                 will
                 cut
                 the
                 Primitive
                 Circle
                 in
                 NS
                 the
                 measure
                 of
                 the
                 Angle
                 KFM
                 or
                 ZFP
                 ,
                 as
                 was
                 propounded
                 .
              
               
                 27.
                 
                 Having
                 shewed
                 how
                 a
                 right
                 or
                 oblique
                 Angled
                 Spherical
                 Triangle
                 may
                 be
                 projected
                 upon
                 the
                 Plane
                 of
                 the
                 Meridian
                 ,
                 as
                 well
                 as
                 delineated
                 upon
                 the
                 Globe
                 ,
                 we
                 will
                 now
                 consider
                 the
                 several
                 Triangles
                 usually
                 represented
                 upon
                 the
                 Globe
                 ,
                 with
                 the
                 several
                 Astronomical
                 and
                 Geographical
                 Problems
                 conteined
                 in
                 them
                 ,
                 and
                 resolved
                 by
                 them
                 .
              
               
                 28.
                 
                 The
                 Spherical
                 Triangles
                 usually
                 represented
                 upon
                 the
                 Globe
                 are
                 eight
                 ,
                 whereof
                 there
                 are
                 five
                 Right
                 angled
                 Triangles
                 ,
                 have
                 their
                 Denomination
                 from
                 their
                 Hypotenusas
                 .
              
               
                 The
                 first
                 is
                 called
                 the
                 Ecliptical
                 Triangle
                 ,
                 whose
                 Hypotenusa
                 is
                 an
                 Arch
                 of
                 the
                 Ecliptick
                 ,
                 the
                 Legs
                 thereof
                 are
                 Arches
                 of
                 the
                 AEquator
                 and
                 Meridian
                 ,
                 this
                 is
                 represented
                 upon
                 the
                 Globe
                 ,
                 by
                 the
                 Triangle
                 ADF
                 ,
                 in
                 Fig.
                 1.
                 
                 In
                 which
                 the
                 five
                 Circular
                 parts
                 ,
                 besides
                 the
                 Right
                 Angle
                 are
                 ;
              
               
                 1.
                 
                 The
                 Hypotenuse
                 or
                 Arch
                 of
                 the
                 Ecliptick
                 AF.
                 
              
               
                 2.
                 
                 The
                 Leg
                 or
                 Arch
                 of
                 the
                 AEquator
                 ,
                 AD.
                 
              
               
                 3.
                 
                 The
                 Leg
                 or
                 Arch
                 of
                 the
                 Meridian
                 DF.
                 
              
               
                 4.
                 
                 The
                 Oblique
                 Angle
                 of
                 the
                 Equator
                 with
                 the
                 Ecliptick
                 and
                 the
                 Suns
                 greatest
                 Declination
                 DAF
                 .
              
               
                 5.
                 
                 The
                 Oblique
                 Angle
                 of
                 the
                 Ecliptick
                 and
                 Meridian
                 ,
                 or
                 the
                 Angle
                 of
                 the
                 Suns
                 position
                 AFD
                 .
              
               
                 The
                 two
                 next
                 I
                 call
                 Meridional
                 ,
                 because
                 the
                 Hypotenusas
                 in
                 them
                 both
                 ,
                 are
                 Arches
                 of
                 a
                 Meridian
                 .
                 One
                 of
                 these
                 is
                 noted
                 with
                 the
                 Letters
                 
                 MPR
                 in
                 Fig.
                 1.
                 
                 In
                 which
                 the
                 five
                 Circular
                 parts
                 are
                 ;
              
               
                 1.
                 
                 The
                 Hypotenusa
                 or
                 Arch
                 of
                 a
                 Meridian
                 PM
                 .
              
               
                 2.
                 
                 The
                 Leg
                 or
                 Arch
                 of
                 the
                 Horizon
                 MR
                 ,
                 the
                 Suns
                 Azimuth
                 North.
                 
              
               
                 3.
                 
                 The
                 Leg
                 or
                 Arch
                 of
                 the
                 Brass
                 Meridian
                 ,
                 representing
                 the
                 height
                 of
                 the
                 Pole
                 PR
                 .
              
               
                 4.
                 
                 The
                 Oblique
                 Angle
                 of
                 the
                 Meridian
                 upon
                 the
                 Globe
                 ;
                 with
                 the
                 Brass
                 Meridian
                 ,
                 or
                 Angle
                 of
                 the
                 Hour
                 from
                 Midnight
                 .
                 P.
                 
              
               
                 5.
                 
                 The
                 Oblique
                 Angle
                 of
                 the
                 Suns
                 Meridian
                 with
                 the
                 Horizon
                 ,
                 or
                 the
                 Complement
                 of
                 the
                 Suns
                 Angle
                 of
                 Position
                 PMR
                 .
              
               
                 The
                 other
                 Right
                 Angled
                 Meridional
                 Triangle
                 is
                 noted
                 with
                 the
                 Letters
                 AEG
                 in
                 Fig.
                 1.
                 
                 In
                 which
                 the
                 5
                 Circular
                 parts
                 are
                 .
              
               
                 1.
                 
                 The
                 Hypotenusa
                 or
                 present
                 Declination
                 of
                 the
                 Sun
                 ,
                 AE
                 .
              
               
                 2.
                 
                 The
                 Leg
                 or
                 Suns
                 Amplitude
                 at
                 the
                 hour
                 of
                 six
                 ,
                 AG.
                 
              
               
                 3.
                 
                 The
                 other
                 Leg
                 or
                 Suns
                 height
                 at
                 the
                 same
                 time
                 EG
                 .
              
               
                 4.
                 
                 The
                 Angle
                 of
                 the
                 Meridian
                 with
                 the
                 Horizon
                 ,
                 or
                 Angle
                 of
                 the
                 Poles
                 elevation
                 ,
                 EAG
                 .
              
               
                 5.
                 
                 The
                 Angle
                 of
                 the
                 Meridian
                 with
                 the
                 Azimuth
                 ,
                 or
                 the
                 Angle
                 of
                 the
                 Suns
                 position
                 ,
                 AEG
                 .
              
               
                 The
                 fourth
                 Right
                 Angled
                 Spherical
                 Triangle
                 ,
                 I
                 call
                 an
                 Azimuth
                 Triangle
                 ,
                 because
                 the
                 Hypotenusa
                 doth
                 cut
                 the
                 Horizon
                 in
                 the
                 East
                 and
                 West
                 Azimuths
                 ,
                 as
                 is
                 represented
                 by
                 the
                 Triangle
                 ADV.
                 in
                 Fig.
                 1.
                 
                 In
                 which
                 the
                 5
                 Circular
                 parts
                 are
                 ,
              
               
               
                 1.
                 
                 The
                 Hypotenusa
                 ,
                 or
                 Arch
                 of
                 the
                 Sun
                 or
                 Stars
                 Altitude
                 AV.
                 
              
               
                 2.
                 
                 The
                 Leg
                 or
                 Declination
                 of
                 the
                 Sun
                 or
                 Star
                 ,
                 DV
                 .
              
               
                 3.
                 
                 The
                 other
                 Leg
                 ,
                 or
                 Right
                 Ascension
                 of
                 the
                 Sun
                 or
                 Star
                 ,
                 AD.
                 
              
               
                 4.
                 
                 The
                 Oblique
                 Angle
                 or
                 Angle
                 of
                 the
                 Poles
                 elevation
                 ,
                 DAV
                 .
              
               
                 5.
                 
                 The
                 other
                 Oblique
                 Angle
                 or
                 Angle
                 of
                 the
                 Sun
                 or
                 Stars
                 Position
                 ,
                 DVA
                 .
              
               
                 The
                 fifth
                 and
                 last
                 Right
                 Angled
                 Spherical
                 Triangle
                 ,
                 that
                 I
                 shall
                 mention
                 ,
                 I
                 call
                 an
                 Horizontal
                 Triangle
                 ,
                 because
                 the
                 Hypotenusa
                 thereof
                 is
                 an
                 Arch
                 of
                 the
                 Horizon
                 ,
                 and
                 is
                 represented
                 by
                 the
                 Triangle
                 AMT
                 in
                 Fig.
                 1.
                 
                 In
                 which
                 the
                 5
                 Circular
                 parts
                 are
                 ;
              
               
                 1.
                 
                 The
                 Hypotenusa
                 and
                 Arch
                 of
                 the
                 Horizon
                 ,
                 or
                 Amplitude
                 of
                 the
                 Sun
                 at
                 his
                 rising
                 or
                 setting
                 ,
                 AM.
                 
              
               
                 2.
                 
                 The
                 Leg
                 conteining
                 the
                 Sun
                 or
                 Stars
                 Declination
                 TM
                 .
              
               
                 3.
                 
                 The
                 other
                 Leg
                 or
                 Ascensional
                 difference
                 AT
                 ,
                 that
                 is
                 ,
                 the
                 difference
                 between
                 DT
                 the
                 Right
                 Ascension
                 and
                 DA
                 the
                 Oblique
                 Angle
                 .
              
               
                 4.
                 
                 The
                 Oblique
                 Angle
                 of
                 the
                 Horizon
                 and
                 Equator
                 ,
                 or
                 height
                 of
                 the
                 Equator
                 TAM
                 .
              
               
                 5.
                 
                 The
                 other
                 Oblique
                 Angle
                 ,
                 or
                 Angle
                 of
                 the
                 Horizon
                 and
                 Meridian
                 AMT
                 .
              
               
                 The
                 Oblique
                 Angled
                 Spherical
                 Triangles
                 usually
                 represented
                 upon
                 the
                 Globe
                 are
                 three
                 .
                 The
                 first
                 I
                 call
                 the
                 Complemental
                 Triangle
                 ,
                 because
                 the
                 sides
                 thereof
                 are
                 all
                 Complements
                 ,
                 and
                 this
                 is
                 represented
                 by
                 the
                 Triangle
                 FZP
                 in
                 Fig.
                 1.
                 
                 Whose
                 Circular
                 parts
                 are
                 ;
              
               
                 1.
                 
                 The
                 Complement
                 of
                 the
                 Poles
                 elevation
                 ZP
                 .
              
               
               
                 2.
                 
                 The
                 Complement
                 of
                 the
                 Suns
                 Declination
                 ,
                 FP
                 .
              
               
                 3.
                 
                 The
                 Complement
                 of
                 the
                 Suns
                 Altitude
                 or
                 Almicantar
                 FZ
                 .
              
               
                 4.
                 
                 The
                 Suns
                 Azimuth
                 or
                 Distance
                 from
                 the
                 North
                 FZP
                 .
              
               
                 5.
                 
                 The
                 hour
                 of
                 the
                 day
                 or
                 distance
                 of
                 the
                 Sun
                 from
                 Noon
                 ZPF
                 .
              
               
                 6.
                 
                 The
                 Angle
                 of
                 the
                 Suns
                 Position
                 ZFP
                 .
              
               
                 The
                 second
                 Oblique
                 Angled
                 Spherical
                 Triangle
                 ,
                 I
                 call
                 a
                 Geographical
                 or
                 Nautical
                 Triangle
                 ,
                 because
                 it
                 serveth
                 to
                 resolve
                 those
                 Problems
                 ,
                 which
                 concern
                 Geographie
                 and
                 Navigation
                 ,
                 and
                 this
                 is
                 also
                 represented
                 by
                 the
                 Triangle
                 FZP
                 in
                 Fig.
                 1.
                 
                 Whose
                 parts
                 are
                 .
              
               
                 1.
                 
                 The
                 Complement
                 of
                 Latitude
                 as
                 before
                 ZP
                 .
              
               
                 2.
                 
                 The
                 distance
                 between
                 the
                 two
                 places
                 at
                 Z
                 and
                 F
                 or
                 side
                 FZ
                 .
              
               
                 3.
                 
                 The
                 Complement
                 of
                 the
                 Latitude
                 of
                 the
                 place
                 at
                 F
                 or
                 side
                 FP
                 .
              
               
                 4.
                 
                 The
                 difference
                 of
                 Longitude
                 between
                 the
                 two
                 places
                 at
                 Z
                 and
                 F
                 or
                 the
                 Angle
                 FBZ.
                 
              
               
                 5.
                 
                 The
                 point
                 of
                 the
                 compass
                 leading
                 from
                 Z
                 to
                 F
                 or
                 Angle
                 FZP
                 .
              
               
                 6.
                 
                 The
                 point
                 of
                 the
                 Compass
                 leading
                 from
                 F
                 to
                 Z
                 ,
                 or
                 Angle
                 ZFP
                 .
              
               
                 The
                 third
                 Oblique
                 Angled
                 Spherical
                 Triangle
                 is
                 called
                 a
                 Polar
                 Triangle
                 ,
                 because
                 one
                 side
                 thereof
                 is
                 the
                 distance
                 between
                 the
                 Poles
                 of
                 the
                 World
                 ,
                 and
                 the
                 Poles
                 of
                 the
                 Zodiack
                 .
                 This
                 Triangle
                 is
                 represented
                 upon
                 the
                 Coelestial
                 Globe
                 ,
                 by
                 the
                 Triangle
                 FSP
                 in
                 Fig.
                 4.
                 
                 In
                 which
                 the
                 Circular
                 parts
                 are
                 ;
              
               
                 1.
                 
                 The
                 distance
                 between
                 the
                 Pole
                 of
                 the
                 
                 World
                 ,
                 and
                 the
                 Pole
                 of
                 the
                 Ecliptick
                 ,
                 or
                 the
                 Arch
                 SP.
                 
              
               
                 2.
                 
                 The
                 Complement
                 of
                 the
                 Stars
                 Declination
                 ,
                 FP
                 .
              
               
                 3.
                 
                 The
                 Complement
                 of
                 the
                 Stars
                 North
                 Latitude
                 ,
                 from
                 the
                 Ecliptick
                 or
                 the
                 Arch
                 FS
                 .
              
               
                 4.
                 
                 The
                 Angle
                 of
                 the
                 Stars
                 Right
                 Ascension
                 FPS
                 .
              
               
                 5.
                 
                 The
                 Complement
                 of
                 the
                 Stars
                 Longitude
                 FSP
                 .
              
               
                 6.
                 
                 The
                 Angle
                 of
                 the
                 Stars
                 Position
                 SFP
                 .
              
               
                 29.
                 
                 And
                 thus
                 at
                 length
                 I
                 have
                 performed
                 ,
                 what
                 was
                 proposed
                 in
                 the
                 15
                 of
                 this
                 Chapter
                 ,
                 that
                 is
                 ,
                 I
                 have
                 shewed
                 how
                 the
                 several
                 Circles
                 of
                 the
                 Globe
                 ,
                 may
                 be
                 projected
                 upon
                 the
                 Plane
                 of
                 the
                 Meridian
                 ,
                 the
                 several
                 useful
                 Triangles
                 that
                 are
                 described
                 by
                 such
                 projection
                 ,
                 with
                 such
                 Astronomical
                 Propositions
                 as
                 are
                 contained
                 and
                 resolveable
                 by
                 those
                 Triangles
                 ;
                 And
                 although
                 the
                 most
                 accurate
                 way
                 of
                 resolution
                 is
                 by
                 the
                 Doctrine
                 of
                 Trigonometry
                 and
                 the
                 Canon
                 of
                 Lines
                 and
                 Tangents
                 ,
                 yet
                 it
                 is
                 not
                 impertinent
                 to
                 do
                 the
                 same
                 upon
                 the
                 Globe
                 it self
                 ,
                 which
                 as
                 to
                 the
                 sides
                 is
                 easie
                 ,
                 but
                 to
                 measure
                 or
                 lay
                 down
                 the
                 Angles
                 is
                 sometimes
                 a
                 little
                 labourious
                 .
              
               
                 In
                 the
                 Right
                 Angled
                 Spherical
                 Triangle
                 AEBZ
                 in
                 Fig.
                 1.
                 
                 The
                 measure
                 of
                 the
                 Angle
                 AEZB
                 is
                 reckoned
                 in
                 the
                 Horizon
                 from
                 H
                 to
                 C
                 but
                 to
                 lay
                 down
                 or
                 measure
                 the
                 Angle
                 AEBZ
                 the
                 readiest
                 way
                 is
                 to
                 describe
                 the
                 Triangle
                 again
                 ,
                 making
                 
                   AEZ
                   =
                   AEB
                
                 and
                 
                   AEB
                   =
                   AEZ
                
                 ,
                 so
                 will
                 the
                 Angle
                 AEBZ
                 stand
                 where
                 the
                 Angle
                 AEZB
                 is
                 ,
                 and
                 may
                 be
                 measured
                 in
                 the
                 Horizon
                 as
                 the
                 other
                 was
                 .
              
               
               
                 And
                 so
                 in
                 the
                 Oblique
                 Angled
                 Spherical
                 Triangle
                 FZP
                 in
                 Fig.
                 1.
                 
                 The
                 Angles
                 at
                 Z
                 and
                 P
                 are
                 easily
                 measured
                 or
                 laid
                 down
                 upon
                 the
                 Globe
                 ,
                 but
                 to
                 perform
                 the
                 same
                 with
                 the
                 Angle
                 ZFP
                 ,
                 you
                 may
                 represent
                 it
                 at
                 the
                 Pole
                 or
                 Zenith
                 and
                 find
                 the
                 measure
                 in
                 the
                 Equator
                 or
                 Horizon
                 .
              
               
                 30.
                 
                 And
                 now
                 having
                 ,
                 as
                 I
                 hope
                 ,
                 sufficiently
                 prepared
                 the
                 young
                 Student
                 for
                 the
                 first
                 part
                 of
                 Astronomy
                 ,
                 the
                 Doctrine
                 of
                 the
                 
                   Primum
                   Mobile
                
                 ,
                 by
                 shewing
                 how
                 the
                 Heavens
                 and
                 the
                 Earth
                 are
                 represented
                 upon
                 the
                 Globe
                 ,
                 or
                 may
                 be
                 projected
                 in
                 Plane
                 ,
                 I
                 will
                 now
                 proceed
                 to
                 such
                 Astronomical
                 Propositions
                 as
                 are
                 generally
                 useful
                 ,
                 and
                 may
                 be
                 sufficient
                 for
                 an
                 Introduction
                 to
                 this
                 noble
                 Science
                 :
                 to
                 go
                 through
                 the
                 several
                 Triangles
                 before
                 propounded
                 ,
                 will
                 be
                 very
                 tedious
                 ,
                 I
                 will
                 therefore
                 shew
                 the
                 several
                 Problems
                 in
                 one
                 Right
                 Angled
                 and
                 one
                 Oblique
                 Angled
                 Spherical
                 Triangle
                 and
                 the
                 Canons
                 by
                 which
                 they
                 are
                 to
                 be
                 resolved
                 ,
                 and
                 leave
                 the
                 rest
                 for
                 the
                 Practice
                 of
                 my
                 Reader
                 .
                 To
                 this
                 purpose
                 I
                 will
                 next
                 acquaint
                 you
                 with
                 my
                 Lord
                 Nepiers
                 Catholick
                 Proposition
                 for
                 the
                 solution
                 of
                 all
                 Right
                 and
                 Oblique
                 Angled
                 Spherical
                 Triangles
                 .
              
            
             
               
               
                 CHAP.
                 IV.
                 
              
               
                 
                   Of
                   the
                   solution
                   of
                   Spherical
                   Triangles
                   .
                
              
               
                 IN
                 Spherical
                 Triangles
                 there
                 are
                 28
                 Varieties
                 or
                 Cases
                 ,
                 16
                 in
                 Rectangular
                 ,
                 and
                 12
                 in
                 Oblique
                 ,
                 whereof
                 all
                 the
                 Rectangular
                 and
                 ten
                 of
                 the
                 Oblique
                 may
                 be
                 resolved
                 by
                 the
                 two
                 Axioms
                 following
                 .
              
               
                 1.
                 
                 Axiom
                 .
                 In
                 all
                 Right
                 Angled
                 Spherical
                 Triangles
                 having
                 the
                 same
                 Acute
                 Angle
                 at
                 the
                 Base
                 ,
                 the
                 Sines
                 of
                 the
                 Hypotenusas
                 are
                 proportional
                 to
                 the
                 Sines
                 of
                 their
                 Perpendicular
                 .
              
               
                 2.
                 
                 Axiom
                 .
                 In
                 all
                 right
                 Angled
                 Spherical
                 Triangles
                 ,
                 the
                 Sines
                 of
                 the
                 Bases
                 and
                 the
                 Tangents
                 of
                 the
                 Perpendicular
                 are
                 proportional
                 .
              
               
                 That
                 all
                 the
                 Cases
                 of
                 a
                 Right
                 Angled
                 Spherical
                 Triangle
                 may
                 be
                 resolved
                 by
                 these
                 two
                 Axioms
                 ,
                 the
                 several
                 parts
                 of
                 the
                 Spherical
                 Triangle
                 proposed
                 ,
                 that
                 so
                 the
                 Angles
                 may
                 be
                 turned
                 into
                 sides
                 ,
                 the
                 Hypotenusa
                 ,
                 into
                 Bases
                 and
                 Perpendiculars
                 and
                 the
                 contrary
                 .
                 By
                 which
                 means
                 the
                 proportions
                 as
                 to
                 the
                 parts
                 of
                 the
                 Triangle
                 given
                 ,
                 are
                 sometimes
                 changed
                 into
                 Co-sines
                 instead
                 of
                 Sines
                 ,
                 and
                 into
                 Co-tangents
                 instead
                 of
                 Tangents
                 .
                 Which
                 the
                 Lord
                 Nepier
                 observing
                 ;
                 those
                 parts
                 of
                 the
                 Right
                 Angled
                 Spherical
                 Triangle
                 ,
                 which
                 in
                 conversion
                 do
                 change
                 their
                 proportion
                 ,
                 he
                 noteth
                 by
                 their
                 Complements
                 .
                 viz.
                 The
                 Hypotenuse
                 and
                 the
                 two
                 Acute
                 Angles
                 :
                 But
                 the
                 sides
                 or
                 Legs
                 are
                 not
                 so
                 noted
                 ,
                 
                 as
                 in
                 the
                 Right
                 Angled
                 Spherical
                 Triangle
                 MPR
                 in
                 Fig.
                 1.
                 
                 And
                 these
                 five
                 he
                 calleth
                 the
                 Circular
                 parts
                 of
                 the
                 Triangle
                 ,
                 amongst
                 which
                 the
                 Right
                 Angle
                 is
                 not
                 reckoned
                 .
              
               
                 2.
                 
                 Now
                 if
                 you
                 reckon
                 five
                 Circulat
                 parts
                 in
                 a
                 Triangle
                 ,
                 one
                 of
                 them
                 must
                 needs
                 be
                 in
                 the
                 middle
                 ,
                 and
                 of
                 the
                 other
                 four
                 ,
                 two
                 are
                 adjacent
                 to
                 that
                 middle
                 part
                 ,
                 the
                 other
                 two
                 are
                 disjunct
                 ,
                 and
                 which
                 soever
                 of
                 the
                 five
                 you
                 call
                 the
                 middle
                 part
                 ,
                 for
                 every
                 one
                 of
                 them
                 may
                 by
                 supposition
                 be
                 made
                 so
                 ;
                 those
                 two
                 Circular
                 parts
                 which
                 are
                 on
                 each
                 side
                 of
                 the
                 middle
                 are
                 called
                 extreams
                 adjunct
                 ,
                 and
                 the
                 other
                 two
                 remaining
                 parts
                 ,
                 are
                 called
                 extream
                 disjunct
                 ,
                 as
                 in
                 the
                 Triangle
                 MPR
                 if
                 you
                 make
                 the
                 Leg
                 PR
                 the
                 middle
                 part
                 ,
                 then
                 the
                 other
                 Leg
                 MR
                 and
                 the
                 Angle
                 Comp.
                 P.
                 Are
                 the
                 extreams
                 conjunct
                 ,
                 the
                 Hyp.
                 Comp.
                 MP
                 and
                 Comp.
                 M
                 ,
                 are
                 the
                 extreams
                 disjunct
                 ,
                 and
                 so
                 of
                 the
                 rest
                 ,
                 as
                 in
                 the
                 following
                 Table
                 .
              
               
               
                 
                   
                     
                       Mid.
                       Part
                    
                     
                       Exctr.
                       conj
                       .
                    
                     
                       Extr.
                       disj●
                    
                  
                   
                     
                        
                    
                     
                       Leg.
                       MR
                    
                     
                       Comp.
                       M
                    
                  
                   
                     
                       Leg
                       PR
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       Comp.
                       P
                    
                     
                       Comp.
                       MP
                    
                  
                   
                     
                        
                    
                     
                       Leg.
                       PR
                    
                     
                       Comp.
                       MP
                    
                  
                   
                     
                       Leg
                       MR
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       Comp.
                       M
                    
                     
                       Comp.
                       P
                    
                  
                   
                     
                        
                    
                     
                       Leg.
                       MR
                    
                     
                       Comp.
                       P
                    
                  
                   
                     
                       Comp.
                       M
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       Comp.
                       MP
                    
                     
                       Leg.
                       PR
                    
                  
                   
                     
                        
                    
                     
                       Comp.
                       M
                    
                     
                       Leg.
                       PR
                    
                  
                   
                     
                       Comp.
                       MP
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       Comp.
                       P.
                       
                    
                     
                       Leg.
                       MR
                    
                  
                   
                     
                        
                    
                     
                       Comp.
                       MP
                    
                     
                       Leg.
                       MR
                    
                  
                   
                     
                       Comp.
                       P
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       Leg.
                       PR
                    
                     
                       Comp.
                       M
                    
                  
                
              
               
                 3.
                 
                 These
                 things
                 premised
                 ,
                 the
                 Ld.
                 Nepier
                 as
                 a
                 consectory
                 from
                 the
                 two
                 preceeding
                 Axioms
                 hath
                 composed
                 this
                 Catholick
                 and
                 Universal
                 Proposition
                 .
              
               
                 The
                 Rectangle
                 made
                 of
                 the
                 Sine
                 of
                 the
                 middle
                 part
                 and
                 Radius
                 is
                 equal
                 to
                 the
                 Rectangle
                 made
                 of
                 the
                 Tangents
                 of
                 the
                 Extremes
                 conjunct
                 or
                 the
                 cosines
                 of
                 the
                 Extremes
                 disjunct
                 .
              
               
                 Therefore
                 if
                 the
                 middle
                 part
                 be
                 sought
                 ,
                 the
                 Radius
                 must
                 be
                 in
                 the
                 first
                 place
                 ;
                 if
                 either
                 of
                 the
                 extremes
                 ,
                 the
                 other
                 extreme
                 must
                 be
                 in
                 the
                 first
                 place
                 .
              
               
                 Only
                 note
                 that
                 if
                 the
                 middle
                 part
                 ,
                 or
                 either
                 of
                 the
                 extremes
                 propounded
                 be
                 noted
                 with
                 its
                 
                 Comp.
                 in
                 the
                 circular
                 parts
                 of
                 the
                 Triangle
                 ,
                 instead
                 of
                 the
                 Sine
                 or
                 Tangent
                 you
                 must
                 use
                 the
                 Cosine
                 or
                 Cotangent
                 of
                 such
                 circular
                 part
                 or
                 parts
                 .
              
               
                 That
                 these
                 directions
                 may
                 be
                 the
                 better
                 conceived
                 ,
                 we
                 have
                 in
                 the
                 Table
                 following
                 set
                 down
                 the
                 circular
                 parts
                 of
                 a
                 Triangle
                 under
                 their
                 respective
                 Titles
                 ,
                 whether
                 they
                 be
                 taken
                 for
                 the
                 middle
                 part
                 ,
                 or
                 for
                 the
                 extremes
                 ,
                 conjunct
                 or
                 disjunct
                 ,
                 and
                 unto
                 these
                 parts
                 ,
                 we
                 have
                 prefixed
                 the
                 Sine
                 or
                 Cosine
                 ,
                 the
                 Tangent
                 or
                 Co-tangent
                 ,
                 as
                 it
                 ought
                 to
                 be
                 by
                 the
                 former
                 Rule
                 .
              
               
                 
                   
                     
                       Mid.
                       Par.
                       
                    
                     
                       Extr.
                       Conj
                       .
                    
                     
                       Ext.
                       Disj
                       .
                    
                  
                   
                     
                        
                    
                     
                       Tang.
                       MR
                    
                     
                       Sine
                       M
                    
                  
                   
                     
                       Sine
                       PR
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       Tang.
                       P.
                       
                    
                     
                       Sine
                       MP
                    
                  
                   
                     
                        
                    
                     
                       Tang.
                       PR
                    
                     
                       Sine
                       MP
                    
                  
                   
                     
                       Sine
                       MR
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       Cotang
                       .
                       M.
                       
                    
                     
                       Sine
                       P
                    
                  
                   
                     
                        
                    
                     
                       Tang.
                       MR
                    
                     
                       Sine
                       P
                    
                  
                   
                     
                       Cosine
                       M
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       Cot.
                       MP
                    
                     
                       Cos.
                       PR
                    
                  
                   
                     
                        
                    
                     
                       Cotang
                       .
                       M.
                       
                    
                     
                       Cos.
                       PR
                    
                  
                   
                     
                       Cos.
                       MP
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       Cotang
                       .
                       P
                    
                     
                       Cos.
                       MR
                    
                  
                   
                     
                        
                    
                     
                       Cot.
                       MP
                    
                     
                       Cos.
                       MR
                    
                  
                   
                     
                       Cosine
                       P
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       Tang.
                       PR
                    
                     
                       Sine
                       M
                    
                  
                
              
               
                 
                 
                   Now
                   then
                   according
                   to
                   this
                   Table
                   and
                   the
                   former
                   Rules
                   .
                
                 
                   1.
                   
                   Sine
                   PR
                   x
                   Rad.
                   =
                   t
                   MR
                   x
                   ct
                   P.
                   
                
                 
                   2.
                   
                   Sine
                   PR
                   x
                   Rad.
                   =
                   s
                   M
                   x
                   s
                   MP
                   .
                
                 
                   3.
                   
                   Sine
                   MR
                   x
                   Rad.
                   =
                   t
                   PR
                   x
                   ct
                   M.
                   
                
                 
                   4.
                   
                   Sine
                   MR
                   x
                   Rad.
                   =
                   s
                   MP
                   x
                   s
                   P.
                   
                
                 
                   5.
                   
                   Cos.
                   M
                   x
                   Rad.
                   =
                   t
                   MR
                   x
                   ct
                   MP
                   .
                
                 
                   6.
                   
                   Cos.
                   M
                   x
                   Rad.
                   =
                   s
                   P
                   x
                   cs
                   PR
                   .
                
                 
                   7
                   Cos.
                   MP
                   x
                   Rad.
                   =
                   ct
                   M
                   x
                   ct
                   P.
                   
                
                 
                   8.
                   
                   Cos.
                   MP
                   x
                   Rad.
                   =
                   cos
                   .
                   PR
                   x
                   cs
                   MR.
                   
                
                 
                   9.
                   
                   Cos.
                   P
                   x
                   Rad.
                   =
                   ct
                   MP
                   x
                   t
                   PR
                   .
                
                 
                   10.
                   
                   Cos.
                   P
                   x
                   Rad.
                   =
                   cos
                   .
                   MR
                   x
                   s
                   M.
                   
                
              
               
                 By
                 these
                 10
                 Rectangles
                 may
                 the
                 16
                 Cases
                 of
                 a
                 Right
                 angled
                 Spherical
                 Triangle
                 be
                 resolved
                 ,
                 and
                 some
                 of
                 them
                 twice
                 over
                 ;
                 for
                 although
                 there
                 are
                 but
                 16
                 varieties
                 in
                 all
                 Right
                 angled
                 Spherical
                 Triangles
                 ,
                 yet
                 30
                 Astronomical
                 Problems
                 may
                 be
                 resolved
                 by
                 one
                 Triangle
                 ,
                 as
                 by
                 the
                 following
                 Examples
                 shall
                 more
                 clearly
                 appear
                 .
              
               
                 
                 
                   Of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                     CASE
                     1.
                     
                  
                   
                     
                       The
                       Legs
                       given
                       ,
                       to
                       find
                       the
                       Angles
                       .
                    
                  
                   
                     IN
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     .
                     The
                     given
                     Legs
                     are
                     MR
                     and
                     RP
                     .
                     The
                     Angles
                     at
                     M
                     and
                     P
                     are
                     required
                     .
                  
                   
                     By
                     the
                     first
                     of
                     the
                     10
                     equal
                     Rectangles
                     s
                     PR
                     x
                     Rad.
                     =
                     t
                     MR
                     x
                     ct
                     P.
                     in
                     which
                     P
                     is
                     fought
                     ,
                     therefore
                     putting
                     MR
                     in
                     the
                     first
                     place
                     .
                     The
                     proportion
                     is
                     .
                     t
                     MR.
                     x
                     Rad.
                     ∷
                     s
                     PR
                     .
                     ct
                     P.
                     
                  
                   
                     And
                     by
                     the
                     third
                     equal
                     Rectangle
                     .
                     t
                     PR
                     .
                     Rad.
                     ∷
                     s
                     MR.
                     ct
                     M.
                     
                  
                
                 
                   
                     CASE
                     2.
                     
                  
                   
                     
                       The
                       Legs
                       given
                       ,
                       to
                       find
                       the
                       Hypotenuse
                       .
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     .
                     The
                     given
                     Legs
                     are
                     MR
                     and
                     PR
                     .
                     The
                     Hypotenuse
                     MP
                     is
                     required
                     .
                  
                   
                     By
                     the
                     eighth
                     of
                     the
                     10
                     Rectangles
                     cos
                     .
                     MP
                     x
                     Rad.
                     =
                     cos
                     .
                     PR
                     x
                     cos
                     .
                     MR
                     in
                     which
                     MP
                     the
                     middle
                     part
                     is
                     sought
                     ,
                     therefore
                     Radius
                     must
                     be
                     put
                     in
                     the
                     first
                     place
                     ,
                     and
                     then
                     the
                     proportion
                     is
                     .
                  
                   
                     Rad
                     :
                     cos
                     .
                     
                       PR
                       ∷
                    
                     cos
                     .
                     
                       M.
                       R.
                    
                     cos
                     .
                     MP
                     .
                  
                
                 
                   
                   
                     CASE
                     3.
                     
                  
                   
                     
                       A
                       Leg
                       with
                       an
                       Angle
                       opposite
                       thereunto
                       being
                       given
                       ,
                       to
                       find
                       the
                       other
                       Leg.
                       
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     ,
                     let
                     there
                     be
                     given
                     .
                     The
                     Leg
                     MR.
                     The
                     Angle
                     P.
                     The
                     Leg
                     PR
                     inquired
                     .
                  
                   
                     By
                     the
                     first
                     of
                     the
                     10
                     Rectangles
                     .
                     Rad.
                     tMR
                     ∷
                     cot
                     .
                     P.
                     Sine
                     PR
                     .
                     or
                     The
                     Leg
                     PR
                     and
                     the
                     Angle
                     M
                     given
                     ,
                     to
                     ●ind
                     MR.
                     
                  
                   
                     By
                     the
                     3
                     of
                     the
                     10
                     Rectangles
                     .
                     Rad.
                     tPR
                     ∷
                     ct
                     M.
                     Sine
                     MR.
                     
                  
                
                 
                   
                     CASE
                     4.
                     
                  
                   
                     
                       A
                       Leg
                       with
                       an
                       Angle
                       conterminate
                       therewith
                       being
                       given
                       ,
                       to
                       find
                       the
                       other
                       Leg.
                       
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     ,
                     MPR
                     ,
                     The
                     given
                     Leg
                     is
                     MR
                     ,
                     with
                     the
                     Angle
                     M.
                     The
                     Leg
                     PR
                     is
                     required
                     .
                  
                   
                     By
                     the
                     3
                     Rectangle
                     .
                     cot
                     .
                     M.
                     Rad
                     ∷
                     Sine
                     
                       MR.
                       tPR
                    
                     .
                  
                   
                     The
                     given
                     Leg
                     RP
                     ,
                     and
                     Angle
                     P.
                     The
                     Leg
                     MR
                     is
                     required
                     .
                  
                   
                     By
                     the
                     1.
                     
                     Rectangle
                     .
                     ctP.
                     Rad
                     ∷
                     sine
                     RP
                     .
                     tang
                     .
                     MR.
                     
                  
                
                 
                   
                   
                     CASE
                     5.
                     
                  
                   
                     
                       A
                       Leg
                       and
                       an
                       Angle
                       conterminate
                       therewith
                       being
                       given
                       ,
                       to
                       find
                       the
                       Hypotenuse
                       .
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     ,
                     let
                     there
                     be
                     given
                     ,
                     
                       
                         The
                         Leg
                         
                           
                             MR
                             and
                             the
                             Angle
                             M
                          
                           
                             PR
                             and
                             the
                             Angle
                             P
                          
                        
                      
                       
                         to
                         find
                         MP
                         .
                      
                    
                  
                   
                     By
                     the
                     5.
                     
                     Rectangle
                     ,
                     t
                     MR.
                     Rad
                     ∷
                     cos
                     .
                     M.
                     ct
                     MP
                     .
                  
                   
                     By
                     the
                     9.
                     
                     Rectangle
                     .
                     t
                     PR
                     .
                     Rad.
                     ∷
                     cos
                     .
                     P.
                     ct
                     MP
                     .
                  
                
                 
                   
                     CASE
                     6.
                     
                  
                   
                     
                       The
                       Hypotenuse
                       and
                       a
                       Leg
                       given
                       ,
                       to
                       find
                       the
                       contained
                       Angle
                       .
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     ,
                     let
                     there
                     be
                     given
                     ,
                     
                       
                         The
                         Hypotenuse
                         MP
                         ,
                      
                       
                         and
                         Leg
                      
                       
                         MR.
                         PR
                         .
                      
                       
                         To
                         find
                      
                       
                         M.
                         
                      
                    
                  
                   
                     By
                     the
                     5.
                     
                     Rectangle
                     ,
                     Rad.
                     ct
                     MP
                     ∷
                     t
                     MR.
                     cos
                     .
                     M.
                     
                  
                   
                     By
                     the
                     9.
                     
                     Rectangle
                     ,
                     Rad.
                     ct
                     MR
                     ∷
                     t
                     PR
                     .
                     cos
                     .
                     P.
                     
                  
                
                 
                   
                     CASE
                     7.
                     
                  
                   
                     
                       The
                       Hypotenuse
                       and
                       one
                       Angle
                       given
                       ,
                       to
                       find
                       the
                       other
                       Angle
                       .
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     ,
                     let
                     there
                     be
                     given
                     ,
                     
                       
                       
                         The
                         Hypotenuse
                         MP
                      
                       
                         &
                         Angle
                      
                       
                         M
                         P.
                         
                      
                       
                         To
                         find
                         the
                         Angle
                      
                       
                         P.
                         M.
                         
                      
                    
                  
                   
                     By
                     the
                     7.
                     
                     Rectangle
                     ,
                     cot
                     .
                     M.
                     Rad
                     ∷
                     cos
                     .
                     MP
                     .
                     cot
                     .
                     P.
                     
                  
                   
                     By
                     the
                     7.
                     
                     Rectangle
                     cot
                     .
                     P.
                     Rad
                     ∷
                     cos
                     .
                     MP
                     .
                     cot
                     .
                     M.
                     
                  
                
                 
                   
                     CASE
                     8.
                     
                  
                   
                     
                       The
                       Oblique
                       A●gles
                       given
                       ,
                       to
                       find
                       the
                       Hypotenuse
                       .
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     ,
                     let
                     there
                     be
                     given
                     The
                     Angles
                     at
                     P
                     and
                     M
                     ,
                     To
                     find
                     the
                     Hypotenuse
                     PM
                     .
                  
                   
                     By
                     the
                     7.
                     
                     Rectangle
                     .
                     Rad.
                     ct
                     P
                     ∷
                     cot
                     .
                     M.
                     cos
                     .
                     MP
                     .
                  
                
                 
                   
                     CASE
                     9.
                     
                  
                   
                     
                       The
                       Hypotenuse
                       and
                       an
                       Angle
                       given
                       ,
                       to
                       find
                       the
                       Leg
                       conterminate
                       with
                       the
                       given
                       Angle
                       .
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     ,
                     let
                     there
                     be
                     given
                     ,
                     
                       
                         The
                         Hypotenuse
                         PM
                      
                       
                         Angle
                      
                       
                         P.
                         M.
                         
                      
                       
                         To
                         find
                      
                       
                         PR
                         .
                         MR.
                         
                      
                    
                  
                   
                     By
                     the
                     9.
                     
                     Rectangle
                     ,
                     ct
                     PM
                     .
                     Rad
                     ∷
                     cos
                     .
                     P.
                     t
                     PR
                     .
                  
                   
                     By
                     the
                     5.
                     
                     Rectangle
                     ,
                     ct
                     PM
                     .
                     Rad
                     ∷
                     cos
                     .
                     
                       M.
                       tMR
                    
                     .
                  
                
                 
                   
                   
                     CASE
                     10.
                     
                  
                   
                     
                       The
                       Hypotenuse
                       and
                       an
                       Angle
                       given
                       ,
                       to
                       find
                       the
                       Leg
                       opposite
                       to
                       the
                       given
                       Angle
                       .
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     ,
                     let
                     there
                     be
                     given
                     ,
                     
                       
                         The
                         Hypotenuse
                         PM
                      
                       
                         and
                         the
                         Angle
                      
                       
                         M.
                         P.
                         
                      
                       
                         To
                         find
                      
                       
                         PR
                         .
                         MR.
                         
                      
                    
                  
                   
                     By
                     the
                     2.
                     
                     Rectangle
                     ,
                     Rad.
                     s
                     MP
                     ∷
                     s
                     M.
                     Sine
                     PR
                     .
                  
                   
                     By
                     the
                     4.
                     
                     Rectangle
                     ,
                     Rad.
                     s
                     MP
                     ∷
                     s
                     P.
                     Sine
                     
                       MR
                       ▪
                    
                  
                
                 
                   
                     CASE
                     11.
                     
                  
                   
                     
                       A
                       Leg
                       and
                       an
                       Angle
                       opposite
                       thereunto
                       being
                       given
                       ,
                       to
                       find
                       the
                       Hypotenuse
                       .
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     ,
                     let
                     there
                     be
                     given
                     ,
                     
                       
                         The
                         Leg
                      
                       
                         PR
                         .
                         MR.
                         
                      
                       
                         and
                         the
                         Angle
                      
                       
                         M
                         P
                      
                       
                         to
                         find
                         the
                         Hypotenuse
                         PM
                         .
                      
                    
                  
                   
                     By
                     the
                     2.
                     
                     Rectangle
                     ,
                     s
                     M.
                     Rad
                     ∷
                     s
                     PR
                     .
                     s
                     MP
                     .
                  
                   
                     By
                     the
                     4.
                     
                     Rectangle
                     ,
                     s
                     P.
                     Rad
                     ∷
                     s
                     MR.
                     s
                     PM
                     .
                  
                
                 
                   
                     CASE
                     12.
                     
                  
                   
                     
                       The
                       Hypotenuse
                       and
                       a
                       Leg
                       given
                       ,
                       to
                       find
                       the
                       Angle
                       opposite
                       to
                       the
                       given
                       Leg.
                       
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     PMR
                     ,
                     
                     the
                     Hypotenuse
                     MP
                     and
                     the
                     Leg
                     MR
                     are
                     given
                     ,
                     the
                     Angle
                     at
                     P
                     is
                     required
                     .
                  
                   
                     By
                     the
                     fourth
                     Rectangle
                     Sine
                     MP
                     to
                     ,
                     Rad
                     ∷
                     s
                     MR.
                     s
                     P.
                     
                  
                   
                     The
                     Hypotenuse
                     MP
                     and
                     Leg
                     PR
                     given
                     ,
                     the
                     Angle
                     M
                     is
                     required
                     .
                  
                   
                     By
                     the
                     second
                     Rectangle
                     .
                     sMP.
                     Rad
                     ∷
                     s
                     PR
                     .
                     s
                     M.
                     
                  
                
                 
                   
                     CASE
                     13.
                     
                  
                   
                     
                       The
                       Angle
                       and
                       Leg
                       conterminate
                       with
                       it
                       being
                       given
                       ,
                       to
                       find
                       the
                       other
                       Angle
                       .
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     PMR
                     ,
                     let
                     there
                     be
                     given
                     ,
                     
                       
                         The
                         Angle
                      
                       
                         M
                         P
                      
                       
                         and
                         the
                         Leg
                      
                       
                         MR
                         PR
                      
                       
                         to
                         find
                         the
                         Angle
                      
                       
                         P.
                         M.
                         
                      
                    
                  
                   
                     By
                     the
                     tenth
                     Rectangle
                     ,
                     Rad.
                     cs
                     MR
                     ∷
                     s
                     M.
                     cs
                     P.
                     
                  
                   
                     By
                     the
                     sixth
                     Rectangle
                     ,
                     Rad.
                     s
                     P
                     ∷
                     cs
                     PR
                     .
                     cs
                     M.
                     
                  
                
                 
                   
                     CASE
                     14.
                     
                  
                   
                     
                       An
                       Angle
                       and
                       a
                       Leg
                       opposite
                       thereunto
                       being
                       given
                       ,
                       to
                       find
                       the
                       other
                       Angle
                       .
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     ,
                     let
                     there
                     be
                     given
                     ,
                     
                       
                         The
                         Angle
                      
                       
                         P
                         M
                      
                       
                         and
                         the
                         Leg
                      
                       
                         MR
                         PR
                      
                       
                         to
                         find
                         the
                         Angle
                      
                       
                         M.
                         P.
                         
                      
                    
                  
                   
                     By
                     the
                     10.
                     
                     Rectangle
                     ,
                     cs
                     MR.
                     Rad
                     ∷
                     cs
                     
                       P.
                       csM.
                    
                     
                  
                   
                     By
                     the
                     6.
                     
                     Rectangle
                     ,
                     cs
                     PR
                     .
                     Rad
                     ∷
                     cs
                     
                       M.
                       sP.
                    
                     
                  
                
                 
                   
                   
                     CASE
                     15.
                     
                  
                   
                     
                       The
                       Oblique
                       Angles
                       given
                       ,
                       to
                       find
                       a
                       Leg.
                       
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     ,
                     let
                     there
                     be
                     given
                     ,
                     the
                     Angles
                     at
                     M
                     and
                     P
                     ,
                     to
                     find
                     the
                     Legs
                     MR
                     and
                     PR
                     .
                  
                   
                     By
                     the
                     10.
                     
                     Rectangle
                     ,
                     sM.
                     Rad
                     ∷
                     cs
                     P.
                     cs
                     MR.
                     
                  
                   
                     By
                     the
                     6.
                     
                     Rectangle
                     ,
                     s
                     P.
                     Rad
                     ∷
                     cs
                     M.
                     cs
                     PR
                     .
                  
                
                 
                   
                     CASE
                     16.
                     
                  
                   
                     
                       The
                       Hypotenuse
                       and
                       one
                       Leg
                       given
                       ,
                       to
                       find
                       the
                       other
                       Leg.
                       
                    
                  
                   
                     In
                     the
                     Right
                     angled
                     Spherical
                     Triangle
                     MPR
                     ,
                     let
                     there
                     be
                     given
                     ,
                     
                       
                         The
                         Hypotenuse
                         MP
                         and
                         the
                         Leg
                      
                       
                         PR
                         MR
                      
                       
                         to
                         find
                         the
                         Leg
                      
                       
                         MR.
                         PR
                         .
                      
                    
                  
                   
                     
                       By
                       the
                       8.
                       
                       Rectangle
                       ,
                    
                     
                       csPR.
                       Rad
                       ∷
                       csMP.
                       csMR.
                       
                    
                     
                       csMR.
                       Rad
                       ∷
                       csMP.
                       csPR.
                       
                    
                  
                   
                     Thus
                     I
                     have
                     given
                     you
                     the
                     Proportions
                     by
                     which
                     the
                     16
                     Cases
                     of
                     a
                     Right
                     angled
                     Spherical
                     Triangle
                     may
                     be
                     resolved
                     ,
                     In
                     which
                     there
                     are
                     contained
                     30
                     Astronomical
                     Problems
                     .
                     Two
                     in
                     every
                     Case
                     except
                     the
                     Second
                     and
                     the
                     Eighth
                     .
                     In
                     both
                     which
                     Cases
                     there
                     are
                     but
                     two
                     Problems
                     .
                     And
                     thus
                     I
                     have
                     done
                     with
                     Right
                     angled
                     Spherical
                     Triangles
                     .
                  
                   
                   
                   
                     5.
                     
                     If
                     the
                     Angles
                     at
                     the
                     Base
                     be
                     both
                     acute
                     or
                     both
                     obtuse
                     ,
                     the
                     Perpendicular
                     shall
                     fall
                     within
                     the
                     Triangle
                     ;
                     but
                     if
                     one
                     of
                     the
                     Angles
                     of
                     the
                     Base
                     be
                     acute
                     and
                     the
                     other
                     obtuse
                     ,
                     the
                     Perpendicular
                     shall
                     fall
                     without
                     the
                     Triangle
                     .
                  
                   
                     6.
                     
                     However
                     the
                     Perpendicular
                     falleth
                     ,
                     it
                     must
                     be
                     always
                     opposite
                     to
                     a
                     known
                     Angle
                     ,
                     for
                     your
                     better
                     direction
                     ,
                     take
                     this
                     General
                     Rule
                     .
                     
                       
                         From
                         the
                         end
                         of
                         a
                         Side
                         given
                         ,
                         being
                         adjacent
                         to
                         an
                         Angle
                         given
                         ,
                         let
                         fall
                         the
                         Perpendicular
                         .
                      
                    
                  
                   
                     As
                     in
                     the
                     Triangle
                     FPS
                     in
                     Fig.
                     4.
                     
                     If
                     there
                     were
                     given
                     the
                     Side
                     
                       F
                       S
                    
                     and
                     the
                     Angle
                     at
                     S
                     ,
                     the
                     Perpendicular
                     by
                     this
                     Rule
                     must
                     fall
                     from
                     P
                     upon
                     the
                     Side
                     
                       S
                       P
                    
                     extended
                     ,
                     if
                     need
                     require
                     .
                  
                   
                     But
                     if
                     there
                     were
                     given
                     the
                     Side
                     
                       P
                       S
                    
                     and
                     the
                     Angle
                     at
                     S
                     ,
                     the
                     Perpendicular
                     must
                     fall
                     from
                     F
                     upon
                     the
                     Side
                     
                       F
                       S.
                    
                     
                  
                   
                     7.
                     
                     To
                     divide
                     an
                     Oblique
                     angled
                     Spherical
                     Triangle
                     into
                     two
                     Right
                     ,
                     by
                     letting
                     fall
                     a
                     Perpendicular
                     upon
                     the
                     Globe
                     it self
                     ,
                     is
                     not
                     necessary
                     ,
                     because
                     all
                     the
                     Cases
                     may
                     be
                     resolved
                     without
                     it
                     ,
                     but
                     in
                     projection
                     it
                     is
                     convenient
                     to
                     inform
                     the
                     fancy
                     :
                     and
                     seeing
                     the
                     reason
                     by
                     which
                     it
                     is
                     done
                     in
                     projection
                     doth
                     depend
                     upon
                     the
                     nature
                     of
                     the
                     Globe
                     ,
                     I
                     will
                     here
                     shew
                     it
                     both
                     ways
                     ,
                     first
                     upon
                     the
                     Globe
                     ,
                     and
                     then
                     by
                     projection
                     .
                  
                   
                   
                     An
                     Oblique
                     angled
                     Spherical
                     Triangle
                     may
                     be
                     divided
                     into
                     two
                     Right
                     ,
                     by
                     letting
                     fall
                     a
                     Perpendicular
                     upon
                     the
                     Globe
                     it self
                     ,
                     in
                     this
                     manner
                     .
                     In
                     the
                     Oblique
                     angled
                     Spherical
                     Triangle
                     FPS
                     in
                     Fig.
                     4.
                     let
                     it
                     be
                     required
                     to
                     let
                     fall
                     a
                     Perpendicular
                     from
                     P
                     upon
                     the
                     Side
                     FS
                     .
                     Suppose
                     the
                     Point
                     P
                     to
                     stand
                     in
                     the
                     Zenith
                     ,
                     where
                     the
                     Arch
                     FS
                     shall
                     cut
                     the
                     Zodiack
                     ,
                     which
                     in
                     this
                     Figure
                     is
                     at
                     K
                     ,
                     make
                     a
                     mark
                     ,
                     and
                     from
                     this
                     Point
                     of
                     Intersection
                     of
                     the
                     Circle
                     upon
                     which
                     the
                     Perpendicular
                     is
                     to
                     fall
                     with
                     the
                     Zodiack
                     ,
                     reckon
                     90
                     Degrees
                     ,
                     which
                     suppose
                     to
                     be
                     at
                     P
                     ;
                     a
                     thin
                     Plate
                     of
                     Brass
                     with
                     a
                     Nut
                     at
                     one
                     end
                     thereof
                     ,
                     whereby
                     to
                     fasten
                     it
                     to
                     the
                     Meridian
                     ,
                     as
                     you
                     do
                     the
                     Quadrant
                     of
                     Altitude
                     ,
                     being
                     graduated
                     as
                     that
                     is
                     ,
                     but
                     of
                     a
                     larger
                     extent
                     (
                     for
                     that
                     a
                     Quadrant
                     in
                     this
                     case
                     will
                     not
                     suffice
                     )
                     being
                     fastned
                     at
                     P
                     and
                     turned
                     about
                     till
                     it
                     cut
                     the
                     Point
                     L
                     in
                     the
                     Zodiack
                     ,
                     will
                     describe
                     upon
                     the
                     Globe
                     the
                     Arch
                     of
                     a
                     great
                     Circle
                     PEL
                     ,
                     intersecting
                     the
                     Side
                     F
                     S
                     at
                     Right
                     Angles
                     in
                     the
                     Point
                     E
                     ,
                     because
                     the
                     Point
                     L
                     in
                     the
                     Zodiack
                     is
                     the
                     Pole
                     of
                     the
                     Circle
                     SFK
                     ,
                     now
                     all
                     great
                     Circles
                     which
                     passing
                     through
                     the
                     Point
                     L
                     ,
                     shall
                     intersect
                     the
                     Circle
                     SKG
                     ,
                     shall
                     intersect
                     it
                     at
                     Right
                     Angles
                     ;
                     by
                     the
                     13.
                     of
                     the
                     2.
                     
                     Chapter
                     .
                  
                   
                     9.
                     
                     And
                     hence
                     to
                     divide
                     an
                     Oblique
                     angled
                     Spherical
                     Triangle
                     into
                     two
                     Right
                     by
                     projection
                     is
                     easie
                     ,
                     as
                     in
                     the
                     Triangle
                     FPS
                     ,
                     the
                     Pole
                     of
                     the
                     Circle
                     SFK
                     is
                     L
                     ,
                     therefore
                     the
                     Circle
                     BLP
                     shall
                     cut
                     the
                     Arch
                     FS
                     at
                     Right
                     Angles
                     in
                     the
                     Point
                     E.
                     And
                     because
                     the
                     Point
                     M
                     is
                     the
                     Pole
                     of
                     the
                     Circle
                     BFP
                     ,
                     therefore
                     the
                     Circle
                     GMS
                     shall
                     cut
                     the
                     Circle
                     BFP
                     at
                     Right
                     Angles
                     in
                     the
                     Point
                     D
                     ,
                     the
                     Side
                     
                       F
                       P
                    
                     being
                     extended
                     .
                     
                     Come
                     we
                     now
                     to
                     the
                     several
                     Cases
                     which
                     after
                     this
                     preparation
                     may
                     be
                     resolved
                     ,
                     by
                     the
                     Catholick
                     Proposition
                     .
                  
                   
                     
                       CASE
                       1.
                       
                    
                     
                       
                         Two
                         Sides
                         with
                         an
                         Angle
                         opposite
                         to
                         one
                         of
                         them
                         being
                         given
                         ,
                         to
                         find
                         the
                         Angle
                         opposite
                         to
                         the
                         other
                         .
                      
                    
                     
                       In
                       the
                       Oblique
                       angled
                       Spherical
                       Triangle
                       
                         F
                         P
                         S
                      
                       ,
                       in
                       Fig.
                       4.
                       the
                       Sides
                       and
                       Angles
                       given
                       and
                       required
                       will
                       admit
                       of
                       six
                       Varieties
                       ;
                       all
                       which
                       may
                       be
                       resolved
                       by
                       the
                       Catholick
                       Proposition
                       ,
                       at
                       two
                       operations
                       ,
                       but
                       those
                       two
                       may
                       be
                       reduced
                       to
                       one
                       ,
                       as
                       by
                       the
                       following
                       Analogies
                       to
                       every
                       Variety
                       will
                       plainly
                       appear
                       .
                       
                         
                           
                             Given
                          
                           
                             Required
                          
                           
                              
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             Rad.
                             s
                             PS
                             ∷
                             s
                             PSF
                             .
                             
                               s
                               PE
                            
                          
                        
                         
                           
                             1.
                             PS
                          
                           
                             PFS
                          
                           
                             
                               s.
                               PF
                            
                             .
                             Rad
                             ∷
                             s
                             PE.
                             
                               s
                               PFS
                            
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             s
                             PF
                             .
                             s
                             PS
                             ∷
                             s
                             PSF
                             .
                             s
                             PFS
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             Rad.
                             
                               s
                               FP
                               ∷
                               s
                               F.
                            
                             s
                             PE
                          
                        
                         
                           
                             2.
                             PS
                          
                           
                             PSF
                          
                           
                             
                               s
                               PS
                            
                             .
                             Rad
                             ∷
                             s
                             PE.
                             
                               s
                               PSF
                            
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             s.
                             PS
                             .
                             s
                             FP
                             ∷
                             s
                             PFS
                             .
                             s
                             PSF
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             Rad.
                             
                               s
                               SF
                               ∷
                               s
                               F.
                            
                             sDS
                          
                        
                         
                           
                             3.
                             FS
                          
                           
                             FPS
                          
                           
                             
                               s
                               PS
                            
                             .
                             Rad
                             ∷
                             s
                             DS.
                             
                               s
                               SPD
                            
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             s.
                             PS
                             .
                             s
                             SF
                             ∷
                             s
                             PFS
                             .
                             s
                             PSF
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             Rad.
                             s
                             PS
                             ∷
                             s
                             SPD
                             .
                             
                               s
                               DS
                            
                          
                        
                         
                           
                             4.
                             FS
                          
                           
                             PFS
                          
                           
                             s
                             FS
                             .
                             
                               Rad
                               ∷
                               s
                               DS.
                            
                             s
                             SF
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             s
                             FS
                             .
                             s
                             PS
                             ∷
                             s
                             SPF.
                             s
                             SF
                          
                        
                         
                           
                             FS
                          
                           
                              
                          
                           
                             Rad.
                             s
                             FS
                             ∷
                             s
                             S.
                             
                               s
                               FC
                            
                          
                        
                         
                           
                             5.
                             FP
                          
                           
                             FPS
                          
                           
                             s.
                             FP
                             .
                             
                               Rad
                               ∷
                               s
                               FC
                            
                             .
                             s
                             FPC
                          
                        
                         
                           
                             FSP
                          
                           
                              
                          
                           
                             s.
                             FP
                             .
                             s
                             FS
                             ∷
                             s
                             PSF
                             .
                             s
                             FPS
                          
                        
                         
                           
                             
                             FS
                          
                           
                              
                          
                           
                             Rad.
                             s
                             FP
                             ∷
                             s
                             FPC
                             .
                             
                               s
                               FC
                            
                          
                        
                         
                           
                             6.
                             FP
                          
                           
                             FSP
                          
                           
                             
                               s
                               FS
                            
                             .
                             Rad
                             ∷
                             s
                             FC
                             .
                             
                               s
                               S
                            
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             s.
                             FS
                             .
                             s
                             FP
                             ∷
                             FPS
                             .
                             s
                             PSF
                             .
                          
                        
                      
                    
                  
                   
                     
                       CASE
                       2.
                       
                    
                     
                       
                         Two
                         Sides
                         with
                         an
                         Angle
                         appo●ite
                         to
                         one
                         of
                         them
                         being
                         given
                         ,
                         to
                         find
                         the
                         contained
                         Angle
                         .
                      
                    
                     
                       In
                       this
                       Case
                       there
                       are
                       six
                       Varieties
                       ,
                       all
                       which
                       may
                       be
                       resolved
                       by
                       the
                       Catholick
                       Proposition
                       ,
                       according
                       to
                       the
                       Table
                       following
                       .
                       
                         
                           
                             Given
                          
                           
                             Required
                          
                           
                              
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             1
                             :
                             cot
                             PSF
                             .
                             Rad
                             ∷
                             cs
                             PS
                             .
                             ct
                             EPS
                          
                        
                         
                           
                             1.
                             PS
                          
                           
                             FPS
                          
                           
                             2.
                             ct
                             PS
                             .
                             Rad
                             ∷
                             cs
                             EPS
                             .
                             t
                             EP
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             3.
                             
                             Rad.
                             t
                             EP
                             ∷
                             ct
                             FP
                             .
                             cs
                             FPE
                          
                        
                         
                           
                             EPS+EPF
                             =
                             FPS
                          
                           
                              
                          
                           
                             ct
                             PS
                             .
                             cs
                             EPS
                             ∷
                             ct
                             FP
                             .
                             ct
                             FPE
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             1.
                             cot
                             PFS
                             .
                             Rad
                             ∷
                             cs
                             PF
                             .
                             ct
                             EPF
                          
                        
                         
                           
                             2.
                             PS
                          
                           
                             FPS
                          
                           
                             2.
                             ct
                             PF
                             .
                             Rad
                             ∷
                             cs
                             EPF
                             .
                             
                               t
                               EP
                            
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             3.
                             
                             Rad.
                             t
                             EP
                             ∷
                             cot
                             PS
                             .
                             cs
                             EPS
                          
                        
                         
                           
                             EPS+EPF
                             =
                             FPS
                          
                           
                              
                          
                           
                             cot
                             PF
                             .
                             cs
                             EPF
                             ∷
                             ct
                             PS
                             ct
                             EPS
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             1.
                             cot
                             PFS
                             .
                             Rad
                             ∷
                             cs
                             FS
                             .
                             ct
                             FSD
                          
                        
                         
                           
                             3.
                             FS
                          
                           
                             PSF
                          
                           
                             2.
                             ct
                             FS
                             .
                             cs
                             FSD
                             ∷
                             
                               Rad.
                               t
                               DS
                            
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             3.
                             
                             Rad.
                             t
                             DS
                             ∷
                             
                               ct
                               PS
                               .
                               cs
                               PSD
                            
                          
                        
                         
                           
                             FSD-PSD
                             =
                             PSF
                          
                           
                              
                          
                           
                             ct
                             FS
                             .
                             cs
                             FSD
                             ∷
                             ct
                             PS
                             .
                             cs
                             PSD
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             1.
                             cot
                             FPS
                             .
                             Rad
                             ∷
                             cs
                             PS
                             .
                             ct
                             PSD
                          
                        
                         
                           
                             4.
                             FS
                          
                           
                             PSF
                          
                           
                             2.
                             ct
                             PS
                             .
                             cs
                             PSD
                             ∷
                             
                               Rad.
                               t
                               DS
                            
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               t
                               DS
                            
                             ∷
                             ct
                             FS
                             .
                             cs
                             FSD
                          
                        
                         
                           
                             FSD-PSD
                             =
                             PSF
                          
                           
                              
                          
                           
                             ct
                             PS
                             .
                             cs
                             PSD
                             ∷
                             ct
                             FS
                             .
                             cs
                             FSD
                          
                        
                         
                           
                             FS
                          
                           
                              
                          
                           
                             1.
                             cot
                             FSP
                             .
                             Rad
                             ∷
                             cs
                             FS
                             .
                             ct
                             SFC
                          
                        
                         
                           
                             5.
                             FP
                          
                           
                             PFS
                          
                           
                             2.
                             ct
                             FS
                             .
                             
                               cs
                               SFC
                            
                             ∷
                             Rad.
                             t
                             FC
                          
                        
                         
                           
                             FSP
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               t
                               FC
                            
                             ∷
                             ct
                             FP
                             .
                             cs
                             PFC
                          
                        
                         
                           
                             SFC-PFC
                             =
                             PFS
                          
                           
                              
                          
                           
                             ct
                             FS
                             .
                             cs
                             SFC
                             ∷
                             ct
                             FP
                             .
                             cs
                             PFC
                          
                        
                         
                           
                             
                             FS
                          
                           
                              
                          
                           
                             1.
                             cot
                             FPS
                             .
                             Rad
                             ∷
                             cs
                             PF
                             .
                             ct
                             PFC
                          
                        
                         
                           
                             6.
                             FF
                          
                           
                             PFS
                          
                           
                             2.
                             cot
                             FP
                             .
                             cs
                             PFC
                             ∷
                             Rad.
                             t
                             FC
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               t
                               FC
                            
                             ∷
                             ct
                             FS
                             .
                             cs
                             SFC
                          
                        
                         
                           
                             SFC-PFC
                             =
                             PFS
                          
                           
                              
                          
                           
                             ct
                             FP
                             .
                             cs
                             PFC
                             ∷
                             ct
                             FS
                             .
                             cs
                             SFC
                             .
                          
                        
                      
                    
                  
                   
                     
                       CASE
                       3.
                       
                    
                     
                       
                         Two
                         Sides
                         and
                         an
                         Angle
                         opposite
                         to
                         one
                         of
                         them
                         being
                         given
                         ,
                         to
                         find
                         the
                         third
                         side
                         .
                      
                    
                     
                       The
                       Varieties
                       in
                       this
                       Case
                       ,
                       with
                       their
                       resolution
                       by
                       the
                       Catholick
                       Proposition
                       ,
                       are
                       as
                       followeth
                       .
                       
                         
                           
                             Given
                          
                           
                             Required
                          
                           
                              
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             1.
                             ct
                             PS
                             ∷
                             cs
                             PSF
                             .
                             t
                             ES
                          
                        
                         
                           
                             1.
                             PS
                          
                           
                             FS
                          
                           
                             2.
                             cs
                             ES.
                             cs
                             PS
                             ∷
                             
                               Rad.
                               cs
                               EP
                            
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               cs
                               EP
                            
                             ∷
                             cs
                             FP
                             .
                             cs
                             FE
                          
                        
                         
                           
                             ES+FE
                             =
                             FS
                          
                           
                              
                          
                           
                             cs
                             ES.
                             cs
                             PS
                             ∷
                             cs
                             FP
                             .
                             cs
                             FE
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             1.
                             cot
                             FP
                             .
                             Rad
                             ∷
                             cos
                             PFS
                             .
                             t
                             FE
                          
                        
                         
                           
                             2.
                             PS
                          
                           
                             FS
                          
                           
                             2.
                             cos
                             FE
                             .
                             cos
                             FP
                             ∷
                             
                               Rad.
                               cos
                               EP
                            
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               cos
                               EP
                            
                             ∷
                             cos
                             PS
                             .
                             cos
                             SE
                          
                        
                         
                           
                             SE+FE
                             =
                             FS
                          
                           
                              
                          
                           
                             cos
                             FE
                             .
                             cos
                             FP
                             ∷
                             cos
                             PS
                             .
                             cos
                             SE
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             1.
                             cot
                             FS
                             .
                             Rad
                             ∷
                             cos
                             PFS
                             .
                             t
                             FD
                          
                        
                         
                           
                             3.
                             FS
                          
                           
                             FP
                          
                           
                             2.
                             cos
                             FD.
                             cos
                             FS
                             ∷
                             
                               Rad.
                               cs
                               SD
                            
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               cos
                               SD
                            
                             ∷
                             cos
                             PS
                             .
                             cs
                             PD
                          
                        
                         
                           
                             FD-PD
                             =
                             FP
                          
                           
                              
                          
                           
                             cos
                             FD.
                             cos
                             FS
                             ∷
                             cs
                             PS
                             .
                             cs
                             PD
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             1.
                             cot
                             PS
                             .
                             Rad
                             ∷
                             cos
                             FPS
                             .
                             t
                             PD
                          
                        
                         
                           
                             4.
                             FS
                          
                           
                             FP
                          
                           
                             2.
                             cos
                             PD
                             .
                             cos
                             PS
                             ∷
                             Rad.
                             cos
                             SD
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             3.
                             
                             Rad.
                             cos
                             SD
                             ∷
                             cos
                             FS
                             .
                             cs
                             FD
                          
                        
                         
                           
                             FD-PD
                             =
                             FP
                          
                           
                              
                          
                           
                             cos
                             PD
                             .
                             cos
                             PS
                             ∷
                             cos
                             FS
                             .
                             cs
                             FD
                          
                        
                         
                           
                             
                             FS
                          
                           
                              
                          
                           
                             1.
                             cot
                             FS
                             .
                             Rad
                             ∷
                             cos
                             FSP
                             .
                             t
                             SC
                          
                        
                         
                           
                             5.
                             FP
                          
                           
                             PS
                          
                           
                             2.
                             cos
                             SC.
                             cos
                             FS
                             ∷
                             
                               Rad.
                               cos
                               FC
                            
                          
                        
                         
                           
                             FSP
                          
                           
                              
                          
                           
                             3.
                             
                             Rad.
                             cos
                             FC
                             ∷
                             
                               cos
                               FP
                               .
                               cos
                               PC
                            
                          
                        
                         
                           
                             SP-PC
                             =
                             PS
                          
                           
                              
                          
                           
                             cos
                             SC.
                             cos
                             FS
                             .
                             cos
                             FP
                             .
                             cos
                             PC
                          
                        
                         
                           
                             FS
                          
                           
                              
                          
                           
                             1.
                             cot
                             FP
                             .
                             Rod
                             ∷
                             cos
                             FPS
                             .
                             t
                             PC
                          
                        
                         
                           
                             6.
                             FP
                          
                           
                             PS
                          
                           
                             2.
                             cos
                             PC
                             .
                             cos
                             FP
                             ∷
                             
                               Rad.
                               cos
                               FC
                            
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               cos
                               FC
                            
                             ∷
                             cos
                             FS
                             .
                             cos
                             SC
                          
                        
                         
                           
                             SC-PC
                             =
                             PS
                          
                           
                              
                          
                           
                             cos
                             PC
                             .
                             cos
                             FP
                             ∷
                             cos
                             FS
                             .
                             cos
                             SC
                          
                        
                      
                    
                  
                   
                     
                       CASE
                       4.
                       
                    
                     
                       
                         Two
                         Angles
                         with
                         a
                         Side
                         opposite
                         to
                         one
                         of
                         them
                         being
                         given
                         ,
                         to
                         find
                         the
                         Side
                         opposite
                         unto
                         the
                         other
                         .
                      
                    
                     
                       The
                       Varieties
                       in
                       this
                       Case
                       ,
                       with
                       their
                       Resolution
                       by
                       the
                       Catholick
                       Proposition
                       ,
                       are
                       as
                       followeth
                       .
                       
                         
                           
                             Given
                          
                           
                             Required
                          
                           
                              
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             Rad.
                             s.
                             PS
                             ∷
                             s
                             DPS.
                             
                               s
                               SD
                            
                          
                        
                         
                           
                             1.
                             FPS
                          
                           
                             FS
                          
                           
                             S.
                             FP
                             .
                             Rad
                             ∷
                             s
                             SD
                             .
                             
                               s
                               FS
                            
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                              
                          
                        
                         
                           
                              
                          
                           
                              
                          
                           
                             s.
                             PFS
                             .
                             s
                             PS
                             ∷
                             s
                             FPS
                             .
                             s
                             FS
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             Rad.
                             s
                             FS
                             ∷
                             s
                             PFS
                             .
                             
                               s.
                               SD
                            
                          
                        
                         
                           
                             2.
                             FPS
                          
                           
                             PS
                          
                           
                             s.
                             FPS
                             .
                             
                               Rad
                               ∷
                               s
                               SD
                            
                             .
                             s
                             PS
                          
                        
                         
                           
                             FS
                          
                           
                              
                          
                           
                              
                          
                        
                         
                           
                              
                          
                           
                              
                          
                           
                             s.
                             FPS
                             .
                             s
                             FS
                             ∷
                             s
                             PFS
                             .
                             s
                             PS
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             Rad.
                             s
                             FP
                             ∷
                             s
                             FPS
                             .
                             
                               s
                               FC
                            
                          
                        
                         
                           
                             3.
                             PSF
                          
                           
                             FS
                          
                           
                             s.
                             PSF
                             .
                             
                               Rad
                               ∷
                               s
                               FC
                            
                             .
                             s
                             FS
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                              
                          
                        
                         
                           
                              
                          
                           
                              
                          
                           
                             s.
                             PSF
                             .
                             s
                             FP
                             ∷
                             s
                             FPS
                             .
                             s
                             FS
                          
                        
                         
                           
                             
                             FPS
                          
                           
                              
                          
                           
                             Rad.
                             s
                             FS
                             ∷
                             s
                             PSF
                             .
                             
                               s
                               FC
                            
                          
                        
                         
                           
                             4.
                             PSF
                          
                           
                             FP
                          
                           
                             s.
                             FPS
                             .
                             
                               Rad
                               ∷
                               s
                               FC
                            
                             .
                             s
                             FP
                          
                        
                         
                           
                             FS
                          
                           
                              
                          
                           
                             s.
                             FPS
                             s
                             FS
                             ∷
                             s
                             PSF
                             .
                             s
                             FP
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             Rad.
                             s
                             PS
                             ∷
                             s
                             PSF
                             .
                             
                               s
                               PE
                            
                          
                        
                         
                           
                             5.
                             SFP
                          
                           
                             FP
                          
                           
                             s.
                             SFP
                             .
                             
                               Rad
                               ∷
                               s
                               PE.
                            
                             s
                             FP
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             s.
                             SFP
                             .
                             s
                             PS
                             ∷
                             s
                             PSF
                             .
                             s
                             FP
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             Rad.
                             s
                             FP
                             ∷
                             s
                             PFS
                             .
                             
                               s
                               PE
                            
                          
                        
                         
                           
                             6.
                             SFP
                          
                           
                             PS
                          
                           
                             s.
                             PSF
                             .
                             
                               Rad
                               ∷
                               s
                               PE.
                            
                             s
                             PS
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             s.
                             PSF
                             .
                             s
                             FP
                             ∷
                             s
                             PFS
                             .
                             s
                             PS
                          
                        
                      
                    
                  
                   
                     
                       CASE
                       5.
                       
                    
                     
                       
                         Two
                         Angles
                         and
                         a
                         side
                         opposite
                         to
                         one
                         of
                         them
                         being
                         given
                         ,
                         to
                         find
                         the
                         Side
                         between
                         them
                         .
                      
                    
                     
                       The
                       Varieties
                       and
                       Proportions
                       ,
                       are
                       as
                       followeth
                       .
                       
                         
                           
                             Given
                          
                           
                             Required
                          
                           
                              
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             1.
                             ct
                             PS
                             .
                             Rad
                             ∷
                             cs
                             DPS.
                             PD
                          
                        
                         
                           
                             1.
                             FPS
                          
                           
                             FP
                          
                           
                             2.
                             ct
                             DPS.
                             s
                             PD
                             ∷
                             
                               Rad.
                               t
                               DS
                            
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               t
                               DS
                            
                             ∷
                             ct
                             PFS
                             .
                             s
                             FD
                          
                        
                         
                           
                             FD-PD
                             =
                             FP
                          
                           
                              
                          
                           
                             ct
                             DPS.
                             s
                             PD
                             ∷
                             ct
                             PFS
                             .
                             s
                             FD
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             1.
                             ct
                             DFS.
                             Rad
                             ∷
                             cs
                             PFS
                             .
                             t
                             FD
                          
                        
                         
                           
                             2.
                             FPS
                          
                           
                             FP
                          
                           
                             2.
                             cot
                             PFS
                             .
                             s
                             FD
                             ∷
                             Rad.
                             t
                             DS
                          
                        
                         
                           
                             FS
                          
                           
                              
                          
                           
                             3.
                             
                             Rad.
                             t
                             DS
                             ∷
                             ct
                             FPS
                             .
                             s
                             PD
                          
                        
                         
                           
                             FD-PD
                             =
                             FP
                          
                           
                              
                          
                           
                              
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             1.
                             cot
                             FP
                             .
                             Rad
                             ∷
                             cs
                             FPC
                             .
                             t
                             PC
                          
                        
                         
                           
                             3.
                             PSF
                          
                           
                             PS
                          
                           
                             2.
                             cot
                             FPC
                             .
                             s
                             PC
                             ∷
                             
                               Rad.
                               t
                               FC
                            
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               t
                               FC
                            
                             ∷
                             ct
                             PSF
                             .
                             s
                             SC
                          
                        
                         
                           
                             SC-PC
                             =
                             PS
                          
                           
                              
                          
                           
                             cot
                             FPC
                             .
                             s
                             PC
                             ∷
                             ct
                             PSF
                             .
                             CS
                          
                        
                         
                           
                             
                             FPS
                          
                           
                              
                          
                           
                             1.
                             cot
                             FS
                             .
                             Rad
                             ∷
                             cs
                             PSF
                             .
                             t
                             SC
                          
                        
                         
                           
                             4.
                             PSF
                          
                           
                             PS
                          
                           
                             2.
                             cot
                             PSF
                             .
                             s
                             SC
                             ∷
                             
                               Rad.
                               t
                               FC
                            
                          
                        
                         
                           
                             FS
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               t
                               FC
                            
                             ∷
                             cot
                             FPS
                             .
                             s
                             PC
                          
                        
                         
                           
                             SC-PC
                             =
                             PS
                          
                           
                              
                          
                           
                             cot
                             PSF
                             .
                             s
                             SC
                             ∷
                             cot
                             FPS
                             .
                             s
                             PC
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             1.
                             cot
                             PS
                             .
                             Rad
                             ∷
                             cs
                             PSF
                             .
                             t
                             SE
                          
                        
                         
                           
                             5.
                             SFP
                          
                           
                             FS
                          
                           
                             2.
                             cot
                             PSF
                             .
                             s
                             SE
                             ∷
                             
                               Rad.
                               t
                               PE
                            
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               t
                               PE
                            
                             ∷
                             cot
                             SFP
                             .
                             s
                             FE
                          
                        
                         
                           
                             FE+SE
                             =
                             FS
                          
                           
                              
                          
                           
                             cot
                             PSF
                             .
                             s
                             SE
                             ∷
                             cot
                             SFP
                             .
                             s
                             FE
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             1.
                             cot
                             FP
                             .
                             Rad
                             ∷
                             cs
                             SFP
                             .
                             t
                             FE
                          
                        
                         
                           
                             6.
                             SFP
                          
                           
                             FS
                          
                           
                             2.
                             cot
                             SFP
                             .
                             s
                             FE
                             ∷
                             
                               Rad.
                               t
                               PE
                            
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               t
                               PE
                            
                             ∷
                             cos
                             PSF
                             .
                             s
                             SE
                          
                        
                         
                           
                             FE+SE
                             =
                             FS
                          
                           
                              
                          
                           
                             cot
                             .
                             SFP
                             .
                             s
                             FE
                             ∷
                             cs
                             PSF
                             .
                             s
                             SE
                          
                        
                      
                    
                  
                   
                     
                       CASE
                       6.
                       
                    
                     
                       
                         Two
                         Angles
                         and
                         a
                         Side
                         opposite
                         to
                         one
                         of
                         them
                         being
                         given
                         ,
                         to
                         find
                         the
                         third
                         Angle
                         .
                      
                    
                     
                       The
                       Varieties
                       and
                       Proportions
                       are
                       as
                       followeth
                       .
                       
                         
                           
                             Given
                          
                           
                             Required
                          
                           
                              
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             1.
                             ct
                             DPS.
                             Rad
                             ∷
                             cs
                             PS
                             .
                             ct
                             PSD
                          
                        
                         
                           
                             1.
                             FPS
                          
                           
                             PSF
                          
                           
                             2.
                             s
                             PSD
                             .
                             cs
                             DPS
                             ∷
                             
                               Rad.
                               cs
                               DS
                            
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             3.
                             
                               cs
                               DS.
                               Rad
                            
                             ∷
                             cs
                             DFS.
                             s
                             FSD
                          
                        
                         
                           
                             FSD-PSD
                             =
                             PSF
                          
                           
                              
                          
                           
                             cs
                             DPS.
                             s
                             PSD
                             ∷
                             cs
                             DFS.
                             s
                             FSD
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             1.
                             ct
                             PFS
                             .
                             Rad
                             ∷
                             cs
                             FS
                             .
                             ct
                             FSD
                          
                        
                         
                           
                             2.
                             FPS
                          
                           
                             PSF
                          
                           
                             2.
                             s
                             FSD
                             .
                             cs
                             PFS
                             ∷
                             
                               Rad.
                               cs
                               DS
                            
                          
                        
                         
                           
                             FS
                          
                           
                              
                          
                           
                             3.
                             
                               cs
                               PDS.
                               Rad
                            
                             ∷
                             cs
                             DPS.
                             cs
                             PSD
                          
                        
                         
                           
                             FSD-PSD
                             =
                             PSF
                          
                           
                              
                          
                           
                             cs
                             PFS
                             .
                             s
                             FSD
                             ∷
                             cs
                             DPS.
                             cs
                             PSD
                          
                        
                         
                           
                             
                             FPS
                          
                           
                              
                          
                           
                             1.
                             ct
                             FPC
                             .
                             Rad
                             ∷
                             cs
                             FP
                             .
                             ct
                             PFC
                          
                        
                         
                           
                             3.
                             PSF
                          
                           
                             PFS
                          
                           
                             2.
                             s
                             PFC
                             .
                             cs
                             FPG
                             ∷
                             
                               Rad.
                               cs
                               FC
                            
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             3.
                             
                               cs
                               FC
                               .
                               Rad
                            
                             ∷
                             cs
                             PSF
                             .
                             s
                             FC
                          
                        
                         
                           
                             SFC-PFC
                             =
                             PFS
                          
                           
                              
                          
                           
                             cs
                             FPC
                             .
                             s
                             PFC
                             ∷
                             cs
                             PSF
                             .
                             s
                             SFC
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             1.
                             cot
                             PSF
                             .
                             Rad
                             ∷
                             cos
                             FS
                             .
                             ct
                             SFC
                          
                        
                         
                           
                             4.
                             PSF
                          
                           
                             PFS
                          
                           
                             2.
                             s
                             SFC
                             .
                             cs
                             PSF
                             ∷
                             
                               Rad.
                               cs
                               FC
                            
                          
                        
                         
                           
                             FS
                          
                           
                              
                          
                           
                             3.
                             
                               cs
                               FC
                               .
                               Rad
                            
                             ∷
                             cs
                             CPF
                             .
                             s
                             PFC
                          
                        
                         
                           
                             SFC-PFC
                             =
                             PFS
                          
                           
                              
                          
                           
                             cs
                             PSF
                             .
                             s
                             SFC
                             ∷
                             cs
                             CPF
                             .
                             s
                             PFC
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             1.
                             cot
                             PSF
                             .
                             Rad
                             ∷
                             cs
                             PS
                             .
                             ct
                             SPE
                          
                        
                         
                           
                             5.
                             SFP
                          
                           
                             FPS
                          
                           
                             2.
                             s
                             SPE
                             .
                             cs
                             PSF
                             ∷
                             
                               Rad.
                               cs
                               PE
                            
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             3.
                             
                               cs
                               PE.
                               Rad
                            
                             ∷
                             cs
                             SFP
                             .
                             s
                             FPE
                          
                        
                         
                           
                             FPE+SPE
                             =
                             FPS
                          
                           
                              
                          
                           
                             cs
                             PSF
                             .
                             s
                             SPE
                             ∷
                             cs
                             SFP
                             .
                             s
                             FPE
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             1.
                             cot
                             SFP
                             .
                             Rad
                             ∷
                             cs
                             FP
                             .
                             ct
                             FPE
                          
                        
                         
                           
                             6.
                             SFP
                          
                           
                             FPS
                          
                           
                             2.
                             s
                             FPE
                             .
                             cs
                             SFP
                             ∷
                             
                               Rad.
                               cs
                               PE
                            
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             3.
                             
                               cos
                               PE
                               Rad
                            
                             ∷
                             cs
                             PSF
                             .
                             s
                             SPE
                          
                        
                         
                           
                             FPE+SPE
                             =
                             FPS
                          
                           
                              
                          
                           
                             cs
                             SFP
                             .
                             s
                             FPE
                             ∷
                             cs
                             PSF
                             .
                             s
                             SPE
                          
                        
                      
                    
                  
                   
                     
                       CASE
                       7.
                       
                    
                     
                       
                         Two
                         Sides
                         and
                         their
                         contained
                         Angle
                         being
                         given
                         ,
                         to
                         find
                         either
                         of
                         the
                         other
                         Angles
                         .
                      
                    
                     
                       The
                       Varieties
                       and
                       Proportions
                       are
                       as
                       followeth
                       .
                       
                         
                           
                             Given
                          
                           
                             Required
                          
                           
                              
                          
                        
                         
                           
                             FS
                          
                           
                              
                          
                           
                             1.
                             ct
                             FP
                             .
                             Rad
                             ∷
                             cs
                             PFS
                             .
                             t
                             FE
                          
                        
                         
                           
                             1.
                             FP
                          
                           
                             FSP
                          
                           
                             2.
                             ct
                             PFS
                             .
                             s
                             FE
                             ∷
                             
                               Rad.
                               t
                               PE
                            
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             3.
                             
                               t
                               PE.
                               Rad.
                            
                             ∷
                             s
                             ES.
                             ct
                             PSF
                          
                        
                         
                           
                             FS-FE
                             =
                             ES
                          
                           
                              
                          
                           
                             s
                             EF.
                             ct
                             PFS
                             ∷
                             s
                             ES.
                             ct
                             PSF
                          
                        
                         
                           
                             
                             FS
                          
                           
                              
                          
                           
                             1.
                             cot
                             FS
                             .
                             Rad
                             :
                             :
                             cs
                             PFS
                             .
                             t
                             DF
                          
                        
                         
                           
                             2.
                             FP
                          
                           
                             FPS
                          
                           
                             2.
                             cot
                             PFS
                             .
                             s
                             DF
                             :
                             :
                             
                               Rad.
                               t
                               DS
                            
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             3.
                             t
                             DS.
                             Rad
                             :
                             :
                             
                               s
                               PD
                               .
                               ct
                               SPD
                            
                          
                        
                         
                           
                             FD
                             -
                             FP
                             =
                             PD
                          
                           
                              
                          
                           
                             s
                             DF.
                             ct
                             PFS
                             :
                             :
                             s
                             PD
                             .
                             ct
                             SPD
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             1.
                             cot
                             FP
                             .
                             Rad
                             :
                             :
                             cos
                             FPC
                             .
                             t
                             PC
                          
                        
                         
                           
                             3.
                             PS
                          
                           
                             PSF
                          
                           
                             2.
                             cot
                             FPC
                             .
                             s
                             PC
                             :
                             :
                             
                               Rad.
                               t
                               FC
                            
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             3.
                             t
                             FC
                             .
                             Rad
                             :
                             :
                             
                               s
                               CS
                               .
                               cot
                               FSP
                            
                          
                        
                         
                           
                             PS+PC
                             =
                             CS
                          
                           
                             s
                             PC
                             .
                             ct
                             FPC
                             :
                             :
                             s
                             CS
                             .
                             ct
                             FSP
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             1.
                             cot
                             PS
                             .
                             Rad
                             :
                             :
                             cos
                             SPD
                             .
                             t
                             PD
                          
                        
                         
                           
                             4.
                             PS
                          
                           
                             SFP
                          
                           
                             2.
                             cot
                             SPD
                             .
                             s
                             PD
                             :
                             :
                             
                               Rad.
                               t
                               DS
                            
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             3.
                             t
                             DS
                             Rad
                             :
                             :
                             
                               s
                               FD.
                               cot
                               SFP
                            
                          
                        
                         
                           
                             FP+PD
                             =
                             FD
                          
                           
                              
                          
                           
                             s
                             PD
                             .
                             ct
                             SPD
                             :
                             :
                             s
                             FD.
                             cot
                             SFP
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             1.
                             cot
                             PS
                             .
                             Rad
                             :
                             :
                             cs
                             PSF
                             .
                             t
                             SE
                          
                        
                         
                           
                             5.
                             FS
                          
                           
                             SFP
                          
                           
                             2.
                             cot
                             PSF
                             .
                             s
                             SE
                             :
                             :
                             
                               Rad.
                               t
                               PE
                            
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             3.
                             t
                             PE.
                             Rad
                             :
                             :
                             
                               s
                               FE
                               .
                               cot
                               SFP
                            
                          
                        
                         
                           
                             FS-SE
                             =
                             FE
                          
                           
                              
                          
                           
                             s
                             SE.
                             ct
                             PSF
                             :
                             :
                             s
                             FE
                             .
                             ct
                             SFP
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             1.
                             cot
                             FS
                             .
                             Rad
                             :
                             :
                             cs
                             PSF
                             .
                             t
                             SC
                          
                        
                         
                           
                             6.
                             FS
                          
                           
                             FPS
                          
                           
                             2.
                             cot
                             PSF
                             .
                             s
                             SC
                             :
                             :
                             
                               Rad.
                               t
                               FC
                            
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             3.
                             t
                             FC
                             .
                             Rad
                             :
                             :
                             
                               s
                               PC
                               .
                               cot
                               FPC
                            
                          
                        
                         
                           
                             SC-PS
                             =
                             PC
                          
                           
                              
                          
                           
                             s
                             SC.
                             cot
                             PSF
                             :
                             :
                             s
                             PC
                             .
                             ct
                             FPC
                          
                        
                      
                    
                  
                   
                     
                       CASE
                       8.
                       
                    
                     
                       
                         Two
                         Sides
                         and
                         their
                         contained
                         Angle
                         being
                         given
                         ,
                         to
                         find
                         the
                         third
                         Side
                         .
                      
                    
                     
                       The
                       Varieties
                       and
                       Proportions
                       are
                       as
                       followeth
                       .
                       
                         
                         
                           
                             Given
                          
                           
                             Required
                          
                           
                              
                          
                        
                         
                           
                             FS
                          
                           
                              
                          
                           
                             1.
                             ct
                             FP
                             .
                             Rad
                             :
                             :
                             cs
                             PFS
                             .
                             t
                             FE
                          
                        
                         
                           
                             1.
                             FP
                          
                           
                             PS
                          
                           
                             2.
                             cs
                             FE
                             .
                             cs
                             FP
                             :
                             :
                             
                               Rad.
                               cos
                               PE
                            
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             3.
                             
                             
                               Rad.
                               cs
                               PE
                            
                             :
                             :
                             cs
                             ES.
                             cs
                             PS
                          
                        
                         
                           
                             FS-FE
                             =
                             ES
                          
                           
                              
                          
                           
                             cs
                             FE
                             .
                             cs
                             FP
                             :
                             :
                             cs
                             ES.
                             cs
                             PS
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             1.
                             ct
                             PS
                             .
                             Rad
                             :
                             :
                             cs
                             SPD
                             .
                             t
                             PD
                          
                        
                         
                           
                             2.
                             SP
                          
                           
                             FS
                          
                           
                             2.
                             cs
                             PD
                             .
                             cs
                             PS
                             :
                             :
                             
                               Rad.
                               cos
                               DS
                            
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             3.
                             
                             Rad.
                             cos
                             DS
                             :
                             :
                             
                               cs
                               FD.
                               cs
                               FS
                            
                          
                        
                         
                           
                             FP+PD
                             =
                             FD
                          
                           
                              
                          
                           
                             cs
                             PD
                             .
                             cs
                             PS
                             :
                             :
                             cs
                             FD.
                             cs
                             FS
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             1.
                             ct
                             PS
                             .
                             Rad
                             :
                             :
                             cs
                             PSF
                             .
                             t.
                             ES
                          
                        
                         
                           
                             3.
                             FS
                          
                           
                             FP
                          
                           
                             2.
                             cs
                             ES.
                             cs
                             PS
                             :
                             :
                             
                               Rad.
                               cos
                               PE
                            
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             3.
                             
                             Rad.
                             cos
                             PE
                             :
                             :
                             
                               cos
                               FE
                               .
                               cos
                               FP
                            
                          
                        
                         
                           
                             FS-ES
                             =
                             FE
                          
                           
                              
                          
                           
                             cs
                             ES.
                             cs
                             PS
                             :
                             :
                             cos
                             FE
                             .
                             cs
                             FP
                          
                        
                      
                    
                  
                   
                     
                       CASE
                       9.
                       
                    
                     
                       
                         Two
                         Angles
                         and
                         their
                         contained
                         Side
                         being
                         given
                         ,
                         to
                         find
                         one
                         of
                         the
                         other
                         Sides
                         .
                      
                    
                     
                       
                         
                           
                             Given
                          
                           
                             Required
                          
                           
                              
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             1.
                             ct
                             PFS
                             .
                             Rad
                             :
                             :
                             cs
                             FP
                             ct
                             FPE
                          
                        
                         
                           
                             1.
                             FPS
                          
                           
                             PS
                          
                           
                             2.
                             ct
                             FP
                             .
                             cs
                             FPE
                             :
                             :
                             
                               Rad.
                               t
                               PE
                            
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             3.
                             t
                             PE.
                             Rad
                             :
                             :
                             
                               cs
                               EPS
                               .
                               ct
                               PS
                            
                          
                        
                         
                           
                             FPS-FPE
                             =
                             EPS
                          
                           
                              
                          
                           
                             cs
                             FPE
                             .
                             ct
                             FP
                             :
                             :
                             cs
                             EPS
                             .
                             ct
                             PS
                          
                        
                         
                           
                             PFS
                          
                           
                              
                          
                           
                             1.
                             cot
                             FPC
                             .
                             Rad
                             :
                             :
                             cs
                             FP
                             .
                             t
                             PFC
                          
                        
                         
                           
                             2.
                             FPS
                          
                           
                             FS
                          
                           
                             2.
                             cot
                             FP
                             .
                             cs
                             PFC
                             :
                             :
                             
                               Rad.
                               t
                               FC
                            
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             3.
                             t
                             FC
                             .
                             Rad
                             :
                             :
                             
                               cs
                               SFC
                               .
                               ct
                               SF
                            
                          
                        
                         
                           
                             SFP+PFC
                             =
                             SFC
                          
                           
                              
                          
                           
                             ct
                             FP
                             .
                             cs
                             PFC
                             :
                             :
                             cs
                             SFC
                             .
                             ct
                             SF
                          
                        
                         
                           
                             
                             FPS
                          
                           
                              
                          
                           
                             1.
                             ct
                             SPD
                             .
                             Rad
                             :
                             :
                             cs
                             PS
                             .
                             ct
                             PSD
                          
                        
                         
                           
                             3.
                             PSF
                          
                           
                             SF
                          
                           
                             2.
                             ct
                             PS
                             .
                             cos
                             PSD
                             :
                             :
                             
                               Rad.
                               t
                               DS
                            
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             3.
                             t
                             DS.
                             Rad
                             :
                             :
                             
                               cs
                               FSD
                               .
                               ct
                               SF
                            
                          
                        
                         
                           
                             PSF+PSD
                             =
                             FSD
                          
                           
                              
                          
                           
                             cs
                             PSD
                             .
                             ct
                             PS
                             :
                             :
                             cs
                             FSD
                             .
                             ct
                             SF
                          
                        
                         
                           
                             FPS
                          
                           
                              
                          
                           
                             1.
                             ct
                             PSF
                             .
                             Rad
                             :
                             :
                             cs
                             PS
                             .
                             ct
                             SPE
                          
                        
                         
                           
                             4.
                             PSF
                          
                           
                             FP
                          
                           
                             2.
                             ct
                             PS
                             .
                             cs
                             SPE
                             :
                             :
                             
                               Rad.
                               t
                               PE
                            
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             3.
                             t
                             PE.
                             Rad
                             :
                             :
                             
                               cs
                               PPE.
                               ct
                               FP
                            
                          
                        
                         
                           
                             FPS-EPS
                             =
                             FPE
                          
                           
                              
                          
                           
                             cs
                             SPE
                             .
                             ct
                             PS
                             :
                             :
                             cs
                             FPE
                             .
                             ct
                             FP
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             1.
                             ct
                             PSF
                             .
                             Rad
                             :
                             :
                             cs
                             SF
                             .
                             ct
                             SFC
                          
                        
                         
                           
                             5.
                             SFP
                          
                           
                             FP
                          
                           
                             2.
                             ct
                             SF
                             .
                             cs
                             SFC
                             :
                             :
                             
                               Rad.
                               t
                               FC
                            
                          
                        
                         
                           
                             SF
                          
                           
                              
                          
                           
                             3.
                             t
                             FC
                             .
                             Rad
                             :
                             :
                             
                               cs
                               CFP
                               .
                               ct
                               FP
                            
                          
                        
                         
                           
                             SFC-SFP
                             =
                             CFP
                          
                           
                              
                          
                           
                             cs
                             SFC
                             .
                             ct
                             SF
                             :
                             :
                             cs
                             CFP
                             .
                             ct
                             FP
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             1.
                             ct
                             SFP
                             .
                             Rad
                             :
                             :
                             cs
                             FS
                             .
                             ct
                             FSD
                          
                        
                         
                           
                             6.
                             SFP
                          
                           
                             PS
                          
                           
                             2.
                             ct
                             FS
                             .
                             cs
                             FSD
                             :
                             :
                             Rad.
                             t
                             SD
                          
                        
                         
                           
                             SF
                          
                           
                              
                          
                           
                             3.
                             t
                             SD
                             .
                             Rad
                             :
                             :
                             cos
                             PSD
                             .
                             ct
                             PS
                          
                        
                         
                           
                             FSD-FSP
                             =
                             PSD
                          
                           
                              
                          
                           
                             cs
                             FSD
                             .
                             ct
                             FS
                             :
                             :
                             cs
                             PSD
                             .
                             ct
                             PS
                          
                        
                      
                    
                  
                   
                     
                       CASE
                       10.
                       
                    
                     
                       
                         Two
                         Angles
                         and
                         the
                         Side
                         between
                         them
                         being
                         given
                         ,
                         to
                         find
                         the
                         third
                         Angle
                         .
                      
                    
                     
                       The
                       Varieties
                       and
                       Proportions
                       are
                       as
                       followeth
                       .
                       
                         
                           
                             Given
                          
                           
                             Required
                          
                           
                              
                          
                        
                         
                           
                             SFP
                          
                           
                              
                          
                           
                             1.
                             ct
                             SFP
                             .
                             Rad
                             :
                             :
                             cs
                             FP
                             .
                             ct
                             FPE
                          
                        
                         
                           
                             1.
                             FPS
                          
                           
                             PSF
                          
                           
                             2.
                             s
                             FPE
                             .
                             cs
                             F
                             :
                             :
                             
                               Rad.
                               cs
                               PE
                            
                          
                        
                         
                           
                             FP
                          
                           
                              
                          
                           
                             3.
                             
                             Rad.
                             cs
                             PE
                             :
                             :
                             
                               s
                               EPS
                               .
                               cs
                               PST
                            
                          
                        
                         
                           
                             FPS-FPE
                             =
                             EPS
                          
                           
                              
                          
                           
                             s
                             FPE
                             .
                             cs
                             PFS
                             :
                             :
                             s
                             SPE
                             .
                             cs
                             PSF
                          
                        
                         
                           
                             
                             FPS
                          
                           
                              
                          
                           
                             1.
                             ct
                             SPD
                             .
                             Rad
                             :
                             :
                             cs
                             PS
                             .
                             ct
                             PSD
                          
                        
                         
                           
                             2.
                             PSF
                          
                           
                             SFP
                          
                           
                             2.
                             s
                             PSD
                             .
                             cs
                             SPD
                             :
                             :
                             
                               Rad.
                               cs
                               DS
                            
                          
                        
                         
                           
                             PS
                          
                           
                              
                          
                           
                             3.
                             
                             Rad.
                             cs
                             DS
                             :
                             :
                             
                               s
                               FSD
                               .
                               cs
                               SFP
                            
                          
                        
                         
                           
                             PSF+PSD
                             =
                             FSD
                          
                           
                              
                          
                           
                             s
                             PSD
                             .
                             cs
                             SPD
                             :
                             :
                             s
                             FSD
                             .
                             cs
                             SFP
                          
                        
                         
                           
                             PSF
                          
                           
                              
                          
                           
                             1.
                             ct
                             PSF
                             .
                             Rad
                             :
                             :
                             cs
                             SF
                             .
                             ct
                             SFC
                          
                        
                         
                           
                             3.
                             SFP
                          
                           
                             FPS
                          
                           
                             2.
                             s
                             SFC
                             .
                             cs
                             PSF
                             :
                             :
                             
                               Rad.
                               cs
                               FC
                            
                          
                        
                         
                           
                             SF
                          
                           
                              
                          
                           
                             3.
                             
                             Rad.
                             cs
                             FC
                             :
                             :
                             
                               s
                               PFC
                               .
                               cs
                               FPS
                            
                          
                        
                         
                           
                             SFC-SFP
                             =
                             PFC
                          
                           
                              
                          
                           
                             s
                             SFC
                             .
                             cs
                             PSF
                             :
                             :
                             s
                             PFC
                             .
                             cs
                             FPS
                          
                        
                      
                    
                  
                   
                     
                       CASE
                       11.
                       
                    
                     
                       
                         The
                         three
                         Sides
                         being
                         given
                         ,
                         to
                         find
                         an
                         Angle
                         .
                      
                    
                     
                       This
                       Case
                       may
                       be
                       resolved
                       by
                       the
                       Catholick
                       Proposition
                       also
                       ,
                       according
                       to
                       the
                       direction
                       of
                       the
                       Lord
                       Nepier
                       ,
                       as
                       I
                       have
                       shewed
                       at
                       large
                       in
                       the
                       Second
                       Book
                       of
                       my
                       
                         Trigonometria
                         Britannica
                         ,
                         Chap.
                         2.
                      
                       but
                       may
                       as
                       I
                       conceive
                       be
                       more
                       conveniently
                       solved
                       ,
                       by
                       this
                       Proposition
                       following
                       .
                    
                     
                       As
                       the
                       Rectangle
                       of
                       the
                       Square
                       of
                       the
                       Sides
                       containing
                       the
                       Angle
                       inquired
                       ;
                    
                     
                       Is
                       to
                       the
                       Square
                       of
                       Radius
                       :
                       So
                       is
                       the
                       Rectangle
                       of
                       the
                       Square
                       of
                       the
                       difference
                       of
                       each
                       containing
                       Side
                       ,
                       and
                       the
                       half
                       sum
                       of
                       the
                       three
                       Sides
                       given
                       .
                    
                     
                       To
                       the
                       Square
                       of
                       the
                       Sine
                       of
                       half
                       the
                       Angle
                       inquired
                       .
                    
                     
                       In
                       this
                       Case
                       there
                       are
                       three
                       Varieties
                       ,
                       as
                       in
                       the
                       Triangle
                       
                         FZP
                         .
                         Fig.
                      
                       3.
                       
                    
                     
                     
                       
                         
                           
                             Given
                          
                           
                             Required
                          
                           
                              
                          
                        
                         
                           
                             ZP
                          
                           
                              
                          
                           
                             s
                             ZP
                             x
                             s
                             PF
                             .
                             Rad.
                             q.
                             
                          
                        
                         
                           
                             1.
                             PF
                          
                           
                             ZPF
                          
                           
                             s
                             ½
                             Z-ZP
                             x
                             s
                             ½
                             Z-PF
                             .
                             Q
                          
                        
                         
                           
                             FZ
                          
                           
                              
                          
                           
                             s
                             ½
                             ZPF
                          
                        
                         
                           
                             ZP
                          
                           
                              
                          
                           
                             s
                             PF
                             x
                             s
                             PZ
                             .
                             Rad.
                             q.
                             
                          
                        
                         
                           
                             2.
                             PF
                          
                           
                             PFZ
                          
                           
                             s
                             ½
                             Z-PF
                             x
                             s
                             ½
                             Z-FZ
                             .
                             Q
                          
                        
                         
                           
                             FZ
                          
                           
                              
                          
                           
                             s
                             ½
                             PFZ
                          
                        
                         
                           
                             ZP
                          
                           
                              
                          
                           
                             s
                             ZP
                             x
                             s
                             FZ
                             Rad.
                             q.
                             
                          
                        
                         
                           
                             3.
                             PF
                          
                           
                             FZP
                          
                           
                             s.
                             ½
                             Z-ZP
                             x
                             ½
                             Z-ZF
                             .
                             Q
                          
                        
                         
                           
                             FZ
                          
                           
                              
                          
                           
                             s
                             ½
                             FZP
                          
                        
                      
                    
                  
                   
                     
                       CASE
                       12.
                       
                    
                     
                       
                         The
                         three
                         Angles
                         given
                         ,
                         to
                         find
                         a
                         Side
                         .
                      
                    
                     
                       This
                       is
                       the
                       Converse
                       of
                       the
                       last
                       ,
                       and
                       to
                       be
                       resolved
                       after
                       the
                       same
                       manner
                       ,
                       if
                       so
                       be
                       we
                       convert
                       the
                       Angles
                       into
                       Sides
                       ,
                       by
                       the
                       tenth
                       of
                       the
                       third
                       Chapter
                       :
                       for
                       so
                       the
                       Sides
                       of
                       the
                       Triangle
                       ACD
                       will
                       be
                       equal
                       to
                       the
                       Angles
                       of
                       the
                       Triangle
                       FZP
                       n
                       Fig.
                       3.
                       
                    
                     
                       
                         That
                         is
                      
                       
                         
                           AD
                           =
                           AEE
                        
                         the
                         measure
                         of
                         the
                         Angle
                         ZPF
                         .
                      
                       
                         
                           DC
                           =
                           KM
                        
                         the
                         measure
                         of
                         the
                         Angle
                         ZFP
                         .
                      
                       
                         AC
                         =
                         HB
                         the
                         Complement
                         of
                         FZP
                         to
                         a
                         Semicircle
                         .
                      
                    
                     
                       
                       
                         The
                         Angle
                      
                       
                         DAC
                         =
                         QR
                         =
                         ZP
                         .
                      
                       
                         ACD
                         =
                         rM
                         =
                         Hf
                         =
                         Zoe
                         =
                         ZF
                         .
                      
                       
                         ADM
                         =
                         sK
                         =
                         AEl
                         =
                         Ph
                         =
                         PF
                         .
                      
                    
                     
                       And
                       thus
                       the
                       Sides
                       of
                       the
                       Triangle
                       ZPF
                       are
                       equal
                       to
                       the
                       Angles
                       of
                       the
                       Triangle
                       ACD
                       .
                       The
                       Complement
                       of
                       the
                       greatest
                       Side
                       PF
                       to
                       a
                       Semicircle
                       being
                       taken
                       for
                       the
                       greatest
                       Angle
                       ADC
                       .
                    
                     
                       And
                       in
                       this
                       Case
                       therefore
                       ,
                       as
                       in
                       the
                       preceding
                       ,
                       there
                       are
                       three
                       Varieties
                       which
                       make
                       up
                       sixty
                       Problems
                       in
                       every
                       Oblique
                       angled
                       Spherical
                       Triangle
                       ;
                       which
                       actually
                       to
                       resolve
                       in
                       so
                       many
                       Triangles
                       ,
                       as
                       have
                       been
                       mentioned
                       ,
                       would
                       be
                       both
                       tedious
                       ,
                       and
                       to
                       little
                       purpose
                       ;
                       I
                       will
                       therefore
                       select
                       some
                       few
                       ,
                       that
                       are
                       of
                       most
                       general
                       use
                       in
                       the
                       Doctrine
                       of
                       the
                       Sphere
                       ,
                       and
                       leave
                       the
                       rest
                       to
                       thine
                       own
                       practice
                       .
                    
                  
                
              
            
             
               
               
                 CHAP.
                 V.
                 
              
               
                 
                   Of
                   such
                   Spherical
                   Problems
                   as
                   are
                   of
                   most
                   General
                   Use
                   in
                   the
                   Doctrine
                   of
                   the
                   Primum
                   Mobile
                   or
                   Diurnal
                   Motion
                   of
                   the
                   Sun
                   and
                   Stars
                   .
                
              
               
                 
                   PROBLEM
                   1.
                   
                
                 
                   
                     The
                     greatest
                     Declination
                     of
                     the
                     Sun
                     being
                     given
                     ,
                     to
                     find
                     the
                     Declination
                     of
                     any
                     Point
                     of
                     the
                     Ecliptick
                     .
                  
                
                 
                   THe
                   Declination
                   of
                   the
                   Sun
                   or
                   other
                   Star
                   ,
                   is
                   his
                   or
                   their
                   distance
                   from
                   the
                   Equator
                   ,
                   and
                   as
                   they
                   decline
                   from
                   thence
                   either
                   Northward
                   or
                   Southward
                   ;
                   so
                   is
                   their
                   Declination
                   reckoned
                   North
                   or
                   South
                   .
                
                 
                   2.
                   
                   The
                   Sun
                   's
                   greatest
                   Declination
                   ,
                   which
                   in
                   this
                   and
                   many
                   other
                   Problems
                   is
                   supposed
                   to
                   be
                   given
                   ,
                   with
                   the
                   Distance
                   of
                   the
                   Tropicks
                   ,
                   Elevation
                   of
                   the
                   Equator
                   ,
                   and
                   Latitude
                   of
                   the
                   Place
                   ,
                   may
                   thus
                   be
                   found
                   .
                
                 
                 
                   
                   
                   
                     The
                     Sun
                     's
                     
                       
                         
                           greatest
                        
                         
                           Meridian
                        
                         
                           H
                           ♋
                           .
                           61.9916
                        
                      
                       
                         
                           least
                        
                         
                           Altitude
                        
                         
                           H
                           ♑
                           .
                           14.9416
                        
                      
                    
                  
                   
                     Their
                     difference
                     is
                     the
                     distance
                     of
                     the
                     Tropicks
                     ♋
                     .
                     ♑
                     .
                     47.
                     050
                  
                   
                     Half
                     that
                     Difference
                     ,
                     is
                     the
                     Sun
                     's
                     greatest
                     Declination
                     AE
                     ♋
                     .
                     23.
                     525
                  
                   
                     Which
                     deduct
                     from
                     the
                     Sun
                     's
                     greatest
                     Altitude
                     ,
                     the
                     remainer
                     is
                     the
                     height
                     of
                     the
                     Equator
                     HAE
                     .
                     38.
                     467
                  
                   
                     The
                     Complement
                     is
                     the
                     height
                     of
                     the
                     Pole
                     AEZ
                     or
                     PR
                     .
                     51.
                     533
                  
                
                 
                   Now
                   then
                   in
                   the
                   Right
                   angled
                   Spherical
                   Triangle
                   ADF
                   in
                   Fig.
                   1.
                   there
                   being
                   given
                   .
                
                 
                   1.
                   
                   The
                   Angle
                   of
                   the
                   Sun
                   's
                   greatest
                   Declination
                   DAF
                   .
                   23.
                   525.
                   
                
                 
                   2.
                   
                   The
                   Sun
                   's
                   supposed
                   distance
                   from
                   ♈
                   to
                   ♎
                   AF.
                   60
                   deg
                   .
                
                 
                   The
                   Sun
                   's
                   present
                   Declination
                   DF
                   may
                   be
                   found
                   ,
                   by
                   the
                   10
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   As
                   the
                   Radius
                   
                     
                       Is
                       to
                       the
                       Sine
                       of
                       DAF
                       .
                       23.
                       525.
                       
                    
                     
                       9.60113517
                    
                     
                       So
                       is
                       the
                       Sine
                       of
                       AF
                       60.
                       
                    
                     
                       9.93753063
                    
                     
                       To
                       the
                       Sine
                       of
                       DF.
                       20.
                       22.
                       
                    
                     
                       9.53866580
                    
                  
                
              
               
                 
                 
                   PROBLEM
                   2.
                   
                
                 
                   
                     The
                     Sun
                     's
                     groatest
                     Declination
                     ,
                     with
                     his
                     Distance
                     from
                     the
                     next
                     AEquinoctial
                     Point
                     being
                     given
                     ,
                     to
                     find
                     his
                     Right
                     Ascension
                     .
                  
                
                 
                   In
                   the
                   Right
                   angled
                   Spherical
                   Triangle
                   ADF
                   in
                   Fig.
                   1.
                   
                   Having
                   the
                   Angle
                   of
                   the
                   Sun
                   's
                   greatest
                   Declination
                   DAF
                   .
                   23.
                   525.
                   
                   And
                   his
                   supposed
                   distance
                   from
                   ♈
                   or
                   ♎
                   ,
                   the
                   
                     Hypotenusa
                     AF.
                     60.
                  
                   
                   The
                   Right
                   Ascension
                   of
                   the
                   Sun
                   ,
                   or
                   Arch
                   of
                   the
                   
                     AEquator
                     ,
                     AD
                  
                   may
                   be
                   found
                   ,
                   by
                   the
                   ninth
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   ,
                
                 
                   
                     As
                     the
                     Cotang
                     .
                     of
                     the
                     Hypot
                     .
                     AF.
                     60.
                     
                  
                   
                     9.76143937
                  
                   
                     Is
                     to
                     the
                     Radius
                  
                   
                     10.00000000
                  
                   
                     So
                     is
                     the
                     Cosine
                     of
                     DAF
                     .
                     23.
                     525.
                     
                  
                   
                     9
                     ▪
                     96231533
                  
                   
                     To
                     the
                     Tang.
                     of
                     AD.
                     57.
                     80.
                     
                  
                   
                     10.20087596
                  
                
              
               
                 
                   PROBLEM
                   3.
                   
                
                 
                   
                     To
                     find
                     the
                     Declination
                     of
                     a
                     Planet
                     or
                     Fixed
                     Star
                     with
                     Latitude
                     .
                  
                
                 
                   In
                   the
                   Oblique
                   angled
                   Spherical
                   Triangle
                   FPS
                   in
                   Fig.
                   4.
                   we
                   have
                   given
                   ,
                   1.
                   
                   
                     PS
                     =
                     AE
                  
                   ♋
                   the
                   greatest
                   Declination
                   of
                   the
                   Ecliptick
                   ,
                   2.
                   
                   The
                   Side
                   FS
                   the
                   Complement
                   of
                   the
                   Stars
                   Latitude
                   from
                   the
                   Ecliptick
                   at
                   K.
                   3.
                   
                   The
                   Angle
                   PSF
                   the
                   Complement
                   of
                   the
                   Stars
                   Longitude
                   .
                   To
                   find
                   PF
                   the
                   Complement
                   of
                   Declination
                   .
                   By
                   the
                   eighth
                   Case
                   of
                   Oblique
                   angled
                   Spherical
                   Triangles
                   ,
                   the
                   Proportions
                   are
                   .
                
                 
                   
                   
                     As
                     the
                     Cot.
                     of
                     PS
                     .
                     23.
                     525.
                     
                  
                   
                     10.3611802
                  
                   
                     Is
                     to
                     the
                     Radius
                     .
                  
                   
                     10.0000000
                  
                   
                     So
                     is
                     the
                     Cos.
                     of
                     PSF
                     .
                     20
                     deg
                     .
                  
                   
                     9.9729858
                  
                   
                     To
                     the
                     Tang.
                     of
                     SE.
                     22.
                     25.
                     
                  
                   
                     9.6118056
                  
                   
                     FS
                     .
                     86
                     deg
                     .
                     -
                     
                       ES.
                       22.
                       25.
                       
                       =
                       FE
                       .
                    
                  
                   
                     63.
                     75.
                     
                  
                
                 
                   
                     As
                     the
                     Cos.
                     of
                     
                       ES.
                       22.
                       25.
                       
                       Comp.
                       Arith.
                       
                    
                  
                   
                     0.0336046
                  
                   
                     To
                     the
                     Cosine
                     of
                     PS
                     .
                     23.
                     525.
                     
                  
                   
                     9.9623154
                  
                   
                     So
                     the
                     Cos.
                     FE
                     .
                     63.
                     75.
                     
                  
                   
                     9.6457058
                  
                   
                     To
                     the
                     Cos.
                     PF
                     .
                     64.
                     01.
                     
                  
                   
                     9.6416258
                  
                
                 
                   Whos
                   's
                   Complement
                   ,
                   is
                   FT
                   .
                   25.
                   99.
                   the
                   Declination
                   sought
                   .
                
              
               
                 
                   PROBLEM
                   4.
                   
                
                 
                   
                     To
                     find
                     the
                     Right
                     Ascension
                     of
                     a
                     Planet
                     ,
                     or
                     other
                     Star
                     with
                     Latitude
                     .
                  
                
                 
                   The
                   Declination
                   being
                   found
                   by
                   the
                   last
                   Problem
                   ,
                   we
                   have
                   in
                   the
                   Oblique
                   angled
                   Spherical
                   Triangle
                   PFS
                   in
                   Fig.
                   4.
                   
                   All
                   the
                   Sides
                   with
                   the
                   Angle
                   FSP
                   20
                   deg
                   .
                   or
                   the
                   Complement
                   of
                   the
                   Stars
                   Longitude
                   .
                   Hence
                   to
                   find
                   FPS
                   by
                   the
                   first
                   Case
                   of
                   Oblique
                   angled
                   Spherical
                   Triangles
                   ,
                   I
                   say
                
                 
                   
                     As
                     the
                     Sine
                     of
                     
                       PF
                       .
                       64.
                       01.
                       
                       Comp.
                       Arith.
                       
                    
                  
                   
                     0.0463059
                  
                   
                     Is
                     to
                     the
                     Sine
                     of
                     FSP
                     .
                     20.
                     
                  
                   
                     9.5340516
                  
                   
                     So
                     is
                     the
                     Sine
                     of
                     FS
                     .
                     86.
                     
                  
                   
                     9.9984407
                  
                   
                     To
                     the
                     Sine
                     of
                     FPS
                     .
                     22.
                     28.
                     
                  
                   
                     9.5787982
                  
                
                 
                   Whos
                   's
                   Complement
                   67.
                   72.
                   is
                   the
                   Right
                   Asc.
                   of
                   a
                   Star
                   II.
                   10.
                   
                   North
                   Lat.
                   4.
                   
                
              
               
                 
                 
                   PROBLEM
                   5.
                   
                
                 
                   
                     The
                     Poles
                     Elevation
                     ,
                     Sun's
                     greatest
                     Declination
                     and
                     Meridian
                     Altitude
                     being
                     given
                     ,
                     to
                     find
                     his
                     true
                     place
                     in
                     the
                     Zodiack
                     .
                  
                
                 
                   If
                   the
                   Meridian
                   Altitude
                   of
                   the
                   Sun
                   be
                   less
                   than
                   the
                   height
                   of
                   the
                   AEquator
                   ,
                   deduct
                   the
                   Meridian
                   Altitude
                   from
                   the
                   height
                   of
                   the
                   AEquator
                   ,
                   the
                   Remainer
                   is
                   the
                   Sun's
                   Declination
                   towards
                   the
                   South
                   Pole
                   :
                   but
                   if
                   the
                   Meridian
                   Altitude
                   of
                   the
                   Sun
                   be
                   more
                   than
                   the
                   height
                   of
                   the
                   AEquator
                   ,
                   deduct
                   the
                   height
                   of
                   the
                   AEquator
                   from
                   the
                   Meridian
                   Altitude
                   ,
                   what
                   remaineth
                   ,
                   is
                   the
                   Sun's
                   Declination
                   towards
                   the
                   North
                   Pole
                   ,
                   in
                   these
                   Northern
                   Parts
                   of
                   the
                   World
                   :
                   the
                   contrary
                   is
                   to
                   be
                   observed
                   in
                   the
                   Southern
                   Parts
                   .
                
                 
                   Then
                   in
                   the
                   Right
                   angled
                   Spherical
                   Triangle
                   ADF
                   in
                   Fig.
                   1.
                   we
                   have
                   given
                   the
                   Angle
                   FAD
                   the
                   Sun's
                   greatest
                   Declination
                   .
                
                 
                   The
                   Leg
                   DF
                   the
                   Sun's
                   present
                   Declination
                   ,
                   To
                   find
                   AF
                   the
                   Sun's
                   distance
                   from
                   the
                   next
                   Equinoctial
                   Point
                   .
                
                 
                   Therefore
                   by
                   the
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                     As
                     the
                     Sine
                     of
                     
                       FAD
                       .
                       23.
                       525.
                       
                       Comp.
                       Ar.
                       
                    
                  
                   
                     0.3988648
                  
                   
                     Is
                     to
                     the
                     Sine
                     of
                     DF.
                     23.
                     5.
                     
                  
                   
                     9.5945468
                  
                   
                     So
                     is
                     the
                     Radius
                     .
                  
                   
                     10.0009000
                  
                   
                     To
                     the
                     Sine
                     of
                     AF.
                     80.
                     04.
                     
                  
                   
                     9.9934116
                  
                
              
               
                 
                 
                   PROBLEM
                   6.
                   
                
                 
                   
                     The
                     Poles
                     Elevation
                     and
                     Sun's
                     Declination
                     being
                     given
                     ,
                     to
                     find
                     his
                     Amplitude
                     .
                  
                
                 
                   The
                   Amplitude
                   of
                   the
                   Sun
                   's
                   rising
                   or
                   setting
                   is
                   an
                   Arch
                   of
                   the
                   Horizon
                   intercepted
                   betwixt
                   the
                   AEquator
                   and
                   the
                   place
                   of
                   the
                   Sun
                   's
                   rising
                   or
                   setting
                   ;
                   and
                   it
                   is
                   either
                   Northward
                   or
                   Southward
                   ,
                   the
                   Northward
                   Amplitude
                   is
                   when
                   he
                   riseth
                   or
                   setteth
                   on
                   this
                   Side
                   of
                   the
                   AEquator
                   towards
                   the
                   North
                   Pole
                   ;
                   and
                   the
                   Southern
                   when
                   he
                   riseth
                   or
                   setteth
                   on
                   that
                   Side
                   of
                   the
                   AEquator
                   which
                   is
                   towards
                   the
                   South
                   Pole
                   :
                   That
                   we
                   may
                   then
                   find
                   the
                   Sun's
                   Amplitude
                   or
                   Distance
                   from
                   the
                   East
                   or
                   West
                   Point
                   ,
                   at
                   the
                   time
                   of
                   his
                   rising
                   or
                   setting
                   .
                   In
                   the
                   Right
                   angled
                   Spherical
                   Triangle
                   ATM
                   ,
                   in
                   Fig.
                   2.
                   let
                   there
                   be
                   given
                   the
                   Angle
                   TAM
                   .
                   38.
                   47.
                   the
                   Complement
                   of
                   the
                   Poles
                   Elevation
                   ;
                   and
                   TM
                   .
                   23.
                   15.
                   the
                   Sun
                   's
                   present
                   Declination
                   :
                   To
                   find
                   AM
                   the
                   Sun's
                   Amplitude
                   .
                
                 
                   By
                   the
                   eleventh
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                     As
                     the
                     Sine
                     of
                     
                       MAT.
                       38.
                       47.
                       
                       Comp.
                       Ar.
                       
                    
                  
                   
                     0.2061365
                  
                   
                     Is
                     to
                     the
                     Radim
                     .
                  
                   
                     10.0000000
                  
                   
                     So
                     is
                     the
                     Sine
                     of
                     MT
                     .
                     23.
                     15.
                     
                  
                   
                     9.5945468
                  
                   
                     To
                     the
                     Sine
                     of
                     AM.
                     39.
                     19.
                     
                  
                   
                     9.8006833
                  
                
              
               
                 
                 
                   PROBLEM
                   7.
                   
                
                 
                   
                     To
                     find
                     the
                     Ascensional
                     Difference
                     .
                  
                
                 
                   The
                   Ascensional
                   Difference
                   is
                   nothing
                   else
                   ,
                   but
                   the
                   Difference
                   between
                   the
                   Ascension
                   of
                   any
                   Point
                   of
                   the
                   Ecliptick
                   in
                   a
                   Right
                   Sphere
                   ,
                   and
                   the
                   Ascension
                   of
                   the
                   same
                   Point
                   in
                   an
                   Oblique
                   Sphere
                   ;
                   As
                   in
                   
                     Fig.
                     1.
                     
                     AT
                  
                   is
                   the
                   Ascensional
                   difference
                   between
                   DA
                   the
                   Sun's
                   Ascension
                   in
                   a
                   Right
                   Sphere
                   ,
                   and
                   DT
                   the
                   Sun's
                   Ascension
                   in
                   an
                   Oblique
                   Sphere
                   .
                   Now
                   then
                   in
                   the
                   Right
                   angled
                   Spherical
                   Triangle
                   AMT
                   ,
                   we
                   have
                   given
                   .
                   The
                   Angle
                   MAT.
                   38.
                   47.
                   the
                   Complement
                   of
                   the
                   Poles
                   Elevation
                   .
                   And
                   MT
                   .
                   23.
                   15.
                   
                   To
                   find
                   AT
                   the
                   Ascensional
                   difference
                   .
                
                 
                   
                     As
                     Rad.
                     
                  
                   
                      
                  
                   
                     To
                     the
                     Cot.
                     of
                     
                       MAT.
                       38.
                       47.
                       
                       Com.
                       Ar.
                       
                    
                  
                   
                     10.0999136
                  
                   
                     So
                     is
                     Tang.
                     MT
                     .
                     23.
                     55.
                     
                  
                   
                     9.6310051
                  
                   
                     To
                     the
                     Sine
                     of
                     AT
                     .
                     32.
                     56.
                     
                  
                   
                     9.7309187
                  
                
              
               
                 
                   PROBLEM
                   8.
                   
                
                 
                   
                     Having
                     the
                     Right
                     Ascension
                     and
                     Ascensional
                     Difference
                     ,
                     to
                     find
                     the
                     Oblique
                     Ascension
                     and
                     Descension
                     .
                  
                
                 
                   In
                   
                     Fig.
                     1.
                     
                     DT
                  
                   represents
                   the
                   Right
                   Ascension
                   ,
                   AT
                   the
                   Ascensional
                   Difference
                   .
                   DA
                   the
                   Oblique
                   Ascension
                   which
                   is
                   found
                   by
                   deducting
                   the
                   Ascensional
                   Difference
                   AT
                   .
                   from
                   the
                   Right
                   Ascension
                   DT
                   .
                   according
                   to
                   the
                   Direction
                   following
                   .
                
                 
                   
                   
                     If
                     the
                     Declination
                     be
                     
                       
                         N.
                         
                      
                       
                         North
                         
                           
                             Subt.
                             
                          
                           
                             Add
                             
                               
                                 The
                                 Ascentional
                                 Difference
                                 from
                                 the
                                 Right
                                 ,
                                 and
                                 it
                                 giveth
                                 the
                                 Oblique
                                 Ascension
                                 .
                              
                               
                                 The
                                 Ascensional
                                 Difference
                                 to
                                 the
                                 Right
                                 ,
                                 and
                                 it
                                 giveth
                                 the
                                 Oblique
                                 Descension
                                 .
                              
                            
                          
                        
                      
                       
                         South
                         
                           
                             Add
                          
                           
                             Subt.
                             
                             
                               
                                 The
                                 Ascensional
                                 Difference
                                 to
                                 the
                                 Right
                                 ,
                                 and
                                 it
                                 giveth
                                 the
                                 Oblique
                                 Ascension
                                 .
                              
                               
                                 The
                                 Ascensional
                                 Difference
                                 from
                                 the
                                 Right
                                 ,
                                 and
                                 it
                                 giveth
                                 the
                                 Oblique
                                 Descension
                                 .
                              
                            
                          
                        
                      
                    
                  
                
                 
                   
                     Right
                     Ascension
                     of
                     ♊
                     .
                     0
                     deg
                     .
                  
                   
                     57.80
                  
                   
                     Ascensional
                     Difference
                  
                   
                     27.62
                  
                   
                     Oblique
                     Ascension
                     ♊
                     .
                     0
                     deg
                     .
                  
                   
                     30.18
                  
                   
                     Oblique
                     Descension
                     ♊
                     .
                     0
                     deg
                     .
                  
                   
                     85.42
                  
                
              
               
                 
                   PROBLEM
                   9.
                   
                
                 
                   
                     To
                     find
                     the
                     time
                     of
                     the
                     Sun
                     's
                     rising
                     and
                     setting
                     ,
                     with
                     the
                     length
                     of
                     the
                     Day
                     and
                     Night
                     .
                  
                
                 
                   The
                   Ascensional
                   Difference
                   of
                   the
                   Sun
                   being
                   added
                   to
                   the
                   Semidiurnal
                   Arch
                   in
                   a
                   Right
                   Sphere
                   ,
                   that
                   is
                   ,
                   to
                   90
                   Degrees
                   in
                   the
                   Northern
                   Signs
                   ,
                   or
                   substracted
                   from
                   it
                   in
                   the
                   Southern
                   ,
                   their
                   Sum
                   or
                   Difference
                   will
                   be
                   the
                   Semidiurnal
                   Arch
                   ,
                   which
                   
                   doubled
                   is
                   the
                   Right
                   Arch
                   ,
                   which
                   bisected
                   is
                   the
                   time
                   of
                   the
                   Sun
                   rising
                   ,
                   and
                   the
                   Day
                   Arch
                   bisected
                   is
                   the
                   time
                   of
                   his
                   setting
                   .
                
                 
                   As
                   when
                   the
                   Sun
                   is
                   in
                   0
                   deg
                   .
                   ♊
                   .
                   his
                   Ascensional
                   Difference
                   is
                   27.
                   62.
                   which
                   being
                   added
                   to
                   90
                   degrees
                   ,
                   because
                   the
                   Declination
                   is
                   North
                   ,
                   the
                   Sum
                   will
                   be
                   117.62
                   the
                   Semidiurnal
                   Arch.
                   
                
                 
                   The
                   double
                   whereof
                   is
                   235.22
                   the
                   Diurnal
                   Arch
                   ,
                   which
                   being
                   converted
                   into
                   time
                   makes
                   15
                   hours
                   41
                   minutes
                   :
                   for
                   the
                   length
                   of
                   the
                   Day
                   ,
                   whose
                   Complement
                   to
                   24
                   ;
                   is
                   8
                   hours
                   19
                   minutes
                   the
                   length
                   of
                   the
                   Night
                   ;
                   the
                   half
                   whereof
                   is
                   4
                   hours
                   9
                   minutes
                   30
                   Seconds
                   the
                   time
                   of
                   the
                   Sun
                   's
                   rising
                   .
                
              
               
                 
                   PROBLEM
                   10.
                   
                
                 
                   
                     The
                     Poles
                     Elevation
                     and
                     the
                     Sun's
                     Declination
                     being
                     given
                     ,
                     to
                     find
                     his
                     Altitude
                     at
                     any
                     time
                     assigned
                     .
                  
                
                 
                   In
                   this
                   Problem
                   there
                   are
                   three
                   Varieties
                   .
                   1.
                   
                   When
                   the
                   Sun
                   is
                   in
                   the
                   
                     AEquator
                     .
                  
                   ,
                   that
                   is
                   ,
                   in
                   the
                   beginning
                   of
                   ♈
                   and
                   ♎
                   in
                   which
                   case
                   supposing
                   the
                   Sun
                   to
                   be
                   at
                   B
                   ,
                   60
                   degrees
                   or
                   four
                   hours
                   distant
                   from
                   the
                   Meridian
                   ,
                   then
                   in
                   the
                   Right
                   angled
                   Spherical
                   Triangle
                   
                     BZ
                     AE
                  
                   ,
                   in
                   Fig.
                   1.
                   we
                   have
                   given
                   ,
                   
                     AE
                     Z
                  
                   ,
                   51.
                   53.
                   the
                   Poles
                   Elevation
                   ,
                   and
                   
                     B
                     AE
                  
                   60
                   degrees
                   ,
                   to
                   find
                   BZ
                   .
                
                 
                   Therefore
                   by
                   the
                   2
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                   
                     As
                     the
                     Radius
                  
                   
                      
                  
                   
                     To
                     the
                     Cosine
                     of
                     
                       AE
                       Z.
                    
                     51.
                     53.
                     
                  
                   
                     9.7938635
                  
                   
                     So
                     is
                     the
                     Cosine
                     of
                     
                       B.
                       AE
                    
                     .
                     60.
                     
                  
                   
                     9.6989700
                  
                   
                     To
                     the
                     Cosine
                     of
                     
                       B
                       Z.
                    
                     71.
                     88.
                     
                  
                   
                     9.4928335
                  
                
                 
                   Whos
                   's
                   Complement
                   BC.
                   18.
                   12.
                   is
                   the
                   ☉
                   Altitude
                   required
                   .
                
                 
                   The
                   second
                   Variety
                   is
                   when
                   the
                   Sun
                   is
                   in
                   the
                   Northern
                   Signs
                   ,
                   that
                   is
                   ,
                   in
                   ♈
                   .
                   ♉
                   .
                   ♊
                   .
                   ♋
                   .
                   ♌
                   .
                   ♍
                   .
                   in
                   which
                   Case
                   supposing
                   the
                   Sun
                   to
                   be
                   at
                   F
                   in
                   
                     Fig.
                     II
                  
                   Then
                   in
                   the
                   Oblique
                   angled
                   Spherical
                   Triangle
                   FZP
                   ,
                   we
                   have
                   given
                   .
                   1.
                   
                   PZ
                   38.
                   47
                   the
                   Complement
                   of
                   the
                   Poles
                   Elevation
                   .
                   2.
                   
                   FP
                   .
                   67.
                   97
                   the
                   Complement
                   of
                   Declination
                   .
                   3.
                   
                   ZPF
                   .
                   45
                   the
                   Distance
                   of
                   the
                   ☉
                   from
                   the
                   Meridian
                   ,
                   To
                   find
                   FZ
                   .
                
                 
                   Therefore
                   by
                   the
                   eighth
                   Case
                   of
                   Oblique
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                     As
                     the
                     Cotang
                     .
                     of
                     ZP
                     .
                     38.
                     47.
                     
                  
                   
                     10.0997059
                  
                   
                     Is
                     to
                     the
                     Radius
                     .
                  
                   
                     10.0000000
                  
                   
                     So
                     is
                     the
                     Cosine
                     of
                     ZPF
                     .
                     45.
                     
                  
                   
                     9.8494850
                  
                   
                     To
                     the
                     Tang.
                     of
                     SP.
                     29.
                     33.
                     
                  
                   
                     9.7497791
                  
                   
                     Then
                     from
                     FP
                     .
                  
                   
                     67.97
                  
                   
                     Deduct
                     SP.
                     
                  
                   
                     29.33
                  
                   
                     There
                     rests
                     FS
                     .
                  
                   
                     38.64
                  
                
                 
                   
                   
                     As
                     the
                     Cosine
                     of
                     
                       SP.
                       29.
                       33.
                       
                       Comp.
                       Ar.
                       
                    
                  
                   
                     0.0595768
                  
                   
                     To
                     the
                     Cosine
                     of
                     PZ
                     .
                     38.
                     47.
                     
                  
                   
                     9.8937251
                  
                   
                     So
                     is
                     the
                     Cosine
                     of
                     FS
                     .
                     38.
                     64.
                     
                  
                   
                     9.8926982
                  
                   
                     To
                     the
                     Cosine
                     of
                     FZ
                     .
                     45.
                     45.
                     
                  
                   
                     9.8460001
                  
                
                 
                   Whos
                   's
                   Complement
                   FC
                   .
                   44.
                   55
                   is
                   the
                   ☉
                   Altitude
                   required
                   .
                
                 
                   The
                   third
                   Variety
                   is
                   when
                   the
                   Sun
                   is
                   in
                   the
                   Southern
                   Signs
                   as
                   in
                   ♎
                   .
                   ♏
                   .
                   ♐
                   .
                   ♑
                   .
                   ♒
                   .
                   ♓
                   .
                   And
                   in
                   this
                   Case
                   supposing
                   the
                   ☉
                   to
                   be
                   ♐
                   10
                   degrees
                   ,
                   and
                   his
                   Declination
                   South
                   Db
                   22.
                   03.
                   and
                   his
                   Distance
                   from
                   the
                   Meridian
                   45
                   as
                   before
                   ,
                   then
                   in
                   the
                   Oblique
                   angled
                   Spherical
                   Triangle
                   
                     Z
                     bP
                  
                   in
                   Fig.
                   1.
                   we
                   have
                   given
                   
                     Z
                     P.
                  
                   38.
                   47.
                   
                   The
                   Side
                   
                     bP
                     112.
                  
                   03.
                   and
                   the
                   Angle
                   ZPb
                   45.
                   
                   To
                   find
                   Zb.
                   
                
                 
                   Therefore
                   by
                   the
                   8
                   Case
                   of
                   Oblique
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                     As
                     the
                     Cotang
                     .
                     of
                     ZP
                     .
                     38.
                     47.
                     
                  
                   
                     10.0997059
                  
                   
                     Is
                     to
                     the
                     Radius
                     .
                  
                   
                     10.0000000
                  
                   
                     So
                     is
                     the
                     Cosine
                     of
                     ZPb
                     .
                     45.
                     
                  
                   
                     9.8494850
                  
                   
                     To
                     the
                     Tang.
                     of
                     SP.
                     29.
                     33.
                     
                  
                   
                     9.7497791
                  
                   
                     Then
                     from
                     bP.
                     
                  
                   
                     112.03
                  
                   
                     Deduct
                     SP.
                     
                  
                   
                     29.33
                  
                   
                     There
                     rests
                     bS.
                     
                  
                   
                     82.70
                  
                   
                     As
                     the
                     Cosine
                     of
                     
                       P
                       S.
                       29.
                       33.
                       
                       Comp.
                       Ar.
                       
                    
                  
                   
                     0.0595768
                  
                   
                     To
                     the
                     Cosine
                     of
                     ZP
                     .
                     38.
                     47.
                     
                  
                   
                     9.8937251
                  
                   
                     So
                     the
                     Cosine
                     of
                     bS.
                     82.
                     70
                  
                   
                     9.1040246
                  
                   
                     To
                     the
                     Cosine
                     of
                     Zb.
                     83.
                     45.
                     
                  
                   
                     9.0573265
                  
                
                 
                   Whos
                   's
                   Complement
                   6.55
                   is
                   the
                   ☉
                   Altitude
                   required
                   .
                
              
               
                 
                 
                   PROBLEM
                   11.
                   
                
                 
                   
                     Having
                     the
                     Altitude
                     of
                     the
                     Sun
                     ,
                     his
                     Distance
                     from
                     the
                     Meridian
                     ,
                     and
                     Declination
                     ,
                     to
                     find
                     his
                     Azimuth
                     .
                  
                
                 
                   The
                   Azimuth
                   of
                   the
                   Sun
                   is
                   an
                   Arch
                   of
                   the
                   Horizon
                   intercepted
                   between
                   the
                   Meridian
                   and
                   the
                   Vertical
                   Line
                   passing
                   by
                   the
                   Sun
                   ,
                   being
                   understood
                   by
                   the
                   Angle
                   HZC
                   in
                   Fig.
                   1.
                   or
                   Arch
                   HC
                   .
                   And
                   in
                   all
                   the
                   Varieties
                   of
                   the
                   last
                   Problem
                   ,
                   may
                   be
                   found
                   ,
                   by
                   the
                   first
                   Case
                   of
                   Oblique
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   Thus
                   in
                   the
                   Triangle
                   ZBP.
                   
                   
                     
                       As
                       the
                       Sine
                       of
                       
                         BZ
                         .
                         71.
                         88.
                         
                         Comp.
                         Ar.
                         
                      
                    
                     
                       0
                       .
                       022090●
                    
                     
                       Is
                       to
                       the
                       Sine
                       of
                       BPZ
                       .
                       60.
                       
                    
                     
                       9.9375306
                    
                     
                       So
                       is
                       the
                       Sine
                       of
                       BP
                       .
                       90.
                       
                    
                     
                       10.0000000
                    
                     
                       To
                       the
                       Sine
                       of
                       BZP.
                       65.
                       67.
                       
                    
                     
                       9.9596209
                    
                  
                
                 
                   In
                   the
                   Triangle
                   ZFP
                   .
                   I
                   say
                   .
                
                 
                   s.
                   ZF
                   .
                   s.
                   ZPF
                   ▪
                   :
                   :
                   s.
                   FP
                   .
                   s.
                   FZP
                   .
                
                 
                   In
                   the
                   Triangle
                   ZbP.
                   I
                   say
                   .
                
                 
                   Sine
                   Zb.
                   Sine
                   ZPb
                   :
                   :
                   Sine
                   bP.
                   Sine
                   bZP.
                   
                
              
               
                 
                 
                   PROBLEM
                   12.
                   
                
                 
                   
                     The
                     Poles
                     Elevation
                     ,
                     with
                     the
                     Sun's
                     Altitude
                     and
                     Declination
                     given
                     ,
                     to
                     find
                     his
                     Azimuth
                     .
                  
                
                 
                   In
                   the
                   Oblique
                   angled
                   Spherical
                   Triangle
                   FZP
                   in
                   Fig.
                   1.
                   let
                   there
                   be
                   given
                   .
                
                 
                   1.
                   
                   FP
                   .
                   67.
                   97
                   the
                   Complement
                   of
                   the
                   ☉
                   Declination
                   .
                
                 
                   2.
                   
                   ZP
                   .
                   38.
                   47
                   the
                   Complement
                   of
                   the
                   Poles
                   Elevation
                   .
                
                 
                   3.
                   
                   FZ
                   .
                   45.
                   46
                   the
                   Complement
                   of
                   the
                   ☉
                   Altitude
                   .
                
                 
                   And
                   let
                   the
                   Angle
                   FZP
                   the
                   ☉
                   Azimuth
                   be
                   required
                   .
                
                 
                   By
                   the
                   11
                   Case
                   of
                   Oblique
                   Angled
                   Spherical
                   Triangles
                   .
                
                 
                   As
                   the
                   Sine
                   ZP
                   x
                   Sine
                   FZ
                   ,
                   Is
                   to
                   the
                   Square
                   of
                   Radius
                   .
                
                 
                   So
                   is
                   the
                   Sine
                   1
                   /
                   2
                   Z
                   of
                   the
                   Sides
                   ZP
                   x
                   1
                   /
                   2
                   
                     Z
                     cr
                     —
                     ZF
                  
                   .
                
                 
                   To
                   the
                   Square
                   of
                   the
                   Sine
                   of
                   half
                   the
                   Angle
                   FZP
                   .
                
                 
                   The
                   Sum
                   of
                   the
                   three
                   Sides
                   is
                   151.89
                
                 
                   The
                   half
                   Sum
                   is
                   75.945
                   from
                   which
                   deduct
                   PZ
                   38.
                   47.
                   
                   The
                   difference
                   is
                   37.475
                   And
                   the
                   Difference
                   between
                   75.945
                   and
                   FZ
                   is
                   30.
                   495.
                   
                
                 
                   
                   
                     
                       Sine
                       of
                    
                     PZ
                     .
                     38.
                     47.
                     
                     Comp.
                     Ar.
                     
                  
                   
                     0.2061365
                  
                   
                     
                       Sine
                       of
                    
                     FZ
                     .
                     45.
                     45.
                     
                     Comp.
                     Ar.
                     
                  
                   
                     0.1471308
                  
                   
                     s.
                     1
                     /
                     2
                     Z
                     cr
                     —
                     PZ
                     .
                     37.
                     475.
                     
                  
                   
                     9.7842000
                  
                   
                     s.
                     1
                     /
                     2
                     Z
                     cr
                     —
                     FZ
                     .
                     30.
                     495.
                     
                  
                   
                     9.7054045
                  
                   
                     Square
                     of
                     the
                     Sine
                     of
                     1
                     /
                     2
                     FZP
                     .
                  
                   
                     19.8428618
                  
                   
                     Sine
                     of
                     57.
                     94.
                     
                  
                   
                     9.9214309
                  
                
                 
                   The
                   double
                   whereof
                   is
                   115.88
                   the
                   ☉
                   Azimuth
                   from
                   the
                   North.
                   And
                   the
                   Complement
                   64.12
                   ,
                   is
                   the
                   ☉
                   Azimuth
                   from
                   the
                   South
                   .
                
              
               
                 
                   PROBLEM
                   13.
                   
                
                 
                   
                     To
                     find
                     the
                     Point
                     of
                     the
                     Ecliptick
                     Culminating
                     ,
                     and
                     its
                     Altitude
                     .
                  
                
                 
                   Before
                   we
                   can
                   know
                   what
                   Sign
                   and
                   Degree
                   of
                   the
                   Ecliptick
                   is
                   in
                   the
                   
                     Medium
                     Coeli
                  
                   ;
                   we
                   must
                   find
                   the
                   Right
                   Ascension
                   thereof
                   ,
                   to
                   do
                   which
                   ,
                   we
                   must
                   add
                   the
                   Sun's
                   Right
                   Ascension
                   to
                   the
                   time
                   afternoon
                   ,
                   being
                   reduced
                   into
                   Degrees
                   and
                   Minutes
                   of
                   the
                   AEquator
                   ,
                   the
                   Sum
                   is
                   the
                   Right
                   Ascension
                   of
                   the
                   
                     Medium
                     Coeli
                  
                   .
                
                 
                   Example
                   .
                   Let
                   the
                   time
                   given
                   ,
                   be
                   March
                   the
                   20.
                   1674.
                   at
                   one
                   of
                   the
                   Clock
                   in
                   the
                   Afternoon
                   .
                
                 
                   At
                   which
                   time
                   the
                   Sun's
                   place
                   is
                   in
                   ♈
                   .
                   10
                   deg
                   .
                   23
                   Centesms
                   .
                
                 
                   To
                   find
                   the
                   Right
                   Ascension
                   thereof
                   ,
                   in
                   the
                   Right
                   angled
                   Spherical
                   T●iangle
                   ADF
                   in
                   
                     Fig.
                     1.
                  
                   we
                   have
                   given
                   ;
                   The
                   Angle
                   of
                   the
                   Sun
                   's
                   greatest
                   Declination
                   DAF
                   23.
                   525
                   and
                   the
                   Sun's
                   distance
                   from
                   the
                   next
                   Equinoctial
                   Point
                   AF
                   10.
                   23.
                   
                
                 
                   Therefore
                   by
                   the
                   ninth
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                   
                     As
                     the
                     
                       ct
                       .
                       AF.
                    
                     10.
                     23.
                     
                  
                   
                     10.7435974
                  
                   
                     Is
                     to
                     Radius
                     .
                  
                   
                     10.0000000
                  
                   
                     So
                     is
                     
                       cs
                       DAF
                    
                     22.
                     525.
                     
                  
                   
                     19.9623154
                  
                   
                     To
                     t
                     AD
                     9.
                     39.
                     
                  
                   
                     9.2187180
                  
                
                 
                   To
                   which
                   adding
                   the
                   Equinoctial
                   Degrees
                   answering
                   to
                   one
                   hour
                   ,
                   viz.
                   15.
                   the
                   Sum
                   is
                   24.39
                   the
                   Right
                   Ascension
                   of
                   the
                   Mid
                   Heaven
                   .
                   Hence
                   to
                   find
                   the
                   Point
                   culminating
                   ;
                   in
                   the
                   Right
                   angled
                   Spherical
                   Triangle
                   ADF
                   in
                   Fig.
                   1.
                   we
                   have
                   given
                   AD
                   24.
                   39
                   and
                   DAF
                   23.
                   525
                   to
                   find
                   AF.
                   
                
                 
                   Therefore
                   by
                   the
                   fifth
                   Case
                   of
                   Right
                   Angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                     As
                     t
                     AD
                     24.
                     39.
                     
                  
                   
                     10.6564908
                  
                   
                     Is
                     to
                     Radius
                     .
                  
                   
                     10.0000000
                  
                   
                     So
                     is
                     
                       cs
                       DAF
                    
                     23.
                     525.
                     
                  
                   
                     9.9623154
                  
                   
                     To
                     ct
                     .
                     AF
                     26.
                     31.
                     
                  
                   
                     10.3058246
                  
                
                 
                   Therefore
                   the
                   Point
                   culminating
                   is
                   ♈
                   26.
                   31.
                   
                
                 
                   To
                   find
                   the
                   Altitude
                   thereof
                   above
                   the
                   Horizon
                   we
                   have
                   given
                   in
                   the
                   same
                   Triangle
                   
                     DAF
                     23.
                  
                   525.
                   and
                   AF
                   26.
                   31.
                   to
                   find
                   DF.
                   
                
                 
                   Therefore
                   by
                   the
                   tenth
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                     As
                     Radius
                     .
                  
                   
                     10.0000000
                  
                   
                     Is
                     to
                     
                       s
                       AF
                       —
                       26
                    
                     ,
                     31.
                     
                  
                   
                     9.6466268
                  
                   
                     So
                     is
                     
                       s
                       DAF
                    
                     23.
                     525.
                     
                  
                   
                     9.6011352
                  
                   
                     To
                     the
                     
                       s
                       DF
                    
                     10.
                     19.
                     
                  
                   
                     9.2477628
                  
                
                 
                 
                   Which
                   is
                   the
                   North
                   Declination
                   of
                   the
                   Point
                   of
                   the
                   Ecliptick
                   culminating
                   ,
                   and
                   being
                   added
                   to
                   the
                   height
                   of
                   the
                   AEquator
                   at
                   London
                   38.
                   47
                   the
                   Sum
                   is
                   48.66
                   the
                   Altitude
                   of
                   the
                   Mid
                   Heaven
                   as
                   was
                   required
                   .
                
              
               
                 
                   PROBLEM
                   14.
                   
                
                 
                   
                     Having
                     the
                     greatest
                     obliquity
                     of
                     the
                     Ecliptick
                     together
                     with
                     the
                     Distance
                     of
                     the
                     Point
                     given
                     from
                     the
                     Equinoctial
                     ,
                     to
                     find
                     the
                     Meridian
                     Angle
                     ,
                     or
                     Intersection
                     of
                     the
                     Meridian
                     with
                     the
                     Ecliptick
                     .
                  
                
                 
                   Having
                   drawn
                   the
                   Primitive
                   Circle
                   HZRN
                   in
                   Fig.
                   5.
                   representing
                   the
                   Meridian
                   ,
                   and
                   the
                   two
                   Diameters
                   HAR
                   ,
                   and
                   ZAN
                   ,
                   set
                   off
                   the
                   height
                   of
                   the
                   Pole
                   from
                   R
                   to
                   P.
                   51.
                   53
                   ,
                   and
                   from
                   N
                   to
                   S
                   ,
                   and
                   draw
                   the
                   Diameters
                   PAS
                   for
                   the
                   Axis
                   of
                   the
                   World
                   ,
                   and
                   
                     AE
                     AQ
                  
                   for
                   the
                   AEquator
                   ;
                   this
                   done
                   ,
                   the
                   Right
                   Ascension
                   of
                   the
                   Mid
                   Heaven
                   being
                   given
                   ,
                   as
                   in
                   the
                   last
                   Problem
                   24.39
                   with
                   the
                   Point
                   culminating
                   .
                   ♈
                   .
                   26.31
                   ,
                   and
                   the
                   Declination
                   thereof
                   10.19
                   ,
                   if
                   you
                   set
                   10
                   deg
                   .
                   19
                   Centesmes
                   from
                   AE
                   to
                   F
                   and
                   e
                   to
                   X
                   ,
                   you
                   may
                   draw
                   the
                   Diameters
                   FAX
                   and
                   cAd
                   at
                   Right
                   Angles
                   thereunto
                   ,
                   and
                   because
                   the
                   
                     Imum
                     Coeli
                  
                   is
                   directly
                   opposite
                   to
                   the
                   Point
                   culminating
                   ,
                   that
                   is
                   ,
                   in
                   ♎
                   26.31
                   ,
                   if
                   you
                   set
                   26.31
                   from
                   X
                   to
                   b
                   ,
                   a
                   Ruler
                   laid
                   from
                   c
                   to
                   b
                   will
                   cut
                   the
                   Diameter
                   FX
                   in
                   G
                   ,
                   and
                   then
                   making
                   
                     Xh
                     Z
                     Xb
                  
                   you
                   have
                   the
                   three
                   Points
                   
                     b
                     G
                     h
                  
                   ,
                   by
                   which
                   to
                   draw
                   that
                   Circle
                   ,
                   which
                   will
                   cut
                   the
                   
                     AEquator
                     AE
                     AQ
                  
                   in
                   ♎
                   ,
                   and
                   so
                   you
                   have
                   the
                   three
                   Points
                   X
                   ♎
                   F
                   by
                   which
                   to
                   describe
                   the
                   Arch
                   of
                   the
                   Ecliptick
                   
                     ♈
                     F
                     ♎
                     X.
                  
                   
                
                 
                 
                   And
                   in
                   the
                   Right
                   angled
                   Spherical
                   Triangle
                   ♈
                   AEF
                   we
                   have
                   given
                   .
                   The
                   Angle
                   AE
                   ♈
                   
                     F.
                     23.525
                  
                   the
                   Sun
                   's
                   greatest
                   Declination
                   ,
                   and
                   ♈
                   
                     F.
                     26.
                  
                   31.
                   the
                   Point
                   culminating
                   ,
                   to
                   find
                   the
                   Angle
                   
                     ♈
                     F
                     AE
                  
                   .
                
                 
                   Therefore
                   by
                   the
                   seventh
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                     
                       As
                       the
                    
                     ct
                     AE
                     ♈
                     F.
                     23.
                     525.
                     
                  
                   
                     10.3611802
                  
                   
                     Is
                     to
                     the
                     Radius
                     .
                  
                   
                     10.0000000
                  
                   
                     So
                     is
                     the
                     cs
                     ♈
                     F.
                     26.
                     31.
                     
                  
                   
                     9.9525062
                  
                   
                     To
                     the
                     cot
                     .
                     ♈
                     FAE
                     .
                     68.
                     60.
                     
                  
                   
                     9.5913260
                  
                
                 
                   Which
                   is
                   the
                   Angle
                   of
                   the
                   Ecliptick
                   with
                   the
                   Meridian
                   .
                
              
               
                 
                   PROBLEM
                   15.
                   
                
                 
                   
                     To
                     find
                     the
                     Angle
                     Orient
                     ,
                     or
                     Altitude
                     of
                     the
                     Nonagesime
                     Degree
                     of
                     the
                     Ecliptick
                     .
                  
                
                 
                   In
                   Fig.
                   5.
                   the
                   Pole
                   of
                   the
                   Ecliptick
                   ♈
                   F
                   ♎
                   X
                   is
                   at
                   m
                   ,
                   and
                   so
                   you
                   have
                   the
                   three
                   Points
                   
                     Z
                     m
                     N
                  
                   to
                   draw
                   the
                   Vertical
                   Circle
                   
                     Z
                     k
                     N
                  
                   cutting
                   the
                   Ecliptick
                   at
                   Right
                   Angles
                   in
                   the
                   Point
                   a
                   :
                   And
                   then
                   in
                   the
                   Right
                   angled
                   Spherical
                   Triangle
                   
                     F
                     a
                     Z
                  
                   ,
                   we
                   have
                   given
                   ;
                   FZ
                   41.
                   34
                   the
                   Complement
                   of
                   FH
                   the
                   Altitude
                   of
                   the
                   Mid
                   Heaven
                   ;
                   And
                   the
                   Angle
                   
                     a
                     FZ
                  
                   68.
                   68
                   the
                   Angle
                   of
                   the
                   Ecliptick
                   with
                   the
                   Meridian
                   .
                   To
                   find
                   
                     Z
                     a.
                  
                   
                
                 
                   Therefore
                   by
                   the
                   tenth
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                 
                   As
                   the
                   Radius
                   .
                
                 
                   
                     To
                     the
                     Sine
                     of
                     FZ
                     .
                     41.
                     34.
                     
                  
                   
                     9
                     .
                     819889●
                  
                   
                     So
                     is
                     the
                     Sine
                     of
                     
                       Z
                       F
                       a.
                    
                     68.
                     68.
                     
                  
                   
                     9.9691128
                  
                   
                     To
                     the
                     Sine
                     of
                     
                       Z
                       a.
                    
                     37.
                     97.
                     
                  
                   
                     9.7891027
                  
                
                 
                   Whos
                   's
                   Complement
                   is
                   ak
                   the
                   Measure
                   of
                   the
                   Angle
                   agk
                   52.
                   03
                   the
                   Angle
                   of
                   the
                   Ecliptick
                   with
                   the
                   Horizon
                   ,
                   or
                   Altitude
                   of
                   the
                   Nonagesime
                   Degree
                   .
                
              
               
                 
                   PROBLEM
                   16.
                   
                
                 
                   
                     To
                     find
                     the
                     place
                     of
                     Nonagosime
                     Degree
                     of
                     the
                     Ecliptick
                     .
                  
                
                 
                   In
                   
                     Fig.
                     5.
                     
                     F
                  
                   represents
                   the
                   Point
                   of
                   the
                   Ecliptick
                   in
                   the
                   Mid
                   Heaven
                   ,
                   which
                   according
                   to
                   Problem
                   14
                   is
                   ♈
                   .
                   26.31
                   which
                   being
                   known
                   ,
                   in
                   the
                   Triangle
                   FZa
                   ,
                   we
                   have
                   also
                   given
                   ,
                   FZ
                   41.
                   34
                   and
                   the
                   Angle
                   ZFa.
                   68.
                   68.
                   
                   To
                   find
                   Fa.
                   
                
                 
                   Therefore
                   by
                   the
                   ninth
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                     As
                     the
                     cot
                     .
                     of
                     FZ
                     .
                     41.
                     34.
                     
                  
                   
                     10.0556361
                  
                   
                     Is
                     to
                     the
                     Radius
                     .
                  
                   
                     10.0000000
                  
                   
                     So
                     is
                     the
                     cos
                     .
                     of
                     ZFa.
                     6.
                     8.
                     6.
                     8.
                     
                  
                   
                     9.5605957
                  
                   
                     To
                     the
                     tang
                     .
                     of
                     Fa.
                     17.
                     73.
                     
                  
                   
                     9.5049596
                  
                
                 
                   Which
                   being
                   added
                   to
                   ♈
                   F
                   26.
                   31
                   the
                   sum
                   is
                   ♈
                   a.
                   44.
                   04
                   the
                   place
                   of
                   the
                   Nonagesime
                   Degree
                   of
                   the
                   Ecliptick
                   at
                   a.
                   
                
              
               
                 
                 
                   PROBLEM
                   17.
                   
                
                 
                   
                     The
                     Mid
                     Heaven
                     being
                     given
                     ,
                     to
                     find
                     the
                     Points
                     of
                     the
                     Ecliptick
                     Ascending
                     and
                     Descending
                     .
                  
                
                 
                   Having
                   found
                   by
                   the
                   last
                   Problem
                   ,
                   the
                   place
                   of
                   Nonagesime
                   Degree
                   of
                   the
                   Ecliptick
                   at
                   a
                   to
                   be
                   in
                   ♉
                   .
                   14.04
                   ,
                   if
                   you
                   add
                   90
                   Degrees
                   or
                   three
                   Signs
                   thereto
                   ,
                   the
                   Ascendant
                   at
                   g
                   will
                   be
                   in
                   ♌
                   14.
                   04
                   ,
                   and
                   the
                   Point
                   descending
                   by
                   adding
                   of
                   six
                   Signs
                   will
                   be
                   in
                   ♒
                   14.
                   02.
                   
                   But
                   these
                   with
                   the
                   Cusps
                   of
                   the
                   other
                   Houses
                   of
                   Heaven
                   may
                   be
                   otherwise
                   found
                   in
                   this
                   manner
                   .
                
                 
                   To
                   the
                   Right
                   Ascension
                   of
                   the
                   
                     Medium
                     Coeli
                  
                   or
                   the
                   tenth
                   House
                   ,
                   add
                   30
                   ,
                   it
                   giveth
                   the
                   Ascension
                   of
                   the
                   eleventh
                   House
                   ,
                   to
                   which
                   adding
                   90
                   Degrees
                   more
                   ,
                   it
                   giveth
                   the
                   Ascension
                   of
                   the
                   twelfth
                   House
                   ,
                   &c.
                   
                   According
                   to
                   which
                   direction
                   ,
                   the
                   Ascensions
                   of
                   the
                   six
                   Houses
                   towards
                   the
                   Orient
                   ,
                   are
                   here
                   set
                   down
                   in
                   the
                   following
                   Table
                   .
                
                 
                   
                     
                       
                         10.
                         
                      
                       
                         24.39
                      
                    
                     
                       
                         11.
                         
                      
                       
                         54.39
                      
                    
                     
                       
                         12.
                         
                      
                       
                         84.39
                      
                    
                     
                       
                         1.
                         
                      
                       
                         114.39
                      
                    
                     
                       
                         2.
                         
                      
                       
                         144.39
                      
                    
                     
                       
                         3.
                         
                      
                       
                         174.39
                      
                    
                  
                
                 
                   Now
                   because
                   the
                   Circles
                   of
                   Position
                   must
                   according
                   to
                   these
                   Directions
                   cut
                   the
                   AEquator
                   at
                   30
                   and
                   30
                   Degrees
                   above
                   the
                   Horizon
                   ,
                   if
                   in
                   Fig.
                   5.
                   you
                   set
                   30
                   Degrees
                   from
                   AE
                   to
                   n
                   ,
                   and
                   n
                   to
                   r.
                   A
                   Ruler
                   laid
                   from
                   P
                   to
                   n
                   and
                   r
                   ,
                   shall
                   cut
                   the
                   AEquator
                   at
                   B
                   and
                   K
                   ,
                   and
                   then
                   you
                   may
                   describe
                   the
                   Circles
                   of
                   Position
                   HBR
                   and
                   HKR
                   ,
                   make
                   
                     AT
                     =
                     AK
                  
                   and
                   
                     AV
                     =
                     AB
                  
                   ,
                   and
                   so
                   you
                   may
                   describe
                   the
                   Circles
                   HTR
                   and
                   HVR
                   ,
                   and
                   where
                   these
                   Circles
                   do
                   cut
                   the
                   
                   Arch
                   of
                   the
                   Ecliptick
                   ♈
                   F
                   ♎
                   there
                   are
                   the
                   Cusps
                   of
                   the
                   Coelestial
                   Houses
                   .
                
                 
                   Thus
                   a
                   Ruler
                   laid
                   from
                   m.
                   the
                   Pole
                   of
                   the
                   Ecliptick
                   to
                   the
                   Intersections
                   
                     ct
                     s.
                     t.
                     g.
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                  
                   .
                   will
                   cut
                   the
                   Primitive
                   Circle
                   in
                   
                     〈◊〉
                     〈◊〉
                     〈◊〉
                     〈◊〉
                     〈◊〉
                  
                   .
                   and
                   the
                   Arches
                   
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     =
                     Fs.
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     =
                     Ft.
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     =
                     Fg.
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     =
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     .
                  
                   and
                   
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     =
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                  
                   being
                   added
                   to
                   
                     〈◊〉
                     〈◊〉
                     〈◊〉
                     〈◊〉
                     〈◊〉
                  
                   B
                   will
                   give
                   you
                   the
                   Cusps
                   of
                   the
                   11.
                   12.
                   1.
                   2
                   and
                   3
                   Houses
                   ,
                   the
                   other
                   six
                   are
                   the
                   same
                   Degrees
                   and
                   Parts
                   in
                   the
                   Opposite
                   Signs
                   .
                
                 
                   Thus
                   a
                   Figure
                   in
                   Heaven
                   may
                   be
                   erected
                   by
                   Projection
                   ,
                   the
                   Arithmetical
                   Computation
                   now
                   followeth
                   ;
                   In
                   which
                   the
                   height
                   of
                   the
                   Pole
                   above
                   each
                   Circle
                   of
                   Position
                   is
                   required
                   ,
                   the
                   which
                   in
                   the
                   Projection
                   is
                   easily
                   found
                   ;
                   as
                   the
                   Pole
                   of
                   the
                   Circle
                   of
                   Position
                   HBR
                   is
                   at
                   the
                   Point
                   D.
                   and
                   so
                   you
                   have
                   the
                   three
                   Points
                   
                     S
                     ,
                     D
                     ,
                     P
                  
                   ,
                   to
                   describe
                   that
                   Circle
                   by
                   ,
                   which
                   will
                   cut
                   the
                   Circle
                   HBR
                   at
                   Right
                   Angles
                   in
                   the
                   Point
                   C.
                   and
                   the
                   Arch
                   PC
                   is
                   the
                   height
                   of
                   the
                   Pole
                   above
                   that
                   Circle
                   of
                   Position
                   ,
                   and
                   may
                   be
                   measured
                   by
                   the
                   Directions
                   given
                   in
                   the
                   nineteenth
                   of
                   the
                   third
                   Chapter
                   .
                
                 
                   In
                   like
                   manner
                   the
                   height
                   of
                   the
                   Pole
                   above
                   the
                   Circle
                   of
                   Position
                   HKR
                   ,
                   will
                   be
                   the
                   Arch
                   PE.
                   
                
                 
                   To
                   compute
                   the
                   same
                   Arithmetically
                   in
                   the
                   Right
                   angled
                   Spherical
                   Triangle
                   HAEB
                   in
                   
                     Fig.
                     5.
                  
                   we
                   have
                   given
                   AEH
                   .
                   38.
                   47
                   the
                   height
                   of
                   the
                   
                     Equator
                     .
                     AEB
                  
                   30.
                   the
                   difference
                   of
                   Ascension
                   between
                   the
                   10
                   and
                   11
                   Houses
                   ,
                   to
                   find
                   HBAE
                   the
                   Angle
                   of
                   that
                   Equator
                   with
                   the
                   Circle
                   of
                   Position
                   .
                
                 
                   Therefore
                   by
                   the
                   first
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   
                   
                     As
                     the
                     Tang.
                     of
                     
                       H
                       AE
                    
                     ,
                     38.
                     47.
                     
                  
                   
                     9.90000652
                  
                   
                     Is
                     to
                     the
                     Radius
                     .
                  
                   
                     10.00000000
                  
                   
                     So
                     is
                     the
                     Sine
                     of
                     
                       AE
                       B.
                    
                     30
                  
                   
                     9.69897000
                  
                   
                     To
                     the
                     Cotang
                     .
                     of
                     
                       AE
                       B
                       H.
                    
                     57.
                     81626.
                     
                  
                   
                     9.79888348
                  
                
                 
                   Whos
                   's
                   Measure
                   in
                   the
                   Scheme
                   is
                   EC
                   ,
                   and
                   the
                   Complement
                   thereof
                   is
                   CP
                   .
                   32.
                   18374
                   the
                   height
                   of
                   the
                   Pole
                   required
                   .
                
                 
                   Therefore
                   the
                   height
                   of
                   the
                   Pole
                   above
                   the
                   Circle
                   of
                   Position
                   HKR
                   .
                   In
                   the
                   Triangle
                   HAEK
                   ,
                   we
                   have
                   given
                   ,
                   
                     H
                     AE
                  
                   as
                   before
                   ,
                   and
                   
                     AE
                     K.
                  
                   60
                   to
                   find
                   HKAE
                   .
                   Therefore
                   .
                
                 
                   
                     As
                     the
                     Tang.
                     of
                     
                       H
                       AE
                    
                     38.
                     47.
                     
                  
                   
                     9.90008652
                  
                   
                     Is
                     to
                     the
                     Radius
                     .
                  
                   
                     10.00000000
                  
                   
                     So
                     is
                     the
                     Sine
                     of
                     
                       AE
                       K
                    
                     60.
                     
                  
                   
                     9.93753063
                  
                   
                     To
                     the
                     Cotang
                     .
                     of
                     
                       HK
                       AE
                    
                     42.
                     53308.
                     
                  
                   
                     10.03744411
                  
                
                 
                   Whos
                   's
                   Measure
                   in
                   the
                   Scheme
                   is
                   GL
                   ,
                   and
                   the
                   Complement
                   thereof
                   is
                   PL
                   47.
                   46692.
                   the
                   height
                   of
                   the
                   Pole
                   required
                   .
                
                 
                   The
                   height
                   of
                   the
                   Pole
                   above
                   HDR
                   is
                   the
                   same
                   with
                   HBR
                   ,
                   and
                   the
                   height
                   of
                   the
                   Pole
                   above
                   HTR
                   is
                   the
                   same
                   with
                   HKR
                   .
                
                 
                   Having
                   found
                   the
                   Ascensions
                   of
                   the
                   several
                   Houses
                   together
                   with
                   the
                   Elevation
                   of
                   the
                   Pole
                   above
                   their
                   Circles
                   of
                   Position
                   ,
                   in
                   the
                   Oblique
                   angled
                   Spherical
                   Triangle
                   ♈
                   BS
                   ,
                   we
                   have
                   given
                   .
                
                 
                   1.
                   
                   The
                   Angle
                   ♈
                   BS
                   the
                   Complement
                   of
                   HBAE
                   .
                
                 
                   2.
                   
                   The
                   Angle
                   
                     B
                     ♈
                     S.
                  
                   23.
                   
                   The
                   Sun
                   's
                   greatest
                   Declination
                   .
                
                 
                   3.
                   
                   Their
                   included
                   Side
                   ♈
                   B.
                   54.
                   39
                   the
                   Ascension
                   of
                   the
                   eleventh
                   House
                   .
                   To
                   find
                   ♈
                   S
                   the
                   
                   Point
                   of
                   the
                   Ecliptick
                   ,
                   which
                   is
                   resolvable
                   by
                   the
                   ninth
                   Case
                   of
                   Right
                   angled
                   Spherical
                   Triangles
                   .
                
                 
                   But
                   in
                   my
                   
                     Trigonometria
                     Britannica
                     ,
                     Problem
                  
                   .
                   5.
                   for
                   the
                   resolving
                   of
                   Oblique
                   angled
                   Spherical
                   Triangles
                   ,
                   I
                   have
                   shewed
                   how
                   this
                   Case
                   as
                   to
                   our
                   present
                   purpose
                   may
                   be
                   resolved
                   ,
                   by
                   these
                   Proportions
                   following
                   .
                
                 
                   
                     1.
                     s
                     1
                     /
                     2
                     Z
                     Ang.
                     s
                     1
                     /
                     2
                     X
                     Ang
                     :
                     :
                     t
                     1
                     /
                     2
                     ♈
                     B.
                     t
                     1
                     /
                     2
                     X
                     Cru
                     .
                  
                   
                     2.
                     cs
                     1
                     /
                     2
                     Z
                     Ang.
                     cs
                     1
                     /
                     2
                     X
                     Ang
                     :
                     :
                     t
                     1
                     /
                     2
                     ♈
                     B.
                     t
                     1
                     /
                     2
                     Z
                     Cru
                     .
                  
                   
                     1
                     /
                     2
                     Z
                     Cru
                     +
                     1
                     /
                     2
                     X
                     Cru
                     =
                     ♈
                     S
                     the
                     Arch
                     of
                     the
                     Ecliptick
                     desired
                     .
                  
                
                 
                   
                     For
                     the
                     Cusp
                     of
                     the
                     Eleventh
                     House
                     .
                  
                   
                     
                       
                         T
                         B
                      
                       Arch
                       ♈
                       B.
                       4439
                       the
                       half
                       whereof
                       is
                       27.
                       195.
                       
                    
                     
                       ♈
                       B
                       S.
                       122.
                       18374.
                       
                    
                     
                       B
                       ♈
                       S.
                       23.
                       525.
                       
                    
                     
                       Z
                       145.70874
                       —
                       1
                       /
                       2
                       Z
                       72.
                       85437.
                       
                    
                     
                       X.
                       198.65874
                       —
                       1
                       /
                       2
                       X.
                       49.
                       32937.
                       
                    
                  
                   
                     
                       s
                       1
                       /
                       2
                       Z.
                       72.
                       85437.
                       
                       Comp.
                       Arith.
                       
                    
                     
                       0.01977589
                    
                     
                       s
                       1
                       /
                       2
                       X.
                       49.
                       32937.
                       
                    
                     
                       9.88000800
                    
                     
                       t
                       1
                       /
                       2
                       ♈
                       B.
                       27.
                       195.
                       
                    
                     
                       9.71081089
                    
                     
                       t
                       1
                       /
                       2
                       X
                       Cru
                       .
                       22.
                       192.
                       
                    
                     
                       9.61059478
                    
                  
                   
                     
                       2.
                       
                       Operation
                       .
                    
                     
                       
                         cs
                         .
                         1
                         /
                         2
                         Z.
                         72.
                         85437.
                         
                         Comp.
                         Arith.
                         
                      
                       
                         0.53012277
                      
                       
                         ss
                         1
                         /
                         2
                         X.
                         49.
                         32937.
                         
                      
                       
                         9.81395860
                      
                       
                         t
                         1
                         /
                         2
                         ♈
                         B.
                         27.
                         195.
                         
                      
                       
                         9.71081089
                      
                       
                         t
                         1
                         /
                         2
                         Z
                         Cru
                         .
                         48.
                         611.
                         
                      
                       
                         10.05489226
                      
                    
                     
                       1.
                       
                       Arch.
                       22.
                       192.
                       
                       Their
                       Sum
                       is
                       70.803
                       the
                       Point
                       of
                       the
                       Ecliptick
                       .
                    
                     
                       
                       
                         cs
                         .
                         ½
                         Z.
                         82.
                         51916.
                         
                         Comp.
                         Arish
                         .
                      
                       
                         0.88517901
                      
                       
                         cs
                         ½
                         X.
                         59.
                         00416.
                         
                      
                       
                         9.71164750
                      
                       
                         t.
                         ½
                         ♈
                         A.
                         57.
                         195.
                         
                      
                       
                         10.19072348
                      
                       
                         
                           t
                           ▪
                           ½
                           Z
                        
                         Cru
                         :
                         78.
                         397.
                         
                      
                       
                         10.68754999
                      
                    
                     
                       1.
                       
                       Arch
                       —
                       53.
                       296.
                       
                       Their
                       Sum
                       121.693
                       is
                       the
                       Point
                       of
                       the
                       Ecliptick
                       for
                       the
                       Ascendant
                       .
                    
                  
                
                 
                   
                     For
                     the
                     Cusp
                     of
                     the
                     Second
                     House
                     .
                  
                   
                     In
                     the
                     Oblique
                     angled
                     Spherical
                     Triangle
                     
                       ♈
                       T
                       
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                      
                    
                     .
                     we
                     have
                     given
                     ,
                     
                       
                         1.
                         
                         
                           ♈
                           T.
                        
                         144.
                         39.
                         
                      
                       
                         The
                         half
                         whereof
                         is
                         72.
                         195.
                         
                      
                       
                         2.
                         
                         ♈
                         T
                         
                           〈◊〉
                           〈◊〉
                           〈◊〉
                           〈◊〉
                           〈◊〉
                        
                         .
                         122.
                         18374
                      
                       
                         To
                         find
                         
                           ♈
                           
                             〈◊〉
                             〈◊〉
                             〈◊〉
                             〈◊〉
                             〈◊〉
                          
                        
                         .
                         The
                         Angles
                         are
                         the
                         same
                         with
                         those
                         of
                         the
                         Twelfth
                         House
                         .
                         Therefore
                         .
                      
                       
                         3.
                         
                         T
                         
                           〈◊〉
                           〈◊〉
                           〈◊〉
                           〈◊〉
                           〈◊〉
                        
                         y.
                         23.
                         525
                      
                       
                          
                      
                    
                  
                   
                     
                       s.
                       ½
                       Z.
                       80.
                       49596.
                       
                       Comp.
                       Arith.
                       
                    
                     
                       0.00601663
                    
                     
                       s
                       ½
                       X.
                       56.
                       97096.
                       
                    
                     
                       9.92351651
                    
                     
                       Their
                       Sum
                    
                     
                       9.92953314
                    
                     
                       t
                       ½
                       ♈
                       T.
                       72.
                       195.
                       
                    
                     
                       10.49327695
                    
                     
                       
                         t
                         ½
                         X
                      
                       Cru
                       .
                       69.
                       306.
                       
                    
                     
                       10.42281009
                    
                  
                   
                     
                       2.
                       
                       Operation
                       .
                    
                     
                       cs
                       ½
                       Z
                       80.
                       49596.
                       
                       Comp.
                       Arith.
                       
                    
                     
                       0.78170174
                    
                     
                       cs
                       ½
                       X
                       56.
                       97096.
                       
                    
                     
                       9.73628614
                    
                     
                       Their
                       Sum
                    
                     
                       10.51798788
                    
                     
                       t
                       ½
                       ♈
                       T.
                       72.
                       195.
                       
                    
                     
                       10.49327695
                    
                     
                       
                         t
                         ½
                         Z
                      
                       Cru
                       .
                       84.
                       34.
                       
                    
                     
                       11.01126483
                    
                  
                   
                     1.
                     
                     Arch.
                     69.
                     306.
                     
                     Their
                     Sum
                     is
                     53.740
                     is
                     the
                     Point
                     of
                     the
                     Ecliptick
                     for
                     the
                     Second
                     House
                     .
                  
                
                 
                   
                   
                     For
                     the
                     Cusp
                     of
                     the
                     Third
                     House
                     .
                  
                   
                     In
                     the
                     Oblique
                     angled
                     Spherical
                     Triangle
                     ♈
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     ,
                     we
                     have
                     ,
                  
                   
                     1.
                     
                     ♈
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     .
                     174.
                     39.
                     
                     The
                     half
                     whereof
                     is
                     87.
                     195.
                     
                     The
                     Angls
                     ♈
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     and
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     ♈
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     are
                     the
                     same
                     with
                     those
                     of
                     the
                     Eleventh
                     House
                     .
                  
                   
                     
                       s
                       ½
                       Z.
                       72.
                       85437.
                       
                       Comp.
                       Arith.
                       
                    
                     
                       0.01977580
                    
                     
                       s
                       ½
                       
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                      
                       49.
                       32937.
                       
                    
                     
                       6.88000800
                    
                     
                       Their
                       Sum
                    
                     
                       9.89978389
                    
                     
                       t
                       ½
                       
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                      
                       .
                       87.
                       195.
                       
                    
                     
                       11.30984054
                    
                  
                   
                     For
                     the
                     Eleventh
                     House
                     .
                  
                
                 
                   
                     For
                     the
                     Cusp
                     of
                     the
                     Twelfth
                     House
                     .
                  
                   
                     In
                     the
                     Oblique
                     angled
                     Spherical
                     Triangle
                     
                       ♈
                       KF
                    
                     ,
                     we
                     have
                     given
                     .
                     
                       
                         1.
                         
                         
                           
                             〈◊〉
                             〈◊〉
                             〈◊〉
                             〈◊〉
                             〈◊〉
                          
                           K.
                        
                         84.
                         39.
                         
                      
                       
                         The
                         half
                         whereof
                         is
                         .
                         42.
                         195.
                         
                      
                       
                         2.
                         
                         ♈
                         Kt.
                         137.46692
                      
                       
                          
                      
                       
                         3.
                         
                         K
                         ♈
                         t.
                         23.525
                      
                       
                         To
                         find
                         
                           ♈
                           t.
                        
                         
                      
                    
                  
                   
                     
                       Z.
                       160.99192
                    
                     
                       ½
                       Z.
                       80.49596
                    
                     
                       X.
                       113.94192
                    
                     
                       ½
                       X.
                       56.97096
                    
                  
                   
                     
                       s
                       ½
                       Z.
                       80.
                       49596.
                       
                       Comp.
                       Arith.
                       
                    
                     
                       0.00601663
                    
                     
                       s
                       ½
                       X.
                       56.
                       97096.
                       
                    
                     
                       9.92351651
                    
                     
                       t
                       ½
                       ♈
                       K.
                       42.
                       195.
                       
                    
                     
                       9.95740882
                    
                     
                       
                         t
                         ½
                         X
                      
                       Cru
                       .
                       37.
                       625.
                       
                    
                     
                       9.88694196
                    
                  
                   
                     
                     
                       2.
                       
                       Operation
                       .
                    
                     
                       cs
                       .
                       ½
                       Z.
                       80.
                       49596.
                       
                       Comp.
                       Arith.
                       
                    
                     
                       0.78170174
                    
                     
                       cs
                       ½
                       X.
                       56.
                       97096.
                       
                    
                     
                       9.73628614
                    
                     
                       t
                       ½
                       ♈
                       K.
                       42.
                       195.
                       
                    
                     
                       9.95740882
                    
                     
                       
                         t
                         ½
                         Z
                      
                       Cru
                       .
                       71.
                       496.
                       
                    
                     
                       10.47539670
                    
                  
                   
                     1.
                     
                     Arch.
                     37.
                     625.
                     
                     Their
                     Sum
                     113.6691
                     is
                     the
                     Point
                     of
                     the
                     Ecliptick
                     for
                     the
                     Twelfth
                     House
                     .
                  
                
                 
                   
                     For
                     the
                     Cusp
                     of
                     the
                     Ascendant
                     .
                  
                   
                     In
                     the
                     Oblique
                     angled
                     Spherical
                     Triangle
                     ♈
                     AG
                     we
                     have
                     ,
                     
                       
                         1.
                         
                         ♈
                         A.
                         114.
                         39.
                         
                      
                       
                         The
                         half
                         whereof
                         is
                         57.
                         195.
                         
                      
                       
                         2.
                         
                         ♈
                         AZ
                         .
                         141.
                         5333.
                         
                      
                       
                         The
                         Complement
                         of
                         HAAE
                         38.
                         46667.
                         
                      
                       
                         3.
                         
                         A
                         
                           〈◊〉
                           〈◊〉
                           〈◊〉
                           〈◊〉
                           〈◊〉
                        
                         y.
                         23.
                         525.
                         
                      
                       
                          
                      
                    
                  
                   
                     
                       Z.
                       165.05833
                    
                     
                       ½
                       Z.
                       82.51916
                    
                     
                       X.
                       118.00833
                    
                     
                       ½
                       X.
                       59.00416
                    
                  
                   
                     
                       s.
                       ½
                       Z.
                       82.
                       51916.
                       
                       Comp.
                       Arith.
                       
                    
                     
                       0
                       .
                       0037162●
                    
                     
                       s.
                       ½
                       X.
                       59.
                       00416.
                       
                    
                     
                       9.93313477
                    
                     
                       t
                       ½
                       ♈
                       A.
                       57.
                       195.
                       
                    
                     
                       10.19072348
                    
                     
                       t
                       ½
                       X.
                       53.
                       296.
                       
                    
                     
                       10.12757454
                    
                  
                   
                     
                       2.
                       
                       Operation
                       .
                    
                     
                       
                         t
                         ½
                         X
                      
                       Cru
                       .
                       86.
                       468.
                       
                    
                     
                       11.20962043
                    
                  
                   
                     
                     
                       2.
                       
                       Operation
                       .
                    
                     
                       cs
                       ½
                       Z.
                       72.
                       85437.
                       
                       Comp.
                       Arith.
                       
                    
                     
                       0.53012277
                    
                     
                       cs
                       ½
                       X.
                       49.
                       32937.
                       
                    
                     
                       9.81395860
                    
                     
                       Their
                       Sum
                    
                     
                       10.34408137
                    
                     
                       t
                       ½
                       ♈
                       
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                      
                       .
                       87.
                       195.
                       
                    
                     
                       11.39984054
                    
                     
                       
                         t
                         ½
                         X
                      
                       Cru
                       .
                       88.
                       729.
                       
                    
                     
                       11.65392191
                    
                  
                   
                     1.
                     
                     Arch.
                     86.
                     468.
                     
                     Their
                     Sum
                     175.197
                     is
                     the
                     Point
                     of
                     the
                     Ecliptick
                     for
                     the
                     Third
                     House
                     .
                  
                   
                     And
                     thus
                     we
                     have
                     not
                     only
                     erected
                     a
                     Figure
                     for
                     the
                     Time
                     given
                     ,
                     but
                     composed
                     a
                     Table
                     for
                     the
                     general
                     erecting
                     of
                     a
                     Figure
                     in
                     that
                     Eatitude
                     ;
                     for
                     by
                     adding
                     together
                     the
                     first
                     and
                     second
                     Numbers
                     in
                     each
                     Proportion
                     for
                     the
                     first
                     ,
                     second
                     and
                     third
                     Houses
                     there
                     is
                     composed
                     two
                     Numbers
                     for
                     each
                     House
                     ,
                     to
                     each
                     of
                     which
                     the
                     Artificial
                     Tangent
                     of
                     half
                     the
                     Ascension
                     of
                     each
                     House
                     being
                     added
                     ,
                     their
                     Aggregates
                     are
                     the
                     Tangents
                     of
                     two
                     Arches
                     ,
                     which
                     being
                     added
                     together
                     ,
                     do
                     give
                     the
                     distance
                     of
                     the
                     Cusp
                     of
                     the
                     House
                     ,
                     from
                     the
                     first
                     Point
                     of
                     Aries
                     ,
                     as
                     in
                     the
                     preceding
                     Operations
                     hath
                     been
                     shewed
                     .
                  
                   
                     Only
                     note
                     ,
                     That
                     if
                     the
                     Ascension
                     of
                     any
                     House
                     be
                     more
                     than
                     a
                     Semicircle
                     ,
                     you
                     must
                     take
                     the
                     Tangent
                     of
                     half
                     the
                     Complement
                     to
                     a
                     whole
                     Circle
                     .
                     And
                     to
                     find
                     the
                     Cusp
                     of
                     the
                     House
                     ,
                     you
                     must
                     also
                     take
                     the
                     Complement
                     of
                     the
                     Sum
                     of
                     the
                     Arches
                     added
                     together
                     .
                  
                   
                     The
                     Numbers
                     according
                     to
                     the
                     former
                     Operations
                     which
                     do
                     constitute
                     a
                     Table
                     of
                     Houses
                     for
                     the
                     Latitude
                     of
                     London
                     .
                     51.
                     53
                     are
                     as
                     followeth
                     .
                  
                   
                   
                     
                       
                         
                            
                        
                         
                           11
                           and
                           3
                           Houses
                        
                         
                           Ascendant
                        
                         
                           12
                           and
                           2
                           Houses
                        
                      
                       
                         
                           1.
                           
                           Oper.
                           
                        
                         
                           9.89978389
                        
                         
                           9.93685106
                        
                         
                           9.92953314
                        
                      
                       
                         
                           2.
                           
                           Oper.
                           
                        
                         
                           10.34408137
                        
                         
                           10.59682651
                        
                         
                           10.51798788
                        
                      
                    
                  
                   
                     The
                     Six
                     Oriental
                     Houses
                     ,
                     by
                     the
                     preceding
                     Operations
                     .
                  
                   
                     
                       The
                       opposite
                       Houses
                       are
                       in
                       the
                       opposite
                       Signs
                       and
                       Degrees
                       .
                    
                     
                       10
                       House
                       ♈
                       26.311
                    
                     
                       11
                       House
                       ♊
                       10.803
                    
                     
                       12
                       House
                       ♋
                       23.691
                    
                     
                       Ascendant
                       ♌
                       11.693
                    
                     
                       2
                       House
                       ♏
                       3.740
                    
                     
                       3
                       House
                       ♏
                       25.197
                    
                     
                       4
                       House
                       ♎
                       26.311
                    
                     
                       5
                       House
                       ♐
                       10.803
                    
                     
                       9
                       House
                       ♑
                       23.691
                    
                     
                       7
                       House
                       ♒
                       11.693
                    
                     
                       8
                       House
                       ♓
                       3.740
                    
                     
                       9
                       House
                       ♓
                       25.197
                    
                  
                   
                     
                       A
                       Figure
                       of
                       the
                       Twelve
                       Coelestial
                       Houses
                       .
                    
                  
                   
                   
                
              
            
          
        
      
       
         
           
             
             
             
               ASTRONOMY
               .
               THE
               Second
               Part
               :
               OR
               ,
               AN
               ACCOUNT
               OF
               THE
               Civil
               Year
               ,
               With
               the
               Reason
               of
               the
               Difference
               Between
               the
               JULIAN
               &
               GREGORIAN
               Calendars
               ,
               And
               the
               manner
               of
               Computing
               the
               Places
               of
               the
               SVN
               and
               MOON
               .
            
             
               LONDON
               ,
               
                 Printed
                 for
              
               Thomas
               Passinger
               ,
               
                 at
                 the
              
               Three
               Bibles
               on
               London-Bridge
               .
               1679.
               
            
          
        
         
           
             
             
             
               AN
               INTRODUCTION
               TO
               Astronomy
               .
            
             
               The
               Second
               Book
               .
            
             
               
                 CHAP.
                 I.
                 
              
               
                 
                   Of
                   the
                   Year
                   Civil
                   and
                   Astronomical
                   .
                
              
               
                 HAving
                 shewed
                 the
                 Motion
                 of
                 the
                 
                   Primum
                   Mobile
                
                 ,
                 or
                 Doctrine
                 of
                 the
                 Sphere
                 ,
                 which
                 I
                 call
                 the
                 Absolute
                 Part
                 of
                 Astronomy
                 ;
                 I
                 come
                 now
                 unto
                 the
                 Comparative
                 ,
                 that
                 is
                 ,
                 to
                 shew
                 the
                 Motion
                 of
                 the
                 Stars
                 in
                 reference
                 to
                 some
                 certain
                 Distinction
                 of
                 Time.
                 
              
               
                 2.
                 
                 And
                 the
                 Distinction
                 of
                 Time
                 is
                 to
                 be
                 considered
                 either
                 according
                 to
                 Nature
                 ,
                 or
                 according
                 to
                 Institution
                 .
              
               
               
                 3.
                 
                 The
                 Distinction
                 of
                 Time
                 according
                 to
                 Nature
                 ,
                 is
                 that
                 space
                 of
                 Time
                 ,
                 in
                 which
                 the
                 Planets
                 do
                 finish
                 their
                 Periodical
                 Revolutions
                 from
                 one
                 certain
                 Point
                 in
                 the
                 Zodiack
                 ,
                 to
                 the
                 same
                 again
                 ,
                 and
                 this
                 in
                 reference
                 to
                 the
                 Sun
                 is
                 called
                 a
                 Year
                 ,
                 in
                 reference
                 to
                 the
                 Moon
                 a
                 Month.
                 
              
               
                 4.
                 
                 The
                 Sun
                 doth
                 pass
                 through
                 the
                 Zodiack
                 in
                 365
                 Days
                 ,
                 5
                 Hours
                 ,
                 and
                 49
                 Minutes
                 .
                 And
                 the
                 Moon
                 doth
                 finish
                 her
                 course
                 in
                 the
                 Zodiack
                 ,
                 and
                 return
                 into
                 Conjunction
                 with
                 the
                 Sun
                 ,
                 in
                 29
                 Days
                 ,
                 12
                 hours
                 ,
                 44
                 Minutes
                 ,
                 and
                 4
                 Seconds
                 .
                 And
                 from
                 the
                 Motion
                 of
                 these
                 two
                 Planets
                 ,
                 the
                 Civil
                 Year
                 in
                 every
                 Nation
                 doth
                 receive
                 its
                 Institution
                 .
              
               
                 5.
                 
                 Twelve
                 Moons
                 or
                 Moneths
                 is
                 the
                 measure
                 of
                 the
                 Common
                 Year
                 ,
                 in
                 Turkey
                 in
                 every
                 Moneth
                 they
                 have
                 29
                 or
                 30
                 Days
                 ,
                 in
                 the
                 whole
                 Year
                 354
                 Days
                 ,
                 and
                 in
                 every
                 third
                 Year
                 355
                 Days
                 .
              
               
                 6.
                 
                 The
                 Persians
                 and
                 Egyptians
                 do
                 also
                 account
                 12
                 Moneths
                 to
                 their
                 Year
                 ;
                 but
                 their
                 moneths
                 are
                 proportioned
                 to
                 the
                 Time
                 of
                 the
                 Suns
                 continuance
                 in
                 every
                 of
                 the
                 Twelve
                 Signs
                 ;
                 in
                 their
                 Year
                 therefore
                 which
                 is
                 Solar
                 ,
                 there
                 are
                 always
                 365
                 Days
                 ,
                 that
                 is
                 eleven
                 Days
                 more
                 than
                 the
                 Lunar
                 Year
                 .
              
               
                 7.
                 
                 And
                 the
                 Iulian
                 Year
                 which
                 is
                 the
                 Account
                 of
                 all
                 Christendom
                 ,
                 doth
                 differ
                 from
                 the
                 other
                 in
                 this
                 ;
                 that
                 by
                 reason
                 of
                 the
                 Sun's
                 Excess
                 in
                 Motion
                 above
                 365
                 Days
                 ,
                 which
                 is
                 5
                 Hours
                 ,
                 49
                 Minutes
                 ,
                 it
                 hath
                 a
                 Day
                 intercalated
                 once
                 in
                 4
                 Years
                 ,
                 and
                 by
                 this
                 intercalation
                 ,
                 it
                 is
                 more
                 agreeable
                 to
                 the
                 Motion
                 of
                 the
                 Sun
                 ,
                 than
                 the
                 former
                 ,
                 and
                 yet
                 there
                 is
                 a
                 considerable
                 difference
                 between
                 them
                 ,
                 which
                 hath
                 occasioned
                 the
                 Church
                 of
                 Rome
                 to
                 make
                 some
                 further
                 amendment
                 of
                 the
                 Solar
                 
                 Year
                 ,
                 but
                 hath
                 not
                 brought
                 it
                 to
                 that
                 exactness
                 ,
                 which
                 might
                 be
                 wished
                 .
              
               
                 8.
                 
                 This
                 intercalation
                 of
                 one
                 Day
                 once
                 in
                 4
                 Years
                 ,
                 doth
                 occasion
                 the
                 Sunday
                 Letter
                 still
                 to
                 alter
                 till
                 28
                 Years
                 be
                 gone
                 about
                 ;
                 The
                 Days
                 of
                 the
                 Week
                 which
                 use
                 to
                 be
                 signed
                 by
                 the
                 seven
                 first
                 Letters
                 in
                 the
                 Alphabet
                 ,
                 do
                 not
                 fall
                 alike
                 in
                 every
                 Common
                 Year
                 ,
                 but
                 because
                 the
                 Year
                 consisteth
                 of
                 52
                 Weeks
                 and
                 one
                 Day
                 ,
                 Sunday
                 this
                 Year
                 will
                 fall
                 out
                 upon
                 the
                 next
                 Year's
                 Monday
                 ,
                 and
                 so
                 forward
                 for
                 seven
                 years
                 ,
                 but
                 every
                 fourth
                 year
                 consisting
                 of
                 52
                 weeks
                 and
                 two
                 days
                 ,
                 doth
                 occasion
                 the
                 Sunday
                 Letter
                 to
                 alter
                 ,
                 till
                 four
                 times
                 seven
                 years
                 ,
                 that
                 is
                 till
                 28
                 years
                 be
                 gone
                 about
                 .
                 This
                 Revolution
                 is
                 called
                 the
                 Cycle
                 of
                 the
                 Sun
                 ,
                 taking
                 its
                 name
                 from
                 the
                 Sunday
                 Letter
                 ,
                 of
                 which
                 it
                 sheweth
                 all
                 the
                 Changes
                 that
                 it
                 can
                 have
                 by
                 reason
                 of
                 the
                 Bissextile
                 or
                 Leap-year
                 .
                 To
                 find
                 which
                 of
                 the
                 28
                 the
                 present
                 is
                 ,
                 add
                 nine
                 to
                 the
                 year
                 of
                 our
                 Lord
                 ,
                 (
                 because
                 this
                 Circle
                 was
                 so
                 far
                 gone
                 about
                 ,
                 at
                 the
                 time
                 of
                 Christs
                 Birth
                 )
                 and
                 divide
                 the
                 whole
                 by
                 28
                 ,
                 what
                 remaineth
                 is
                 the
                 present
                 year
                 ,
                 if
                 nothing
                 remain
                 the
                 Cycle
                 is
                 out
                 ,
                 and
                 that
                 you
                 must
                 call
                 the
                 last
                 year
                 of
                 the
                 Cycle
                 ,
                 or
                 28.
                 
              
               
                 9.
                 
                 This
                 Intercalation
                 of
                 one
                 day
                 in
                 four
                 years
                 ,
                 doth
                 occasion
                 the
                 Letter
                 F
                 to
                 be
                 twice
                 repeated
                 in
                 February
                 ,
                 in
                 which
                 Moneth
                 the
                 day
                 is
                 added
                 ,
                 that
                 is
                 ,
                 the
                 Letter
                 F
                 is
                 set
                 to
                 the
                 24
                 and
                 25
                 days
                 of
                 that
                 Moneth
                 ,
                 and
                 in
                 such
                 a
                 year
                 S.
                 Matthias
                 day
                 is
                 to
                 be
                 observed
                 upon
                 the
                 25
                 day
                 ,
                 and
                 the
                 next
                 Sunday
                 doth
                 change
                 or
                 alter
                 his
                 Letter
                 ,
                 from
                 which
                 leaping
                 or
                 changing
                 ,
                 such
                 a
                 year
                 is
                 called
                 Leap-year
                 ,
                 aud
                 the
                 number
                 of
                 days
                 in
                 each
                 Moneth
                 is
                 well
                 expressed
                 by
                 these
                 old
                 Verses
                 .
              
               
               
                 
                   Thirty
                   days
                   hath
                
                 September
                 ,
                 April
                 ,
                 June
                 and
                 November
                 .
              
               
                 February
                 hath
                 28
                 alone
                 ,
                 All
                 the
                 rest
                 have
                 thirty
                 and
                 one
                 .
              
               
                 
                   But
                   when
                   of
                   Leap-year
                   cometh
                   the
                   Time
                   ,
                
                 
                   Then
                   days
                   hath
                   February
                   twenty
                   and
                   nine
                   .
                
              
               
                 That
                 this
                 year
                 is
                 somewhat
                 too
                 long
                 ,
                 is
                 acknowledged
                 by
                 the
                 most
                 skilful
                 Astronomers
                 ,
                 as
                 for
                 the
                 number
                 of
                 days
                 in
                 a
                 year
                 the
                 Emperours
                 Mathematicians
                 were
                 in
                 the
                 right
                 ,
                 for
                 it
                 is
                 certain
                 ,
                 that
                 no
                 year
                 can
                 consist
                 of
                 more
                 than
                 365
                 days
                 ,
                 but
                 for
                 the
                 odd
                 hours
                 it
                 is
                 as
                 certain
                 that
                 they
                 cannot
                 be
                 fewer
                 than
                 five
                 ,
                 nor
                 yet
                 so
                 many
                 as
                 six
                 ;
                 so
                 then
                 the
                 doubt
                 is
                 upon
                 the
                 minutes
                 ,
                 60
                 whereof
                 do
                 make
                 an
                 hour
                 ,
                 a
                 small
                 matter
                 one
                 would
                 think
                 ,
                 but
                 how
                 great
                 in
                 the
                 consequence
                 we
                 shall
                 see
                 .
                 The
                 Emperours
                 year
                 being
                 more
                 than
                 10
                 minutes
                 greater
                 than
                 the
                 Suns
                 ,
                 will
                 in
                 134
                 years
                 rise
                 to
                 one
                 whole
                 day
                 ,
                 and
                 by
                 this
                 means
                 the
                 Vernal
                 or
                 Spring
                 Equinox
                 ,
                 which
                 in
                 Iulius
                 Caesar's
                 time
                 was
                 upon
                 the
                 24
                 of
                 March
                 ,
                 is
                 now
                 in
                 our
                 time
                 upon
                 the
                 10
                 of
                 March
                 ,
                 13
                 days
                 backward
                 ,
                 and
                 somewhat
                 more
                 ,
                 and
                 so
                 if
                 it
                 be
                 let
                 alone
                 will
                 go
                 back
                 to
                 the
                 first
                 of
                 March
                 ,
                 and
                 first
                 of
                 February
                 ,
                 and
                 by
                 degrees
                 more
                 and
                 more
                 backward
                 still
                 .
              
               
                 10.
                 
                 To
                 reform
                 this
                 difference
                 ,
                 some
                 of
                 the
                 late
                 Roman
                 Bishops
                 have
                 earnestly
                 endeavoured
                 .
                 And
                 the
                 thing
                 was
                 brought
                 to
                 that
                 perfection
                 it
                 now
                 standeth
                 ,
                 by
                 Gregory
                 the
                 Thirteenth
                 ,
                 in
                 the
                 year
                 1582.
                 
                 His
                 Mathematicians
                 ,
                 whereof
                 Lilius
                 was
                 the
                 Chief
                 ,
                 advised
                 him
                 thus
                 :
                 That
                 considering
                 there
                 had
                 been
                 an
                 Agitation
                 in
                 the
                 
                 Council
                 of
                 Nice
                 somewhat
                 concerned
                 in
                 this
                 matter
                 upon
                 the
                 motion
                 of
                 that
                 Question
                 ,
                 about
                 the
                 Celebration
                 of
                 Easter
                 .
                 And
                 that
                 the
                 Fathers
                 of
                 the
                 Assembly
                 ,
                 after
                 due
                 deliberation
                 with
                 the
                 Astronomers
                 of
                 that
                 time
                 ,
                 had
                 fixed
                 the
                 Vernal
                 Equinox
                 at
                 the
                 21
                 of
                 March
                 ,
                 and
                 considering
                 also
                 that
                 since
                 that
                 time
                 a
                 difference
                 of
                 ten
                 whole
                 days
                 had
                 past
                 over
                 in
                 the
                 Calendar
                 ,
                 that
                 is
                 ,
                 that
                 the
                 Vernal
                 Equinox
                 ,
                 which
                 began
                 upon
                 the
                 21
                 of
                 March
                 ,
                 had
                 prevented
                 so
                 much
                 ,
                 as
                 to
                 begin
                 in
                 
                 Gregorie's
                 days
                 at
                 the
                 10
                 of
                 the
                 same
                 ,
                 they
                 advised
                 ,
                 that
                 10
                 days
                 should
                 be
                 cut
                 off
                 from
                 the
                 Calendar
                 ,
                 which
                 was
                 done
                 ,
                 and
                 the
                 10
                 days
                 taken
                 out
                 of
                 October
                 in
                 the
                 year
                 1582.
                 as
                 being
                 the
                 moneth
                 of
                 that
                 year
                 in
                 which
                 that
                 Pope
                 was
                 born
                 ;
                 so
                 that
                 when
                 they
                 came
                 to
                 the
                 fifth
                 of
                 the
                 moneth
                 they
                 reckoned
                 the
                 15
                 ,
                 and
                 so
                 the
                 Equinox
                 was
                 come
                 up
                 to
                 its
                 place
                 again
                 ,
                 and
                 happened
                 upon
                 the
                 21
                 of
                 March
                 ,
                 as
                 at
                 the
                 Council
                 of
                 Nice
                 .
              
               
                 But
                 that
                 Lilius
                 should
                 bring
                 back
                 the
                 beginning
                 of
                 the
                 year
                 to
                 the
                 time
                 of
                 the
                 Nicene
                 Council
                 and
                 no
                 further
                 ,
                 is
                 to
                 be
                 marvelled
                 at
                 ,
                 he
                 should
                 have
                 brought
                 it
                 back
                 to
                 the
                 Emperours
                 own
                 time
                 ,
                 where
                 the
                 mistake
                 was
                 first
                 entered
                 ,
                 and
                 instead
                 of
                 10
                 ,
                 cut
                 off
                 13
                 days
                 ;
                 however
                 this
                 is
                 the
                 reason
                 why
                 these
                 two
                 Calendars
                 differ
                 the
                 space
                 of
                 10
                 days
                 from
                 one
                 another
                 .
                 And
                 thus
                 I
                 have
                 given
                 you
                 an
                 account
                 of
                 the
                 year
                 as
                 it
                 now
                 stands
                 with
                 us
                 in
                 England
                 ,
                 and
                 with
                 the
                 rest
                 of
                 the
                 Christian
                 World
                 in
                 respect
                 of
                 the
                 Sun
                 ,
                 some
                 other
                 particulars
                 there
                 are
                 between
                 us
                 and
                 them
                 which
                 do
                 depend
                 upon
                 the
                 motion
                 of
                 the
                 Moon
                 ,
                 as
                 well
                 as
                 of
                 the
                 Sun
                 ,
                 and
                 for
                 the
                 better
                 underderstanding
                 of
                 them
                 ,
                 I
                 will
                 also
                 give
                 you
                 a
                 brief
                 
                 account
                 of
                 her
                 revolution
                 .
                 But
                 first
                 I
                 will
                 shew
                 you
                 ,
                 how
                 the
                 day
                 of
                 the
                 moneth
                 in
                 any
                 year
                 propounded
                 in
                 one
                 Couutry
                 ,
                 may
                 be
                 reduced
                 to
                 its
                 correspondent
                 time
                 in
                 another
                 .
              
               
                 11.
                 
                 Taking
                 therefore
                 the
                 length
                 of
                 the
                 year
                 ,
                 to
                 be
                 in
                 several
                 Nations
                 as
                 hath
                 been
                 before
                 declared
                 ,
                 if
                 we
                 would
                 find
                 what
                 day
                 of
                 the
                 moneth
                 in
                 one
                 Conntry
                 is
                 correspondent
                 to
                 the
                 day
                 of
                 that
                 moneth
                 given
                 in
                 another
                 ,
                 there
                 must
                 be
                 some
                 beginning
                 to
                 every
                 one
                 of
                 these
                 Accounts
                 ,
                 and
                 that
                 beginning
                 must
                 be
                 referred
                 to
                 some
                 one
                 ,
                 as
                 to
                 the
                 common
                 measure
                 of
                 the
                 rest
                 .
              
               
                 12.
                 
                 The
                 most
                 natural
                 beginning
                 of
                 All
                 Accounts
                 ,
                 is
                 the
                 time
                 of
                 the
                 Worlds
                 Creation
                 ,
                 but
                 they
                 who
                 could
                 not
                 attain
                 to
                 the
                 Worlds
                 Beginning
                 ,
                 have
                 reckoned
                 from
                 their
                 own
                 ,
                 as
                 the
                 Romans
                 from
                 the
                 building
                 of
                 Rome
                 ,
                 the
                 Greeks
                 from
                 their
                 Olympicks
                 ,
                 the
                 Assyrians
                 from
                 Nabonassar
                 ,
                 and
                 all
                 Christians
                 from
                 the
                 Birth
                 of
                 Christ
                 :
                 the
                 beginning
                 of
                 which
                 and
                 all
                 other
                 the
                 most
                 notable
                 Epochaes
                 ,
                 we
                 have
                 ascertained
                 to
                 their
                 correspondent
                 times
                 in
                 the
                 Julian
                 Period
                 ,
                 which
                 Scaliger
                 contrived
                 by
                 the
                 continual
                 Multiplication
                 of
                 those
                 Circles
                 ,
                 all
                 in
                 former
                 time
                 of
                 good
                 use
                 ,
                 and
                 two
                 of
                 them
                 do
                 yet
                 remain
                 ;
                 the
                 Circles
                 yet
                 in
                 use
                 are
                 those
                 of
                 the
                 Sun
                 and
                 Moon
                 ,
                 the
                 one
                 ,
                 to
                 wit
                 ,
                 the
                 Sun
                 ,
                 is
                 a
                 Circle
                 of
                 28
                 years
                 ,
                 and
                 the
                 Circle
                 of
                 the
                 Moon
                 is
                 19
                 ,
                 as
                 shall
                 be
                 shewed
                 hereafter
                 .
                 The
                 third
                 Circle
                 which
                 now
                 serves
                 for
                 no
                 other
                 use
                 than
                 the
                 constituting
                 of
                 the
                 Julian
                 Period
                 ,
                 is
                 the
                 Roman
                 Indiction
                 ,
                 or
                 a
                 Circle
                 of
                 15
                 years
                 ;
                 if
                 you
                 multiply
                 28
                 the
                 Circle
                 of
                 the
                 Sun
                 ,
                 by
                 19
                 the
                 Circle
                 of
                 the
                 Moon
                 ,
                 the
                 Product
                 is
                 532
                 ,
                 which
                 being
                 multiplied
                 by
                 15
                 ,
                 the
                 Circle
                 of
                 the
                 Roman
                 Indiction
                 ,
                 the
                 Product
                 is
                 7980
                 ,
                 the
                 
                 Number
                 of
                 years
                 in
                 the
                 Julian
                 Period
                 :
                 whose
                 admirable
                 condition
                 is
                 to
                 distinguish
                 every
                 year
                 within
                 the
                 whole
                 Circle
                 by
                 a
                 several
                 certain
                 Character
                 ,
                 the
                 year
                 of
                 the
                 Sun
                 ,
                 Moon
                 ,
                 and
                 Indiction
                 being
                 never
                 the
                 same
                 again
                 until
                 the
                 revolution
                 of
                 7980
                 years
                 be
                 gone
                 about
                 ,
                 the
                 beginning
                 of
                 this
                 Period
                 was
                 764
                 Julian
                 years
                 before
                 the
                 most
                 reputed
                 time
                 of
                 the
                 Worlds
                 Creation
                 ;
                 which
                 being
                 premised
                 ,
                 we
                 will
                 now
                 by
                 Example
                 shew
                 you
                 how
                 to
                 reduce
                 the
                 years
                 of
                 Forreigners
                 to
                 our
                 Julian
                 years
                 ,
                 and
                 the
                 contrary
                 .
              
               
                 
                   1.
                   
                   Example
                   .
                
                 
                   I
                   desire
                   to
                   know
                   at
                   what
                   time
                   in
                   the
                   Turkish
                   Account
                   ,
                   the
                   fifth
                   of
                   Iune
                   in
                   the
                   year
                   of
                   our
                   Lord
                   1640.
                   doth
                   fall
                   .
                
                 
                   The
                   Julian
                   years
                   complete
                   are
                   1648
                   ,
                   and
                   are
                   thus
                   turned
                   into
                   days
                   ,
                   by
                   the
                   Table
                   of
                   days
                   in
                   Julian
                   years
                   .
                
                 
                   
                     1000
                     Julian
                     years
                     give
                     days
                  
                   
                     365250
                  
                   
                     600
                     Julian
                     years
                     give
                     days
                     ▪
                  
                   
                     219150
                  
                   
                     40
                     Julian
                     years
                     give
                     days
                  
                   
                     14610
                  
                   
                     8
                     Years
                     give
                     days
                  
                   
                     2922
                  
                   
                     May
                     complete
                  
                   
                     151
                  
                   
                     Days
                  
                   
                     5
                  
                   
                     The
                     Sum
                     is
                  
                   
                     602088
                  
                
                 
                   Now
                   because
                   the
                   Turkish
                   Account
                   began
                   
                     Iuly
                     16.
                     
                     Anno
                     Christi
                  
                   .
                   622.
                   you
                   must
                   convert
                   these
                   years
                   into
                   days
                   also
                   .
                
                 
                   
                   
                     600
                     Julian
                     years
                     give
                     days
                  
                   
                     219150
                  
                   
                     20
                     Years
                     give
                     days
                  
                   
                     7305
                  
                   
                     1
                     Year
                     giveth
                     days
                  
                   
                     365
                  
                   
                     Iune
                     complete
                  
                   
                     181
                  
                   
                     Days
                  
                   
                     15
                  
                   
                     The
                     Sum
                     is
                  
                   
                     227016
                  
                
                 
                   
                     Which
                     being
                     substracted
                     from
                  
                   
                     602088
                  
                   
                     There
                     resteth
                     days
                  
                   
                     375072
                  
                   
                     900
                     Turkish
                     years
                     give
                     days
                  
                   
                     318930
                  
                   
                     There
                     resteth
                  
                   
                     56142
                  
                   
                     150
                     Turkish
                     years
                     give
                     days
                  
                   
                     53155
                  
                   
                     There
                     resteth
                  
                   
                     02987
                  
                   
                     8
                     Turkish
                     years
                     give
                     days
                  
                   
                     2835
                  
                   
                     There
                     resteth
                  
                   
                     152
                  
                   
                     Giumadi
                     .
                     4.
                     
                  
                   
                     148
                  
                   
                     There
                     resteth
                  
                   
                     4
                  
                
                 
                   Therefore
                   the
                   fifth
                   of
                   Iune
                   1649.
                   in
                   our
                   English
                   Account
                   doth
                   fall
                   in
                   the
                   year
                   1058.
                   of
                   Mahomet
                   ,
                   or
                   the
                   Turkish
                   Hegira
                   ,
                   the
                   fourth
                   day
                   of
                   the
                   moneth
                   Giumadi
                   .
                   11
                
              
               
                 
                   2.
                   
                   Example
                   .
                
                 
                   I
                   desire
                   to
                   know
                   upon
                   what
                   day
                   of
                   our
                   Julian
                   year
                   the
                   17
                   day
                   of
                   the
                   moneth
                   in
                   the
                   1069
                   year
                   complete
                   of
                   the
                   Persian
                   Account
                   from
                   Ieshagile
                   doth
                   fall
                   .
                
                 
                   
                   
                     The
                     beginning
                     of
                     this
                     Epocha
                     is
                     from
                     the
                     Epocha
                     of
                     Christ
                     in
                     complete
                     days
                  
                   
                     230639
                  
                   
                     1000
                     Persian
                     years
                     give
                  
                   
                     365000
                  
                   
                     60
                     Years
                     give
                  
                   
                     21900
                  
                   
                     9
                     Years
                     give
                  
                   
                     3285
                  
                   
                     Chortal
                     complete
                  
                   
                     90
                  
                   
                     Days
                     complete
                  
                   
                     16
                  
                   
                     The
                     Sum
                  
                   
                     620930
                  
                   
                     1000
                     Julian
                     years
                     Substracted
                  
                   
                     365250
                  
                   
                     There
                     rests
                  
                   
                     255680
                  
                   
                     700
                     Julian
                     years
                  
                   
                     255675
                  
                   
                     There
                     rests
                  
                   
                     5
                  
                
                 
                   Therefore
                   it
                   falls
                   out
                   in
                   the
                   Julian
                   year
                   from
                   Christ
                   1700.
                   the
                   fifth
                   day
                   of
                   Ianuary
                   .
                
                 
                   He
                   that
                   understands
                   this
                   may
                   by
                   the
                   like
                   method
                   convert
                   the
                   years
                   of
                   other
                   Epochas
                   ,
                   into
                   our
                   Julian
                   years
                   and
                   the
                   contrary
                   .
                
                 
                   The
                   Anticipation
                   of
                   the
                   Gregorian
                   Calendar
                   is
                   more
                   easily
                   obtained
                   ,
                   for
                   if
                   you
                   enter
                   the
                   Table
                   with
                   the
                   years
                   of
                   Christ
                   complete
                   ,
                   you
                   have
                   the
                   days
                   to
                   be
                   added
                   to
                   the
                   time
                   in
                   the
                   Julian
                   Account
                   ,
                   to
                   make
                   it
                   answer
                   to
                   the
                   Gregorian
                   ,
                   which
                   will
                   be
                   but
                   ten
                   days
                   difference
                   till
                   the
                   year
                   1700.
                   and
                   then
                   the
                   difference
                   will
                   be
                   a
                   day
                   more
                   ,
                   until
                   the
                   year
                   1800.
                   and
                   so
                   forward
                   three
                   days
                   difference
                   more
                   in
                   every
                   400
                   years
                   to
                   come
                   ,
                   unless
                   our
                   year
                   shall
                   be
                   reformed
                   as
                   well
                   as
                   theirs
                   .
                
              
            
             
               
               
                 CHAP.
                 II.
                 
              
               
                 
                   Of
                   the
                   Cycle
                   of
                   the
                   Moon
                   ,
                   what
                   it
                   is
                   ,
                   how
                   placed
                   in
                   the
                   Calendar
                   ,
                   and
                   to
                   what
                   purpose
                   .
                
              
               
                 THat
                 the
                 Civil
                 Year
                 in
                 use
                 with
                 us
                 and
                 all
                 Christians
                 ,
                 doth
                 consist
                 of
                 365
                 days
                 ,
                 and
                 every
                 fourth
                 year
                 of
                 366
                 ,
                 hath
                 been
                 already
                 shewed
                 ,
                 with
                 the
                 return
                 of
                 the
                 Sunday
                 Letter
                 in
                 28
                 years
                 .
                 In
                 which
                 time
                 the
                 Moon
                 doth
                 finish
                 her
                 course
                 in
                 the
                 Zodiack
                 no
                 less
                 than
                 twelve
                 times
                 ,
                 which
                 twelve
                 Moons
                 ,
                 or
                 354
                 days
                 ,
                 do
                 fall
                 short
                 of
                 the
                 Sun's
                 year
                 ,
                 eleven
                 days
                 in
                 every
                 common
                 year
                 ,
                 and
                 twelve
                 in
                 the
                 Bissextile
                 or
                 Leap-year
                 .
              
               
                 And
                 by
                 Observation
                 of
                 Meton
                 an
                 Athenian
                 ,
                 it
                 was
                 found
                 out
                 about
                 432
                 years
                 before
                 Christ
                 ,
                 that
                 the
                 Moon
                 in
                 nineteen
                 years
                 did
                 return
                 to
                 be
                 in
                 Conjunction
                 with
                 the
                 Sun
                 on
                 the
                 self
                 same
                 day
                 ,
                 and
                 this
                 Circle
                 of
                 nineteen
                 years
                 is
                 called
                 the
                 Cycle
                 of
                 the
                 Moon
                 ,
                 which
                 being
                 written
                 in
                 the
                 Calendar
                 against
                 the
                 day
                 in
                 every
                 Moneth
                 ,
                 in
                 which
                 the
                 Moon
                 did
                 change
                 ,
                 in
                 Letters
                 of
                 Gold
                 ,
                 was
                 also
                 called
                 the
                 Golden
                 Number
                 ,
                 or
                 from
                 the
                 excellent
                 use
                 thereof
                 ,
                 which
                 was
                 at
                 first
                 ,
                 only
                 to
                 find
                 the
                 New
                 Moons
                 in
                 every
                 Moneth
                 for
                 ever
                 ,
                 but
                 amongst
                 Christians
                 it
                 serveth
                 for
                 another
                 purpose
                 also
                 ,
                 even
                 the
                 finding
                 of
                 the
                 time
                 when
                 the
                 Feast
                 of
                 Easter
                 is
                 to
                 be
                 observed
                 .
                 The
                 New
                 Moons
                 by
                 this
                 Number
                 are
                 thus
                 found
                 .
                 In
                 the
                 first
                 year
                 of
                 the
                 Circle
                 ,
                 or
                 when
                 the
                 Golden
                 Number
                 is
                 1
                 ,
                 where
                 the
                 Number
                 1
                 was
                 set
                 in
                 the
                 Calendar
                 in
                 any
                 Moneth
                 ,
                 that
                 day
                 is
                 New
                 Moon
                 ,
                 in
                 
                 the
                 second
                 Year
                 where
                 you
                 find
                 the
                 golden
                 Number
                 2
                 ,
                 in
                 the
                 third
                 Year
                 where
                 you
                 find
                 the
                 golden
                 Number
                 3
                 ,
                 and
                 so
                 forward
                 till
                 the
                 whole
                 Circle
                 be
                 expired
                 ;
                 then
                 you
                 must
                 begin
                 with
                 one
                 again
                 ,
                 and
                 run
                 through
                 the
                 whole
                 Circle
                 as
                 before
                 .
              
               
                 2.
                 
                 And
                 the
                 reason
                 why
                 the
                 Calendar
                 begins
                 with
                 the
                 golden
                 Number
                 3
                 ,
                 not
                 1
                 ,
                 is
                 this
                 .
                 The
                 Christians
                 in
                 Alexandria
                 had
                 used
                 this
                 Circle
                 of
                 the
                 Moon
                 two
                 Years
                 before
                 the
                 Nicene
                 Council
                 .
                 And
                 in
                 the
                 first
                 of
                 these
                 Years
                 the
                 new
                 Moon
                 next
                 to
                 the
                 Vernal
                 Equinox
                 was
                 upon
                 the
                 27th
                 Day
                 of
                 the
                 Egyptian
                 month
                 Phamenoth
                 answering
                 to
                 the
                 23d
                 of
                 our
                 March
                 ,
                 against
                 that
                 Day
                 therefore
                 they
                 placed
                 the
                 golden
                 Number
                 1.
                 
                 And
                 because
                 there
                 are
                 29
                 Days
                 and
                 a
                 half
                 from
                 one
                 new
                 Moon
                 to
                 another
                 ,
                 they
                 made
                 the
                 distance
                 between
                 the
                 new
                 Moons
                 to
                 be
                 interchangeably
                 29
                 and
                 30
                 Days
                 ,
                 and
                 so
                 they
                 placed
                 the
                 same
                 golden
                 Number
                 against
                 the
                 26
                 Day
                 of
                 Phurmuthi
                 the
                 Month
                 following
                 ,
                 and
                 against
                 the
                 26
                 Day
                 of
                 the
                 Month
                 Pachon
                 and
                 so
                 forward
                 ,
                 and
                 upon
                 this
                 ground
                 by
                 the
                 like
                 progression
                 was
                 the
                 golden
                 Number
                 set
                 in
                 the
                 Roman
                 Calendar
                 ;
                 and
                 so
                 the
                 golden
                 Number
                 1
                 by
                 their
                 example
                 was
                 set
                 against
                 
                   March
                   23.
                   
                   April
                   21.
                   
                   Iune
                   19.
                   
                   Iuly
                   19.
                   
                   August
                   17.
                   
                   September
                   16.
                   
                   October
                   15.
                   
                   November
                   14.
                   
                   December
                   .
                
                 13.
                 
                 But
                 then
                 because
                 in
                 the
                 following
                 Year
                 the
                 golden
                 Number
                 was
                 2.
                 reckoning
                 30
                 Days
                 from
                 the
                 13th
                 of
                 December
                 ,
                 the
                 golden
                 Number
                 2
                 was
                 set
                 to
                 
                   Innuary
                   12.
                   
                   February
                   10.
                   
                   March
                   12.
                   
                   April
                   10.
                   
                   May
                   10.
                   
                   Iune
                   8.
                   
                   Iuly
                   8.
                   
                   August
                   6.
                   
                   September
                   5.
                   
                   October
                   4.
                   
                   November
                   3.
                   
                   December
                   .
                
                 2.
                 
                 From
                 whence
                 reckoning
                 13
                 Days
                 as
                 before
                 ,
                 the
                 golden
                 Number
                 3
                 
                 comes
                 in
                 course
                 for
                 the
                 third
                 Year
                 to
                 be
                 set
                 against
                 the
                 first
                 of
                 Ianuary
                 .
              
               
                 But
                 that
                 you
                 may
                 know
                 how
                 the
                 golden
                 Number
                 comes
                 to
                 be
                 distributed
                 in
                 the
                 Calendar
                 according
                 to
                 the
                 form
                 in
                 which
                 it
                 now
                 is
                 ,
                 you
                 must
                 consider
                 that
                 in
                 19
                 Solar
                 Years
                 there
                 are
                 not
                 only
                 228
                 Lunar
                 Months
                 or
                 12
                 times
                 19
                 Lunar
                 Months
                 but
                 235
                 for
                 the
                 11
                 Days
                 which
                 the
                 common
                 Solar
                 Year
                 doth
                 exceed
                 the
                 Lunar
                 ,
                 do
                 in
                 19
                 Years
                 arise
                 to
                 209
                 Days
                 ,
                 out
                 of
                 which
                 there
                 may
                 be
                 appointed
                 7
                 Months
                 ,
                 6
                 whereof
                 will
                 contain
                 30
                 Days
                 apiece
                 ,
                 and
                 one
                 Month
                 29
                 days
                 ;
                 and
                 these
                 7
                 Months
                 are
                 called
                 Embolismical
                 Months
                 ,
                 because
                 by
                 a
                 kind
                 of
                 injection
                 or
                 interposition
                 they
                 are
                 reckoned
                 in
                 some
                 of
                 the
                 19
                 Years
                 .
                 And
                 those
                 Years
                 in
                 which
                 they
                 are
                 reckoned
                 are
                 called
                 Embolismical
                 Years
                 ,
                 to
                 distinguish
                 them
                 from
                 the
                 common
                 Years
                 which
                 always
                 contain
                 354
                 Days
                 ,
                 whereas
                 6
                 of
                 these
                 Embolismical
                 Years
                 do
                 each
                 of
                 them
                 contain
                 384
                 Days
                 ,
                 and
                 the
                 seventh
                 Embolismical
                 Year
                 in
                 which
                 the
                 Month
                 of
                 29
                 Days
                 is
                 reckoned
                 ,
                 doth
                 contain
                 383
                 Days
                 .
              
               
                 3.
                 
                 The
                 Embolismical
                 Years
                 in
                 the
                 Cycle
                 of
                 the
                 Moon
                 are
                 properly
                 these
                 Seven
                 .
                 3
                 ,
                 6
                 ,
                 9
                 ,
                 11
                 ,
                 14
                 ,
                 17
                 ,
                 19.
                 because
                 in
                 the
                 third
                 Year
                 11
                 Days
                 being
                 thrice
                 reckoned
                 do
                 amount
                 to
                 33
                 Days
                 ,
                 that
                 is
                 one
                 Month
                 of
                 30
                 Days
                 and
                 3
                 Days
                 over
                 .
                 Again
                 in
                 the
                 sixth
                 Year
                 the
                 11
                 Days
                 which
                 the
                 Solar
                 exceed
                 the
                 Lunar
                 ,
                 being
                 thrice
                 numbred
                 ,
                 do
                 amount
                 to
                 33
                 Days
                 .
                 which
                 with
                 the
                 3
                 Days
                 formerly
                 reserved
                 do
                 make
                 36
                 Days
                 ,
                 that
                 is
                 one
                 Month
                 of
                 30
                 Days
                 and
                 6
                 Days
                 over
                 .
                 Again
                 in
                 the
                 Ninth
                 Year
                 there
                 are
                 also
                 33
                 Days
                 ,
                 to
                 which
                 the
                 6
                 Days
                 reserved
                 being
                 added
                 ,
                 there
                 will
                 arise
                 one
                 Month
                 more
                 and
                 9
                 Days
                 over
                 .
                 But
                 in
                 
                 the
                 Eleventh
                 Year
                 twice
                 11
                 Days
                 being
                 added
                 to
                 the
                 9
                 Days
                 reserved
                 ,
                 do
                 make
                 31
                 Days
                 ,
                 that
                 is
                 ,
                 one
                 Month
                 of
                 30
                 days
                 and
                 one
                 day
                 over
                 ,
                 which
                 being
                 added
                 to
                 the
                 supernumerary
                 days
                 in
                 the
                 fourteenth
                 Year
                 do
                 make
                 another
                 Month
                 of
                 30
                 Days
                 and
                 4
                 Days
                 over
                 ,
                 and
                 these
                 being
                 added
                 to
                 the
                 supernumerary
                 Days
                 in
                 the
                 sevententh
                 Year
                 do
                 make
                 another
                 Month
                 of
                 30
                 and
                 7
                 Days
                 over
                 ,
                 and
                 these
                 7
                 Days
                 being
                 added
                 to
                 the
                 22
                 supernumerary
                 Days
                 in
                 the
                 Ninteenth
                 Year
                 of
                 the
                 Moons
                 Cycle
                 do
                 make
                 another
                 Month
                 of
                 29
                 Days
                 .
              
               
                 4.
                 
                 But
                 because
                 there
                 are
                 6939
                 Days
                 and
                 18
                 Hours
                 in
                 19
                 Solar
                 Years
                 ,
                 that
                 is
                 ,
                 4
                 Days
                 18
                 Hours
                 more
                 then
                 in
                 the
                 common
                 and
                 Embolismical
                 Lunar
                 Years
                 ,
                 in
                 which
                 the
                 excess
                 between
                 the
                 Lunar
                 and
                 the
                 Solar
                 Year
                 is
                 supposed
                 to
                 be
                 no
                 more
                 then
                 11
                 Days
                 in
                 each
                 Year
                 ,
                 whereas
                 in
                 every
                 fourth
                 Year
                 the
                 excess
                 is
                 one
                 Day
                 more
                 ,
                 that
                 is
                 ,
                 12
                 Days
                 ,
                 that
                 is
                 ,
                 in
                 16
                 Years
                 4
                 Days
                 ,
                 and
                 in
                 the
                 remaining
                 3
                 Years
                 three
                 fourths
                 of
                 a
                 day
                 more
                 .
                 And
                 that
                 the
                 new
                 Moons
                 after
                 19
                 Lunar
                 Years
                 or
                 235
                 Lunations
                 do
                 not
                 return
                 to
                 the
                 same
                 days
                 again
                 ,
                 but
                 want
                 almost
                 5
                 days
                 ,
                 it
                 is
                 evident
                 that
                 the
                 civil
                 Lunations
                 do
                 not
                 agree
                 with
                 the
                 Astronomical
                 and
                 that
                 there
                 must
                 be
                 yet
                 some
                 kind
                 of
                 intercalation
                 used
                 .
              
               
                 5.
                 
                 Now
                 therefore
                 in
                 distributing
                 the
                 golden
                 Number
                 throughout
                 the
                 Calendar
                 .
                 If
                 the
                 new
                 Moons
                 should
                 interchangeably
                 consist
                 of
                 30
                 and
                 29
                 days
                 ,
                 and
                 so
                 but
                 228
                 Lunations
                 in
                 19
                 Years
                 ;
                 we
                 might
                 proceed
                 in
                 the
                 same
                 order
                 in
                 which
                 we
                 have
                 begun
                 ,
                 and
                 by
                 which
                 as
                 hath
                 been
                 shewed
                 the
                 third
                 Year
                 of
                 the
                 Golden
                 Number
                 falls
                 upon
                 the
                 Calends
                 of
                 Ianuary
                 .
                 But
                 for
                 as
                 much
                 as
                 there
                 are
                 first
                 six
                 Lunations
                 of
                 30
                 days
                 apiece
                 and
                 
                 one
                 of
                 29
                 days
                 to
                 be
                 interposed
                 ,
                 therefore
                 there
                 must
                 be
                 6
                 times
                 2
                 Lunations
                 together
                 consisting
                 of
                 30
                 days
                 and
                 once
                 three
                 Lunations
                 of
                 29
                 days
                 .
                 And
                 that
                 respect
                 may
                 be
                 also
                 had
                 to
                 the
                 Bissextile
                 days
                 ,
                 although
                 they
                 are
                 not
                 exprest
                 in
                 the
                 Calendar
                 ,
                 that
                 Lunation
                 which
                 doth
                 contain
                 the
                 Bissertile
                 day
                 ,
                 if
                 it
                 should
                 have
                 been
                 29
                 days
                 ,
                 it
                 must
                 be
                 30
                 ,
                 if
                 it
                 should
                 have
                 consisted
                 of
                 30
                 days
                 it
                 must
                 consist
                 of
                 31.
                 
              
               
                 6.
                 
                 And
                 because
                 it
                 was
                 thought
                 convenient
                 ,
                 as
                 hath
                 been
                 shewed
                 ,
                 to
                 begin
                 with
                 the
                 third
                 Year
                 of
                 the
                 Cycle
                 of
                 the
                 Moon
                 ,
                 because
                 the
                 Golden
                 Number
                 3
                 is
                 set
                 to
                 the
                 Calends
                 of
                 Ianuary
                 ,
                 therefore
                 in
                 this
                 Cycle
                 the
                 Embolismical
                 Years
                 are
                 ,
                 2
                 ,
                 5
                 ,
                 8
                 ,
                 11
                 ,
                 13
                 ,
                 16
                 ,
                 19.
                 
                 But
                 yet
                 that
                 it
                 may
                 appear
                 ,
                 that
                 these
                 Years
                 are
                 in
                 effect
                 the
                 same
                 ,
                 as
                 if
                 we
                 had
                 begun
                 with
                 the
                 first
                 Year
                 of
                 the
                 Golden
                 Number
                 ,
                 save
                 only
                 that
                 the
                 eighth
                 Year
                 instead
                 of
                 the
                 ninth
                 is
                 to
                 be
                 accounted
                 Embolismical
                 ,
                 I
                 have
                 added
                 the
                 Table
                 follwing
                 ,
                 in
                 which
                 it
                 is
                 apparent
                 that
                 the
                 former
                 Embolismical
                 years
                 do
                 agree
                 with
                 these
                 last
                 mentioned
                 .
              
               
                 7.
                 
                 But
                 as
                 I
                 said
                 before
                 ,
                 it
                 was
                 thought
                 more
                 convenient
                 to
                 begin
                 the
                 account
                 from
                 the
                 number
                 3
                 set
                 to
                 the
                 Calends
                 of
                 Ianuary
                 ,
                 because
                 by
                 so
                 reckoning
                 30
                 and
                 29
                 days
                 to
                 each
                 Lunation
                 interchangeably
                 ,
                 the
                 same
                 Number
                 3
                 falls
                 upon
                 
                   Ianuary
                   31.
                   
                   March
                
                 1
                 ,
                 and
                 31.
                 
                 
                   April
                   29.
                   
                   May
                   29.
                   
                   Iune
                   27.
                   
                   Iuly
                   27.
                   
                   August
                   25.
                   
                   September
                   14.
                   
                   October
                   23.
                   
                   November
                   22.
                   
                   December
                
                 21.
                 
                 As
                 if
                 the
                 Lunar
                 years
                 were
                 compleated
                 upon
                 the
                 20
                 of
                 December
                 there
                 remain
                 just
                 11
                 Days
                 ,
                 which
                 the
                 Solar
                 years
                 doth
                 exceed
                 the
                 Lunar
                 .
              
               
                 8.
                 
                 And
                 by
                 ranking
                 on
                 and
                 accounting
                 4
                 for
                 the
                 Golden
                 Number
                 of
                 the
                 next
                 year
                 ,
                 you
                 will
                 
                 find
                 it
                 set
                 on
                 
                   Ianuary
                   20
                   ,
                   February
                   18
                   ,
                   March
                   20
                   ,
                   April
                   18
                   ,
                   May
                   18
                   ,
                   Iune
                   16
                   ,
                   Iuly
                   16
                   ,
                   August
                   14
                   ,
                   September
                   13
                   ,
                   Octob.
                   12
                   ,
                   Novemb
                   .
                   11
                   ,
                   Decemb.
                
                 10.
                 
              
               
                 
                   
                     
                       Cycle
                       of
                       the
                       Moon
                       .
                    
                     
                       Cycle
                       of
                       the
                       Moon
                       .
                    
                     
                       Embolismical
                       Years
                       .
                    
                     
                       Number
                       of
                       Days
                       .
                    
                  
                   
                     
                       1
                    
                     
                       3
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                       2
                    
                     
                       4
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                       3
                    
                     
                       5
                    
                     
                       Embol
                       .
                    
                     
                       384
                    
                  
                   
                     
                       4
                    
                     
                       6
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                       5
                    
                     
                       7
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                       6
                    
                     
                       8
                    
                     
                       Embol
                       .
                    
                     
                       384
                    
                  
                   
                     
                       7
                    
                     
                       9
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                       8
                    
                     
                       10
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                       9
                    
                     
                       11
                    
                     
                       Embol
                       .
                    
                     
                       384
                    
                  
                   
                     
                       10
                    
                     
                       12
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       11
                    
                     
                       13
                    
                     
                       Embol
                       .
                    
                     
                       384
                    
                  
                   
                     
                       12
                    
                     
                       14
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                       13
                    
                     
                       15
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                       14
                    
                     
                       16
                    
                     
                       Embol
                       .
                    
                     
                       384
                    
                  
                   
                     
                       15
                    
                     
                       17
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                       16
                    
                     
                       18
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                       17
                    
                     
                       19
                    
                     
                       Embol
                       .
                    
                     
                       384
                    
                  
                   
                     
                       18
                    
                     
                       1
                    
                     
                        
                    
                     
                       354
                    
                  
                   
                     
                       19
                    
                     
                       2
                    
                     
                       Embol
                       .
                    
                     
                       384
                    
                  
                
              
               
                 9.
                 
                 But
                 in
                 going
                 on
                 ,
                 and
                 taking
                 5
                 for
                 the
                 Golden
                 Number
                 in
                 the
                 third
                 year
                 ,
                 we
                 must
                 remember
                 that
                 that
                 is
                 an
                 Embolismical
                 Year
                 ,
                 and
                 therefore
                 that
                 somewhere
                 there
                 must
                 be
                 2
                 Months
                 together
                 of
                 30
                 days
                 .
                 And
                 for
                 this
                 reason
                 the
                 Golden
                 Number
                 5
                 ,
                 is
                 set
                 to
                 
                   Ianuary
                   9
                   ,
                   February
                   7
                   ,
                   March
                   9
                   ,
                   April
                   7
                   ,
                   May
                   7
                   ,
                   Iune
                   5
                   ,
                   Iuly
                   5
                   ,
                   August
                   3
                   ,
                   September
                   2
                   ,
                
                 as
                 also
                 upon
                 the
                 second
                 day
                 of
                 October
                 ,
                 and
                 not
                 upon
                 the
                 first
                 ,
                 that
                 so
                 there
                 may
                 be
                 2
                 Lunations
                 together
                 of
                 30
                 ,
                 and
                 the
                 same
                 Number
                 5
                 is
                 also
                 set
                 to
                 the
                 thirty
                 first
                 of
                 October
                 ,
                 to
                 make
                 the
                 Lunation
                 to
                 consist
                 of
                 29
                 days
                 ,
                 and
                 to
                 the
                 thirtieth
                 of
                 November
                 instead
                 of
                 the
                 twenty
                 ninth
                 ,
                 that
                 so
                 a
                 Lunation
                 of
                 
                 30
                 may
                 again
                 succeed
                 as
                 it
                 ought
                 .
              
               
                 10.
                 
                 In
                 like
                 manner
                 in
                 the
                 sixth
                 Year
                 ,
                 having
                 gone
                 through
                 the
                 fourth
                 and
                 fifth
                 as
                 common
                 years
                 ,
                 you
                 may
                 see
                 the
                 Golden
                 Number
                 8
                 set
                 to
                 the
                 fifth
                 of
                 April
                 ,
                 which
                 should
                 have
                 been
                 upon
                 the
                 fourth
                 ,
                 and
                 in
                 the
                 ninth
                 Year
                 the
                 Golden
                 Number
                 11
                 is
                 set
                 to
                 the
                 second
                 of
                 February
                 which
                 should
                 have
                 been
                 upon
                 the
                 first
                 .
              
               
                 And
                 there
                 is
                 a
                 particular
                 reason
                 ,
                 for
                 which
                 these
                 numbers
                 are
                 otherwise
                 placed
                 from
                 the
                 eighth
                 of
                 March
                 to
                 the
                 fifth
                 of
                 April
                 ,
                 namely
                 ,
                 that
                 all
                 the
                 paschal
                 Lunations
                 may
                 consist
                 of
                 29
                 days
                 :
                 For
                 thus
                 from
                 the
                 eighth
                 of
                 March
                 to
                 the
                 sixth
                 of
                 April
                 ,
                 to
                 both
                 which
                 days
                 the
                 Golden
                 Number
                 is
                 16
                 ,
                 there
                 are
                 but
                 29
                 days
                 .
                 And
                 from
                 the
                 ninth
                 of
                 March
                 to
                 the
                 seventh
                 of
                 April
                 ,
                 to
                 both
                 which
                 days
                 the
                 Golden
                 Number
                 is
                 5
                 ,
                 there
                 are
                 also
                 29
                 days
                 ,
                 and
                 so
                 of
                 the
                 rest
                 till
                 you
                 come
                 to
                 the
                 fifth
                 of
                 April
                 ,
                 which
                 is
                 the
                 last
                 Paschal
                 Lunation
                 ,
                 as
                 the
                 eighth
                 of
                 March
                 is
                 the
                 first
                 ,
                 but
                 at
                 any
                 other
                 time
                 of
                 the
                 Year
                 ,
                 the
                 length
                 of
                 the
                 Month
                 in
                 the
                 Embolismical
                 Year
                 ,
                 may
                 be
                 fixed
                 as
                 you
                 please
                 .
              
               
                 12.
                 
                 And
                 in
                 this
                 manner
                 in
                 the
                 17
                 years
                 ,
                 in
                 which
                 the
                 lunations
                 of
                 the
                 whole
                 Circle
                 are
                 finished
                 ,
                 and
                 in
                 which
                 the
                 Golden
                 Number
                 is
                 19
                 ,
                 the
                 Month
                 of
                 Iuly
                 is
                 taken
                 at
                 pleasure
                 ,
                 to
                 the
                 thirtieth
                 day
                 whereof
                 is
                 set
                 the
                 Golden
                 Number
                 19
                 ,
                 which
                 should
                 have
                 been
                 upon
                 the
                 thirty
                 first
                 ,
                 and
                 the
                 same
                 Number
                 being
                 notwithstanding
                 placed
                 upon
                 the
                 twenty
                 eighth
                 of
                 August
                 ,
                 that
                 by
                 the
                 two
                 Lunations
                 of
                 29
                 days
                 together
                 ,
                 it
                 might
                 be
                 understood
                 ,
                 that
                 the
                 seventh
                 Embolismical
                 Month
                 consisting
                 of
                 29
                 days
                 is
                 there
                 inserted
                 ,
                 instead
                 of
                 a
                 Month
                 of
                 30
                 days
                 .
                 In
                 which
                 place
                 the
                 Embolismical
                 or
                 leaping
                 Year
                 of
                 the
                 Moon
                 may
                 
                 plainly
                 be
                 observed
                 for
                 that
                 year
                 is
                 one
                 day
                 less
                 than
                 the
                 rest
                 ,
                 which
                 the
                 Moon
                 doth
                 as
                 it
                 were
                 pass
                 over
                 .
                 The
                 which
                 one
                 day
                 is
                 again
                 added
                 to
                 the
                 29
                 days
                 of
                 the
                 last
                 Month
                 ,
                 that
                 we
                 may
                 by
                 that
                 means
                 come
                 ,
                 as
                 in
                 other
                 Years
                 ,
                 to
                 the
                 Golden
                 Number
                 ,
                 which
                 sheweth
                 the
                 New
                 Moon
                 in
                 Ianuary
                 following
                 .
                 And
                 for
                 this
                 reason
                 the
                 Epact
                 then
                 doth
                 not
                 consist
                 of
                 11
                 but
                 of
                 12
                 days
                 .
                 And
                 thus
                 you
                 see
                 the
                 reason
                 ,
                 for
                 which
                 the
                 Golden
                 Numbers
                 are
                 thus
                 set
                 in
                 the
                 Calendar
                 as
                 here
                 you
                 see
                 .
                 In
                 which
                 we
                 may
                 also
                 observe
                 ,
                 that
                 every
                 following
                 Number
                 is
                 made
                 by
                 adding
                 8
                 to
                 the
                 Number
                 preceding
                 ,
                 and
                 every
                 preceding
                 Number
                 is
                 also
                 made
                 by
                 adding
                 11
                 to
                 the
                 Number
                 next
                 following
                 ,
                 and
                 casting
                 away
                 19
                 when
                 the
                 addition
                 shall
                 exceed
                 it
                 .
              
               
                 For
                 Example
                 ,
                 if
                 you
                 add
                 8
                 to
                 the
                 Golden
                 Number
                 3
                 set
                 against
                 the
                 first
                 of
                 Ianuary
                 ,
                 it
                 maketh
                 11
                 ,
                 to
                 which
                 add
                 8
                 more
                 and
                 it
                 maketh
                 19
                 ,
                 to
                 which
                 adding
                 8
                 it
                 maketh
                 27
                 ,
                 from
                 which
                 substracting
                 19
                 the
                 remainer
                 is
                 8
                 ,
                 to
                 which
                 again
                 adding
                 8
                 ,
                 the
                 sum
                 is
                 19
                 ,
                 to
                 which
                 adding
                 8
                 the
                 sum
                 is
                 24
                 ,
                 from
                 which
                 deducting
                 19
                 the
                 remainer
                 is
                 5
                 ,
                 and
                 so
                 of
                 the
                 rest
                 .
                 In
                 like
                 manner
                 receding
                 backward
                 ,
                 to
                 the
                 5
                 add
                 11
                 they
                 make
                 16
                 ,
                 to
                 the
                 16
                 add
                 11
                 they
                 make
                 27
                 ,
                 from
                 which
                 deducting
                 19
                 the
                 remainer
                 is
                 8
                 ,
                 to
                 which
                 11
                 being
                 added
                 the
                 same
                 is
                 19
                 ,
                 to
                 which
                 11
                 being
                 added
                 the
                 sum
                 is
                 30
                 ,
                 from
                 which
                 deducting
                 19
                 the
                 remainer
                 is
                 11
                 ,
                 to
                 which
                 11
                 being
                 added
                 the
                 sum
                 is
                 22
                 ,
                 from
                 which
                 deducting
                 19
                 the
                 remainer
                 is
                 3.
                 
                 And
                 by
                 this
                 we
                 may
                 see
                 that
                 every
                 following
                 number
                 will
                 be
                 in
                 use
                 8
                 years
                 after
                 the
                 preceding
                 ,
                 and
                 every
                 preceding
                 Number
                 will
                 be
                 in
                 use
                 11
                 years
                 after
                 the
                 following
                 ,
                 that
                 is
                 ,
                 the
                 same
                 will
                 return
                 to
                 be
                 in
                 use
                 after
                 
                 8
                 Years
                 and
                 11
                 ,
                 and
                 the
                 other
                 after
                 11
                 Years
                 and
                 8
                 ,
                 or
                 once
                 in
                 19
                 years
                 .
              
            
             
               
                 CHAP.
                 III.
                 
              
               
                 
                   Of
                   the
                   Vse
                   of
                   the
                   Golden
                   Number
                   in
                   finding
                   the
                   Feast
                   of
                   Easter
                   .
                
              
               
                 THe
                 Cycle
                 of
                 the
                 Moon
                 or
                 Golden
                 Number
                 is
                 a
                 circle
                 of
                 19
                 years
                 ,
                 as
                 hath
                 been
                 said
                 already
                 ,
                 which
                 being
                 distributed
                 in
                 the
                 Calendar
                 as
                 hath
                 been
                 shewn
                 in
                 the
                 last
                 Chapter
                 ,
                 doth
                 shew
                 the
                 day
                 of
                 the
                 New
                 Moon
                 for
                 ever
                 ;
                 though
                 not
                 exactly
                 :
                 But
                 the
                 use
                 for
                 which
                 it
                 was
                 chiefly
                 intended
                 ,
                 was
                 to
                 find
                 the
                 Paschal
                 New
                 Moons
                 ,
                 that
                 is
                 ,
                 those
                 new
                 Moons
                 on
                 which
                 the
                 Feast
                 of
                 Easter
                 and
                 other
                 moveable
                 Feasts
                 depend
                 .
                 To
                 this
                 purpose
                 we
                 must
                 remember
                 ,
              
               
                 1.
                 
                 That
                 the
                 vernal
                 Equinox
                 is
                 supposed
                 to
                 be
                 fixed
                 to
                 the
                 twenty
                 first
                 day
                 of
                 March.
                 
              
               
                 2.
                 
                 That
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 on
                 which
                 the
                 Feast
                 of
                 Easter
                 doth
                 depend
                 ,
                 can
                 never
                 happen
                 before
                 the
                 Equinox
                 ;
                 though
                 it
                 may
                 fall
                 upon
                 it
                 or
                 upon
                 the
                 day
                 following
                 .
              
               
                 3.
                 
                 That
                 the
                 Feast
                 of
                 Easter
                 is
                 never
                 observed
                 upon
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 ,
                 but
                 upon
                 the
                 Sunday
                 following
                 ;
                 so
                 that
                 if
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 be
                 Sunday
                 ,
                 the
                 Sunday
                 following
                 is
                 Easter
                 day
                 .
              
               
                 4.
                 
                 That
                 the
                 Feast
                 of
                 Easter
                 may
                 fall
                 upon
                 the
                 fifteenth
                 day
                 of
                 the
                 Moon
                 ,
                 or
                 upon
                 any
                 other
                 day
                 unto
                 the
                 twenty
                 first
                 ,
                 inclusively
                 .
              
               
                 5.
                 
                 That
                 the
                 Paschal
                 Sunday
                 is
                 discovered
                 by
                 
                 the
                 proper
                 and
                 Dominical
                 Letter
                 for
                 every
                 Year
                 The
                 which
                 may
                 be
                 found
                 as
                 hath
                 been
                 already
                 declared
                 ,
                 or
                 by
                 the
                 proper
                 Table
                 for
                 that
                 purpose
                 .
                 Hence
                 it
                 followeth
                 ,
              
               
                 1.
                 
                 That
                 the
                 New
                 Moon
                 immediately
                 preceding
                 the
                 Feast
                 of
                 Easter
                 ,
                 cannot
                 be
                 before
                 the
                 eighth
                 day
                 of
                 March
                 ,
                 for
                 if
                 you
                 suppose
                 it
                 to
                 be
                 upon
                 March
                 6
                 ,
                 the
                 Moon
                 will
                 be
                 14
                 days
                 old
                 March
                 19
                 ,
                 which
                 is
                 before
                 the
                 Equinox
                 ,
                 contrary
                 to
                 the
                 second
                 Rule
                 before
                 given
                 ,
                 and
                 upon
                 the
                 seventh
                 day
                 of
                 March
                 there
                 is
                 no
                 Golden
                 Number
                 fixed
                 ;
                 and
                 therefore
                 the
                 Golden
                 Number
                 16
                 ,
                 which
                 standeth
                 against
                 March
                 8
                 ,
                 is
                 the
                 first
                 by
                 which
                 the
                 Paschal
                 New
                 Moon
                 may
                 be
                 discovered
                 .
              
               
                 2.
                 
                 It
                 followeth
                 hence
                 ,
                 That
                 the
                 last
                 Paschal
                 New
                 Moon
                 cannot
                 happen
                 beyond
                 the
                 fifth
                 day
                 of
                 April
                 ,
                 because
                 all
                 the
                 19
                 Golden
                 Numbers
                 are
                 expressed
                 from
                 the
                 eighth
                 of
                 March
                 to
                 that
                 day
                 .
                 And
                 if
                 a
                 New
                 Moon
                 should
                 happen
                 upon
                 the
                 sixth
                 of
                 April
                 ,
                 there
                 would
                 be
                 two
                 Paschal
                 New
                 Moons
                 that
                 year
                 ,
                 one
                 upon
                 the
                 eighth
                 of
                 March
                 and
                 another
                 upon
                 the
                 sixth
                 of
                 April
                 ,
                 the
                 same
                 Golden
                 Number
                 16
                 being
                 proper
                 to
                 them
                 both
                 ,
                 but
                 this
                 is
                 absurd
                 because
                 Easter
                 cannot
                 be
                 observed
                 twice
                 in
                 one
                 year
                 .
              
               
                 3.
                 
                 It
                 followeth
                 hence
                 ,
                 That
                 the
                 Feast
                 of
                 Easter
                 can
                 never
                 happen
                 before
                 the
                 twenty
                 second
                 day
                 of
                 March
                 ,
                 nor
                 after
                 the
                 twenty
                 fifth
                 day
                 of
                 April
                 :
                 For
                 if
                 the
                 first
                 New
                 Moon
                 be
                 upon
                 the
                 eighth
                 of
                 March
                 ,
                 and
                 that
                 the
                 Feast
                 of
                 Easter
                 must
                 be
                 upon
                 the
                 Sunday
                 following
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 ;
                 it
                 is
                 plain
                 that
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 must
                 be
                 March
                 21
                 at
                 the
                 soonest
                 :
                 So
                 that
                 supposing
                 the
                 next
                 day
                 to
                 be
                 Sunday
                 ,
                 Easter
                 cannot
                 
                 not
                 be
                 before
                 March
                 the
                 twenty
                 second
                 .
                 And
                 because
                 the
                 fourteenth
                 day
                 of
                 the
                 last
                 Moon
                 falleth
                 upon
                 the
                 eighteenth
                 day
                 of
                 April
                 ,
                 if
                 that
                 day
                 be
                 Saturday
                 ,
                 and
                 the
                 Dominical
                 Letter
                 
                   D
                   ,
                   Easter
                
                 shall
                 be
                 upon
                 the
                 nineteenth
                 day
                 ,
                 but
                 if
                 it
                 be
                 Sunday
                 ,
                 Easter
                 cannot
                 be
                 till
                 the
                 twenty
                 fifth
                 .
              
               
                 4.
                 
                 It
                 followeth
                 hence
                 ,
                 That
                 although
                 there
                 are
                 but
                 19
                 days
                 ,
                 on
                 which
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 can
                 happen
                 ,
                 as
                 there
                 are
                 but
                 19
                 Golden
                 Numbers
                 ,
                 yet
                 there
                 are
                 35
                 days
                 from
                 the
                 twenty
                 second
                 of
                 March
                 to
                 the
                 twenty
                 fifth
                 of
                 April
                 ,
                 on
                 which
                 the
                 Feast
                 of
                 Easter
                 may
                 happen
                 ,
                 because
                 there
                 is
                 no
                 day
                 within
                 those
                 Limits
                 ,
                 but
                 may
                 be
                 the
                 Sunday
                 following
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 .
                 And
                 although
                 the
                 Feast
                 of
                 Easter
                 can
                 never
                 happen
                 upon
                 March
                 22
                 ,
                 but
                 when
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 is
                 upon
                 the
                 twenty
                 first
                 ,
                 and
                 the
                 Sunday
                 Letter
                 D
                 ,
                 nor
                 upon
                 the
                 twenty
                 fifth
                 of
                 April
                 ,
                 but
                 when
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 is
                 upon
                 April
                 18
                 ,
                 and
                 the
                 Dominical
                 Letter
                 C.
                 Yet
                 Easter
                 may
                 fall
                 upon
                 March
                 23
                 ,
                 not
                 only
                 when
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 is
                 upon
                 the
                 twenty
                 second
                 day
                 which
                 is
                 Saturday
                 ,
                 but
                 also
                 if
                 it
                 fall
                 upon
                 the
                 twenty
                 first
                 which
                 is
                 Friday
                 .
                 In
                 like
                 manner
                 Easter
                 may
                 fall
                 upon
                 April
                 24
                 ,
                 not
                 only
                 when
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 is
                 upon
                 the
                 eighteenth
                 day
                 which
                 is
                 Monday
                 ,
                 but
                 also
                 if
                 it
                 happen
                 upon
                 the
                 seventeenth
                 being
                 Sunday
                 .
                 And
                 for
                 the
                 same
                 reason
                 it
                 may
                 fall
                 oftner
                 upon
                 other
                 days
                 that
                 are
                 further
                 distant
                 from
                 the
                 said
                 twenty
                 second
                 of
                 March
                 and
                 twenty
                 fifth
                 of
                 April
                 .
              
               
                 5.
                 
                 It
                 followeth
                 hence
                 ,
                 That
                 the
                 Feast
                 of
                 Easter
                 may
                 be
                 easily
                 found
                 in
                 any
                 Year
                 propounded
                 :
                 For
                 the
                 Golden
                 Number
                 in
                 any
                 Year
                 being
                 given
                 ,
                 if
                 
                 you
                 look
                 the
                 same
                 between
                 the
                 eighth
                 of
                 March
                 and
                 fifth
                 of
                 April
                 both
                 inclusively
                 ,
                 and
                 reckon
                 14
                 days
                 from
                 that
                 day
                 ,
                 which
                 answereth
                 to
                 the
                 Golden
                 Number
                 given
                 ,
                 where
                 your
                 account
                 doth
                 end
                 is
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 :
                 Then
                 consider
                 which
                 is
                 the
                 Dominical
                 Letter
                 for
                 that
                 Year
                 ,
                 and
                 that
                 which
                 followeth
                 next
                 after
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 is
                 Easter
                 day
                 .
                 Example
                 ,
                 In
                 the
                 year
                 1674
                 the
                 Golden
                 Number
                 is
                 3
                 ,
                 and
                 the
                 Sunday
                 Letter
                 D
                 ,
                 which
                 being
                 sought
                 in
                 the
                 Calendar
                 between
                 the
                 aforesaid
                 limits
                 ,
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 is
                 upon
                 April
                 the
                 thirteenth
                 ,
                 and
                 the
                 D
                 next
                 following
                 is
                 April
                 19.
                 
                 And
                 therefore
                 Easter
                 day
                 that
                 Year
                 is
                 April
                 19.
                 
                 Otherwise
                 thus
                 .
              
               
                 
                   In
                   March
                   after
                   the
                   first
                   C
                   ,
                
                 
                   Look
                   the
                   Prime
                   wherever
                   it
                   be
                   ,
                
                 
                   The
                   third
                   Sunday
                   after
                   Easter
                   day
                   shall
                   be
                   .
                
                 
                   And
                   if
                   the
                   Prime
                   on
                   Sunday
                   be
                   ,
                
                 
                   Reckon
                   that
                   for
                   one
                   of
                   the
                   Three
                   .
                
              
               
                 6.
                 
                 Thus
                 the
                 Feast
                 of
                 Easter
                 may
                 be
                 found
                 in
                 the
                 Calendar
                 ,
                 and
                 from
                 thence
                 a
                 brief
                 Table
                 shewing
                 the
                 same
                 ,
                 may
                 be
                 extracted
                 in
                 this
                 manner
                 .
                 Write
                 in
                 one
                 Column
                 the
                 several
                 Golden
                 Numbers
                 in
                 the
                 Calendar
                 from
                 the
                 eighth
                 of
                 March
                 to
                 the
                 fifth
                 of
                 April
                 ,
                 in
                 the
                 same
                 order
                 observing
                 the
                 same
                 distance
                 .
                 In
                 the
                 second
                 Column
                 set
                 the
                 Dominical
                 Letters
                 in
                 number
                 35
                 so
                 disposed
                 ,
                 as
                 that
                 no
                 Dominical
                 Letter
                 may
                 stand
                 against
                 the
                 Golden
                 Number
                 16
                 ,
                 but
                 setting
                 the
                 Letter
                 D
                 against
                 the
                 Golden
                 Number
                 5
                 ,
                 write
                 the
                 rest
                 in
                 
                 this
                 order
                 .
                 
                   E
                   ,
                   F
                   ,
                   G
                   ,
                   A
                   ,
                   B
                   ,
                   &c.
                
                 and
                 when
                 you
                 come
                 to
                 the
                 Golden
                 Number
                 8
                 ,
                 set
                 the
                 Letter
                 C
                 ,
                 and
                 there
                 continue
                 the
                 Letters
                 till
                 you
                 come
                 to
                 C
                 again
                 ,
                 because
                 when
                 the
                 Golden
                 Number
                 is
                 16
                 ,
                 which
                 in
                 the
                 Calendar
                 is
                 set
                 to
                 the
                 eighth
                 day
                 of
                 March
                 ,
                 is
                 new
                 Moon
                 ,
                 and
                 the
                 fourteenth
                 day
                 of
                 that
                 Moon
                 doth
                 fall
                 upon
                 the
                 twenty
                 first
                 ,
                 to
                 which
                 the
                 Dominical
                 Letter
                 is
                 C
                 ,
                 upon
                 which
                 the
                 Feast
                 of
                 Easter
                 cannot
                 happen
                 ;
                 and
                 therefore
                 in
                 the
                 third
                 Column
                 containing
                 the
                 day
                 in
                 which
                 the
                 Feast
                 of
                 Easter
                 is
                 to
                 be
                 observed
                 ,
                 is
                 also
                 void
                 .
                 But
                 in
                 the
                 next
                 place
                 immediately
                 following
                 ,
                 to
                 wit
                 ,
                 against
                 the
                 letter
                 D
                 is
                 set
                 March
                 22
                 ,
                 because
                 if
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 shall
                 fall
                 upon
                 the
                 twenty
                 first
                 of
                 March
                 being
                 Saturday
                 ,
                 the
                 next
                 day
                 being
                 Sunday
                 ,
                 shall
                 be
                 the
                 Feast
                 of
                 Easter
                 .
              
               
                 To
                 the
                 Letters
                 following
                 ,
                 
                   E
                   ,
                   F
                   ,
                   G
                   ,
                   A
                   ,
                   B
                   ,
                   &c.
                
                 are
                 set
                 23
                 ,
                 24
                 ,
                 25
                 ,
                 and
                 so
                 orderly
                 to
                 the
                 last
                 of
                 March
                 ,
                 and
                 so
                 forward
                 till
                 you
                 come
                 to
                 the
                 twenty
                 fifth
                 of
                 April
                 ,
                 by
                 which
                 Table
                 thus
                 made
                 ,
                 the
                 Feast
                 of
                 Easter
                 may
                 be
                 found
                 until
                 the
                 Calendar
                 shall
                 be
                 reformed
                 .
              
               
                 For
                 having
                 found
                 the
                 Golden
                 Number
                 in
                 the
                 first
                 Column
                 ,
                 the
                 Dominical
                 Letter
                 for
                 the
                 Year
                 next
                 after
                 it
                 ,
                 doth
                 shew
                 the
                 Feast
                 of
                 Easter
                 ,
                 as
                 in
                 the
                 former
                 Example
                 ,
                 the
                 Golden
                 Number
                 is
                 3
                 and
                 the
                 Dominicall
                 Letter
                 D
                 ,
                 therefore
                 Easter
                 day
                 is
                 upon
                 April
                 19.
                 
                 The
                 other
                 moveable
                 Feasts
                 are
                 thus
                 found
                 .
              
               
                 Advent
                 Sunday
                 is
                 always
                 the
                 nearest
                 Sunday
                 to
                 St.
                 Andrews
                 ,
                 whether
                 before
                 or
                 after
                 .
              
               
               
                 Septuagesima
                 Sunday
                 is
                 Nine
                 Weeks
                 before
                 Easter
                 .
              
               
                 Sexagesima
                 Sunday
                 is
                 Eight
                 Weeks
                 before
                 Easter
                 .
              
               
                 Qainquagesima
                 Sunday
                 is
                 Seven
                 Weeks
                 before
                 Easter
                 .
              
               
                 Quadragesima
                 Sunday
                 is
                 Six
                 Weeks
                 before
                 Easter
                 .
              
               
                 Rogation
                 Sunday
                 is
                 five
                 Weeks
                 after
                 Easter
                 .
              
               
                 Ascension
                 day
                 is
                 Forty
                 Days
                 after
                 Easter
                 .
              
               
                 Whitsunday
                 is
                 Seven
                 Weeks
                 after
                 Easter
                 .
              
               
                 Trinity
                 Sunday
                 is
                 Eight
                 Weeks
                 after
                 Easter
                 .
              
               
                 
                   
                     
                       G.
                       N.
                       
                    
                     
                       D.
                       L.
                       
                    
                     
                       Easter
                       .
                    
                  
                   
                     
                       XVI
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       V
                    
                     
                       D
                    
                     
                       22
                       March
                    
                  
                   
                     
                        
                    
                     
                       E
                    
                     
                       23
                    
                  
                   
                     
                       XIII
                    
                     
                       F
                    
                     
                       24
                    
                  
                   
                     
                       II
                    
                     
                       G
                    
                     
                       25
                    
                  
                   
                     
                        
                    
                     
                       A
                    
                     
                       26
                    
                  
                   
                     
                       X
                    
                     
                       B
                    
                     
                       27
                    
                  
                   
                     
                        
                    
                     
                       C
                    
                     
                       28
                    
                  
                   
                     
                       XVIII
                    
                     
                       D
                    
                     
                       29
                    
                  
                   
                     
                       VII
                    
                     
                       E
                    
                     
                       30
                    
                  
                   
                     
                        
                    
                     
                       F
                    
                     
                       31
                    
                  
                   
                     
                       XV
                    
                     
                       G
                    
                     
                       1
                       April
                    
                  
                   
                     
                       IV
                    
                     
                       A
                    
                     
                       2
                    
                  
                   
                     
                        
                    
                     
                       B
                    
                     
                       3
                    
                  
                   
                     
                       XII
                    
                     
                       C
                    
                     
                       4
                    
                  
                   
                     
                       I
                    
                     
                       D
                    
                     
                       5
                    
                  
                   
                     
                        
                    
                     
                       E
                    
                     
                       6
                    
                  
                   
                     
                       IX
                    
                     
                       F
                    
                     
                       7
                    
                  
                   
                     
                        
                    
                     
                       G
                    
                     
                       8
                    
                  
                   
                     
                       XVII
                    
                     
                       A
                    
                     
                       9
                    
                  
                   
                     
                       VI
                    
                     
                       B
                    
                     
                       10
                    
                  
                   
                     
                        
                    
                     
                       C
                    
                     
                       11
                    
                  
                   
                     
                       XIV
                    
                     
                       D
                    
                     
                       12
                    
                  
                   
                     
                       III
                    
                     
                       E
                    
                     
                       13
                    
                  
                   
                     
                        
                    
                     
                       F
                    
                     
                       14
                    
                  
                   
                     
                       XI
                    
                     
                       G
                    
                     
                       15
                    
                  
                   
                     
                        
                    
                     
                       A
                    
                     
                       16
                    
                  
                   
                     
                       XIX
                    
                     
                       B
                    
                     
                       17
                    
                  
                   
                     
                       VIII
                    
                     
                       C
                    
                     
                       18
                    
                  
                   
                     
                        
                    
                     
                       D
                    
                     
                       19
                    
                  
                   
                     
                        
                    
                     
                       E
                    
                     
                       20
                    
                  
                   
                     
                        
                    
                     
                       F
                    
                     
                       21
                    
                  
                   
                     
                        
                    
                     
                       G
                    
                     
                       22
                    
                  
                   
                     
                        
                    
                     
                       A
                    
                     
                       23
                    
                  
                   
                     
                        
                    
                     
                       B
                    
                     
                       24
                    
                  
                   
                     
                        
                    
                     
                       C
                    
                     
                       25
                    
                  
                
              
            
             
               
               
                 CHAP.
                 IV.
                 
              
               
                 
                   Of
                   the
                   Reformation
                   of
                   the
                   Calendar
                   by
                   Pope
                   Gregory
                   the
                   Thirteenth
                   ;
                   and
                   substituting
                   a
                   Cycle
                   of
                   Epacts
                   in
                   the
                   room
                   of
                   the
                   Golden
                   Number
                   .
                
              
               
                 HItherto
                 we
                 have
                 spoken
                 of
                 the
                 Calendar
                 which
                 is
                 in
                 use
                 with
                 us
                 ,
                 we
                 will
                 now
                 shew
                 you
                 for
                 what
                 reasons
                 it
                 is
                 alter'd
                 in
                 the
                 Church
                 of
                 Rome
                 ,
                 and
                 how
                 the
                 Feast
                 of
                 Easter
                 is
                 by
                 them
                 observed
                 .
              
               
                 The
                 Year
                 by
                 the
                 appointment
                 of
                 
                   Iulius
                   Caesar
                
                 consisting
                 of
                 365
                 days
                 6
                 hours
                 ,
                 whereas
                 the
                 Sun
                 doth
                 finish
                 his
                 course
                 in
                 the
                 Zodiack
                 ,
                 in
                 365
                 days
                 5
                 hours
                 49
                 minutes
                 or
                 thereabouts
                 ,
                 it
                 cometh
                 to
                 pass
                 that
                 in
                 134
                 Years
                 or
                 less
                 ,
                 there
                 is
                 a
                 whole
                 day
                 in
                 the
                 Calendar
                 more
                 than
                 there
                 ought
                 ;
                 in
                 268
                 years
                 2
                 days
                 more
                 ;
                 in
                 4002
                 years
                 3
                 days
                 :
                 and
                 so
                 since
                 Iulius
                 Caesar's
                 time
                 the
                 vernal
                 Equinox
                 hath
                 gone
                 backward
                 13
                 or
                 14
                 days
                 ,
                 namely
                 from
                 the
                 24
                 of
                 March
                 to
                 the
                 tenth
                 .
                 Now
                 because
                 the
                 Equinox
                 was
                 at
                 the
                 time
                 of
                 the
                 Nicene
                 Council
                 upon
                 the
                 twenty
                 first
                 of
                 March
                 ,
                 when
                 the
                 time
                 for
                 the
                 observing
                 of
                 Easter
                 was
                 first
                 universally
                 established
                 ,
                 they
                 thought
                 it
                 sufficient
                 to
                 bring
                 the
                 Equinox
                 back
                 to
                 that
                 time
                 ,
                 by
                 cutting
                 off
                 10
                 days
                 in
                 the
                 Calendar
                 as
                 hath
                 been
                 declared
                 ,
                 and
                 to
                 prevent
                 any
                 anticipation
                 for
                 the
                 time
                 to
                 come
                 ,
                 have
                 appointed
                 ,
                 that
                 the
                 Leap-year
                 shall
                 be
                 thrice
                 omitted
                 in
                 every
                 400
                 Years
                 to
                 come
                 ,
                 and
                 for
                 memory
                 sake
                 ,
                 appointed
                 the
                 first
                 omission
                 to
                 be
                 accounted
                 from
                 the
                 Year
                 1600
                 ,
                 not
                 from
                 1582
                 ,
                 in
                 which
                 the
                 reformation
                 was
                 made
                 ,
                 because
                 it
                 was
                 not
                 only
                 near
                 the
                 time
                 ,
                 in
                 which
                 the
                 emendation
                 was
                 begun
                 ,
                 but
                 also
                 because
                 the
                 Equinox
                 has
                 not
                 fully
                 made
                 an
                 anticipation
                 of
                 10
                 days
                 from
                 the
                 
                 place
                 thereof
                 ,
                 at
                 the
                 time
                 of
                 the
                 Nicene
                 Council
                 ,
                 which
                 was
                 March
                 21.
                 
              
               
                 The
                 Years
                 then
                 1700
                 ,
                 1800
                 ,
                 1900
                 ,
                 which
                 should
                 have
                 been
                 Bissextile
                 Years
                 ,
                 are
                 to
                 he
                 accounted
                 common
                 years
                 ,
                 but
                 the
                 Year
                 2000
                 must
                 be
                 a
                 Bissextile
                 :
                 In
                 like
                 manner
                 the
                 Years
                 2100
                 ,
                 2200
                 ,
                 2300
                 ,
                 shall
                 be
                 common
                 years
                 ,
                 and
                 the
                 Year
                 2400
                 Bissextile
                 ,
                 and
                 so
                 forward
                 .
              
               
                 2.
                 
                 Again
                 ,
                 because
                 it
                 was
                 supposed
                 that
                 the
                 Cycle
                 of
                 the
                 Moon
                 ,
                 or
                 Golden
                 Number
                 was
                 so
                 fixed
                 ,
                 that
                 the
                 new
                 and
                 full
                 Moons
                 would
                 in
                 every
                 19
                 years
                 return
                 to
                 the
                 same
                 days
                 again
                 ;
                 whereas
                 their
                 not
                 returning
                 the
                 same
                 hours
                 ,
                 but
                 making
                 an
                 anticipation
                 of
                 one
                 hour
                 27
                 minutes
                 or
                 thereabouts
                 ,
                 it
                 must
                 needs
                 be
                 that
                 in
                 17
                 Cycles
                 or
                 little
                 more
                 than
                 300
                 Years
                 ,
                 there
                 would
                 be
                 an
                 anticipation
                 of
                 a
                 whole
                 day
                 .
                 And
                 hence
                 it
                 is
                 evident
                 that
                 in
                 1300
                 Years
                 since
                 the
                 Nicene
                 Council
                 ,
                 the
                 New
                 and
                 Full
                 Moons
                 do
                 happen
                 more
                 than
                 4
                 days
                 sooner
                 than
                 the
                 Cycle
                 of
                 the
                 Moon
                 or
                 Golden
                 Number
                 doth
                 demonstrate
                 :
                 Whence
                 also
                 it
                 comes
                 to
                 pass
                 ,
                 that
                 the
                 fourteenth
                 day
                 of
                 the
                 Moon
                 by
                 the
                 Cycle
                 is
                 in
                 truth
                 the
                 eighteenth
                 day
                 ,
                 and
                 so
                 the
                 Feast
                 of
                 Easter
                 should
                 be
                 observed
                 not
                 from
                 the
                 fifteenth
                 day
                 of
                 the
                 Moon
                 to
                 the
                 twenty
                 first
                 ,
                 but
                 from
                 the
                 nineteenth
                 to
                 the
                 twenty
                 fifth
                 .
              
               
                 3.
                 
                 That
                 the
                 Moon
                 therefore
                 being
                 once
                 brought
                 into
                 order
                 ,
                 might
                 not
                 make
                 any
                 anticipation
                 for
                 the
                 time
                 to
                 come
                 ,
                 it
                 is
                 appointed
                 that
                 a
                 Cycle
                 of
                 30
                 Epacts
                 should
                 be
                 placed
                 in
                 the
                 Calendar
                 instead
                 of
                 the
                 Golden
                 Number
                 ,
                 answering
                 to
                 every
                 day
                 in
                 the
                 Year
                 ;
                 to
                 shew
                 the
                 New
                 Moons
                 in
                 these
                 days
                 ,
                 not
                 only
                 for
                 300
                 Years
                 or
                 thereabouts
                 ,
                 but
                 that
                 there
                 might
                 be
                 new
                 Epacts
                 without
                 
                 altering
                 the
                 Calendar
                 ,
                 to
                 perform
                 the
                 same
                 thing
                 upon
                 other
                 days
                 as
                 need
                 shall
                 require
                 .
              
               
                 4.
                 
                 For
                 the
                 better
                 understanding
                 whereof
                 ,
                 to
                 the
                 Calendar
                 in
                 use
                 with
                 us
                 ,
                 we
                 have
                 annexed
                 the
                 Gregorian
                 Calendar
                 also
                 :
                 In
                 the
                 first
                 Column
                 whereof
                 you
                 have
                 30
                 numbers
                 from
                 1
                 to
                 30
                 ,
                 save
                 only
                 that
                 in
                 the
                 place
                 of
                 30
                 you
                 have
                 this
                 Asterisk
                 *
                 ,
                 But
                 they
                 begin
                 with
                 the
                 Calends
                 of
                 Ianuary
                 ,
                 and
                 we
                 continued
                 and
                 repeated
                 after
                 a
                 Retrograde
                 order
                 in
                 this
                 manner
                 ,
                 *
                 29
                 ,
                 28
                 ,
                 27
                 ,
                 &c.
                 and
                 that
                 for
                 this
                 cause
                 especially
                 ,
                 that
                 the
                 number
                 being
                 given
                 which
                 sheweth
                 the
                 New
                 Moons
                 in
                 every
                 Month
                 for
                 one
                 Year
                 ,
                 you
                 might
                 by
                 numbring
                 11
                 upwards
                 exclusively
                 find
                 the
                 number
                 which
                 will
                 shew
                 the
                 New
                 Moons
                 the
                 Year
                 following
                 ,
                 to
                 wit
                 ,
                 the
                 Number
                 which
                 falleth
                 in
                 the
                 eleventh
                 place
                 .
              
               
                 5.
                 
                 And
                 these
                 Numbers
                 are
                 called
                 Epacts
                 ,
                 because
                 they
                 do
                 in
                 order
                 shew
                 those
                 11
                 days
                 ,
                 which
                 are
                 yearly
                 to
                 be
                 added
                 to
                 the
                 Lunar
                 Year
                 consisting
                 of
                 354
                 days
                 ,
                 that
                 it
                 may
                 be
                 in
                 conformity
                 with
                 the
                 Solar
                 Year
                 consisting
                 of
                 365
                 days
                 .
                 To
                 this
                 purpose
                 ,
                 as
                 hath
                 been
                 said
                 concerning
                 the
                 Golden
                 Number
                 ,
                 these
                 Epacts
                 being
                 repeated
                 12
                 times
                 ,
                 and
                 ending
                 upon
                 the
                 twentieth
                 day
                 of
                 December
                 ,
                 the
                 same
                 Numbers
                 must
                 be
                 added
                 to
                 the
                 11
                 remaining
                 days
                 ,
                 which
                 were
                 added
                 to
                 the
                 first
                 11
                 days
                 in
                 the
                 Month
                 of
                 Ianuary
                 .
              
               
                 6.
                 
                 And
                 because
                 12
                 times
                 30
                 do
                 make
                 360
                 ,
                 whereas
                 from
                 the
                 first
                 of
                 Ianuary
                 to
                 the
                 twentieth
                 of
                 December
                 inclusively
                 ,
                 there
                 are
                 but
                 354
                 days
                 ,
                 you
                 must
                 know
                 that
                 to
                 gain
                 the
                 other
                 six
                 days
                 ,
                 the
                 numbers
                 25
                 and
                 24
                 are
                 in
                 every
                 other
                 Month
                 both
                 placed
                 against
                 one
                 day
                 ,
                 namely
                 ,
                 to
                 
                   February
                   5
                   ,
                   April
                   5
                   ,
                   Iune
                   3
                   ,
                   August
                   1
                   ,
                   September
                
                 29
                 ,
                 and
                 
                 November
                 27.
                 
                 But
                 why
                 these
                 two
                 Numbers
                 are
                 chosen
                 rather
                 then
                 any
                 other
                 ,
                 and
                 why
                 in
                 these
                 6
                 Months
                 the
                 number
                 25
                 is
                 sometimes
                 writ
                 to
                 XVI
                 ,
                 sometimes
                 to
                 XXV
                 in
                 a
                 common
                 character
                 ,
                 and
                 why
                 the
                 number
                 19
                 is
                 set
                 to
                 the
                 last
                 day
                 of
                 December
                 in
                 a
                 common
                 Character
                 ,
                 shall
                 be
                 declared
                 hereafter
                 .
              
               
                 7.
                 
                 Here
                 only
                 note
                 that
                 this
                 Asterisk
                 *
                 is
                 set
                 instead
                 of
                 the
                 Epact
                 30
                 ,
                 because
                 the
                 Epact
                 shewing
                 the
                 Number
                 of
                 days
                 which
                 do
                 remain
                 after
                 the
                 Lunation
                 in
                 the
                 Month
                 of
                 December
                 ,
                 it
                 may
                 sometimes
                 fall
                 out
                 that
                 2
                 Lunations
                 may
                 so
                 end
                 ,
                 that
                 the
                 one
                 may
                 require
                 30
                 for
                 the
                 Epact
                 ,
                 and
                 the
                 other
                 0
                 ,
                 which
                 would
                 ,
                 if
                 both
                 were
                 written
                 ,
                 cause
                 some
                 inconveniences
                 ,
                 and
                 therefore
                 this
                 *
                 Asterisk
                 is
                 there
                 set
                 ,
                 that
                 it
                 might
                 indifferently
                 serve
                 to
                 both
                 .
                 And
                 the
                 Epact
                 29
                 is
                 therefore
                 set
                 to
                 the
                 second
                 day
                 of
                 Ianuary
                 ,
                 because
                 after
                 the
                 compleat
                 Lunation
                 in
                 the
                 second
                 of
                 December
                 there
                 are
                 29
                 days
                 ,
                 and
                 for
                 the
                 like
                 reason
                 the
                 Epact
                 28
                 is
                 set
                 against
                 the
                 third
                 of
                 Ianuary
                 ,
                 because
                 after
                 the
                 compleat
                 Lunation
                 in
                 the
                 third
                 of
                 December
                 there
                 are
                 then
                 28
                 days
                 over
                 ,
                 and
                 so
                 the
                 rest
                 in
                 order
                 till
                 you
                 come
                 to
                 the
                 thirtieth
                 of
                 Ianuary
                 ,
                 where
                 you
                 find
                 the
                 Epact
                 1.
                 because
                 after
                 the
                 compleat
                 Lunation
                 on
                 the
                 thirtieth
                 day
                 there
                 is
                 only
                 one
                 day
                 over
                 .
              
               
                 8.
                 
                 And
                 besides
                 the
                 shewing
                 of
                 the
                 New
                 Moons
                 in
                 every
                 Month
                 ,
                 which
                 is
                 and
                 may
                 be
                 done
                 by
                 the
                 Golden
                 Number
                 ,
                 the
                 Epacts
                 have
                 this
                 advantage
                 ,
                 that
                 they
                 may
                 be
                 perpetual
                 and
                 keep
                 the
                 same
                 place
                 in
                 the
                 Calendar
                 in
                 all
                 future
                 ages
                 ,
                 which
                 can
                 hardly
                 be
                 effected
                 with
                 the
                 Golden
                 Number
                 ,
                 for
                 in
                 little
                 more
                 then
                 700
                 years
                 ,
                 the
                 New
                 Moons
                 do
                 make
                 an
                 anticipation
                 of
                 one
                 day
                 ,
                 and
                 then
                 it
                 
                 will
                 be
                 necessary
                 to
                 set
                 the
                 Golden
                 Number
                 one
                 degree
                 backward
                 ,
                 and
                 so
                 the
                 Golden
                 Number
                 which
                 at
                 the
                 time
                 of
                 the
                 Nicene
                 Council
                 was
                 set
                 to
                 the
                 first
                 of
                 Ianuary
                 ,
                 should
                 in
                 300
                 years
                 be
                 set
                 to
                 the
                 last
                 of
                 December
                 ,
                 and
                 so
                 of
                 the
                 rest
                 ,
                 but
                 the
                 Epacts
                 being
                 once
                 fixed
                 shall
                 not
                 need
                 any
                 such
                 retraction
                 or
                 commutation
                 .
                 For
                 as
                 often
                 as
                 the
                 New
                 Moons
                 do
                 change
                 their
                 day
                 either
                 by
                 Anticipation
                 or
                 by
                 Suppression
                 of
                 the
                 Bissextile
                 year
                 ,
                 you
                 shall
                 not
                 need
                 to
                 do
                 any
                 more
                 than
                 to
                 take
                 another
                 rank
                 of
                 19
                 Epacts
                 ,
                 insteed
                 of
                 those
                 which
                 were
                 before
                 in
                 use
                 .
                 For
                 instance
                 ,
                 the
                 Epacts
                 which
                 are
                 and
                 have
                 been
                 in
                 use
                 in
                 the
                 Church
                 of
                 Rome
                 since
                 the
                 year
                 of
                 reformation
                 1582
                 ,
                 and
                 will
                 continue
                 till
                 the
                 year
                 1700
                 ,
                 are
                 these
                 10
                 following
                 1.
                 12.
                 23.
                 4.
                 15.
                 26.
                 7.
                 18.
                 29.
                 10.
                 21.
                 2.
                 13.
                 24.
                 5.
                 16.
                 27.
                 8.
                 19.
                 
                 And
                 from
                 the
                 year
                 1700
                 the
                 Epacts
                 which
                 will
                 be
                 in
                 use
                 are
                 these
                 .
                 *
                 11.
                 22.
                 3.
                 14.
                 25.
                 6.
                 17.
                 28.
                 9.
                 20.
                 1.
                 12.
                 23.
                 4.
                 15.
                 26.
                 7.
                 18.
                 and
                 shall
                 continue
                 not
                 only
                 to
                 the
                 year
                 1800
                 ,
                 but
                 from
                 thence
                 until
                 the
                 year
                 1900
                 also
                 ;
                 and
                 although
                 in
                 the
                 year
                 1800
                 the
                 Bissextile
                 is
                 to
                 be
                 suppressed
                 ,
                 yet
                 is
                 there
                 a
                 compensation
                 for
                 that
                 Suppression
                 ,
                 by
                 the
                 Moons
                 Anticipation
                 .
                 To
                 make
                 this
                 a
                 little
                 more
                 plain
                 ,
                 the
                 motion
                 of
                 the
                 Moon
                 ,
                 which
                 doth
                 occasion
                 the
                 change
                 of
                 the
                 Epact
                 ,
                 must
                 be
                 more
                 fully
                 considered
                 .
              
            
             
               
               
                 CHAP.
                 V.
                 
              
               
                 
                   Of
                   the
                   Moons
                   mean
                   Motion
                   ,
                   and
                   how
                   the
                   Anticipation
                   of
                   the
                   New
                   Moons
                   may
                   be
                   discovered
                   by
                   the
                   Epacts
                   .
                
              
               
                 THe
                 Moon
                 according
                 to
                 her
                 middle
                 motion
                 doth
                 finish
                 her
                 course
                 in
                 the
                 Zodiack
                 in
                 29
                 days
                 ,
                 12
                 hours
                 44
                 minutes
                 ,
                 three
                 seconds
                 or
                 thereabout
                 ,
                 and
                 therefore
                 a
                 common
                 Lunar
                 year
                 doth
                 consist
                 of
                 354
                 days
                 ,
                 8
                 hours
                 ,
                 48
                 minutes
                 ,
                 38
                 seconds
                 and
                 some
                 few
                 thirds
                 ,
                 but
                 an
                 Embolismical
                 year
                 doth
                 consist
                 of
                 383
                 days
                 ,
                 21
                 hours
                 ,
                 32
                 minutes
                 ,
                 41
                 seconds
                 and
                 somewhat
                 more
                 ;
                 and
                 therefore
                 in
                 19
                 years
                 it
                 doth
                 exceed
                 the
                 motion
                 of
                 the
                 Sun
                 1
                 hour
                 ,
                 27
                 minutes
                 ,
                 33
                 seconds
                 feré
                 .
              
               
                 2.
                 
                 Hence
                 it
                 cometh
                 to
                 pass
                 ,
                 that
                 although
                 the
                 New
                 Moons
                 do
                 after
                 19
                 years
                 return
                 to
                 the
                 same
                 days
                 ;
                 yet
                 is
                 there
                 an
                 Anticipation
                 of
                 1
                 hour
                 ,
                 27
                 minutes
                 ,
                 33
                 seconds
                 .
                 And
                 in
                 twice
                 19
                 years
                 ,
                 that
                 is
                 ,
                 in
                 38
                 years
                 ,
                 there
                 is
                 an
                 Anticipation
                 of
                 2
                 hours
                 ,
                 55
                 minutes
                 ,
                 6
                 seconds
                 ,
                 and
                 after
                 312
                 years
                 and
                 a
                 half
                 ,
                 there
                 is
                 an
                 Anticipation
                 of
                 one
                 whole
                 day
                 and
                 some
                 few
                 Minutes
                 .
                 And
                 therefore
                 after
                 312
                 years
                 no
                 new
                 Moon
                 can
                 happen
                 upon
                 the
                 same
                 day
                 it
                 did
                 19
                 years
                 before
                 ,
                 but
                 a
                 day
                 sooner
                 .
                 Hence
                 it
                 comes
                 to
                 pass
                 that
                 in
                 the
                 Julian
                 Calendar
                 ,
                 in
                 which
                 no
                 regard
                 is
                 had
                 to
                 this
                 Anticipation
                 ,
                 the
                 New
                 Moons
                 found
                 out
                 by
                 the
                 Golden
                 Number
                 must
                 needs
                 be
                 erroneous
                 ,
                 and
                 from
                 the
                 time
                 of
                 the
                 Nicene
                 Council
                 4
                 days
                 after
                 the
                 New
                 Moons
                 by
                 a
                 regular
                 Computation
                 .
              
               
                 3.
                 
                 And
                 hence
                 it
                 follows
                 also
                 ,
                 that
                 if
                 the
                 Golden
                 Number
                 ,
                 after
                 312
                 were
                 upon
                 due
                 consideration
                 
                 removed
                 a
                 day
                 forwarder
                 or
                 nearer
                 the
                 beginning
                 of
                 the
                 Months
                 ,
                 they
                 would
                 shew
                 the
                 New
                 Moons
                 for
                 312
                 years
                 to
                 come
                 .
                 And
                 being
                 again
                 removed
                 after
                 those
                 years
                 ,
                 a
                 day
                 more
                 would
                 by
                 the
                 like
                 reason
                 do
                 the
                 same
                 again
                 .
                 But
                 it
                 was
                 thought
                 more
                 convenient
                 so
                 to
                 dispose
                 30
                 Epacts
                 ,
                 that
                 they
                 keeping
                 their
                 constant
                 places
                 ,
                 19
                 of
                 them
                 should
                 perform
                 the
                 work
                 of
                 the
                 Golden
                 Number
                 ,
                 until
                 by
                 this
                 means
                 there
                 should
                 be
                 an
                 Anticipation
                 of
                 one
                 day
                 .
                 And
                 when
                 such
                 an
                 Anticipation
                 should
                 happen
                 ,
                 those
                 19
                 Epacts
                 being
                 let
                 alone
                 ,
                 other
                 19
                 should
                 be
                 used
                 ,
                 which
                 do
                 belong
                 to
                 the
                 preceding
                 day
                 ,
                 without
                 making
                 any
                 alteration
                 in
                 the
                 Calendar
                 .
              
               
                 4.
                 
                 And
                 if
                 this
                 Anticipation
                 would
                 do
                 the
                 whole
                 work
                 ,
                 nothing
                 were
                 more
                 plain
                 ,
                 then
                 to
                 make
                 that
                 commutation
                 of
                 the
                 19
                 Epact
                 once
                 in
                 312
                 years
                 :
                 but
                 because
                 the
                 detraction
                 of
                 the
                 Bissextile
                 days
                 doth
                 variously
                 interpose
                 and
                 cause
                 the
                 19
                 Epacts
                 sometimes
                 to
                 be
                 changed
                 into
                 these
                 that
                 do
                 precede
                 ,
                 sometimes
                 into
                 these
                 that
                 follow
                 ,
                 sometimes
                 into
                 neither
                 ,
                 but
                 to
                 continue
                 still
                 the
                 same
                 ;
                 therefore
                 some
                 Tables
                 are
                 to
                 be
                 made
                 ,
                 by
                 which
                 we
                 may
                 know
                 ,
                 when
                 the
                 commutation
                 was
                 to
                 be
                 made
                 and
                 into
                 what
                 Epacts
                 .
              
               
                 4.
                 
                 First
                 therefore
                 there
                 was
                 made
                 a
                 Table
                 called
                 
                   Tabula
                   Epactarum
                   Expansa
                
                 ,
                 in
                 this
                 manner
                 .
              
               
                 First
                 on
                 the
                 top
                 were
                 placed
                 the
                 19
                 Golden
                 Numbers
                 in
                 order
                 ,
                 beginning
                 with
                 the
                 Number
                 3
                 ,
                 which
                 in
                 the
                 old
                 Calendar
                 is
                 placed
                 against
                 the
                 Calends
                 of
                 Ianuary
                 ,
                 and
                 under
                 every
                 one
                 of
                 these
                 Golden
                 Numbers
                 there
                 are
                 placed
                 30
                 Epacts
                 all
                 constituted
                 from
                 the
                 lowest
                 number
                 in
                 the
                 first
                 rank
                 in
                 which
                 the
                 Epact
                 is
                 1
                 ,
                 and
                 in
                 that
                 first
                 rank
                 the
                 Golden
                 Number
                 is
                 3
                 ,
                 the
                 rest
                 from
                 
                 thence
                 towards
                 the
                 right
                 Hand
                 are
                 made
                 by
                 the
                 constant
                 addition
                 of
                 it
                 ,
                 and
                 the
                 casting
                 away
                 of
                 30
                 ,
                 as
                 often
                 as
                 they
                 shall
                 exceed
                 that
                 number
                 ,
                 only
                 when
                 you
                 come
                 to
                 the
                 27
                 ,
                 the
                 Epact
                 under
                 the
                 Golden
                 Number
                 19
                 ,
                 there
                 must
                 be
                 added
                 12
                 instead
                 of
                 11
                 ,
                 that
                 so
                 the
                 Epact
                 following
                 may
                 be
                 9
                 not
                 8
                 ,
                 for
                 the
                 Reasons
                 already
                 given
                 in
                 this
                 Discourse
                 concerning
                 the
                 Golden
                 Number
                 and
                 Embolismical
                 years
                 .
                 And
                 this
                 rank
                 being
                 thus
                 made
                 ,
                 the
                 other
                 Epacts
                 are
                 disposed
                 in
                 their
                 natural
                 order
                 ascending
                 upwards
                 ,
                 and
                 the
                 number
                 once
                 again
                 resumed
                 after
                 the
                 Epact
                 30
                 or
                 rather
                 this
                 Asterisk
                 *
                 set
                 in
                 the
                 place
                 thereof
                 :
                 only
                 observe
                 that
                 under
                 the
                 Golden
                 Number
                 12.
                 13.
                 14.
                 15.
                 16.
                 17.
                 18.
                 19.
                 in
                 the
                 place
                 of
                 XX
                 there
                 is
                 yet
                 25
                 in
                 the
                 common
                 Character
                 .
                 And
                 to
                 the
                 Epacts
                 under
                 the
                 Golden
                 Number
                 19
                 ,
                 12
                 must
                 still
                 be
                 added
                 to
                 make
                 that
                 Epact
                 under
                 the
                 Golden
                 Number
                 1.
                 
                 As
                 was
                 said
                 before
                 concerning
                 the
                 lowest
                 Rank
                 .
              
               
                 5.
                 
                 And
                 on
                 the
                 left
                 hand
                 of
                 these
                 Epacts
                 before
                 those
                 under
                 the
                 Golden
                 Number
                 3.
                 are
                 set
                 30
                 Letters
                 of
                 the
                 Alphabet
                 ,
                 19
                 in
                 a
                 small
                 Character
                 ,
                 and
                 11
                 in
                 a
                 great
                 ,
                 in
                 which
                 some
                 are
                 passed
                 by
                 ,
                 for
                 no
                 other
                 reason
                 save
                 only
                 this
                 ,
                 that
                 their
                 similitude
                 with
                 some
                 of
                 the
                 small
                 Letters
                 ,
                 should
                 not
                 occasion
                 any
                 mistake
                 in
                 their
                 use
                 ,
                 which
                 shall
                 be
                 shewed
                 in
                 its
                 place
                 .
              
               
                 6.
                 
                 Besides
                 this
                 Table
                 there
                 was
                 another
                 Table
                 made
                 which
                 is
                 called
                 
                   Tabula
                   AEquationis
                   Epactarum
                
                 ,
                 in
                 which
                 there
                 is
                 a
                 series
                 of
                 years
                 ,
                 in
                 which
                 the
                 Moon
                 ,
                 by
                 reason
                 of
                 her
                 mentioned
                 anticipation
                 doth
                 need
                 AEquation
                 ,
                 and
                 in
                 which
                 the
                 number
                 of
                 Epacts
                 signed
                 with
                 the
                 letters
                 of
                 the
                 Alphabet
                 ,
                 are
                 to
                 be
                 changed
                 ;
                 being
                 otherwise
                 AEquated
                 
                 where
                 it
                 needeth
                 ,
                 by
                 the
                 suppression
                 of
                 the
                 Bissextile
                 days
                 .
              
               
                 7.
                 
                 But
                 it
                 supposeth
                 ,
                 that
                 it
                 was
                 convenient
                 to
                 suppress
                 the
                 Bissextiles
                 once
                 only
                 in
                 100
                 years
                 ;
                 and
                 the
                 Moon
                 to
                 be
                 aequated
                 ,
                 or
                 as
                 far
                 as
                 concerns
                 her self
                 ,
                 the
                 rank
                 of
                 Epacts
                 to
                 be
                 changed
                 ,
                 once
                 only
                 in
                 300
                 years
                 ,
                 and
                 the
                 12
                 years
                 and
                 a
                 half
                 more
                 ,
                 to
                 be
                 referred
                 till
                 after
                 the
                 years
                 2400
                 ,
                 they
                 do
                 amount
                 unto
                 100
                 years
                 ,
                 and
                 then
                 an
                 aequation
                 to
                 be
                 made
                 :
                 but
                 then
                 it
                 must
                 be
                 made
                 by
                 reason
                 of
                 the
                 interposing
                 this
                 hundred
                 not
                 in
                 the
                 three
                 hundredth
                 but
                 the
                 hundredth
                 year
                 .
                 Moreover
                 this
                 aequation
                 is
                 to
                 be
                 made
                 as
                 in
                 referece
                 to
                 the
                 Moon
                 only
                 ,
                 because
                 as
                 the
                 suppression
                 of
                 the
                 Bissextiles
                 intervene
                 ,
                 the
                 order
                 of
                 changing
                 the
                 ranks
                 of
                 Epacts
                 is
                 varied
                 ,
                 as
                 shall
                 be
                 shewed
                 hereafter
                 .
              
               
                 8.
                 
                 Again
                 this
                 Table
                 supposeth
                 ,
                 that
                 seeing
                 the
                 New
                 Moon
                 at
                 the
                 time
                 of
                 the
                 Nicene
                 Council
                 was
                 upon
                 the
                 Calends
                 of
                 Ianuary
                 ,
                 the
                 golden
                 Number
                 3
                 being
                 there
                 placed
                 ,
                 that
                 it
                 would
                 have
                 been
                 the
                 same
                 if
                 the
                 Epact
                 *
                 had
                 been
                 set
                 to
                 the
                 same
                 Calends
                 ,
                 that
                 is
                 if
                 the
                 Epacts
                 had
                 been
                 then
                 in
                 use
                 .
                 And
                 therefore
                 at
                 that
                 time
                 the
                 highest
                 or
                 last
                 rank
                 of
                 Epacts
                 was
                 to
                 be
                 used
                 ,
                 whose
                 Index
                 is
                 P
                 ,
                 and
                 then
                 after
                 300
                 years
                 ,
                 the
                 lowest
                 or
                 first
                 rank
                 should
                 succeed
                 ,
                 whose
                 Index
                 is
                 a
                 ,
                 (
                 for
                 the
                 letters
                 return
                 in
                 a
                 Circle
                 )
                 and
                 after
                 300
                 years
                 more
                 ,
                 the
                 following
                 rank
                 whose
                 Index
                 is
                 b
                 and
                 so
                 forward
                 ;
                 but
                 that
                 it
                 is
                 conceived
                 ,
                 that
                 the
                 New
                 Moon
                 in
                 the
                 Calends
                 of
                 Ianuary
                 ,
                 is
                 more
                 agreeable
                 to
                 the
                 year
                 of
                 Christ
                 500
                 ,
                 than
                 the
                 time
                 of
                 the
                 Nicene
                 Councel
                 ;
                 and
                 therefore
                 as
                 if
                 the
                 rank
                 of
                 Epacts
                 under
                 the
                 letter
                 l
                 were
                 sutable
                 to
                 the
                 year
                 500
                 ,
                 it
                 seemed
                 
                 good
                 to
                 make
                 use
                 of
                 that
                 rank
                 under
                 the
                 letter
                 a
                 in
                 the
                 year
                 of
                 Christ
                 800
                 ,
                 and
                 those
                 under
                 the
                 letter
                 b
                 ,
                 in
                 the
                 year
                 1100
                 ,
                 and
                 those
                 under
                 the
                 letter
                 e
                 in
                 the
                 year
                 1400.
                 
              
               
                 9.
                 
                 Which
                 being
                 granted
                 ,
                 because
                 in
                 the
                 year
                 1582
                 ,
                 ten
                 days
                 were
                 cut
                 off
                 from
                 the
                 Calendar
                 ,
                 we
                 must
                 run
                 backward
                 ,
                 or
                 in
                 an
                 inverted
                 order
                 count
                 10
                 series
                 ,
                 designed
                 ,
                 suppose
                 ,
                 by
                 the
                 letters
                 
                   b.
                   a.
                   P.
                   N.
                   M.
                   H.
                   G.
                   F.
                   E.
                   D.
                
                 so
                 that
                 from
                 the
                 year
                 1582
                 the
                 series
                 of
                 Epacts
                 whose
                 literal
                 Index
                 is
                 D
                 ,
                 is
                 to
                 be
                 used
                 ,
                 and
                 this
                 is
                 that
                 rank
                 of
                 Epacts
                 which
                 is
                 now
                 used
                 in
                 the
                 Church
                 of
                 Rome
                 .
              
               
                 10.
                 
                 And
                 therefore
                 as
                 if
                 this
                 Table
                 had
                 its
                 beginning
                 from
                 that
                 year
                 ;
                 the
                 first
                 number
                 in
                 the
                 second
                 column
                 is
                 1582
                 ,
                 and
                 then
                 in
                 order
                 under
                 it
                 .
                 1600.
                 1700.
                 1800.
                 1900.
                 2000.
                 
                 &c.
                 And
                 in
                 the
                 third
                 Column
                 every
                 fourth
                 hundred
                 year
                 is
                 marked
                 for
                 a
                 Bissextile
                 ,
                 that
                 is
                 ,
                 1600.
                 2400.
                 2800
                 ,
                 &c.
                 and
                 in
                 the
                 fourth
                 Column
                 to
                 every
                 three
                 hundreth
                 ▪
                 Year
                 is
                 set
                 this
                 Character
                 C
                 ,
                 to
                 shew
                 in
                 what
                 year
                 the
                 Moon
                 by
                 her
                 Anticipation
                 of
                 one
                 day
                 ,
                 doth
                 need
                 aequation
                 ;
                 but
                 in
                 the
                 year
                 1800
                 the
                 double
                 character
                 is
                 set
                 CC
                 ,
                 to
                 signify
                 that
                 then
                 another
                 hundred
                 years
                 are
                 gotten
                 by
                 the
                 12
                 years
                 and
                 a
                 half
                 reserved
                 ,
                 besides
                 and
                 above
                 the
                 other
                 300
                 years
                 ;
                 and
                 this
                 character
                 is
                 also
                 set
                 to
                 the
                 years
                 4300.
                 6800
                 ,
                 and
                 for
                 the
                 same
                 reason
                 .
              
               
                 But
                 in
                 the
                 first
                 Column
                 ,
                 or
                 on
                 the
                 left
                 hand
                 of
                 these
                 years
                 are
                 placed
                 the
                 Letters
                 or
                 Indices
                 of
                 those
                 ranks
                 of
                 Epacts
                 in
                 the
                 former
                 Table
                 ,
                 which
                 are
                 to
                 be
                 used
                 in
                 those
                 years
                 and
                 when
                 the
                 Letters
                 are
                 charged
                 .
                 Thus
                 against
                 the
                 year
                 1600
                 the
                 Letter
                 D
                 is
                 continued
                 ,
                 to
                 shew
                 that
                 from
                 that
                 
                 year
                 ,
                 to
                 the
                 year
                 1700
                 the
                 rank
                 of
                 Epacts
                 is
                 still
                 to
                 be
                 used
                 ,
                 which
                 do
                 belong
                 to
                 that
                 Letter
                 .
                 And
                 for
                 as
                 much
                 as
                 the
                 Letter
                 C
                 is
                 set
                 to
                 the
                 year
                 1700
                 ,
                 it
                 sheweth
                 that
                 that
                 rank
                 of
                 Epacts
                 is
                 then
                 to
                 be
                 used
                 ,
                 which
                 do
                 belong
                 thereto
                 ,
                 and
                 so
                 of
                 the
                 rest
                 .
              
               
                 11.
                 
                 The
                 reason
                 why
                 these
                 Letters
                 in
                 the
                 first
                 Column
                 are
                 sometimes
                 changed
                 in
                 100
                 years
                 ,
                 sometimes
                 in
                 200
                 ,
                 sometimes
                 not
                 in
                 less
                 then
                 300
                 Years
                 ,
                 and
                 that
                 they
                 are
                 sometimes
                 taken
                 forward
                 ,
                 sometimes
                 backward
                 ,
                 according
                 to
                 the
                 order
                 of
                 the
                 Alphabet
                 ,
                 is
                 because
                 the
                 suppression
                 of
                 the
                 Bissextiles
                 do
                 intervene
                 with
                 the
                 lunar
                 aequation
                 :
                 for
                 if
                 the
                 Bissextile
                 were
                 only
                 to
                 be
                 suppressed
                 ,
                 in
                 these
                 300
                 or
                 sometimes
                 400
                 years
                 ,
                 in
                 which
                 the
                 Moon
                 needeth
                 aequation
                 ,
                 the
                 rank
                 of
                 Epacts
                 in
                 that
                 case
                 would
                 need
                 no
                 commutation
                 ,
                 but
                 would
                 continue
                 the
                 same
                 for
                 ever
                 ;
                 and
                 the
                 golden
                 Number
                 would
                 have
                 been
                 sufficient
                 ,
                 if
                 the
                 suppression
                 of
                 the
                 Bissextile
                 ,
                 and
                 anticipation
                 of
                 the
                 Moon
                 ,
                 did
                 by
                 a
                 perpetual
                 compensation
                 cause
                 the
                 new
                 Moons
                 still
                 to
                 return
                 to
                 the
                 same
                 days
                 :
                 but
                 because
                 the
                 Bissextile
                 is
                 ofttimes
                 suppressed
                 ,
                 when
                 the
                 Moon
                 hath
                 no
                 aequation
                 ,
                 the
                 Moon
                 hath
                 sometimes
                 an
                 aequation
                 when
                 the
                 Bissextile
                 is
                 not
                 suppressed
                 ,
                 sometimes
                 also
                 both
                 are
                 to
                 be
                 done
                 and
                 sometimes
                 neither
                 ;
                 all
                 which
                 varieties
                 may
                 yet
                 be
                 reduced
                 to
                 these
                 three
                 Rules
                 .
              
               
                 1.
                 
                 As
                 often
                 as
                 the
                 Bissextile
                 is
                 suppressed
                 without
                 any
                 aequation
                 of
                 the
                 Moon
                 ,
                 then
                 the
                 letter
                 which
                 served
                 to
                 that
                 time
                 shall
                 be
                 changed
                 to
                 the
                 next
                 below
                 it
                 contrary
                 to
                 the
                 order
                 of
                 the
                 Alphabet
                 .
                 And
                 the
                 new
                 Moons
                 shall
                 be
                 removed
                 
                 one
                 day
                 towards
                 the
                 end
                 of
                 the
                 Year
                 .
              
               
                 2.
                 
                 As
                 often
                 as
                 the
                 Moon
                 needeth
                 aequation
                 ,
                 without
                 suppression
                 of
                 the
                 Bissextile
                 ,
                 then
                 the
                 Letter
                 which
                 was
                 in
                 use
                 to
                 that
                 time
                 shall
                 be
                 changed
                 to
                 the
                 next
                 above
                 it
                 according
                 to
                 the
                 order
                 of
                 the
                 Alphabet
                 ,
                 that
                 the
                 New
                 Moons
                 may
                 again
                 return
                 one
                 day
                 towards
                 the
                 beginning
                 of
                 the
                 year
                 .
              
               
                 3.
                 
                 As
                 often
                 as
                 there
                 is
                 a
                 Suppression
                 and
                 an
                 aequation
                 both
                 ,
                 or
                 when
                 there
                 is
                 neither
                 ,
                 the
                 Letter
                 is
                 not
                 changed
                 at
                 all
                 but
                 that
                 which
                 served
                 for
                 the
                 former
                 Centenary
                 ,
                 shall
                 also
                 continue
                 in
                 the
                 succeeding
                 ;
                 because
                 the
                 compensation
                 so
                 made
                 ,
                 the
                 New
                 Moons
                 do
                 neither
                 go
                 forward
                 nor
                 backward
                 ,
                 but
                 happen
                 in
                 the
                 compass
                 of
                 the
                 same
                 days
                 .
              
               
                 1.
                 
                 And
                 this
                 is
                 enough
                 to
                 shew
                 for
                 what
                 reason
                 the
                 letters
                 are
                 so
                 placed
                 in
                 the
                 Table
                 ,
                 as
                 there
                 you
                 see
                 them
                 :
                 for
                 in
                 the
                 year
                 1600
                 the
                 Bissextile
                 being
                 neither
                 suppressed
                 ,
                 nor
                 the
                 Moon
                 aequated
                 ,
                 the
                 letter
                 D
                 used
                 in
                 the
                 former
                 Centenary
                 or
                 in
                 the
                 latter
                 part
                 thereof
                 from
                 the
                 year
                 1582
                 ,
                 is
                 still
                 the
                 same
                 .
              
               
                 In
                 the
                 year
                 1700
                 ,
                 because
                 there
                 is
                 a
                 suppression
                 ,
                 but
                 no
                 aequation
                 ,
                 the
                 commutation
                 is
                 made
                 to
                 the
                 Letter
                 C
                 descending
                 .
              
               
                 In
                 the
                 Year
                 1800
                 ,
                 because
                 there
                 is
                 both
                 a
                 suppression
                 and
                 an
                 aequation
                 ,
                 the
                 same
                 letter
                 C
                 doth
                 still
                 continue
                 .
              
               
                 In
                 the
                 Year
                 2400
                 ,
                 because
                 there
                 is
                 an
                 aequation
                 and
                 no
                 suppression
                 ,
                 there
                 is
                 an
                 ascension
                 to
                 the
                 Letter
                 A.
                 
              
               
                 And
                 thus
                 you
                 see
                 not
                 only
                 the
                 construction
                 of
                 this
                 Table
                 ,
                 but
                 how
                 it
                 may
                 be
                 continued
                 to
                 any
                 other
                 Year
                 ,
                 as
                 long
                 as
                 the
                 World
                 shall
                 last
                 .
              
               
               
                 12.
                 
                 And
                 by
                 these
                 two
                 Tables
                 we
                 may
                 easily
                 know
                 which
                 rank
                 of
                 the
                 30
                 Epacts
                 doth
                 belong
                 to
                 ,
                 or
                 is
                 proper
                 for
                 any
                 particular
                 age
                 :
                 for
                 as
                 in
                 our
                 age
                 ,
                 that
                 is
                 ,
                 from
                 the
                 Year
                 1600
                 to
                 the
                 Year
                 1700
                 exclusively
                 ,
                 that
                 series
                 is
                 proper
                 whose
                 Index
                 is
                 D.
                 Namely
                 ,
                 23
                 ,
                 4
                 ,
                 15
                 ,
                 26
                 ,
                 &c.
                 so
                 in
                 the
                 two
                 Ages
                 following
                 ,
                 that
                 is
                 ,
                 from
                 the
                 Year
                 1700
                 to
                 the
                 Year
                 1900
                 exclusively
                 ,
                 that
                 series
                 is
                 proper
                 whose
                 Index
                 is
                 C
                 ,
                 namely
                 these
                 ,
                 22
                 ,
                 3
                 ,
                 14
                 ,
                 25.
                 and
                 in
                 the
                 three
                 ages
                 following
                 thence
                 ,
                 that
                 is
                 from
                 the
                 Year
                 1900
                 to
                 the
                 Year
                 2100
                 exclusively
                 ,
                 that
                 series
                 is
                 proper
                 whose
                 Index
                 is
                 B
                 ,
                 namely
                 these
                 ,
                 21
                 ,
                 2
                 ,
                 13
                 ,
                 24
                 ,
                 &c.
                 
                 And
                 so
                 for
                 any
                 other
                 .
              
               
                 Hence
                 also
                 it
                 may
                 be
                 known
                 ,
                 which
                 of
                 the
                 19
                 doth
                 belong
                 to
                 any
                 particular
                 Year
                 ,
                 for
                 which
                 no
                 more
                 is
                 necessary
                 ,
                 than
                 only
                 to
                 know
                 the
                 Golden
                 Number
                 for
                 the
                 year
                 given
                 ,
                 which
                 being
                 sought
                 in
                 the
                 head
                 of
                 the
                 Table
                 ,
                 and
                 the
                 Index
                 of
                 that
                 Age
                 in
                 the
                 side
                 ,
                 the
                 common
                 Angle
                 ,
                 or
                 meeting
                 of
                 these
                 two
                 ,
                 will
                 shew
                 you
                 the
                 Epact
                 desired
                 :
                 As
                 in
                 the
                 year
                 1674
                 the
                 Golden
                 Number
                 is
                 3
                 and
                 the
                 
                   Index
                   D
                
                 ;
                 therefore
                 in
                 the
                 common
                 Angle
                 I
                 find
                 23
                 for
                 the
                 Epact
                 that
                 year
                 ,
                 and
                 sheweth
                 the
                 New
                 Moons
                 in
                 every
                 Month
                 thereof
                 .
              
               
                 And
                 here
                 it
                 will
                 not
                 be
                 unseasonable
                 to
                 give
                 the
                 reason
                 ,
                 for
                 which
                 the
                 Epact
                 25
                 not
                 XXV
                 is
                 written
                 under
                 the
                 Golden
                 Numbers
                 12
                 ,
                 13
                 ,
                 14
                 ,
                 15
                 ,
                 16
                 ,
                 17
                 ,
                 18
                 ,
                 19.
                 namely
                 ,
                 because
                 the
                 ranks
                 of
                 Epacts
                 ,
                 which
                 under
                 these
                 greater
                 Numbers
                 hath
                 this
                 Epact
                 25
                 ,
                 hath
                 also
                 XXIV
                 ,
                 it
                 would
                 follow
                 that
                 in
                 these
                 Ages
                 in
                 which
                 any
                 of
                 these
                 Ranks
                 were
                 in
                 use
                 ,
                 the
                 New
                 Moon
                 in
                 19
                 years
                 will
                 happen
                 twice
                 upon
                 the
                 same
                 days
                 ;
                 in
                 those
                 six
                 Months
                 in
                 which
                 the
                 Epacts
                 XXV
                 and
                 XXIV
                 are
                 set
                 to
                 the
                 same
                 day
                 :
                 Whereas
                 the
                 New
                 Moons
                 do
                 not
                 happen
                 
                 on
                 the
                 same
                 day
                 till
                 19
                 years
                 be
                 gone
                 about
                 .
                 To
                 avoid
                 this
                 inconvenience
                 ,
                 the
                 Epact
                 25
                 not
                 XXV
                 is
                 set
                 under
                 these
                 great
                 numbers
                 ,
                 and
                 the
                 Epact
                 25
                 is
                 in
                 the
                 Calendar
                 ,
                 in
                 these
                 Months
                 set
                 with
                 the
                 Epact
                 XXVI
                 ,
                 but
                 in
                 the
                 other
                 Months
                 with
                 the
                 Epact
                 XXV
                 .
              
               
                 14.
                 
                 Hence
                 it
                 cometh
                 to
                 pass
                 ,
                 1.
                 
                 That
                 in
                 these
                 Years
                 the
                 Epacts
                 25
                 and
                 XXIV
                 do
                 never
                 meet
                 on
                 the
                 same
                 day
                 .
                 2.
                 
                 That
                 there
                 is
                 no
                 danger
                 that
                 the
                 Epacts
                 25
                 and
                 XXVI
                 should
                 in
                 these
                 6
                 Months
                 cause
                 the
                 same
                 inconvenience
                 ,
                 seeing
                 that
                 the
                 Epacts
                 25
                 and
                 XXVI
                 are
                 never
                 both
                 found
                 in
                 the
                 same
                 Rank
                 .
                 3.
                 
                 That
                 the
                 Epact
                 25
                 may
                 in
                 other
                 Months
                 without
                 inconvenience
                 be
                 set
                 to
                 the
                 same
                 day
                 with
                 the
                 Epact
                 XXVI
                 ,
                 because
                 in
                 these
                 there
                 is
                 no
                 danger
                 of
                 their
                 meeting
                 with
                 the
                 Epact
                 XXIV
                 on
                 the
                 same
                 days
                 .
                 4.
                 
                 That
                 there
                 is
                 no
                 fear
                 that
                 the
                 Epacts
                 XXV
                 and
                 XXIV
                 being
                 set
                 on
                 the
                 same
                 days
                 ,
                 should
                 in
                 future
                 Ages
                 cause
                 the
                 same
                 inconvenience
                 ,
                 because
                 the
                 Epacts
                 XXV
                 and
                 XXIV
                 are
                 not
                 found
                 together
                 in
                 any
                 of
                 the
                 other
                 Ranks
                 .
                 But
                 that
                 either
                 one
                 or
                 both
                 of
                 them
                 are
                 wanting
                 .
                 Besides
                 ,
                 when
                 one
                 of
                 these
                 Epacts
                 is
                 in
                 use
                 ,
                 the
                 other
                 is
                 not
                 ,
                 and
                 that
                 only
                 which
                 is
                 in
                 use
                 is
                 proper
                 to
                 the
                 day
                 .
                 As
                 in
                 this
                 our
                 Age
                 until
                 the
                 Year
                 1700
                 the
                 Epacts
                 in
                 use
                 are
                 those
                 in
                 the
                 rank
                 whose
                 Index
                 is
                 D.
                 In
                 which
                 these
                 two
                 XXIV
                 and
                 XXV
                 are
                 not
                 both
                 found
                 .
                 And
                 in
                 the
                 two
                 following
                 Ages
                 ,
                 because
                 the
                 rank
                 of
                 Epacts
                 in
                 use
                 is
                 that
                 whose
                 Index
                 is
                 C
                 ,
                 in
                 which
                 there
                 is
                 the
                 Epact
                 XXV
                 ,
                 not
                 XXIV
                 ,
                 the
                 New
                 Moons
                 are
                 shewed
                 by
                 the
                 Epact
                 XXV
                 not
                 by
                 XXIV
                 .
                 But
                 because
                 in
                 three
                 following
                 Ages
                 ,
                 the
                 rank
                 of
                 Epacts
                 in
                 use
                 is
                 that
                 whose
                 Index
                 is
                 B
                 ,
                 in
                 which
                 25
                 and
                 XXIV
                 are
                 both
                 found
                 ,
                 the
                 New
                 
                 Moons
                 are
                 shewed
                 by
                 the
                 Epact
                 XXIV
                 when
                 the
                 golden
                 Number
                 is
                 6.
                 
                 And
                 by
                 the
                 Epact
                 25
                 when
                 the
                 golden
                 Number
                 is
                 17
                 ,
                 and
                 not
                 by
                 the
                 Epact
                 XXV
                 .
              
               
                 15.
                 
                 And
                 if
                 it
                 be
                 asked
                 why
                 the
                 Epact
                 19
                 in
                 the
                 common
                 Character
                 is
                 set
                 with
                 the
                 Epact
                 XX
                 against
                 the
                 last
                 day
                 of
                 December
                 ;
                 know
                 that
                 for
                 the
                 reasons
                 before
                 declared
                 ,
                 the
                 last
                 Embolismical
                 Month
                 within
                 the
                 space
                 of
                 19
                 years
                 ,
                 ought
                 to
                 be
                 but
                 29
                 days
                 and
                 not
                 30
                 ,
                 as
                 the
                 rest
                 are
                 ;
                 and
                 therefore
                 when
                 the
                 Epact
                 19
                 doth
                 concur
                 with
                 the
                 golden
                 Number
                 19
                 ,
                 the
                 last
                 Month
                 or
                 last
                 Lunation
                 beginning
                 the
                 second
                 of
                 December
                 ,
                 shall
                 end
                 upon
                 the
                 30
                 and
                 not
                 upon
                 the
                 31
                 of
                 that
                 Month
                 ,
                 and
                 the
                 New
                 Moon
                 should
                 be
                 supposed
                 to
                 happen
                 upon
                 the
                 31
                 under
                 the
                 same
                 Epact
                 19
                 ,
                 that
                 12
                 being
                 added
                 to
                 19
                 and
                 not
                 11
                 ,
                 you
                 may
                 have
                 one
                 for
                 the
                 Epact
                 of
                 the
                 year
                 following
                 ,
                 which
                 may
                 be
                 found
                 upon
                 the
                 30
                 of
                 Ianuary
                 ,
                 as
                 if
                 the
                 Lunation
                 of
                 30
                 days
                 had
                 been
                 accomplished
                 the
                 Day
                 before
                 .
              
            
             
               
                 CHAP.
                 VI.
                 
              
               
                 
                   How
                   to
                   find
                   the
                   Dominical
                   Letter
                   and
                   Feast
                   of
                   Easter
                   according
                   to
                   the
                   Gregorian
                   account
                   .
                
              
               
                 HAving
                 shewed
                 for
                 what
                 reason
                 ,
                 and
                 in
                 what
                 manner
                 the
                 Epacts
                 are
                 substituted
                 in
                 the
                 place
                 of
                 the
                 golden
                 Number
                 ,
                 and
                 how
                 the
                 New
                 Moons
                 may
                 be
                 by
                 them
                 found
                 in
                 the
                 Calendar
                 for
                 ever
                 ;
                 I
                 shall
                 now
                 shew
                 you
                 how
                 to
                 find
                 the
                 Feast
                 of
                 Easter
                 and
                 the
                 other
                 moveable
                 
                 Feasts
                 according
                 to
                 the
                 Gregorian
                 or
                 new
                 account
                 ;
                 and
                 to
                 this
                 purpose
                 I
                 must
                 first
                 shew
                 you
                 how
                 to
                 find
                 the
                 Dominical
                 Letter
                 ,
                 for
                 that
                 the
                 Cycle
                 of
                 28
                 years
                 will
                 not
                 serve
                 the
                 turn
                 ,
                 because
                 of
                 the
                 suppression
                 of
                 the
                 Bissextile
                 once
                 in
                 a
                 hundred
                 years
                 ,
                 but
                 doth
                 require
                 7
                 Cycles
                 of
                 28
                 years
                 apeice
                 .
                 The
                 first
                 whereof
                 begins
                 with
                 CB
                 ,
                 and
                 endeth
                 in
                 D.
                 The
                 second
                 begins
                 with
                 DC
                 ,
                 and
                 endeth
                 in
                 E.
                 The
                 third
                 begins
                 with
                 ED
                 ,
                 and
                 endeth
                 in
                 
                   F
                   &c.
                
                 
                 The
                 first
                 of
                 these
                 Cycles
                 began
                 to
                 be
                 in
                 use
                 1582
                 ,
                 in
                 which
                 year
                 the
                 dominical
                 Letter
                 according
                 to
                 the
                 Julian
                 account
                 was
                 G
                 ,
                 but
                 upon
                 the
                 fifteenth
                 day
                 of
                 October
                 ,
                 that
                 Year
                 was
                 changed
                 to
                 C
                 :
                 for
                 the
                 fifth
                 of
                 October
                 being
                 Friday
                 and
                 then
                 called
                 the
                 fifteenth
                 ,
                 the
                 Letter
                 A
                 became
                 Friday
                 ,
                 B
                 Saturday
                 ,
                 and
                 C
                 Sunday
                 ,
                 the
                 remaining
                 part
                 of
                 the
                 year
                 ,
                 in
                 which
                 the
                 Cycle
                 of
                 the
                 Sun
                 was
                 23
                 ,
                 and
                 the
                 second
                 after
                 the
                 Bissextile
                 or
                 leap
                 Year
                 ,
                 and
                 so
                 making
                 C
                 ,
                 which
                 answereth
                 to
                 the
                 fifteenth
                 year
                 of
                 that
                 Circle
                 ,
                 to
                 be
                 23
                 ,
                 the
                 Circle
                 will
                 end
                 at
                 D
                 ;
                 and
                 consequently
                 CB
                 ,
                 which
                 in
                 the
                 old
                 account
                 doth
                 belong
                 to
                 the
                 21
                 year
                 of
                 the
                 Circle
                 ,
                 hath
                 ever
                 since
                 been
                 called
                 the
                 first
                 ,
                 and
                 so
                 shall
                 continue
                 until
                 the
                 year
                 1700
                 ,
                 in
                 which
                 the
                 Bissextile
                 being
                 suppressed
                 ,
                 the
                 next
                 Cycle
                 will
                 begin
                 with
                 DC
                 as
                 hath
                 been
                 said
                 already
                 .
                 Under
                 the
                 first
                 rank
                 or
                 order
                 of
                 Dominical
                 Letters
                 are
                 written
                 the
                 years
                 1582
                 and
                 1600
                 ,
                 under
                 the
                 second
                 1700
                 ,
                 under
                 the
                 third
                 1800
                 ,
                 under
                 the
                 fourth
                 1900
                 and
                 2000
                 ,
                 under
                 the
                 fifth
                 2100
                 ,
                 under
                 the
                 sixth
                 2200
                 and
                 under
                 the
                 seventh
                 2300
                 and
                 2400.
                 
                 And
                 again
                 under
                 the
                 first
                 Order
                 ,
                 2500
                 ,
                 under
                 the
                 second
                 2600
                 ,
                 under
                 the
                 third
                 2700
                 and
                 2800
                 ,
                 and
                 so
                 forward
                 as
                 far
                 as
                 you
                 
                 please
                 ,
                 always
                 observing
                 the
                 same
                 order
                 ,
                 that
                 the
                 100
                 Bissextile
                 years
                 may
                 still
                 be
                 joyned
                 with
                 the
                 not
                 Bissextile
                 immediately
                 preceding
                 .
              
               
                 1.
                 
                 And
                 hence
                 it
                 appears
                 ,
                 that
                 the
                 seven
                 orders
                 of
                 Dominical
                 Letters
                 ,
                 are
                 so
                 many
                 Tables
                 ,
                 successively
                 serving
                 all
                 future
                 Generations
                 .
                 For
                 as
                 the
                 first
                 Order
                 serveth
                 from
                 the
                 year
                 1582
                 and
                 1600
                 to
                 the
                 year
                 1700
                 exclusively
                 ,
                 and
                 the
                 second
                 Order
                 from
                 thence
                 to
                 the
                 year
                 1800
                 exclusively
                 ,
                 so
                 shall
                 all
                 the
                 rest
                 in
                 like
                 manner
                 which
                 here
                 are
                 set
                 down
                 ,
                 and
                 to
                 be
                 set
                 down
                 at
                 pleasure
                 .
                 And
                 hence
                 the
                 Dominical
                 Letter
                 or
                 Letters
                 may
                 be
                 found
                 for
                 any
                 year
                 propounded
                 ,
                 as
                 if
                 it
                 were
                 required
                 to
                 find
                 the
                 dominical
                 Letter
                 for
                 the
                 year
                 1674
                 ,
                 because
                 the
                 year
                 given
                 is
                 contained
                 in
                 the
                 centenary
                 1600.
                 
                 I
                 find
                 the
                 Cycle
                 of
                 the
                 Sun
                 by
                 the
                 Rule
                 already
                 given
                 to
                 be
                 3.
                 
                 In
                 the
                 first
                 order
                 against
                 the
                 number
                 3
                 ,
                 I
                 find
                 G
                 for
                 the
                 Sunday
                 Letter
                 of
                 that
                 year
                 ,
                 in
                 like
                 manner
                 because
                 the
                 year
                 1750
                 is
                 contained
                 under
                 the
                 Centenary
                 1700
                 ,
                 the
                 Cycle
                 of
                 the
                 Sun
                 being
                 27
                 ,
                 I
                 find
                 in
                 the
                 second
                 rank
                 the
                 Letter
                 D
                 answering
                 to
                 that
                 Number
                 ,
                 and
                 that
                 is
                 the
                 Dominical
                 Letter
                 for
                 that
                 year
                 ,
                 and
                 so
                 of
                 the
                 rest
                 .
              
               
                 3.
                 
                 Again
                 for
                 as
                 much
                 as
                 the
                 fifth
                 Order
                 is
                 the
                 same
                 with
                 that
                 Table
                 ,
                 which
                 serves
                 for
                 the
                 old
                 account
                 ,
                 therefore
                 that
                 order
                 will
                 serve
                 the
                 turn
                 for
                 ever
                 where
                 that
                 Calendar
                 is
                 in
                 use
                 ,
                 and
                 so
                 this
                 last
                 will
                 be
                 of
                 perpetual
                 use
                 to
                 both
                 the
                 Calendars
                 .
              
               
                 4.
                 
                 Now
                 then
                 to
                 find
                 the
                 time
                 in
                 which
                 the
                 Feast
                 of
                 Easter
                 is
                 to
                 be
                 observed
                 ,
                 there
                 is
                 but
                 little
                 to
                 be
                 added
                 to
                 that
                 which
                 hath
                 been
                 already
                 said
                 concerning
                 the
                 Julian
                 Calendar
                 .
                 For
                 the
                 Paschal
                 
                 Limits
                 are
                 the
                 same
                 in
                 both
                 ,
                 the
                 difference
                 is
                 only
                 in
                 the
                 Epacts
                 ,
                 which
                 here
                 are
                 used
                 instead
                 of
                 the
                 golden
                 Number
                 .
              
               
                 5.
                 
                 For
                 the
                 terms
                 of
                 the
                 Paschal
                 New
                 Moons
                 are
                 always
                 the
                 eighth
                 of
                 March
                 and
                 the
                 fifth
                 of
                 April
                 :
                 but
                 whereas
                 there
                 are
                 11
                 days
                 within
                 these
                 Limits
                 to
                 which
                 no
                 golden
                 Number
                 is
                 affixed
                 ,
                 there
                 is
                 now
                 one
                 day
                 to
                 which
                 an
                 Epact
                 is
                 not
                 appointed
                 ,
                 because
                 there
                 is
                 no
                 day
                 within
                 those
                 Limits
                 ,
                 on
                 which
                 in
                 process
                 of
                 time
                 a
                 New
                 Moon
                 may
                 not
                 happen
                 .
                 And
                 the
                 reason
                 for
                 which
                 the
                 two
                 Epacts
                 XXV
                 and
                 XXIV
                 are
                 both
                 set
                 to
                 the
                 fifth
                 of
                 April
                 ,
                 is
                 first
                 general
                 ,
                 which
                 was
                 shewed
                 before
                 ,
                 namly
                 that
                 by
                 doing
                 the
                 same
                 in
                 5
                 other
                 Months
                 ,
                 the
                 12
                 time
                 30
                 Epacts
                 might
                 be
                 contracted
                 to
                 the
                 Limits
                 of
                 the
                 lunar
                 Year
                 which
                 consists
                 of
                 354
                 days
                 :
                 but
                 there
                 is
                 a
                 particular
                 reason
                 also
                 for
                 it
                 ,
                 that
                 the
                 Antients
                 having
                 appointed
                 that
                 all
                 the
                 Paschal
                 lunations
                 should
                 consist
                 of
                 29
                 days
                 ,
                 it
                 was
                 necessary
                 that
                 some
                 two
                 of
                 the
                 Epacts
                 should
                 be
                 set
                 to
                 one
                 of
                 these
                 days
                 in
                 which
                 the
                 Paschal
                 lunation
                 might
                 happen
                 ,
                 the
                 Epacts
                 being
                 30
                 in
                 number
                 .
                 And
                 it
                 was
                 thought
                 convenient
                 to
                 choose
                 the
                 last
                 day
                 ,
                 to
                 which
                 the
                 Epact
                 XXV
                 belonging
                 ,
                 the
                 Epact
                 XXIV
                 should
                 also
                 be
                 set
                 ;
                 and
                 hence
                 by
                 imitation
                 it
                 comes
                 to
                 pass
                 ,
                 that
                 these
                 and
                 not
                 other
                 Epacts
                 are
                 set
                 to
                 that
                 day
                 in
                 other
                 Months
                 ,
                 in
                 which
                 two
                 Epacts
                 are
                 to
                 be
                 set
                 to
                 the
                 same
                 days
                 .
              
               
                 6.
                 
                 The
                 use
                 of
                 these
                 Epacts
                 in
                 finding
                 the
                 Feast
                 of
                 Easter
                 ,
                 is
                 the
                 same
                 with
                 that
                 which
                 hath
                 been
                 shewed
                 concerning
                 the
                 golden
                 Numbers
                 .
                 For
                 the
                 Epact
                 and
                 the
                 Sunday
                 Letter
                 for
                 that
                 year
                 propounded
                 being
                 given
                 ,
                 the
                 Feast
                 of
                 Easter
                 may
                 be
                 found
                 in
                 the
                 Calendar
                 after
                 the
                 same
                 
                 manner
                 .
                 Thus
                 in
                 the
                 year
                 1674
                 ,
                 the
                 Epact
                 is
                 23
                 and
                 the
                 Sunday
                 Letter
                 G
                 ,
                 and
                 therefore
                 reckoning
                 fourteen
                 days
                 from
                 the
                 eighth
                 of
                 March
                 to
                 which
                 the
                 Epact
                 is
                 set
                 ,
                 the
                 Sunday
                 following
                 is
                 March
                 25
                 ,
                 which
                 is
                 the
                 day
                 on
                 which
                 the
                 Feast
                 of
                 Easter
                 is
                 observed
                 .
              
               
                 7.
                 
                 And
                 hence
                 as
                 hath
                 been
                 shewed
                 in
                 the
                 third
                 Chapter
                 concerning
                 the
                 Julian
                 Calendar
                 ,
                 a
                 brief
                 table
                 may
                 be
                 made
                 to
                 shew
                 the
                 feast
                 of
                 Easter
                 and
                 the
                 other
                 moveable
                 Feasts
                 for
                 ever
                 ,
                 in
                 which
                 there
                 is
                 no
                 other
                 difference
                 ,
                 save
                 only
                 that
                 the
                 Epacts
                 as
                 they
                 are
                 in
                 this
                 new
                 Calendar
                 ,
                 are
                 to
                 be
                 used
                 as
                 the
                 golden
                 Numbers
                 are
                 ,
                 which
                 stand
                 in
                 the
                 old
                 Calendar
                 .
                 And
                 a
                 Table
                 having
                 the
                 golden
                 Numbers
                 of
                 the
                 old
                 Calendar
                 set
                 in
                 one
                 Column
                 ,
                 and
                 the
                 Epacts
                 as
                 they
                 are
                 in
                 the
                 new
                 Calendar
                 set
                 in
                 another
                 ,
                 will
                 indifferently
                 shew
                 the
                 movable
                 Feasts
                 in
                 both
                 accounts
                 ,
                 as
                 in
                 the
                 Year
                 1674
                 ,
                 the
                 golden
                 Number
                 is
                 3
                 and
                 the
                 Sunday
                 Letter
                 according
                 to
                 the
                 Julian
                 account
                 is
                 D
                 ,
                 according
                 to
                 the
                 Gregorian
                 G
                 ,
                 and
                 the
                 Epact
                 23
                 ,
                 and
                 therefore
                 according
                 to
                 this
                 Table
                 our
                 Easter
                 is
                 April
                 19
                 ,
                 and
                 the
                 other
                 ,
                 to
                 wit
                 ,
                 the
                 Gregorian
                 ,
                 is
                 March
                 25.
                 
                 The
                 like
                 may
                 be
                 done
                 for
                 any
                 other
                 year
                 past
                 or
                 to
                 come
                 .
              
            
             
               
               
                 CHAP.
                 VII
                 .
              
               
                 
                   How
                   to
                   reduce
                   Sexagenary
                   numbers
                   into
                   Decimal
                   ,
                   and
                   the
                   Contrary
                   .
                
              
               
                 EVery
                 Circle
                 hath
                 antiently
                 ,
                 and
                 is
                 yet
                 generally
                 supposed
                 to
                 be
                 divided
                 into
                 300
                 degrees
                 ,
                 each
                 degree
                 into
                 60
                 Minutes
                 ,
                 each
                 Minute
                 into
                 60
                 Seconds
                 ,
                 and
                 so
                 forward
                 as
                 far
                 as
                 need
                 shall
                 require
                 .
                 But
                 this
                 partition
                 is
                 somewhat
                 troublesom
                 in
                 Addition
                 and
                 Subtraction
                 ,
                 much
                 more
                 in
                 Multiplication
                 and
                 Division
                 ;
                 and
                 the
                 Tables
                 hitherto
                 contrived
                 to
                 ease
                 that
                 manner
                 of
                 computation
                 ,
                 do
                 scarce
                 sufficiently
                 perform
                 the
                 work
                 ,
                 for
                 which
                 they
                 are
                 intended
                 .
                 And
                 although
                 the
                 Canon
                 published
                 by
                 the
                 learned
                 
                   H.
                   Gellibrand
                
                 ,
                 in
                 which
                 the
                 Division
                 of
                 the
                 Circle
                 into
                 360
                 degrees
                 is
                 retained
                 ,
                 but
                 every
                 degree
                 is
                 divided
                 into
                 100
                 parts
                 ,
                 is
                 much
                 better
                 than
                 the
                 old
                 Sexagenary
                 Canon
                 ,
                 yet
                 some
                 are
                 of
                 opinion
                 ,
                 that
                 if
                 the
                 Antients
                 had
                 divided
                 the
                 whole
                 circle
                 into
                 100
                 or
                 1000
                 parts
                 ,
                 it
                 would
                 have
                 proved
                 much
                 better
                 then
                 either
                 ;
                 only
                 they
                 think
                 Custome
                 such
                 a
                 Tyrant
                 ,
                 that
                 the
                 alteration
                 of
                 it
                 now
                 will
                 not
                 be
                 perhaps
                 so
                 advantagious
                 ;
                 leaving
                 them
                 therefore
                 to
                 injoy
                 their
                 own
                 opinions
                 ,
                 they
                 will
                 not
                 I
                 hope
                 be
                 offended
                 if
                 others
                 be
                 of
                 another
                 mind
                 :
                 for
                 their
                 sakes
                 therefore
                 ,
                 that
                 do
                 rather
                 like
                 the
                 Decimal
                 way
                 of
                 calculation
                 ▪
                 Having
                 made
                 a
                 Canon
                 of
                 artificial
                 Signs
                 and
                 Tangents
                 for
                 the
                 degrees
                 and
                 parts
                 of
                 a
                 Circle
                 divided
                 into
                 100
                 parts
                 ,
                 I
                 shall
                 here
                 also
                 shew
                 you
                 ,
                 how
                 to
                 reduce
                 sexagenary
                 Numbers
                 into
                 Decimal
                 ,
                 and
                 the
                 contrary
                 ,
                 
                 as
                 well
                 in
                 time
                 as
                 motion
                 .
              
               
                 2.
                 
                 The
                 parts
                 of
                 a
                 Circle
                 consisting
                 of
                 360
                 degrees
                 ,
                 may
                 be
                 reduced
                 into
                 the
                 parts
                 of
                 a
                 circle
                 divided
                 into
                 100
                 degrees
                 or
                 parts
                 ,
                 by
                 the
                 rule
                 of
                 Three
                 in
                 this
                 manner
                 .
              
               
                 As
                 360
                 is
                 to
                 100
                 ,
                 so
                 is
                 any
                 other
                 Number
                 of
                 degrees
                 ,
                 in
                 the
                 one
                 ,
                 to
                 the
                 correspondent
                 degrees
                 and
                 parts
                 in
                 the
                 other
                 .
              
               
                 But
                 if
                 the
                 sexagenary
                 degrees
                 have
                 Minutes
                 and
                 Seconds
                 joyned
                 with
                 them
                 ,
                 you
                 must
                 reduce
                 the
                 whole
                 Circle
                 as
                 well
                 as
                 the
                 parts
                 propounded
                 into
                 the
                 least
                 Denomination
                 ,
                 and
                 so
                 proceed
                 according
                 to
                 the
                 rule
                 given
                 .
              
               
                 Example
                 .
                 Let
                 it
                 be
                 required
                 to
                 convert
                 125
                 degrees
                 of
                 the
                 Sexagenary
                 Circle
                 ,
                 into
                 their
                 correspondent
                 parts
                 in
                 the
                 Decimal
                 .
                 I
                 say
                 ,
                 as
                 360
                 is
                 to
                 100
                 ,
                 so
                 is
                 125
                 to
                 34
                 ,
                 722222
                 ,
                 &c.
                 that
                 is
                 ,
                 34
                 degrees
                 and
                 722222
                 Parts
                 .
              
               
                 2.
                 
                 Example
                 .
                 Let
                 the
                 Decimal
                 of
                 238
                 degrees
                 47
                 Minutes
                 be
                 required
                 .
                 In
                 a
                 whole
                 Circle
                 there
                 are
                 21600
                 Minutes
                 ,
                 and
                 in
                 238
                 degrees
                 ,
                 there
                 are
                 14280
                 Minutes
                 ,
                 to
                 which
                 47
                 being
                 added
                 the
                 sum
                 is
                 14327.
                 
                 Now
                 then
                 I
                 say
                 if
                 21600
                 give
                 100
                 ,
                 what
                 shall
                 14327.
                 
                 The
                 Answ.
                 is
                 66
                 ,
                 3287
                 &c.
                 
                 In
                 like
                 manner
                 if
                 it
                 were
                 required
                 to
                 convert
                 the
                 Hours
                 and
                 Minutes
                 of
                 a
                 Day
                 into
                 decimal
                 Parts
                 ,
                 say
                 thus
                 ,
                 if
                 24
                 Hours
                 give
                 100
                 ,
                 what
                 shall
                 any
                 other
                 number
                 of
                 Hours
                 give
                 .
                 Thus
                 if
                 the
                 Decimal
                 of
                 18
                 hours
                 were
                 required
                 ,
                 the
                 answer
                 would
                 be
                 75
                 ,
                 and
                 the
                 Decimal
                 answering
                 to
                 16
                 Hours
                 30
                 Minutes
                 is
                 68
                 ,
                 75.
                 
              
               
                 But
                 if
                 it
                 be
                 required
                 to
                 convert
                 the
                 Decimal
                 Parts
                 of
                 a
                 Circle
                 into
                 its
                 correspondent
                 Parts
                 in
                 Sexagenary
                 .
                 The
                 proportion
                 is
                 ;
                 as
                 100
                 is
                 
                 to
                 the
                 Decimal
                 given
                 ,
                 so
                 is
                 360
                 to
                 the
                 Sexagenary
                 degrees
                 and
                 parts
                 required
                 .
              
               
                 Example
                 .
                 Let
                 the
                 Decimal
                 given
                 be
                 349
                 722222
                 ,
                 if
                 you
                 multiply
                 this
                 Number
                 given
                 by
                 360
                 ,
                 the
                 Product
                 will
                 be
                 1249999992
                 ,
                 that
                 is
                 cutting
                 off
                 7
                 Figures
                 ,
                 124
                 degrees
                 and
                 9999992
                 parts
                 of
                 a
                 degree
                 .
                 If
                 Minutes
                 be
                 required
                 ,
                 multiply
                 the
                 Decimal
                 parts
                 by
                 60
                 ,
                 and
                 from
                 the
                 product
                 cut
                 off
                 as
                 many
                 Figures
                 ,
                 as
                 were
                 in
                 the
                 Decimal
                 parts
                 given
                 ,
                 the
                 rest
                 shall
                 be
                 the
                 Minutes
                 desired
                 .
              
               
                 But
                 to
                 avoid
                 this
                 trouble
                 ,
                 I
                 have
                 here
                 exhibited
                 two
                 Tables
                 ,
                 the
                 one
                 for
                 converting
                 sexagenary
                 degrees
                 and
                 Minutes
                 into
                 Decimals
                 ,
                 and
                 the
                 contrary
                 .
                 The
                 other
                 for
                 converting
                 Hours
                 and
                 Minutes
                 into
                 Decimals
                 ,
                 and
                 the
                 contrary
                 .
                 The
                 use
                 of
                 which
                 Tables
                 I
                 will
                 explain
                 by
                 example
                 .
              
               
                 Let
                 it
                 be
                 required
                 to
                 convert
                 258
                 degrees
                 34′
                 .
                 47″
                 ,
                 into
                 the
                 parts
                 of
                 a
                 Circle
                 decimally
                 divided
                 .
              
               
                 The
                 Table
                 for
                 this
                 purpose
                 doth
                 consist
                 of
                 two
                 Leaves
                 ,
                 the
                 first
                 Leaf
                 is
                 divided
                 into
                 21
                 Columns
                 ,
                 of
                 which
                 the
                 1.
                 3.
                 5.
                 7.
                 9.
                 11.
                 13.
                 15.
                 17.
                 19
                 doth
                 contain
                 the
                 degrees
                 in
                 a
                 sexagenary
                 Circle
                 ,
                 the
                 2.
                 4.
                 6.
                 8.
                 10.
                 12.
                 14.
                 16.
                 18
                 and
                 20
                 doth
                 contain
                 the
                 degrees
                 of
                 a
                 Circle
                 Decimally
                 divided
                 ,
                 answering
                 to
                 the
                 former
                 ,
                 and
                 the
                 last
                 Column
                 doth
                 contain
                 the
                 Decimal
                 parts
                 ,
                 to
                 be
                 annexed
                 to
                 the
                 Decimal
                 degrees
                 .
                 Thus
                 the
                 Decimal
                 degrees
                 answering
                 to
                 26
                 Sexagenary
                 are
                 7
                 ,
                 and
                 the
                 parts
                 in
                 the
                 last
                 Column
                 are
                 22222222
                 and
                 therefore
                 the
                 degrees
                 and
                 parts
                 answering
                 to
                 26
                 Sexagenary
                 degrees
                 are
                 7.
                 22222222.
                 
              
               
               
                 In
                 like
                 manner
                 the
                 Decimal
                 of
                 62
                 degrees
                 ,
                 17.
                 22222222.
                 
                 And
                 the
                 Decimal
                 of
                 258
                 degrees
                 ,
                 34′
                 .
                 47″
                 ,
                 is
                 thus
                 found
                 .
              
               
                 
                   The
                   Decimal
                   of
                   258
                   degrees
                   is
                
                 
                   71.66666666
                
                 
                   The
                   Decimal
                   of
                   34
                   Minutes
                   is
                
                 
                   .15747040
                
                 
                   The
                   Decimal
                   of
                   47
                   seconds
                   is
                
                 
                   .00362652
                
                 
                   Their
                   Sum
                
                 
                   71.82776358
                
              
               
                 is
                 the
                 Decimal
                 of
                 258
                 degrees
                 ,
                 34′
                 .
                 47″
                 as
                 was
                 required
                 .
              
               
                 In
                 like
                 mauner
                 the
                 Decimal
                 of
                 any
                 Hours
                 and
                 Minutes
                 may
                 be
                 found
                 by
                 the
                 Table
                 for
                 that
                 purpose
                 .
              
               
                 Example
                 .
                 Let
                 the
                 Decimal
                 of
                 7
                 Hours
                 28′
                 be
                 required
                 .
              
               
                 
                   The
                   Decimal
                   answering
                   to
                   7h
                   .
                   is
                
                 
                   29.16666667
                
                 
                   The
                   Decimal
                   of
                   28
                   Minutes
                   is
                
                 
                   1.94444444
                
                 
                   The
                   Sum
                
                 
                   31.11111111
                
              
               
                 is
                 the
                 Decimal
                 Sought
                 .
              
               
                 To
                 find
                 the
                 degrees
                 and
                 Minutes
                 in
                 a
                 sexagenary
                 Circle
                 ,
                 answering
                 to
                 the
                 degrees
                 and
                 parts
                 of
                 a
                 Circle
                 Decimally
                 divided
                 ,
                 is
                 but
                 the
                 contrary
                 work
                 .
              
               
                 As
                 if
                 it
                 were
                 required
                 to
                 find
                 the
                 Degrees
                 and
                 minutes
                 answering
                 to
                 this
                 decimal
                 71.
                 02776359
                 ,
                 the
                 Degrees
                 or
                 Integers
                 being
                 sought
                 in
                 the
                 2.
                 4.
                 6
                 or
                 8
                 Columns
                 &c.
                 of
                 the
                 first
                 Leaf
                 of
                 that
                 Table
                 ,
                 right
                 against
                 71.
                 
                 I
                 find
                 256
                 and
                 in
                 the
                 last
                 Column
                 these
                 parts
                 11111111
                 ,
                 which
                 being
                 less
                 than
                 the
                 Decimal
                 given
                 ,
                 I
                 proceed
                 
                 till
                 I
                 come
                 to
                 6666667
                 ,
                 which
                 being
                 the
                 nearest
                 to
                 my
                 number
                 given
                 ,
                 I
                 find
                 against
                 these
                 parts
                 under
                 71.
                 
                 Degrees
                 258
                 ,
                 so
                 then
                 258
                 are
                 the
                 degrees
                 answering
                 to
                 the
                 Decimal
                 given
                 and
                 ,
              
               
                 
                   To
                   find
                   the
                   Minutes
                   and
                   Seconds
                   from
                
                 
                   71.82776359
                
                 
                   I
                   Substract
                   the
                   number
                   in
                   the
                   Table
                
                 
                   71.66666667
                
                 
                   The
                   remainer
                   is
                
                 
                   16109692
                
                 
                   which
                   being
                   Sought
                   in
                   the
                   next
                   Leaf
                   under
                   the
                   title
                   Minutes
                   ,
                   the
                   next
                   leaf
                   is
                
                 
                   11747640
                
                 
                   And
                   the
                   Minutes
                   34
                   ,
                   and
                   this
                   number
                   being
                   Subtracted
                   the
                   remainer
                   is
                
                 
                   00362652
                
              
               
                 Which
                 is
                 the
                 Decimal
                 of
                 47
                 seconds
                 ,
                 and
                 so
                 the
                 degrees
                 and
                 Minutes
                 answering
                 to
                 the
                 Decimal
                 given
                 are
                 258
                 degrees
                 34′
                 and
                 47″
                 ,
                 the
                 like
                 may
                 be
                 done
                 for
                 any
                 other
                 .
              
            
             
               
                 CHAP.
                 VIII
                 .
              
               
                 
                   Of
                   the
                   difference
                   of
                   Meridiens
                   .
                
              
               
                 HAving
                 in
                 the
                 first
                 part
                 shewed
                 how
                 the
                 places
                 of
                 the
                 Planets
                 in
                 the
                 Zodiack
                 may
                 be
                 found
                 by
                 observation
                 ,
                 and
                 how
                 to
                 reduce
                 the
                 time
                 of
                 an
                 observation
                 made
                 in
                 one
                 Country
                 ,
                 to
                 the
                 correspondent
                 time
                 in
                 another
                 ,
                 as
                 to
                 the
                 day
                 of
                 the
                 Month
                 ,
                 by
                 considering
                 the
                 several
                 
                 measures
                 of
                 the
                 year
                 in
                 several
                 Nations
                 ,
                 there
                 is
                 yet
                 onething
                 wanting
                 ,
                 which
                 is
                 ,
                 by
                 an
                 observation
                 made
                 of
                 a
                 Planets
                 place
                 in
                 one
                 Country
                 to
                 find
                 when
                 the
                 Planet
                 is
                 in
                 that
                 place
                 in
                 reference
                 to
                 another
                 ;
                 as
                 suppose
                 the
                 ☉
                 by
                 observation
                 was
                 found
                 at
                 Vraniburg
                 to
                 be
                 in
                 
                   ♈
                   .
                   3d.
                   13′
                   .
                   14″
                   .
                   March
                
                 the
                 fourteenth
                 1583
                 at
                 what
                 time
                 was
                 the
                 Sun
                 in
                 the
                 same
                 place
                 at
                 London
                 ?
                 To
                 resolve
                 this
                 and
                 the
                 like
                 questions
                 ,
                 the
                 Longitude
                 of
                 places
                 from
                 some
                 certain
                 Meridian
                 must
                 be
                 known
                 ;
                 to
                 which
                 purpose
                 I
                 have
                 here
                 exhibited
                 a
                 Table
                 shewing
                 the
                 difference
                 of
                 Meridians
                 in
                 Hours
                 and
                 Minutes
                 ,
                 of
                 most
                 of
                 the
                 eminent
                 places
                 in
                 England
                 from
                 the
                 City
                 of
                 London
                 ,
                 and
                 of
                 some
                 places
                 beyond
                 the
                 Seas
                 also
                 .
                 The
                 use
                 whereof
                 is
                 either
                 to
                 reduce
                 the
                 time
                 given
                 under
                 the
                 Meridian
                 of
                 London
                 to
                 some
                 other
                 Meridian
                 ,
                 or
                 the
                 time
                 given
                 in
                 some
                 other
                 Meridian
                 to
                 the
                 Meridian
                 of
                 London
                 .
              
               
                 1.
                 
                 If
                 it
                 be
                 required
                 to
                 reduce
                 the
                 time
                 given
                 under
                 the
                 Meridian
                 of
                 London
                 to
                 some
                 other
                 Meridian
                 ,
                 seek
                 the
                 place
                 desired
                 in
                 the
                 Catalogue
                 ,
                 and
                 the
                 difference
                 of
                 time
                 there
                 found
                 ,
                 either
                 add
                 to
                 or
                 subtract
                 from
                 the
                 times
                 given
                 at
                 London
                 ,
                 according
                 as
                 the
                 Titles
                 of
                 Addition
                 or
                 Subtraction
                 shew
                 ,
                 so
                 will
                 the
                 time
                 be
                 reduced
                 to
                 the
                 Meridian
                 of
                 the
                 other
                 place
                 as
                 was
                 required
                 .
                 Example
                 .
                 The
                 same
                 place
                 at
                 London
                 was
                 in
                 the
                 first
                 Point
                 of
                 ♉
                 ,
                 6
                 Hours
                 
                   P.
                   M.
                
                 and
                 it
                 is
                 required
                 to
                 reduce
                 the
                 same
                 to
                 the
                 Meridian
                 of
                 Vraniburg
                 I
                 therefore
                 seek
                 in
                 Vraniburg
                 in
                 the
                 Catalogue
                 of
                 places
                 ,
                 against
                 which
                 I
                 find
                 50′
                 with
                 the
                 Letter
                 A
                 annexed
                 ,
                 therefore
                 I
                 conclude
                 ,
                 that
                 the
                 Sun
                 was
                 that
                 day
                 at
                 Vraniburg
                 in
                 the
                 first
                 point
                 of
                 ♉
                 ,
                 6
                 Hours
                 50′
                 .
                 
                   P.
                   M.
                
                 
              
               
               
                 2.
                 
                 If
                 the
                 time
                 given
                 be
                 under
                 some
                 other
                 Meridian
                 ,
                 and
                 it
                 be
                 required
                 to
                 reduce
                 the
                 same
                 to
                 the
                 Meridian
                 of
                 London
                 ,
                 you
                 must
                 seek
                 the
                 place
                 given
                 in
                 the
                 Catalogue
                 ,
                 and
                 the
                 difference
                 of
                 time
                 there
                 found
                 ,
                 contrary
                 to
                 the
                 Title
                 is
                 to
                 be
                 added
                 or
                 subtracted
                 from
                 the
                 time
                 there
                 given
                 .
              
               
                 Example
                 .
                 Suppose
                 the
                 place
                 of
                 the
                 Sun
                 had
                 been
                 at
                 Vraniburg
                 ,
                 at
                 6
                 Hours
                 50′
                 .
                 
                   P.
                   M.
                
                 and
                 I
                 would
                 reduce
                 the
                 same
                 to
                 the
                 Meridian
                 of
                 London
                 ;
                 against
                 Vraniburg
                 as
                 before
                 I
                 find
                 50′
                 A.
                 therefore
                 contrary
                 to
                 the
                 Title
                 I
                 Subtract
                 50′
                 and
                 the
                 remainder
                 6
                 Hours
                 is
                 the
                 time
                 of
                 the
                 Suns
                 place
                 in
                 the
                 Meridian
                 of
                 London
                 .
              
            
             
               
                 CHAP.
                 IX
                 .
              
               
                 
                   Of
                   the
                   Theory
                   of
                   the
                   Sun
                   's
                   or
                   Earth's
                   Motion
                   .
                
              
               
                 IN
                 the
                 first
                 part
                 of
                 this
                 Treatise
                 we
                 have
                 spoken
                 of
                 the
                 primary
                 Motion
                 of
                 the
                 Planets
                 and
                 Stars
                 ,
                 as
                 they
                 are
                 wheeled
                 about
                 in
                 their
                 diurnal
                 motion
                 from
                 East
                 to
                 West
                 ,
                 but
                 here
                 we
                 are
                 to
                 shew
                 their
                 own
                 proper
                 motions
                 in
                 their
                 several
                 Orbs
                 from
                 West
                 to
                 East
                 ,
                 which
                 we
                 call
                 their
                 second
                 motions
                 .
              
               
                 1.
                 
                 And
                 these
                 Orbs
                 are
                 supposed
                 to
                 be
                 Elliptical
                 ,
                 as
                 the
                 ingenious
                 Repler
                 ,
                 by
                 the
                 help
                 of
                 Tycho's
                 accurate
                 observations
                 ,
                 hath
                 demonstrated
                 in
                 the
                 Motions
                 of
                 Mars
                 and
                 Mercury
                 ,
                 and
                 may
                 therefore
                 be
                 conceived
                 to
                 be
                 the
                 Figure
                 in
                 which
                 the
                 rest
                 do
                 move
                 .
              
               
                 2.
                 
                 Here
                 then
                 we
                 are
                 to
                 consider
                 what
                 an
                 Ellipsis
                 is
                 ,
                 how
                 it
                 may
                 be
                 drawn
                 ,
                 and
                 by
                 what
                 Method
                 
                 the
                 motions
                 of
                 the
                 Planets
                 according
                 to
                 that
                 Figure
                 may
                 be
                 computed
                 .
              
               
                 3.
                 
                 What
                 an
                 Ellipsis
                 is
                 
                   Apollonius
                   Pergaeus
                   in
                   Conicis
                   ,
                   Claudius
                   Mydorgius
                
                 and
                 others
                 have
                 well
                 defined
                 and
                 explained
                 ,
                 but
                 here
                 I
                 think
                 it
                 sufficient
                 to
                 tell
                 the
                 Reader
                 ,
                 that
                 it
                 is
                 a
                 long
                 Circle
                 ,
                 or
                 a
                 circular
                 Line
                 drawn
                 within
                 or
                 without
                 a
                 long
                 Square
                 ;
                 or
                 a
                 circular
                 Line
                 drawn
                 between
                 two
                 Circles
                 of
                 different
                 Diameters
                 .
              
               
                 4.
                 
                 The
                 usual
                 and
                 Mechanical
                 way
                 of
                 drawing
                 this
                 Ellipsis
                 is
                 thus
                 ;
                 first
                 draw
                 a
                 line
                 to
                 that
                 length
                 which
                 you
                 would
                 have
                 the
                 greatest
                 Diameter
                 to
                 be
                 ,
                 as
                 the
                 Line
                 AP
                 in
                 Figure
                 8
                 ,
                 and
                 from
                 the
                 middle
                 of
                 this
                 Line
                 at
                 X
                 ,
                 set
                 off
                 with
                 your
                 compasses
                 the
                 Equal
                 distance
                 XM
                 and
                 XH
                 .
              
               
                 5.
                 
                 Then
                 take
                 a
                 piece
                 of
                 thred
                 of
                 the
                 same
                 length
                 with
                 the
                 Diameter
                 AP
                 and
                 fasten
                 one
                 end
                 thereof
                 in
                 the
                 point
                 M
                 and
                 the
                 other
                 in
                 the
                 point
                 H
                 ,
                 and
                 with
                 your
                 Pen
                 extend
                 the
                 thred
                 thus
                 fastened
                 to
                 the
                 point
                 A
                 ,
                 and
                 from
                 thence
                 towards
                 P
                 keeping
                 the
                 thread
                 stiff
                 upon
                 your
                 Pen
                 ,
                 draw
                 a
                 line
                 from
                 A
                 by
                 B
                 to
                 P
                 ,
                 the
                 line
                 so
                 drawn
                 shall
                 be
                 half
                 an
                 Ellipsis
                 ,
                 and
                 in
                 like
                 manner
                 you
                 may
                 draw
                 the
                 other
                 half
                 from
                 P
                 by
                 D
                 to
                 A.
                 In
                 which
                 because
                 the
                 whole
                 thred
                 is
                 equal
                 to
                 the
                 Diameter
                 AP.
                 therefore
                 the
                 two
                 Lines
                 made
                 by
                 thred
                 in
                 drawing
                 of
                 the
                 Ellipsis
                 ,
                 must
                 in
                 every
                 point
                 of
                 the
                 said
                 Ellipsis
                 be
                 also
                 equal
                 to
                 the
                 same
                 Diameter
                 AP.
                 They
                 that
                 desire
                 a
                 demonstration
                 thereof
                 geometrically
                 ,
                 may
                 consult
                 
                   Apollonius
                   Pergaeus
                   ,
                   Claudius
                   Mydorgius
                
                 or
                 others
                 ,
                 in
                 their
                 treatises
                 of
                 Conical
                 Sections
                 ,
                 this
                 is
                 sufficient
                 for
                 our
                 present
                 purpose
                 ,
                 and
                 from
                 the
                 equality
                 of
                 these
                 two
                 Lines
                 with
                 the
                 Diameter
                 ,
                 a
                 brief
                 Method
                 of
                 calculation
                 of
                 the
                 
                 Planets
                 place
                 in
                 an
                 Ellipsis
                 ,
                 is
                 thus
                 Demonstrated
                 by
                 Dr.
                 Ward
                 now
                 Bishop
                 of
                 Salisbury
                 .
              
               
                 6.
                 
                 In
                 this
                 
                   Ellipsis
                   H
                
                 denotes
                 the
                 place
                 of
                 the
                 Suns
                 Center
                 ,
                 to
                 which
                 the
                 true
                 motion
                 of
                 the
                 Planet
                 is
                 referred
                 ,
                 M
                 the
                 other
                 Focus
                 whereunto
                 the
                 equal
                 or
                 middle
                 motion
                 is
                 numbred
                 ,
                 A
                 the
                 Aphelion
                 where
                 the
                 Planet
                 is
                 farthest
                 distant
                 from
                 the
                 Sun
                 and
                 slowest
                 in
                 motion
                 ,
                 P
                 the
                 Perihelion
                 where
                 the
                 Planet
                 is
                 nearest
                 the
                 Sun
                 and
                 slowest
                 in
                 motion
                 .
                 In
                 the
                 points
                 A
                 and
                 P
                 the
                 Line
                 of
                 the
                 mean
                 and
                 true
                 motion
                 do
                 convene
                 ,
                 and
                 therefore
                 in
                 either
                 of
                 these
                 places
                 the
                 Planet
                 is
                 from
                 P
                 in
                 aequality
                 ,
                 but
                 in
                 all
                 other
                 points
                 the
                 mean
                 and
                 true
                 motion
                 differ
                 ,
                 and
                 in
                 D
                 and
                 C
                 is
                 the
                 greatest
                 elliptick
                 AEquation
                 .
              
               
                 8.
                 
                 Now
                 suppose
                 the
                 Planet
                 in
                 B
                 ,
                 the
                 line
                 of
                 the
                 middle
                 motion
                 according
                 to
                 this
                 Figure
                 is
                 MB
                 ,
                 the
                 line
                 of
                 the
                 true
                 motion
                 HB
                 .
                 The
                 mean
                 Anomaly
                 AMB.
                 The
                 Eliptick
                 aequation
                 or
                 
                   Prosthaphaeresis
                   MBH
                
                 ,
                 which
                 in
                 this
                 Example
                 subtracted
                 from
                 AMB
                 ,
                 the
                 remainer
                 AHB
                 is
                 the
                 true
                 Anomaly
                 .
                 And
                 here
                 note
                 that
                 in
                 the
                 right
                 lined
                 Triangle
                 MBH
                 ,
                 the
                 side
                 MH
                 is
                 always
                 the
                 same
                 ,
                 being
                 the
                 distance
                 of
                 the
                 Foci
                 ,
                 the
                 other
                 two
                 sides
                 MB
                 and
                 HB
                 are
                 together
                 equal
                 to
                 AP.
                 Now
                 then
                 if
                 you
                 continue
                 the
                 side
                 MB
                 till
                 BE
                 be
                 equal
                 to
                 BH
                 and
                 draw
                 the
                 line
                 HE
                 ,
                 in
                 the
                 right
                 lined
                 Triangle
                 MEH
                 ,
                 we
                 have
                 given
                 
                   ME
                   =
                   AD
                
                 and
                 MH
                 with
                 the
                 Angle
                 EMH
                 ,
                 to
                 find
                 the
                 Angles
                 MEH
                 and
                 MHE
                 which
                 in
                 this
                 case
                 are
                 equal
                 ,
                 because
                 
                   EB
                   =
                   BH
                
                 by
                 Contraction
                 ,
                 and
                 therefore
                 the
                 double
                 of
                 BEH
                 or
                 
                   BHE
                   =
                   MBH
                
                 ,
                 which
                 is
                 the
                 Angle
                 required
                 .
              
               
                 And
                 that
                 which
                 yet
                 remaineth
                 to
                 be
                 done
                 ,
                 is
                 
                 the
                 finding
                 the
                 place
                 of
                 the
                 Aphelion
                 ,
                 the
                 true
                 Excentricity
                 or
                 distance
                 of
                 the
                 umbilique
                 points
                 ,
                 and
                 the
                 stating
                 of
                 the
                 Planets
                 middle
                 motion
                 .
              
            
             
               
                 CHAP.
                 X.
                 
              
               
                 
                   Of
                   the
                   finding
                   of
                   the
                   Suns
                   Apogeon
                   ,
                   quantity
                   of
                   Excentricity
                   aend
                   middle
                   motion
                   .
                
              
               
                 THe
                 place
                 of
                 the
                 Suns
                 Apogaeon
                 and
                 quantity
                 of
                 Excentricity
                 may
                 from
                 the
                 observations
                 of
                 our
                 countrey
                 man
                 Mr.
                 
                   Edward
                   Wright
                
                 be
                 obtained
                 in
                 this
                 manner
                 ,
                 in
                 the
                 years
                 1596
                 ,
                 and
                 1497
                 ,
                 the
                 Suns
                 entrance
                 into
                 ♈
                 and
                 ♎
                 and
                 into
                 the
                 midst
                 of
                 ♉
                 .
                 ♌
                 .
                 ♍
                 .
                 and
                 ♒
                 were
                 as
                 in
                 the
                 Table
                 following
                 expressed
                 .
              
               
                 
                   
                     
                        
                    
                     
                       1596
                    
                     
                       1597
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       D.
                       H.
                       M.
                       
                    
                     
                       D.
                       H.
                       M.
                       
                    
                     
                        
                    
                  
                   
                     
                       Ianuary
                       .
                    
                     
                       25.
                       00.07
                    
                     
                       24.
                       05.54
                    
                     
                       ♒
                       .
                       15
                    
                  
                   
                     
                       March.
                       
                    
                     
                       9.
                       18.43
                    
                     
                       10.
                       00.37
                    
                     
                       ♈
                       .
                       0
                    
                  
                   
                     
                       April
                       .
                    
                     
                       24.
                       21.47
                    
                     
                       25.
                       03.54
                    
                     
                       ♉
                       .
                       15
                    
                  
                   
                     
                       Iuly
                       .
                    
                     
                       28.
                       01.43
                    
                     
                       28.
                       09.56
                    
                     
                       ♌
                       .
                       15
                    
                  
                   
                     
                       September
                       .
                    
                     
                       12.
                       13.48
                    
                     
                       12.
                       19.15
                    
                     
                       ♎
                       .
                       0
                    
                  
                   
                     
                       October
                       .
                    
                     
                       27.
                       15.23
                    
                     
                       27.
                       21.50
                    
                     
                       ♍
                       .
                       15
                    
                  
                
              
               
                 And
                 hence
                 the
                 Suns
                 continuance
                 in
                 the
                 Northern
                 Semicircle
                 from
                 ♈
                 to
                 ♎
                 in
                 the
                 year
                 1596
                 being
                 Leap
                 year
                 ,
                 was
                 thus
                 found
                 .
                 
                   
                   
                      
                  
                   
                     d.
                     h.
                     
                  
                   
                     From
                     the
                     1.
                     of
                     Ianuary
                     to
                     ☉
                     Entrance
                     ♎
                     .
                  
                   
                     256.
                     13.
                     48.
                     
                  
                   
                     From
                     the
                     1.
                     of
                     Iun
                     to
                     ☉
                     Entrance
                     ♈
                  
                   
                     69.
                     18.43
                  
                   
                     Their
                     difference
                     .
                  
                   
                     186.
                     19.05
                  
                
                 
                   
                     In
                     the
                     year
                     1597
                     from
                     the
                     1
                     of
                     Ianuary
                     to
                     the
                     time
                     of
                     the
                     ☉
                     Entrance
                     into
                     ♎
                     .
                  
                   
                     255.
                     19.15
                  
                   
                     To
                     the
                     ☉
                     entrance
                     into
                     ♈
                     .
                  
                   
                     69.
                     09.37
                  
                   
                     Their
                     difference
                     is
                  
                   
                     186.
                     18.38
                  
                
              
               
                 And
                 the
                 difference
                 of
                 the
                 Suns
                 continuance
                 in
                 these
                 Arks
                 in
                 the
                 year
                 1596
                 and
                 1597
                 is
                 27′
                 .
                 and
                 therefore
                 the
                 mean
                 time
                 of
                 his
                 continuance
                 in
                 those
                 Arks
                 is
                 days
                 186.
                 hours
                 18.
                 minutes
                 51.
                 seconds
                 30.
                 
                 And
                 by
                 consequence
                 his
                 continuance
                 in
                 the
                 Southern
                 Semicircle
                 that
                 is
                 from
                 ♎
                 to
                 ♈
                 is
                 178
                 days
                 .
                 11
                 hours
                 ,
                 8
                 minutes
                 and
                 30
                 seconds
                 .
                 
                   
                     In
                     like
                     manner
                     in
                     the
                     year
                     1596
                     between
                     his
                     entrance
                     into
                     ♉
                     15.
                     and
                     ♍
                     15
                     ,
                     there
                     are
                     days
                  
                   
                     185.
                     17.36
                  
                   
                     And
                     in
                     the
                     year
                     1597
                     there
                     are
                     days
                  
                   
                     185.
                     17.56
                  
                
              
               
                 And
                 to
                 find
                 the
                 middle
                 motion
                 answering
                 to
                 days
                 186.
                 hours
                 18.
                 
                 Minutes
                 51.
                 seconds
                 30
                 I
                 say
                 .
              
               
                 As
                 365
                 days
                 ,
                 6
                 hours
                 ,
                 the
                 length
                 of
                 the
                 Julian
                 ,
                 year
                 is
                 to
                 360
                 ,
                 the
                 degrees
                 in
                 a
                 Circle
                 .
              
               
                 So
                 is
                 186
                 days
                 ,
                 18
                 hours
                 ,
                 51′
                 .
                 30″
                 to
                 184
                 degrees
                 .
                 03′
                 .
                 56″
                 .
              
               
                 In
                 like
                 manner
                 the
                 mean
                 motion
                 answering
                 
                 to
                 185
                 days
                 ,
                 17
                 h.
                 46′
                 is
                 183
                 degrees
                 ,
                 02′
                 .
                 09
                 .
                 
                   
                     Apparent
                     motion
                     from
                     ♈
                     to
                     ♎
                  
                   
                     180.
                     00.00
                  
                   
                     Middle
                     motion
                  
                   
                     184.
                     03.56
                  
                   
                     Their
                     Sum
                  
                   
                     364.
                     03.56
                  
                   
                     Half
                     Sum
                     is
                     the
                     Arch.
                     SME
                  
                   
                     182.
                     01.58
                  
                
              
               
                 In
                 1596
                 from
                 15
                 ♒
                 to
                 15
                 ♌
                 there
                 are
                 days
                 185
                 ,
                 hours
                 01
                 ,
                 minutes
                 36.
                 
                 In
                 1597.
                 days
                 135.
                 hours
                 4.
                 
                 02′
                 .
              
               
                 And
                 the
                 mean
                 motion
                 answering
                 thereunto
                 is
                 .
                 182
                 d.
                 30′
                 .
                 36″
                 .
                 
                   
                     Apparent
                     motion
                     from
                  
                   
                     15
                     ♉
                     to
                     15
                     ♍
                     .
                     180.
                     
                  
                   
                     Middle
                     motion
                  
                   
                     185.
                     17.
                     56.
                     181.
                     04.53
                  
                   
                     Half
                     Sum
                     is
                  
                   
                     183.
                     32.
                     26
                  
                
              
               
                 From
                 15
                 ♒
                 to
                 15
                 ♌
                 Days
                 .
                 185.
                 04
                 h.
                 02′
                 
                   
                     Apparent
                     motion
                  
                   
                     180.
                     
                  
                   
                     Middle
                     motion
                  
                   
                     182.
                     30.
                     36
                  
                   
                     Half
                     Sum
                  
                   
                     181.
                     15.
                     18
                  
                
              
               
                 Now
                 then
                 in
                 Fig.
                 from
                 PGC.
                 181.
                 32.
                 26
                 deduct
                 NKD
                 180
                 ,
                 the
                 Remainer
                 is
                 
                   DC+NP
                   .
                   1.
                
                 32.
                 26.
                 
                 Therefore
                 DC
                 or
                 NP.
                 46.
                 13
                 ,
                 whose
                 Sine
                 is
                 HA.
                 
              
               
                 And
                 from
                 XPG.
                 181.
                 15.
                 18
                 deduct
                 
                   TNK
                   180
                
                 ,
                 the
                 Remainer
                 is
                 KG+TX
                 1.
                 15.
                 18.
                 
                 Therefore
                 KG
                 or
                 TX
                 37.
                 39
                 ,
                 whose
                 Sine
                 is
                 HR
                 .
              
               
               
                 
                   
                     Now
                     then
                     to
                     find
                     the
                     Apogaeon
                     .
                  
                   
                     As
                     
                       HA
                       46′
                       .
                       13″
                    
                  
                   
                     5.12851105
                  
                   
                     To
                     Rad.
                     So
                     
                       HR
                       37′
                       .
                       39″
                    
                  
                   
                     15.03948202
                  
                   
                     To
                     
                       Tang.
                       HAR.
                    
                     39
                     d.
                     10′.04″
                  
                   
                     9.91097097
                  
                   
                     GAM
                     .
                  
                   
                     45
                  
                   
                     Apogaeon
                  
                   
                     95.
                     49.
                     56.
                     
                  
                
                 
                   
                     Hence
                     to
                     find
                     the
                     excentricity
                     AR.
                     
                  
                   
                     As
                     the
                     Sine
                     HAR.
                     39.
                     10.04
                  
                   
                     9.80043756
                  
                   
                     To
                     Rad.
                     So
                     HR
                     .
                     37.39
                  
                   
                     15.03948202
                  
                   
                     To
                     RA.
                     1733.99
                  
                   
                     5.23904446
                  
                
              
               
                 Or
                 thus
                 ,
              
               
                 In
                 the
                 Triangle
                 
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                
                 we
                 have
                 given
                 
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                
                 .
                 and
                 
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                
                 .
                 
                   
                     As
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     .
                     37.39
                  
                   
                     5.03948202
                  
                   
                     To
                     Rad.
                     So
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     .
                     46.
                     13.
                     
                  
                   
                     15.12851105
                  
                   
                     To
                     Tang.
                     R
                     
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                       〈◊〉
                    
                     .
                     50.
                     49.56
                  
                   
                     10.08902903
                  
                   
                     PAS
                     .
                  
                   
                     45.
                     
                  
                
              
               
                 Apogaeon
                 95
                 deg
                 .
                 49′
                 .
                 56″
                 .
                 
                   as
                   before
                
                 .
                 
                   
                     Then
                     for
                     the
                     Excentricity
                     RA.
                     
                  
                   
                     As
                     the
                     Sine
                     of
                     
                       R
                       
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                      
                    
                     .
                     50.
                     49.
                     56
                  
                   
                     9.88945938
                  
                   
                     Is
                     to
                     
                       
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                         〈◊〉
                      
                       .
                       46′
                       .
                       13″
                    
                  
                   
                     5.12851105
                  
                   
                     So
                     is
                     Radius
                     .
                     To
                     
                       RA.
                       1734.01
                    
                  
                   
                     5.23905167
                  
                
              
               
                 And
                 this
                 agreeth
                 with
                 the
                 excentricity
                 ,
                 used
                 
                 by
                 Mr.
                 Street
                 in
                 his
                 
                   Astron.
                   Carolina
                
                 ,
                 Pag.
                 23.
                 
                 But
                 Mr.
                 Wing
                 as
                 well
                 by
                 observation
                 in
                 former
                 ages
                 ,
                 as
                 our
                 own
                 ,
                 in
                 his
                 
                   Astron.
                   Instaur
                
                 .
                 Pag.
                 39.
                 doth
                 find
                 it
                 to
                 be
                 1788
                 or
                 1791.
                 
                 The
                 work
                 by
                 both
                 observations
                 as
                 followeth
                 .
              
               
                 2.
                 
                 And
                 first
                 in
                 the
                 time
                 of
                 
                   Ptolemy
                   ,
                   Anno
                   Christi
                
                 139
                 by
                 comparing
                 many
                 observations
                 together
                 ,
                 he
                 sets
                 down
                 for
                 the
                 measure
                 nearest
                 truth
                 ,
                 the
                 interval
                 between
                 the
                 vernal
                 Equinox
                 and
                 the
                 Tropick
                 of
                 Cancer
                 to
                 be
                 days
                 93.
                 hours
                 23.
                 and
                 minutes
                 03.
                 
                 And
                 from
                 the
                 Vernal
                 to
                 the
                 Autumnal
                 Equinox
                 ,
                 days
                 186.
                 hours
                 13.
                 and
                 minutes
                 5.
                 
                 
                   
                      
                  
                   
                     D.
                     
                  
                   
                     The
                     apparent
                     motion
                     from
                     ♈
                     to
                     ♎
                  
                   
                     90.
                     36.00
                  
                   
                     Middle
                     motion
                     for
                     93
                     d.
                     23
                     h.
                     3′
                     .
                     is
                  
                   
                     92.
                     36.42
                  
                   
                     The
                     half
                     Sum
                     is
                     GP
                  
                   
                     91.
                     18.21
                  
                
                 
                   
                     Apparent
                     motion
                     from
                     ♈
                     to
                     ♎
                  
                   
                     180.
                     00.00
                  
                   
                     Middle
                     motion
                     for
                     186
                     d.
                     13
                     h.
                     5′
                     .
                     is
                  
                   
                     183.
                     52.03
                  
                   
                     The
                     half
                     Sum
                     is
                     GEK
                  
                   
                     181.
                     56.02
                  
                
                 
                   
                     The
                     half
                     of
                     GEK
                     is
                     GE.
                     
                  
                   
                     90.
                     58.01
                  
                   
                     And
                     GP
                     less
                     GE
                     is
                  
                   
                     00.
                     20.20
                  
                   
                     Whos
                     's
                     Sum
                     is
                     AC
                     59146.
                     
                  
                   
                      
                  
                
              
               
                 Again
                 from
                 GEK
                 181.
                 56.
                 02.
                 deduct
                 the
                 Semicircle
                 FED
                 180.
                 the
                 remainer
                 is
                 the
                 summ
                 DK
                 and
                 FG.
                 1.
                 56.
                 2.
                 and
                 therefore
                 
                   DK
                   =
                   FG.
                   58′
                   .
                   01″
                   .
                
                 whose
                 sign
                 is
                 
                   BC.
                   168755.
                   
                   L
                
                 is
                 the
                 place
                 of
                 the
                 Aphelion
                 ,
                 and
                 AB
                 the
                 Excentricity
                 .
              
               
                 Now
                 then
                 in
                 the
                 Triangle
                 ABC
                 .
                 in
                 the
                 Fig.
                 6
                 we
                 have
                 given
                 the
                 two
                 sides
                 AC
                 and
                 BC.
                 To
                 find
                 the
                 Angle
                 BAC
                 and
                 the
                 Hypotenuse
                 AB
                 .
                 
                 For
                 which
                 the
                 proportions
                 are
                 .
                 
                   
                     As
                     the
                     side
                     AC
                     .
                     59146
                  
                   
                     4.77192538
                  
                   
                     Is
                     to
                     the
                     Radius
                     .
                  
                   
                     10.00000000
                  
                   
                     So
                     is
                     the
                     side
                     
                       BC
                       ▪
                    
                     168755
                  
                   
                     5.22725665
                  
                   
                     To
                     Tang.
                     BAC
                     .
                     70.
                     41.
                     10.
                     
                  
                   
                     10.45533127
                  
                
                 
                   
                     Secondly
                     for
                     AB
                     .
                  
                   
                     As
                     the
                     Sine
                     of
                     BAC
                     .
                     70.
                     41.
                     10.
                     
                  
                   
                     9.97484352
                  
                   
                     Is
                     to
                     the
                     side
                     AB
                     .
                     168755.
                     
                  
                   
                     5.22725665
                  
                   
                     So
                     is
                     the
                     Radius
                     .
                  
                   
                     10.00000000
                  
                   
                     To
                     the
                     Hypot
                     .
                     AB
                     .
                     1788.
                     10.
                     
                  
                   
                     5.25241313
                  
                
              
               
                 Therefore
                 the
                 Aphelion
                 at
                 that
                 time
                 was
                 in
                 II
                 10.
                 41.
                 10.
                 
                 And
                 the
                 excentricity
                 .
                 1788.
                 
              
               
                 3.
                 
                 Again
                 
                   Anno
                   Christi
                
                 1652
                 the
                 Suns
                 place
                 by
                 observation
                 was
                 found
                 to
                 be
                 as
                 followeth
                 .
              
               
                 
                   
                     
                       April
                       .
                       24.
                       
                    
                     
                       hours
                       .
                       10.
                       
                    
                     
                       ♉
                       .
                       15
                    
                  
                   
                     
                       October
                       .
                       27.
                       
                    
                     
                       hours
                       .
                       7.
                       10′
                    
                     
                       ♍
                       .
                       15
                    
                  
                   
                     
                       Ianuary
                       .
                       24.
                       
                    
                     
                       hours
                       .
                       11
                       .
                       20′
                    
                     
                       ♒
                       .
                       15
                    
                  
                   
                     
                       Iuly
                       .
                       27.
                       
                    
                     
                       hours
                       .
                       16.30
                       ,
                    
                     
                       ♌
                       .
                       15
                    
                  
                
              
               
                 Hence
                 it
                 appeareth
                 that
                 the
                 Sun
                 is
                 running
                 through
                 one
                 Semicircle
                 of
                 the
                 Ecliptick
                 ,
                 that
                 is
                 from
                 ♉
                 15
                 to
                 ♍
                 15.
                 185
                 days
                 21
                 hours
                 and
                 10′
                 .
                 And
                 through
                 the
                 other
                 Semicircle
                 from
                 ♒
                 15
                 to
                 ♌
                 15
                 ,
                 days
                 184.
                 hours
                 5.
                 therefore
                 the
                 Suns
                 mean
                 motion
                 ,
                 according
                 to
                 the
                 practice
                 in
                 the
                 last
                 example
                 ,
                 from
                 ♉
                 15
                 to
                 ♍
                 15
                 is
                 181.
                 30.
                 26.
                 and
                 from
                 ♒
                 15
                 to
                 ♌
                 15.
                 181.
                 16.
                 30.
                 
              
               
                 Now
                 then
                 in
                 Fig.
                 7.
                 if
                 we
                 subtract
                 the
                 semicircle
                 of
                 the
                 Orb
                 KMH
                 .
                 180.
                 from
                 
                   WPV
                   181.
                   36.
                
                 26.
                 the
                 remainer
                 is
                 the
                 sum
                 of
                 KW
                 and
                 HV
                 
                 1.
                 36.
                 26.
                 the
                 Sine
                 of
                 half
                 thereof
                 48′
                 .
                 13″
                 is
                 equal
                 to
                 AC
                 .
                 140252.
                 
              
               
                 Again
                 the
                 mean
                 motion
                 of
                 the
                 Sun
                 in
                 his
                 Orb
                 from
                 ♒
                 15
                 to
                 ♉
                 15
                 is
                 the
                 Arch
                 
                   SKP.
                   181.
                   16.
                   30.
                
                 whose
                 excess
                 above
                 the
                 Semicircle
                 being
                 bisected
                 is
                 38.
                 15.
                 whos
                 's
                 Sine
                 CB.
                 111345.
                 now
                 then
                 in
                 the
                 Triangle
                 ABC
                 to
                 find
                 the
                 Angle
                 BAC
                 ,
                 the
                 proportion
                 is
                 .
                 
                   
                     As
                     the
                     side
                     AC
                     .
                     140252
                  
                   
                     5.14690906
                  
                   
                     Is
                     to
                     the
                     Radius
                     .
                  
                   
                     10.00000000
                  
                   
                     So
                     is
                     the
                     Side
                     CB
                     111345
                  
                   
                     5.04667072
                  
                   
                     To
                     Tang.
                     BAC
                     .
                     38.
                     36.
                     21
                     ,
                  
                   
                     9.89966166
                  
                
              
               
                 Which
                 being
                 deducted
                 out
                 of
                 the
                 Angle
                 .
                 69
                 
                   A
                   ♌
                
                 .
                 45
                 it
                 leaveth
                 the
                 Angle
                 69
                 AL
                 6.
                 33.
                 39.
                 the
                 place
                 of
                 the
                 ☉
                 Aphelion
                 sought
                 ,
                 and
                 this
                 is
                 the
                 quantity
                 which
                 we
                 retain
                 .
                 
                   
                     And
                     for
                     the
                     excentricity
                     BC.
                     
                  
                   
                     As
                     the
                     Sum
                     of
                     BAC
                     .
                     38.
                     26.
                     21
                  
                   
                     9.79356702
                  
                   
                     Is
                     to
                     the
                     Radius
                     .
                  
                   
                     10.00000000
                  
                   
                     So
                     is
                     the
                     side
                     BC
                     111345
                  
                   
                     5.04667072
                  
                   
                     To
                     the
                     Hypot
                     .
                     AB
                     .
                     179103
                  
                   
                     5.25310370
                  
                
                 
                   
                     
                       So
                       then
                    
                     Anno
                     Christi
                     .
                     1652.
                     
                     Aphel
                     .
                  
                   
                     96.
                     33.39
                  
                   
                     Anno
                     Christi
                     .
                     139.
                     the
                     Aphelion
                  
                   
                     70.
                     41.10
                  
                   
                     Their
                     difference
                     is
                  
                   
                     25.
                     52.29
                  
                
              
               
                 And
                 the
                 difference
                 of
                 time
                 is
                 1513
                 Julian
                 years
                 .
              
               
                 Hence
                 to
                 find
                 the
                 motion
                 of
                 the
                 Aphelion
                 for
                 2.
                 years
                 ,
                 say
                 I
                 ,
                 if
                 1513
                 years
                 give
                 25.
                 52.29
                 ,
                 what
                 shall
                 one
                 year
                 give
                 ,
                 and
                 the
                 answer
                 is
                 00
                 d.
                 01′
                 
                 01″
                 .
                 33‴
                 .
                 56
                 iv
                 .
                 44v.
                 that
                 is
                 in
                 Decimal
                 numbers
                 .
                 0.
                 00475.
                 04447.
                 0555.
                 
              
               
                 And
                 the
                 motion
                 for
                 .
                 1651
                 years
                 .
                 7.
                 84298.
                 4208862
                 ,
                 which
                 being
                 deducted
                 from
                 the
                 place
                 of
                 the
                 
                   Aphelion
                   Anno
                   Christi
                   .
                   1652
                   —
                   26.
                   82245.
                   3703703.
                   
                
                 The
                 remainer
                 ,
                 
                   viz.
                   18.
                   97946.
                   9494841
                
                 is
                 the
                 place
                 thereof
                 in
                 the
                 beginning
                 of
                 the
                 Christian
                 AEra
                 ,
                 which
                 being
                 reduced
                 is
                 ,
                 68
                 deg
                 .
                 19.
                 min.
                 33.
                 sec.
                 56.
                 thirds
                 .
              
               
                 4.
                 
                 The
                 Earths
                 middle
                 motion
                 ,
                 Aphelion
                 and
                 Excentricity
                 being
                 thus
                 found
                 ,
                 we
                 will
                 now
                 shew
                 how
                 the
                 same
                 may
                 be
                 stated
                 to
                 any
                 particular
                 time
                 desired
                 ,
                 and
                 this
                 must
                 be
                 done
                 by
                 help
                 of
                 the
                 Sun
                 or
                 Earths
                 place
                 taken
                 by
                 observation
                 .
                 In
                 the
                 178
                 year
                 then
                 from
                 the
                 death
                 of
                 
                   Alexander
                   ,
                   Mechir
                
                 the
                 27
                 at
                 11
                 hours
                 
                   P.
                   M.
                   Hipparcus
                
                 found
                 in
                 the
                 Meridian
                 of
                 Alexand.
                 that
                 the
                 Sun
                 entered
                 ♈
                 0.
                 the
                 which
                 Vernal
                 Equinox
                 happened
                 in
                 the
                 Meridian
                 of
                 London
                 according
                 to
                 Mr.
                 Wings
                 computation
                 at
                 9
                 hours
                 14′
                 ,
                 and
                 the
                 Suns
                 Aphelion
                 then
                 may
                 thus
                 be
                 found
                 .
              
               
                 The
                 motion
                 of
                 the
                 Aphelion
                 for
                 one
                 year
                 ,
                 was
                 before
                 found
                 to
                 be
                 .
                 0.
                 00475.
                 04447.
                 0555.
                 therefore
                 the
                 motion
                 thereof
                 for
                 one
                 day
                 is
                 0.
                 00001.
                 501491722.
                 
                 The
                 Christian
                 AEra
                 began
                 in
                 the
                 4713
                 year
                 compleat
                 of
                 the
                 Julian
                 Period
                 ,
                 in
                 which
                 there
                 are
                 days
                 1721423.
                 
                 The
                 
                   AEra
                   Alexandri
                
                 began
                 November
                 the
                 twelfth
                 ,
                 in
                 the
                 year
                 4390
                 of
                 the
                 Julian
                 Period
                 ,
                 in
                 which
                 there
                 are
                 1603397
                 days
                 .
                 And
                 from
                 the
                 death
                 of
                 Alexander
                 to
                 the
                 27
                 of
                 Mechir
                 178
                 ,
                 there
                 are
                 days
                 64781
                 ,
                 therefore
                 from
                 the
                 beginning
                 of
                 the
                 Julian
                 Period
                 ,
                 to
                 the
                 178
                 year
                 of
                 the
                 
                   AEra
                   Alexandri
                
                 ,
                 there
                 are
                 days
                 1668178
                 which
                 being
                 deducted
                 from
                 the
                 days
                 in
                 the
                 Christian
                 AEra
                 ,
                 
                 1721423
                 ,
                 the
                 remainer
                 is
                 53245
                 ,
                 the
                 number
                 of
                 days
                 between
                 the
                 178
                 year
                 after
                 the
                 death
                 of
                 
                   Alexander
                   ,
                   Mechir
                
                 27
                 ,
                 and
                 the
                 beginning
                 of
                 the
                 Christian
                 AEra
                 .
              
               
                 Or
                 thus
                 .
                 From
                 the
                 
                   AEra
                   Alexandri
                
                 to
                 the
                 
                   AEra
                   Christi
                
                 there
                 are
                 323
                 Julian
                 years
                 ,
                 and
                 51
                 days
                 ,
                 that
                 is
                 118026
                 days
                 .
                 And
                 from
                 the
                 
                   AEra
                   Alexandri
                
                 to
                 the
                 time
                 of
                 the
                 observation
                 ,
                 there
                 are
                 64781
                 days
                 ,
                 which
                 being
                 deducted
                 from
                 the
                 former
                 ,
                 the
                 remainer
                 is
                 53245
                 as
                 before
                 .
                 Now
                 then
                 if
                 you
                 multiply
                 the
                 motion
                 of
                 the
                 Aphelion
                 for
                 one
                 day
                 ,
                 viz.
                 0.
                 00001.
                 3014917
                 by
                 53245
                 ,
                 the
                 product
                 is
                 0.
                 69297.
                 9255665
                 ,
                 which
                 being
                 deducted
                 from
                 the
                 place
                 of
                 the
                 Aphelion
                 in
                 the
                 beginning
                 of
                 the
                 Christian
                 AEra
                 ,
                 before
                 found
                 .
                 18.
                 97946.
                 9494841.
                 the
                 remainer
                 18.
                 28649.
                 0239176
                 is
                 the
                 place
                 of
                 the
                 Aphelion
                 at
                 the
                 time
                 of
                 the
                 observation
                 ,
                 that
                 is
                 in
                 Sexagenary
                 numbers
                 .
                 deg
                 .
                 65.
                 
                 49′
                 .
                 53″
                 .
              
               
                 5.
                 
                 The
                 place
                 of
                 the
                 Aphelion
                 at
                 the
                 time
                 of
                 the
                 observation
                 being
                 thus
                 found
                 to
                 be
                 deg
                 .
                 65.
                 
                 49′
                 .
                 53″
                 .
                 The
                 Suns
                 mean
                 Longitude
                 at
                 that
                 time
                 ,
                 may
                 be
                 thus
                 computed
                 .
              
               
                 In
                 Fig.
                 8.
                 
                 In
                 the
                 Triangle
                 EMH
                 we
                 have
                 given
                 the
                 side
                 ME
                 200000
                 ,
                 the
                 side
                 MH
                 3576
                 ,
                 the
                 double
                 excentricity
                 before
                 found
                 ,
                 and
                 the
                 Angle
                 EMH
                 114.
                 
                 10′
                 .
                 07″
                 .
                 the
                 complement
                 of
                 the
                 Aphelion
                 to
                 a
                 Semicircle
                 ,
                 to
                 find
                 the
                 Angle
                 MEH
                 ,
                 for
                 which
                 the
                 proportion
                 is
                 ,
              
               
                 As
                 the
                 Summ
                 of
                 the
                 sides
                 ,
                 is
                 to
                 the
                 difference
                 of
                 the
                 sides
                 ,
                 so
                 is
                 the
                 Tangent
                 of
                 the
                 half
                 Summ
                 of
                 the
                 opposite
                 Angles
                 ,
                 to
                 the
                 Tangent
                 of
                 half
                 their
                 difference
                 .
                 
                   
                     The
                     side
                     ME.
                     200000.
                     
                  
                   
                      
                  
                   
                     The
                     side
                     MH
                     3576.
                     
                  
                   
                      
                  
                   
                   
                     Z.
                     Of
                     the
                     sides
                     .
                     203576.
                     
                     
                       Co.
                       ar
                    
                     .
                  
                   
                     4.69127343
                  
                   
                     X.
                     Of
                     the
                     sides
                     .
                     196424.
                     
                  
                   
                     5.29321855
                  
                   
                     Tang.
                     ½
                     Z
                     Angles
                     .
                     32′
                     .
                     54′
                     .
                     56.
                     
                  
                   
                     9.91111512
                  
                   
                     Tang.
                     ½
                     X
                     Angles
                     .
                     31.
                     59.
                     21.
                     
                  
                   
                      
                  
                   
                     Angle
                     MEH
                     .
                     0.
                     55.
                     35.
                     
                  
                   
                     9.79560710
                  
                
              
               
                 The
                 double
                 whereof
                 is
                 the
                 Angle
                 
                   MBH
                   1.
                
                 51.
                 10.
                 which
                 being
                 Subtracted
                 from
                 360
                 the
                 remainer
                 358.
                 08.
                 50.
                 is
                 the
                 estimate
                 middle
                 motion
                 of
                 the
                 Sun
                 ,
                 from
                 which
                 subtracting
                 the
                 Aphelion
                 before
                 found
                 ,
                 65.
                 49.
                 53.
                 the
                 remainer
                 292.
                 18.
                 57.
                 is
                 the
                 mean
                 Anomaly
                 by
                 which
                 the
                 absolute
                 AEquation
                 may
                 be
                 found
                 according
                 to
                 the
                 former
                 operation
                 .
                 
                   
                     Z.
                     ME+MH
                     .
                     203576.
                     
                     Co.
                     ar
                     .
                  
                   
                     4.69127343
                  
                   
                     X.
                     ME-MH
                     .
                     196424
                  
                   
                     5.29321855
                  
                   
                     Tang.
                     ½
                     Anom
                     .
                     56.
                     09.
                     28.
                     
                  
                   
                     10.17359517
                  
                   
                     Tang.
                     ½
                     X.
                     55.
                     12.
                     18.
                     
                  
                   
                     10.15808715
                  
                   
                     Differ
                     .
                     00.
                     57.
                     10.
                     
                  
                   
                      
                  
                
              
               
                 Doubled
                 1.
                 54.
                 20
                 ,
                 which
                 added
                 to
                 the
                 middle
                 motion
                 before
                 found
                 gives
                 the
                 ☉
                 true
                 place
                 ♈
                 .
                 00.
                 
                 3′
                 .
                 10″
                 ,
                 which
                 exceeds
                 the
                 observation
                 3′
                 .
                 10″
                 .
                 therefore
                 I
                 deduct
                 the
                 same
                 from
                 the
                 middle
                 motion
                 before
                 found
                 ,
                 and
                 the
                 remainer
                 358.
                 05.
                 50.
                 is
                 the
                 middle
                 motion
                 at
                 the
                 time
                 of
                 the
                 observation
                 of
                 Hipparchus
                 ,
                 to
                 which
                 if
                 you
                 add
                 the
                 middle
                 motion
                 of
                 the
                 Sun
                 for
                 53245
                 days
                 ,
                 or
                 for
                 323
                 AEgyptian
                 years
                 131
                 days
                 ,
                 280.
                 46.
                 
                 08′
                 the
                 Summ
                 ,
                 rejecting
                 the
                 whole
                 Circles
                 ,
                 is
                 278.
                 51.
                 48
                 the
                 Suns
                 mean
                 Longitude
                 in
                 the
                 beginning
                 of
                 the
                 Christian
                 AEra
                 .
              
               
                 6.
                 
                 But
                 one
                 observation
                 is
                 not
                 sufficient
                 ,
                 whereby
                 
                 to
                 state
                 the
                 middle
                 motion
                 for
                 any
                 desired
                 Epocha
                 ,
                 we
                 will
                 therefore
                 examine
                 the
                 same
                 by
                 another
                 observation
                 made
                 by
                 Albategnius
                 at
                 Aracta
                 in
                 the
                 year
                 of
                 Christ
                 882
                 ,
                 March
                 :
                 15.
                 hours
                 22.
                 21.
                 but
                 in
                 the
                 Meridian
                 of
                 London
                 at
                 18
                 hours
                 .
                 58′
                 .
              
               
                 The
                 motion
                 of
                 the
                 Aphelion
                 for
                 881
                 years
                 ,
                 74
                 days
                 is
                 3.
                 806068653737
                 ,
                 which
                 being
                 added
                 to
                 the
                 place
                 thereof
                 in
                 the
                 beginning
                 of
                 the
                 Christian
                 AEra
                 ,
                 the
                 place
                 at
                 the
                 time
                 of
                 the
                 observation
                 will
                 be
                 found
                 to
                 be
                 22.
                 785538148578
                 ,
                 that
                 is
                 reduced
                 ,
                 Deg.
                 82.
                 
                 01′
                 .
                 40″
                 .
                 And
                 hence
                 the
                 AEquation
                 according
                 to
                 the
                 former
                 operations
                 is
                 Deg.
                 2.
                 
                 01′
                 .
                 16″
                 which
                 being
                 deducted
                 from
                 a
                 whole
                 Circle
                 ,
                 the
                 remainer
                 357
                 d.
                 58′
                 .
                 44″
                 is
                 the
                 estimate
                 middle
                 motion
                 at
                 that
                 time
                 ,
                 from
                 which
                 deducting
                 the
                 Aphelion
                 deg
                 .
                 82.
                 01.
                 40.
                 the
                 remainer
                 275.
                 57.
                 04
                 is
                 the
                 mean
                 anomaly
                 ,
                 and
                 the
                 AEquation
                 answering
                 thereto
                 is
                 deg
                 .
                 2.
                 
                 02′
                 .
                 18″
                 which
                 being
                 added
                 to
                 the
                 middle
                 motion
                 before
                 found
                 ,
                 gives
                 the
                 ☉
                 place
                 ♈
                 .
                 00.
                 
                 01′
                 .
                 02″
                 which
                 exceeds
                 the
                 observation
                 01′
                 .
                 02″
                 .
                 therefore
                 deduct
                 the
                 same
                 from
                 the
                 middle
                 motion
                 before
                 found
                 ,
                 the
                 remainer
                 357.
                 
                 57′
                 .
                 22″
                 is
                 the
                 middle
                 motion
                 of
                 the
                 ☉
                 at
                 the
                 time
                 of
                 the
                 observation
                 ,
                 from
                 which
                 deducting
                 the
                 middle
                 motion
                 for
                 881
                 years
                 ,
                 74
                 days
                 ,
                 18
                 hours
                 ,
                 58
                 minutes
                 ,
                 viz.
                 80d.
                 06′
                 .
                 10″
                 .
                 the
                 remainer
                 277
                 deg
                 .
                 51′
                 .
                 12″
                 .
                 is
                 the
                 ☉
                 mean
                 Longitude
                 in
                 the
                 beginning
                 of
                 the
                 Christian
                 AEra
                 .
                 
                   
                     By
                     the
                     first
                     observation
                     it
                     is
                     deg
                     .
                  
                   
                     278.
                     
                     51′
                     .
                     48″
                  
                   
                     By
                     the
                     second
                  
                   
                     277.
                     51.
                     12
                  
                   
                     Their
                     difference
                     is
                  
                   
                     1.
                     00.
                     36
                  
                
              
               
               
                 He
                 that
                 desires
                 the
                 same
                 to
                 this
                 or
                 any
                 other
                 Epocha
                 ,
                 to
                 more
                 exactness
                 ,
                 must
                 take
                 the
                 pains
                 to
                 compare
                 the
                 Collection
                 thereof
                 from
                 sundry
                 Observations
                 ,
                 with
                 one
                 another
                 ,
                 this
                 is
                 sufficient
                 to
                 shew
                 how
                 it
                 is
                 to
                 be
                 found
                 .
                 Here
                 therefore
                 I
                 will
                 only
                 add
                 the
                 measures
                 set
                 down
                 by
                 some
                 of
                 our
                 own
                 Nation
                 ,
                 and
                 leave
                 it
                 to
                 the
                 Readers
                 choice
                 to
                 make
                 use
                 of
                 that
                 which
                 pleaseth
                 him
                 best
                 .
              
               
                 
                   The
                   ☉
                   mean
                   Longitude
                   in
                   the
                   beginning
                   of
                   the
                   Christian
                   AEra
                   according
                   to
                   .
                
                 
                   
                     Vincent
                     Wing
                  
                   is
                
                 
                   9.
                   8d.
                   00′
                   .
                   31″
                
                 
                   Tho.
                   Street
                   is
                
                 
                   9.
                   7.
                   55.
                   56
                
                 
                   Iohn
                   Flamsted
                   is
                
                 
                   9.
                   7.
                   54.
                   39
                
                 
                   By
                   our
                   first
                   Computation
                
                 
                   9.
                   8.
                   51.
                   48
                
                 
                   By
                   our
                   second
                
                 
                   9.
                   7.
                   51.
                   12
                
              
               
                 In
                 the
                 Ensuing
                 Tables
                 of
                 the
                 ☉
                 mean
                 Longitude
                 ,
                 we
                 have
                 made
                 use
                 of
                 that
                 measure
                 given
                 by
                 Mr.
                 Flamsted
                 ,
                 a
                 little
                 pains
                 will
                 fit
                 the
                 Tables
                 to
                 any
                 other
                 measure
                 .
              
            
             
               
                 CHAP.
                 XI
                 .
              
               
                 
                   Of
                   the
                   quantity
                   of
                   the
                   Tropical
                   and
                   Sydereal
                   Year
                   .
                
              
               
                 THe
                 year
                 Natural
                 or
                 Tropical
                 (
                 so
                 called
                 from
                 the
                 Greek
                 word
                 
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                
                 ,
                 (
                 which
                 signifies
                 to
                 turn
                 )
                 because
                 the
                 year
                 doth
                 still
                 turn
                 or
                 return
                 into
                 it self
                 )
                 is
                 that
                 part
                 of
                 time
                 in
                 which
                 the
                 ☉
                 doth
                 finish
                 his
                 course
                 in
                 the
                 Zodiack
                 
                 by
                 coming
                 to
                 the
                 same
                 point
                 from
                 whence
                 it
                 began
                 .
              
               
                 2.
                 
                 That
                 we
                 may
                 determine
                 the
                 true
                 quantity
                 thereof
                 ,
                 we
                 must
                 first
                 find
                 the
                 time
                 of
                 the
                 ☉
                 Ingress
                 into
                 the
                 AEquinoctial
                 Points
                 ,
                 about
                 which
                 there
                 is
                 no
                 small
                 difference
                 amongst
                 Astronomers
                 ,
                 and
                 therefore
                 an
                 absolute
                 exactness
                 is
                 not
                 to
                 be
                 expected
                 ,
                 it
                 is
                 well
                 that
                 we
                 are
                 arrived
                 so
                 near
                 the
                 Truth
                 as
                 we
                 are
                 .
                 Leaving
                 it
                 therefore
                 to
                 the
                 scrutiny
                 of
                 after
                 Ages
                 ,
                 to
                 make
                 and
                 compare
                 sundry
                 Observations
                 of
                 the
                 ☉
                 entrance
                 into
                 the
                 AEquinoctial
                 Points
                 ,
                 it
                 shall
                 suffice
                 to
                 shew
                 here
                 how
                 the
                 quantity
                 of
                 the
                 Tropical
                 year
                 may
                 be
                 determined
                 ,
                 from
                 these
                 following
                 observations
                 .
              
               
                 3.
                 
                 
                   Albategnius
                   ,
                   Anno
                   Christi
                
                 882
                 observed
                 the
                 ☉
                 entrance
                 into
                 the
                 Autumnal
                 AEquinox
                 at
                 Aracta
                 in
                 Syria
                 to
                 be
                 Sept.
                 19.
                 1
                 hour
                 15′
                 in
                 the
                 Morning
                 .
                 But
                 according
                 to
                 Mr.
                 Wings
                 correction
                 in
                 his
                 
                   Astron.
                   Instaur
                
                 .
                 Page
                 44
                 ,
                 it
                 was
                 at
                 1
                 hour
                 43′
                 in
                 the
                 Morning
                 ,
                 and
                 therefore
                 according
                 to
                 the
                 ☉
                 middle
                 motion
                 ,
                 the
                 mean
                 time
                 of
                 this
                 Autumnal
                 AEquinox
                 was
                 Sept.
                 16.
                 12
                 h.
                 14′
                 .
                 25″
                 .
                 that
                 is
                 at
                 London
                 at
                 8
                 h.
                 54′
                 .
                 25″
                 .
              
               
                 4.
                 
                 Again
                 by
                 sundry
                 observations
                 made
                 in
                 the
                 year
                 1650.
                 the
                 second
                 from
                 Bissextile
                 as
                 that
                 of
                 Albategnius
                 was
                 ,
                 the
                 true
                 time
                 of
                 the
                 ☉
                 ingress
                 into
                 ♎
                 was
                 found
                 to
                 be
                 Sept.
                 12.
                 14
                 h.
                 40′
                 .
                 and
                 therefore
                 his
                 ingress
                 according
                 to
                 his
                 middle
                 motion
                 was
                 Sept.
                 10.
                 13
                 h.
                 02.
                 
              
               
                 5.
                 
                 Now
                 the
                 interval
                 of
                 these
                 two
                 observations
                 is
                 the
                 time
                 of
                 768
                 years
                 ,
                 in
                 which
                 space
                 by
                 subtracting
                 the
                 lesser
                 from
                 the
                 greater
                 ,
                 I
                 find
                 an
                 anticipation
                 of
                 5
                 days
                 ,
                 9
                 hours
                 ,
                 52′
                 .
                 25″
                 .
                 which
                 divided
                 by
                 768
                 giveth
                 in
                 the
                 quotient
                 
                 10′
                 .
                 55″
                 .
                 39
                 which
                 being
                 subtracted
                 for
                 365
                 days
                 ,
                 6
                 hours
                 ,
                 the
                 quantity
                 of
                 the
                 Julian
                 year
                 ,
                 the
                 true
                 quantity
                 of
                 the
                 Tropical
                 year
                 will
                 be
                 365
                 days
                 ,
                 5
                 hours
                 ,
                 49′
                 .
                 04″
                 .
                 21‴
                 .
                 Others
                 from
                 other
                 observations
                 have
                 found
                 it
                 somewhat
                 less
                 ,
                 our
                 worthy
                 countryman
                 Mr.
                 
                   Edward
                   Wright
                
                 takes
                 it
                 to
                 be
                 365
                 d.
                 5
                 hours
                 .
                 48′
                 .
              
               
                 Mr.
                 
                   Iohn
                   Flamsted
                
                 ,
                 5
                 h.
                 29′
                 .
                 Mr.
                 
                   Tho.
                   Street
                
                 5
                 h.
                 49′
                 .
                 01″
                 .
                 taking
                 therefore
                 the
                 Tropical
                 year
                 to
                 consist
                 of
                 365
                 days
                 ,
                 5
                 hours
                 ,
                 49
                 Minutes
                 ,
                 the
                 Suns
                 mean
                 motion
                 for
                 one
                 day
                 is
                 0
                 deg
                 .
                 59′
                 .
                 8″
                 .
                 19‴
                 .
                 43
                 iv
                 .
                 47
                 v.
                 21
                 vi
                 .
                 29
                 vii
                 .
                 23
                 viii
                 .
                 or
                 in
                 decimal
                 Numbers
                 ,
                 the
                 whole
                 Circle
                 being
                 divided
                 into
                 100
                 degrees
                 ,
                 the
                 ☉
                 daily
                 motion
                 is
                 0.
                 27379.
                 08048.
                 11873.
                 
              
               
                 6.
                 
                 The
                 Sydereal
                 or
                 Starry
                 year
                 is
                 found
                 from
                 the
                 Solar
                 by
                 adding
                 the
                 Annual
                 Motion
                 of
                 the
                 eighth
                 Orb
                 or
                 praecession
                 of
                 the
                 AEquinoctial
                 Points
                 thereunto
                 ,
                 that
                 praecession
                 being
                 first
                 converted
                 into
                 time
                 .
              
               
                 7.
                 
                 Now
                 the
                 motion
                 of
                 the
                 fixed
                 Stars
                 is
                 found
                 to
                 be
                 about
                 50″
                 .
                 in
                 a
                 years
                 time
                 ,
                 as
                 Mr.
                 Wing
                 hath
                 collected
                 from
                 the
                 several
                 observations
                 of
                 
                   Timocharis
                   ,
                   Hipparchus
                   ,
                   Tycho
                
                 and
                 others
                 ;
                 and
                 to
                 shew
                 the
                 manner
                 of
                 this
                 Collection
                 ,
                 I
                 will
                 mention
                 onely
                 two
                 ,
                 one
                 in
                 the
                 time
                 of
                 Timocharis
                 ,
                 and
                 another
                 in
                 the
                 time
                 of
                 Tycho
                 .
              
               
                 8.
                 
                 Timocharis
                 then
                 as
                 Ptolemy
                 hath
                 it
                 in
                 his
                 Almagist
                 ,
                 sets
                 down
                 the
                 Virgins
                 Spike
                 more
                 northwardly
                 than
                 the
                 AEquinoctial
                 ,
                 1
                 deg
                 .
                 24′
                 .
                 the
                 time
                 of
                 this
                 observation
                 is
                 supposed
                 to
                 be
                 about
                 291
                 years
                 before
                 Christ
                 ,
                 the
                 Latitude
                 1
                 deg
                 .
                 59′
                 South
                 ,
                 and
                 therefore
                 the
                 place
                 of
                 the
                 Star
                 was
                 in
                 ♍
                 .
                 21
                 d.
                 59′
                 .
                 And
                 by
                 the
                 observation
                 of
                 Tycho
                 1601
                 current
                 ,
                 it
                 was
                 in
                 ♎
                 
                 18.
                 
                 16′
                 .
                 and
                 therefore
                 the
                 motion
                 in
                 one
                 year
                 50″
                 ,
                 which
                 being
                 divided
                 by
                 365
                 days
                 ,
                 6
                 hours
                 ,
                 the
                 quotient
                 is
                 the
                 motion
                 thereof
                 in
                 a
                 days
                 time
                 .
                 00′
                 .
                 8‴
                 .
                 12
                 iv
                 .
                 48
                 v.
                 47
                 vi
                 .
                 18
                 vii
                 .
                 30
                 viii
                 .
                 13
                 ix
                 .
                 and
                 in
                 decimal
                 Numbers
                 ,
                 the
                 motion
                 for
                 a
                 year
                 is
                 00385.
                 80246.
                 91358.
                 
                 The
                 motion
                 for
                 a
                 day
                 .
                 00001.
                 05626.
                 95938.
                 
              
               
                 9.
                 
                 Now
                 the
                 time
                 in
                 which
                 the
                 Sun
                 moveth
                 50″
                 ,
                 is
                 20′
                 .
                 17″
                 .
                 28‴
                 ,
                 therefore
                 the
                 length
                 of
                 the
                 sydereal
                 year
                 is
                 365
                 days
                 ,
                 6
                 hours
                 ,
                 9′
                 .
                 17″
                 .
                 28‴
                 .
                 And
                 the
                 Suns
                 mean
                 motion
                 for
                 a
                 day
                 59′
                 .
                 8″
                 .
                 19‴
                 .
                 43
                 iv
                 .
                 47
                 v.
                 21
                 vi
                 .
                 29
                 vii
                 .
                 23
                 viii
                 .
                 converted
                 into
                 time
                 is
                 00.
                 
                 03′
                 .
                 56″
                 .
                 33‴
                 .
                 18
                 iv
                 .
                 55
                 v.
                 9
                 vi
                 .
                 23
                 vii
                 .
                 57
                 viii
                 .
                 which
                 being
                 added
                 to
                 the
                 AEquinoctial
                 day
                 ,
                 24
                 hours
                 ,
                 giveth
                 the
                 mean
                 solar
                 day
                 ,
                 24
                 hours
                 .
                 3.
                 
                 ′
                 56″
                 .
                 33‴
                 .
                 18
                 iv
                 .
                 55.
                 9.
                 23.
                 57.
                 
              
               
                 10.
                 
                 And
                 the
                 daily
                 motion
                 of
                 the
                 fixed
                 Stars
                 ,
                 being
                 converted
                 into
                 time
                 is
                 32
                 iv
                 .
                 51
                 v.
                 15
                 vi
                 .
                 9
                 vii
                 .
                 14
                 viii
                 .
                 24
                 ix
                 .
                 and
                 therefore
                 the
                 AEquinoctial
                 day
                 being
                 24
                 hours
                 ,
                 the
                 sydereal
                 day
                 is
                 24
                 hours
                 ,
                 00′
                 .
                 00″
                 .
                 00‴
                 .
                 32
                 iv
                 .
                 51.
                 15.
                 9.
                 14
                 24.
                 
              
               
                 11.
                 
                 Hence
                 to
                 find
                 the
                 praecession
                 of
                 the
                 AEquinoctial
                 Points
                 ,
                 or
                 Longitude
                 of
                 any
                 fixed
                 Star
                 ,
                 you
                 must
                 add
                 or
                 subtract
                 the
                 motion
                 thereof
                 ,
                 from
                 the
                 time
                 of
                 the
                 observation
                 ,
                 to
                 the
                 time
                 given
                 ,
                 to
                 or
                 from
                 the
                 place
                 given
                 by
                 observation
                 ,
                 and
                 you
                 have
                 your
                 desire
                 .
              
               
                 Example
                 .
                 The
                 place
                 of
                 the
                 first
                 Star
                 in
                 Aries
                 found
                 by
                 Tycho
                 in
                 the
                 year
                 1601
                 current
                 ,
                 was
                 in
                 ♈
                 .
                 27
                 d.
                 37′
                 .
                 00.
                 and
                 I
                 would
                 know
                 the
                 place
                 thereof
                 in
                 the
                 beginning
                 of
                 the
                 Christian
                 AEra
                 .
              
               
               
                 
                   
                     The
                     motion
                     of
                     the
                     fixed
                     Stars
                     for
                     1600
                     years
                     ,
                  
                   
                     22
                     d.
                     13′
                     .
                     20″
                  
                   
                     Which
                     being
                     deducted
                     from
                     the
                     place
                     found
                     by
                     observ
                     .
                  
                   
                     27.
                     37.
                     00
                  
                   
                     The
                     remainer
                     .
                  
                   
                     5.
                     231.
                     40
                  
                
                 is
                 the
                 place
                 thereof
                 in
                 the
                 beginning
                 of
                 the
                 Christian
                 AEra
                 .
              
               
                 12.
                 
                 Having
                 thus
                 found
                 the
                 ☉
                 middle
                 motion
                 ,
                 the
                 motion
                 of
                 the
                 Aphelion
                 and
                 fixed
                 Stars
                 ,
                 with
                 their
                 places
                 ,
                 in
                 the
                 beginning
                 of
                 the
                 Christian
                 AEra
                 ;
                 we
                 will
                 now
                 set
                 down
                 the
                 numbers
                 here
                 exhibited
                 
                   AEra
                   Christi
                
                 .
                 Mr.
                 Wing
                 from
                 the
                 like
                 observations
                 ,
                 takes
                 the
                 ☉
                 motion
                 to
                 be
                 as
                 followeth
                 .
              
               
                 
                   
                     The
                     ☉
                     mean
                     Longitude
                  
                   
                     9.
                     8.
                     00.
                     31
                  
                   
                     Place
                     of
                     Aphelion
                  
                   
                     2.
                     8.
                     20.
                     03
                  
                   
                     The
                     Anomaly
                  
                   
                     06.
                     29.
                     40.
                     28
                  
                
                 
                   
                     The
                     which
                     in
                     decimal
                     Numbers
                     are
                  
                   
                     The
                     ☉
                     mean
                     Longitude
                  
                   
                     77.
                     22460.
                     86419
                  
                   
                     Place
                     of
                     the
                     Aphelion
                  
                   
                     18.
                     98171.
                     29629
                  
                   
                     The
                     Anomaly
                  
                   
                     58.
                     24289.
                     56790
                  
                
                 
                   
                     The
                     mean
                     motions
                     for
                     one
                     year
                     .
                  
                   
                     The
                     ☉
                     mean
                     Longitude
                  
                   
                     99.
                     93364.
                     37563.
                     34
                  
                   
                     The
                     Aphelion
                  
                   
                     00.
                     00475.
                     04447.
                     05
                  
                   
                     The
                     ☉
                     mean
                     Anomaly
                  
                   
                     99.
                     92889.
                     33116.
                     29
                  
                
                 
                   
                     The
                     ☉
                     mean
                     motions
                     for
                     one
                     day
                     .
                  
                   
                   
                     The
                     ☉
                     mean
                     Longitude
                  
                   
                     00.
                     27379.
                     08048.
                     11
                  
                   
                     The
                     Aphelion
                  
                   
                     00.
                     00001.
                     30149.
                     17
                  
                   
                     The
                     mean
                     Anomaly
                  
                   
                     00.
                     27377.
                     77898.
                     94
                  
                
              
               
                 And
                 according
                 to
                 these
                 measures
                 are
                 the
                 Tables
                 made
                 shewing
                 the
                 ☉
                 mean
                 Longitude
                 and
                 Anomaly
                 ,
                 for
                 Years
                 ,
                 Months
                 ,
                 Days
                 and
                 Hours
                 .
              
            
             
               
                 CHAP.
                 XII
                 .
              
               
                 
                   The
                   Suns
                   mean
                   motions
                   otherwise
                   stated
                   .
                
              
               
                 SOme
                 there
                 are
                 in
                 our
                 present
                 age
                 ,
                 that
                 will
                 not
                 allow
                 the
                 Aphelion
                 to
                 have
                 any
                 motion
                 ,
                 or
                 alteration
                 ,
                 but
                 what
                 proceeds
                 from
                 the
                 motion
                 of
                 the
                 fixed
                 Stars
                 ,
                 the
                 which
                 as
                 hath
                 been
                 shewed
                 ,
                 do
                 move
                 50
                 seconds
                 in
                 a
                 year
                 ,
                 and
                 hence
                 the
                 place
                 of
                 the
                 first
                 Star
                 in
                 Aries
                 ,
                 in
                 the
                 beginning
                 of
                 the
                 Christian
                 AEra
                 was
                 found
                 to
                 be
                 ♈
                 .
                 5.
                 23d.
                 40.
                 
              
               
                 Now
                 then
                 ,
                 if
                 from
                 the
                 place
                 of
                 the
                 
                   Aphelion
                   Anno
                   Christi
                
                 .
                 1652
                 as
                 was
                 shewed
                 in
                 the
                 tenth
                 Chapter
                 ,
                 deg
                 .
                 96.
                 
                 33′
                 .
                 39.
                 we
                 deduct
                 the
                 motion
                 of
                 the
                 fixed
                 Stars
                 for
                 that
                 time
                 .
                 28.
                 19.
                 12.
                 the
                 remainer
                 68.
                 14.
                 27
                 is
                 the
                 constant
                 place
                 of
                 the
                 Aphelion
                 ;
                 but
                 Mr.
                 Street
                 in
                 his
                 
                   Astronomia
                   Carolina
                
                 Page
                 23
                 ,
                 makes
                 the
                 constant
                 place
                 of
                 the
                 Aphelion
                 to
                 be
                 68d.
                 20.
                 00
                 ,
                 and
                 the
                 ☉
                 excentricity
                 1732.
                 
              
               
               
               
                 
                   The
                   place
                   of
                   the
                   Sun
                   observed
                
                 
                   ♈
                   .
                   0.
                   33.
                   19
                
                 
                   The
                   praecession
                   of
                   AEquinox
                
                 
                   0.
                   27.
                   27.
                   22
                
                 
                   The
                   Earths
                   Sydereal
                   Longitude
                
                 
                   5.
                   03.
                   05.
                   57
                
                 
                   The
                   place
                   of
                   the
                   Aphelion
                   Subtract
                
                 
                   8.
                   08.
                   20.
                   00
                
              
               
                 
                   The
                   Earths
                   true
                   Anomaly
                
                 
                   8.
                   24.
                   45.
                   57
                
                 
                   AEquation
                   Subtract
                
                 
                   1.
                   58.
                   47
                
              
               
                 
                   The
                   remainer
                   is
                   the
                   Estimate
                   M.
                   Anom
                   .
                
                 
                   8.
                   22.
                   47.
                   10
                
                 
                   AEquation
                   answering
                   thereto
                   add
                   .
                
                 
                   1.
                   58.
                   27
                
              
               
                 
                   The
                   Earths
                   true
                   Anomaly
                
                 
                   8.
                   24.
                   45.
                   37
                
                 
                   The
                   place
                   of
                   the
                   Aphelion
                
                 
                   8.
                   08.
                   20.
                   00
                
                 
                   Praecession
                   of
                   the
                   AEquinox
                
                 
                   0.
                   27.
                   27.
                   22
                
              
               
                 
                   Place
                   of
                   the
                   Sun
                
                 
                   ♈
                   .
                   00.
                   32.
                   59
                
                 
                   But
                   the
                   place
                   by
                   observation
                
                 
                   ♈
                   .
                   00.
                   33.
                   19
                
                 
                   The
                   difference
                   is
                
                 
                   001.
                   001.
                   20
                
                 
                   Which
                   being
                   added
                   to
                   the
                   mean
                   Anom
                   .
                
                 
                   8.
                   22.
                   47.
                   10
                
                 
                   The
                   mean
                   Anomaly
                   is
                
                 
                   8.
                   22.
                   47.
                   30
                
                 
                   The
                   absolute
                   AEquation
                
                 
                   1.
                   58.
                   27
                
                 
                   The
                   true
                   Anomaly
                
                 
                   8.
                   24.
                   45.
                   57
                
                 
                   Agreeing
                   with
                   observation
                   .
                
                 
                    
                
              
               
                 And
                 so
                 the
                 mean
                 Anomaly
                 
                   AEra
                   Christi
                
                 is
                 6.
                 23.
                 19.
                 56.
                 
                 But
                 Mr.
                 Flamsted
                 according
                 to
                 whose
                 measure
                 the
                 ensuing
                 Tables
                 are
                 composed
                 ,
                 takes
                 the
                 mean
                 Anomaly
                 
                   AEra
                   Christi
                
                 .
                 to
                 be
                 6.
                 24.
                 07.
                 091.
                 
                 The
                 place
                 of
                 the
                 Aphelion
                 to
                 be
                 8
                 ,
                 08.
                 23.
                 50.
                 
                 And
                 so
                 the
                 Praecession
                 of
                 the
                 AEquinox
                 and
                 Aphelion
                 in
                 the
                 beginning
                 of
                 
                 the
                 Christian
                 AEra
                 .
                 8
                 ,
                 13.
                 47.
                 30.
                 in
                 decimal
                 Numbers
                 .
              
               
                 
                   AEra
                   Christi
                   .
                
                 
                   The
                   Suns
                   mean
                   Anomaly
                
                 
                   56.
                   69976.
                   85185
                
                 
                   The
                   Suns
                   Apogaeon
                   and
                   Praec
                   .
                   AEq.
                   
                
                 
                   20.
                   49768.
                   51851
                
              
               
                 
                   The
                   ☉
                   mean
                   motions
                   for
                   one
                   Year
                   .
                
                 
                   The
                   ☉
                   mean
                   Longitude
                
                 
                   99.
                   93364.
                   37563.
                   34
                
                 
                   The
                   Praecession
                   of
                   AEquin
                   .
                
                 
                   00385.
                   80246.
                   91
                
                 
                   The
                   ☉
                   mean
                   Anomal
                   .
                
                 
                   99.
                   92978.
                   57316.
                   43
                
              
               
                 
                   The
                   ☉
                   mean
                   Motions
                   for
                   one
                   Day
                   .
                
                 
                   The
                   ☉
                   mean
                   Longitude
                
                 
                   00.
                   27379.
                   08048.
                   11
                
                 
                   The
                   Praecession
                   of
                   AEqui
                   .
                
                 
                   00.
                   00001.
                   05699.
                   30
                
                 
                   The
                   ☉
                   mean
                   Anom
                   .
                
                 
                   00.
                   27378.
                   02348.
                   81
                
              
            
             
               
                 CHAP.
                 XIII
                 .
              
               
                 
                   How
                   to
                   Calculate
                   the
                   Suns
                   true
                   place
                   by
                   either
                   of
                   the
                   Tables
                   of
                   middle
                   motion
                   .
                
              
               
                 VVRite
                 out
                 the
                 Epocha
                 next
                 before
                 the
                 given
                 time
                 ,
                 and
                 severally
                 under
                 that
                 set
                 the
                 motions
                 belonging
                 to
                 the
                 years
                 ,
                 months
                 and
                 days
                 compleat
                 ,
                 to
                 the
                 hours
                 ,
                 scruples
                 ,
                 current
                 every
                 one
                 under
                 his
                 like
                 (
                 only
                 remember
                 that
                 in
                 the
                 Bissextile
                 years
                 after
                 the
                 end
                 of
                 Frebruary
                 the
                 days
                 must
                 be
                 increased
                 by
                 an
                 unite
                 )
                 then
                 adding
                 all
                 together
                 ,
                 the
                 sum
                 shall
                 be
                 the
                 ☉
                 mean
                 motion
                 for
                 the
                 time
                 given
                 .
              
               
               
                 Example
                 .
              
               
                 Let
                 the
                 given
                 time
                 be
                 
                   Anno
                   Christi
                   1672.
                   
                   February
                   23.
                
                 hours
                 11.
                 
                 34′
                 .
                 54″
                 .
                 by
                 the
                 Tables
                 of
                 the
                 ☉
                 mean
                 Longitude
                 and
                 Anomaly
                 ,
                 the
                 numbers
                 are
                 as
                 followeth
                 .
              
               
                 
                   
                     
                        
                    
                     
                        
                    
                     
                       M.
                       Longitud
                       .
                    
                     
                       M.
                       Anomal
                       .
                    
                  
                   
                     
                       The
                       Epocha
                    
                     
                       1660
                    
                     
                       80.
                       67440.
                       
                    
                     
                       53.79815
                    
                  
                   
                     
                       Years
                    
                     
                       11
                    
                     
                       99.
                       81766.
                       
                    
                     
                       99.76526
                    
                  
                   
                     
                       Ianuary
                    
                     
                        
                    
                     
                       08.
                       48751.
                       
                    
                     
                       08.48711
                    
                  
                   
                     
                       Day
                       .
                    
                     
                       23
                    
                     
                       06.
                       29718.
                       
                    
                     
                       06.29688
                    
                  
                   
                     
                       Hours
                    
                     
                       11
                    
                     
                       00.
                       12548.
                       
                    
                     
                       00.12548
                    
                  
                   
                     
                        
                    
                     
                       34
                    
                     
                       00.
                       00646.
                       
                    
                     
                       00.00646
                    
                  
                   
                     
                        
                    
                     
                       54
                    
                     
                       00.
                       00017.
                       
                    
                     
                       00.00017
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       95.
                       40886.
                       
                    
                     
                       68.47951
                    
                  
                
              
               
                 By
                 the
                 Tables
                 of
                 the
                 Suns
                 mean
                 Anomaly
                 and
                 praecession
                 of
                 the
                 AEquinox
                 ,
                 the
                 numbers
                 are
                 these
                 .
              
               
                 
                   
                     
                        
                    
                     
                        
                    
                     
                       Anomaly
                       .
                    
                     
                       Praece
                       .
                       AEqui
                       .
                    
                  
                   
                     
                       The
                       Epocha
                    
                     
                       1660
                    
                     
                       53.
                       76721.
                       
                    
                     
                       26.90200
                    
                  
                   
                     
                       Years
                    
                     
                       11
                    
                     
                       99.
                       77520.
                       
                    
                     
                       00.04243
                    
                  
                   
                     
                       Ianuary
                    
                     
                        
                    
                     
                       8.
                       48718.
                       
                    
                     
                       00032
                    
                  
                   
                     
                       Days
                    
                     
                       23
                    
                     
                       6.
                       29694.
                       
                    
                     
                       00024
                    
                  
                   
                     
                       Hours
                    
                     
                       11
                    
                     
                       0.
                       12548.
                       
                    
                     
                       26.94499
                    
                  
                   
                     
                        
                    
                     
                       34′
                    
                     
                       .00646
                       .
                    
                     
                       68.45882
                    
                  
                   
                     
                        
                    
                     
                       54″
                    
                     
                       .00035
                       .
                    
                     
                       95.40381
                    
                  
                   
                     
                       ☉
                       mean
                       Anomaly
                    
                     
                        
                    
                     
                       68.45882
                    
                     
                        
                    
                  
                
              
               
               
                 There
                 is
                 no
                 great
                 difference
                 between
                 the
                 ☉
                 mean
                 Longitude
                 and
                 Anomaly
                 found
                 by
                 the
                 Tables
                 of
                 mean
                 Longitude
                 and
                 Anomaly
                 ,
                 and
                 that
                 found
                 by
                 the
                 Tables
                 of
                 mean
                 Anomaly
                 and
                 Precession
                 of
                 the
                 AEquinox
                 .
                 The
                 method
                 of
                 finding
                 the
                 Elliptical
                 AEquation
                 is
                 the
                 same
                 in
                 both
                 ,
                 we
                 will
                 instance
                 in
                 the
                 latter
                 only
                 ,
                 in
                 which
                 the
                 ☉
                 mean
                 Anomaly
                 is
                 Degrees
                 68.
                 45882.
                 
                 And
                 the
                 precession
                 of
                 AEquin
                 .
                 deg
                 .
                 26.
                 94499.
                 
              
               
                 But
                 because
                 there
                 is
                 no
                 Canon
                 of
                 Sines
                 and
                 Tangents
                 as
                 yet
                 published
                 ,
                 suitable
                 to
                 this
                 division
                 of
                 the
                 Circle
                 into
                 an
                 100
                 deg
                 .
                 or
                 parts
                 :
                 We
                 must
                 first
                 convert
                 the
                 ☉
                 mean
                 Anomaly
                 ,
                 and
                 prec
                 .
                 of
                 of
                 the
                 AEquin
                 ,
                 given
                 ,
                 into
                 the
                 degrees
                 and
                 parts
                 of
                 the
                 common
                 Circle
                 :
                 And
                 this
                 may
                 be
                 done
                 either
                 into
                 degrees
                 and
                 decimal
                 parts
                 of
                 a
                 degree
                 ,
                 or
                 into
                 deg
                 .
                 and
                 minutes
                 :
                 if
                 it
                 were
                 required
                 to
                 be
                 done
                 into
                 degrees
                 and
                 minutes
                 ,
                 the
                 Table
                 here
                 exhibited
                 for
                 that
                 purpose
                 will
                 serve
                 the
                 turn
                 ,
                 but
                 if
                 it
                 be
                 required
                 to
                 be
                 done
                 into
                 degrees
                 and
                 decimal
                 parts
                 ,
                 I
                 judge
                 the
                 following
                 method
                 to
                 be
                 more
                 convenient
                 .
              
               
                 Multiply
                 the
                 degrees
                 and
                 parts
                 given
                 by
                 36
                 ,
                 the
                 Product
                 ,
                 if
                 you
                 cut
                 off
                 one
                 figure
                 more
                 towards
                 the
                 right
                 hand
                 than
                 there
                 are
                 parts
                 in
                 the
                 number
                 given
                 ,
                 shall
                 be
                 the
                 degrees
                 and
                 parts
                 of
                 the
                 common
                 Circle
                 .
              
               
                 
                   
                     
                       Anomaly
                       .
                       68.
                       45882
                    
                     
                       Praec
                       .
                       AEquinox
                       .
                       26.
                       94499
                    
                  
                   
                     
                       36
                    
                     
                        
                    
                     
                       36
                    
                  
                   
                     
                       41075292
                    
                     
                        
                    
                     
                       16166994
                    
                  
                   
                     
                       20537646
                    
                     
                        
                    
                     
                       8983497
                    
                  
                   
                     
                       Anom
                       .
                       246.
                       451752
                    
                     
                        
                    
                     
                       Prae.
                       AEq.
                       97.
                       001964
                    
                  
                
              
               
               
                 And
                 if
                 you
                 multiply
                 the
                 parts
                 of
                 these
                 Products
                 ,
                 you
                 will
                 convert
                 them
                 into
                 minutes
                 .
              
               
                 Otherwise
                 thus
                 .
                 Multiply
                 the
                 degrees
                 and
                 parts
                 given
                 by
                 6
                 continually
                 ,
                 the
                 second
                 Product
                 ,
                 if
                 you
                 cut
                 off
                 one
                 figure
                 more
                 towards
                 the
                 right
                 hand
                 than
                 are
                 parts
                 in
                 the
                 number
                 given
                 ,
                 shall
                 be
                 the
                 degrees
                 and
                 parts
                 of
                 the
                 common
                 Circle
                 .
                 The
                 third
                 Product
                 of
                 the
                 parts
                 only
                 shall
                 give
                 minutes
                 ,
                 the
                 fourth
                 seconds
                 ,
                 and
                 so
                 forward
                 as
                 far
                 as
                 you
                 please
                 .
                 Example
                 .
              
               
                 
                   ☉
                   Mean
                   Anom
                   .
                   68.
                   45882
                
                 
                   Praec
                   .
                   AEq.
                   26.
                   94499
                
                 
                   6
                
                 
                   6
                
                 
                   41075292
                
                 
                   16166994
                
                 
                   246.451752
                
                 
                   97.001964
                
                 
                   6
                
                 
                   6
                
                 
                   27.10512
                
                 
                   0.11784
                
                 
                   6
                
                 
                   6
                
                 
                   6.3072
                
                 
                   7.0704
                
              
               
                 And
                 thus
                 the
                 mean
                 Anom
                 .
                 is
                 deg
                 .
                 246.
                 451742
                 or
                 27′
                 .
                 06.
                 
                 The
                 Prec
                 .
                 AEq.
                 97.
                 001964.
                 or
                 00′
                 .
                 07″
                 .
              
               
                 Hence
                 to
                 find
                 the
                 Elliptical
                 AEquation
                 in
                 degrees
                 and
                 decimal
                 parts
                 :
                 In
                 Fig.
                 8.
                 we
                 have
                 given
                 in
                 the
                 right
                 lined
                 plain
                 Triangle
                 EMH
                 ,
                 the
                 sides
                 ME
                 ,
                 and
                 MH
                 ,
                 and
                 the
                 Angle
                 EMH
                 ,
                 66.
                 451742.
                 the
                 excess
                 of
                 the
                 mean
                 Anomaly
                 above
                 a
                 Semicircle
                 ,
                 to
                 find
                 the
                 Angle
                 MEH
                 .
              
               
                 
                 
                   The
                   side
                   ME
                
                 
                   200000
                
                 
                   The
                   side
                   MH
                
                 
                   3468
                
              
               
                 
                   
                     
                       Zcru
                       .
                    
                     
                       203468
                    
                     
                       
                         Co.
                         ar
                      
                       .
                    
                     
                       4.69150389
                    
                  
                   
                     
                       Xcru
                       .
                    
                     
                       196532
                    
                     
                        
                    
                     
                       5.29343327
                    
                  
                   
                     
                       
                         t
                         frac12
                      
                       Zangle
                       .
                    
                     
                       56.774129
                    
                     
                        
                    
                     
                       10.18374097
                    
                  
                   
                     
                       
                         t
                         frac12
                      
                       Xangle
                       .
                    
                     
                       55.857087
                    
                     
                        
                    
                     
                       10.16867813
                    
                  
                
              
               
                 MEH
                 .
                 0.
                 917042
                 the
                 double
                 whereof
                 is
                 the
                 Angle
                 MBH
                 .
                 1.
                 834084
                 or
                 Elliptick
                 AEquation
                 sought
                 ,
                 which
                 being
                 added
                 to
                 the
                 mean
                 Anomaly
                 and
                 praecession
                 of
                 the
                 AEquinox
                 ,
                 because
                 the
                 Anomaly
                 is
                 more
                 than
                 a
                 Semicircle
                 ,
                 the
                 same
                 is
                 the
                 Suns
                 true
                 place
                 .
              
               
                 
                   The
                   ☉
                   mean
                   Anomaly
                
                 
                   246.451742
                
                 
                   The
                   Praecession
                   of
                   the
                   AEquinox
                
                 
                   97.001964
                
                 
                   Elliptick
                   AEquation
                
                 
                   1.834084
                
                 
                   The
                   Suns
                   true
                   place
                   .
                
                 
                   345.287790
                
              
               
                 But
                 because
                 the
                 Elliptick
                 AEquation
                 thus
                 found
                 doth
                 not
                 so
                 exactly
                 agree
                 to
                 observation
                 as
                 is
                 desired
                 ,
                 Bullialdus
                 in
                 Chap.
                 3.
                 of
                 his
                 Book
                 entituled
                 
                   Astronomiae
                   Philolaicae
                   fundamenta
                   clarius
                   explicata
                
                 ,
                 Printed
                 at
                 Paris
                 ,
                 1657.
                 shews
                 how
                 to
                 correct
                 the
                 same
                 by
                 an
                 Angle
                 applied
                 to
                 the
                 Focus
                 of
                 middle
                 motion
                 ,
                 subtended
                 by
                 the
                 part
                 of
                 the
                 ordinate
                 line
                 ,
                 intercepted
                 between
                 the
                 Ellipsis
                 and
                 the
                 Circle
                 circumscribing
                 it
                 .
                 This
                 Mr.
                 Street
                 maketh
                 use
                 of
                 in
                 his
                 
                   Astronomia
                   Carolina
                
                 ,
                 and
                 this
                 I
                 thought
                 not
                 amiss
                 to
                 add
                 here
                 .
              
               
               
                 XN
                 .
                 GX
                 ∷
                 OB
                 tang
                 .
                 OEB.
                 OM
                 tang
                 .
                 OEM.
                 
              
               
                 And
                 the
                 Angle
                 
                   OEM-OEB
                   =
                   BEM
                   =
                   ETY
                
                 ,
                 the
                 variation
                 to
                 be
                 deducted
                 from
                 the
                 Elliptick
                 AEquation
                 ETH
                 ,
                 the
                 Remainer
                 is
                 the
                 absolute
                 AEquation
                 YTS
                 in
                 the
                 first
                 Quadrant
                 .
              
               
                 In
                 the
                 second
                 and
                 third
                 Quadrants
                 ,
                 the
                 variation
                 or
                 difference
                 between
                 the
                 mean
                 and
                 corrected
                 Anomaly
                 ,
                 must
                 be
                 added
                 to
                 the
                 Elliptick
                 AEquation
                 ,
                 to
                 find
                 the
                 true
                 and
                 absolute
                 AEquation
                 .
              
               
                 For
                 
                   XN
                   .
                   XG
                   .
                   QV.
                   tang
                   .
                   QEV.
                
                 the
                 
                   comp
                   .
                   m.
                   Anom
                   .
                   QR
                   .
                   t.
                   QER.
                
                 and
                 the
                 Angle
                 
                   VER
                   =
                   ECO
                
                 is
                 the
                 variation
                 ,
                 and
                 
                   ECO+ECH
                   =
                   OCH
                
                 is
                 the
                 absolute
                 AEquation
                 sought
                 in
                 the
                 second
                 Quadrant
                 .
              
               
                 Again
                 ,
                 
                   XN
                   .
                   SG
                   ∷
                   a
                   D
                   ,
                   tang
                   .
                   a
                   ED.
                   a
                   b
                   ,
                   tang
                   .
                   aEB
                   .
                
                 And
                 
                   aEB
                   —
                   aED
                   =
                   DEf
                
                 the
                 variation
                 =
                 EFO
                 and
                 
                   EfO+EfH
                   =
                   OfH
                
                 the
                 absolute
                 AEquation
                 sought
                 in
                 the
                 third
                 Quadrant
                 .
              
               
                 Lastly
                 ,
                 in
                 the
                 fourth
                 Quadrant
                 of
                 mean
                 Anomaly
                 it
                 is
                 .
              
               
                 
                   XN
                   .
                   XG
                   ∷
                   ch
                   .
                   tang
                   .
                   eEH.
                   eg
                   .
                   tang
                   .
                   eFg.
                
                 and
                 hEg
                 is
                 the
                 variation
                 :
                 And
                 
                   EFH
                   —
                   
                     〈◊〉
                     〈◊〉
                     〈◊〉
                     〈◊〉
                     〈◊〉
                  
                   =
                   
                     〈◊〉
                     〈◊〉
                     〈◊〉
                     〈◊〉
                     〈◊〉
                  
                
                 the
                 absolute
                 AEquation
                 sought
                 in
                 the
                 fourth
                 Quadrant
                 .
              
               
                 And
                 to
                 find
                 XN
                 the
                 conjugate
                 Semi-diameter
                 ,
                 in
                 the
                 right
                 angled
                 Triangle
                 ENX
                 ,
                 we
                 have
                 given
                 ,
                 
                   EN
                   =
                   AX
                
                 and
                 EX
                 the
                 semi-distance
                 of
                 the
                 umbilick
                 points
                 .
                 And
                 Mr.
                 Briggs
                 in
                 Chap.
                 19.
                 of
                 his
                 Arithm.
                 Logar
                 .
                 hath
                 shewed
                 ,
                 that
                 the
                 half
                 Sum
                 of
                 the
                 Logarith
                 .
                 of
                 the
                 sum
                 and
                 difference
                 of
                 the
                 Hypotenuse
                 ,
                 and
                 the
                 given
                 leg
                 .
                 shall
                 be
                 the
                 Logarith
                 .
                 of
                 the
                 other
                 leg
                 .
              
               
                 
                   
                     
                       
                       Now
                       then
                       
                         EN
                         =
                         AX.
                      
                       100000
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       The
                       Leg
                       EX
                       .
                    
                     
                       1734
                    
                     
                        
                    
                  
                   
                     
                       Their
                       Sum
                    
                     
                       101734
                    
                     
                       5.00745001
                    
                  
                   
                     
                       Their
                       difference
                    
                     
                       98266
                    
                     
                       4.99240328
                    
                  
                   
                     
                        
                    
                     
                       The
                       Z
                       of
                       the
                       Logarithms
                       ,
                    
                     
                       9.99985329
                    
                  
                   
                     
                        
                    
                     
                       frac12
                       ;
                       Z.
                       Logarith
                       .
                       XN
                       .
                       99983
                    
                     
                       4.99992664
                    
                  
                
              
               
                 Now
                 then
                 in
                 the
                 former
                 Example
                 the
                 mean
                 Anomaly
                 is
                 246
                 deg
                 .
                 451741.
                 and
                 the
                 excess
                 above
                 a
                 semicircle
                 is
                 the
                 ang
                 .
                 aED
                 .
                 66.
                 451742.
                 
                 Therefore
                 .
              
               
                 
                   As
                   XN
                   .
                   99983
                
                 
                   4.99992664
                
                 
                   Is
                   to
                   XG
                   .
                   100000
                
                 
                   5.00000000
                
                 
                   So
                   is
                   the
                   tang
                   .
                   aED
                   66.451742
                
                 
                   10.36069857
                
                 
                   To
                   the
                   tang
                   .
                   aEB
                   66.455296
                
                 
                   10.36077193
                
              
               
                 
                   aEB
                   —
                   aED
                   =
                   DEf
                
                 .003544
                 the
                 variation
                 ,
                 which
                 being
                 added
                 to
                 the
                 Elliptick
                 AEquation
                 before
                 found
                 ,
                 the
                 absolute
                 AEquation
                 is
                 1.
                 837628.
                 and
                 therefore
                 the
                 ☉
                 true
                 place
                 345.
                 291334.
                 that
                 is
                 X.
                 15.
                 17.
                 28.
                 
              
            
             
               
                 CHAP.
                 XIV
                 .
              
               
                 
                   To
                   find
                   the
                   place
                   of
                   the
                   fixed
                   Stars
                   .
                
              
               
               
                 Example
                 .
                 Let
                 the
                 given
                 time
                 be
                 1500
                 ,
                 the
                 difference
                 of
                 time
                 is
                 100
                 years
                 ,
                 and
                 the
                 motion
                 of
                 the
                 fixed
                 Stars
                 for
                 100
                 years
                 is
                 0.
                 38580.
                 
              
               
                 
                   The
                   place
                   of
                   the
                   1
                   *
                   in
                   ♈
                   ,
                   1600
                
                 
                   7.67129
                
                 
                   Motion
                   for
                   100
                   years
                   subtract
                
                 
                   0.38580
                
                 
                   Place
                   required
                   in
                   the
                   year
                   1500
                
                 
                   7.28549
                
              
               
                 2.
                 
                 Example
                 .
              
               
                 
                   Let
                   the
                   time
                   given
                   be
                
                 
                   1674.
                   
                
                 
                   The
                   place
                   of
                   the
                   first
                   Star
                   in
                   ♈
                   1600
                   was
                
                 
                   7.67129
                
                 
                   Motion
                   for
                   60
                   years
                   is
                
                 
                   0.23148
                
                 
                   Motion
                   for
                   14
                   years
                   is
                
                 
                   0.05401
                
                 
                   Place
                   required
                   in
                   the
                   year
                   1674
                   compl
                   .
                
                 
                   7.95678
                
              
            
             
               
                 CHAP.
                 XV.
                 
              
               
                 
                   Of
                   the
                   Theory
                   of
                   the
                   Moon
                   ,
                   and
                   the
                   finding
                   the
                   place
                   of
                   her
                   Apogaeon
                   ,
                   quantity
                   of
                   excentricity
                   and
                   middle
                   motion
                   .
                
              
               
                 THe
                 Moon
                 is
                 a
                 secondary
                 Planet
                 ,
                 moving
                 about
                 the
                 Earth
                 ,
                 as
                 the
                 Earth
                 and
                 other
                 
                 Planets
                 do
                 about
                 the
                 Sun
                 ,
                 and
                 so
                 not
                 only
                 the
                 Earth
                 but
                 the
                 whole
                 System
                 of
                 the
                 Moon
                 ,
                 is
                 also
                 carried
                 about
                 the
                 Sun
                 in
                 a
                 year
                 .
                 And
                 hence
                 ,
                 according
                 to
                 Hipparchus
                 ,
                 there
                 arises
                 a
                 twofold
                 ,
                 but
                 according
                 to
                 Tycho
                 a
                 three-fold
                 Inequality
                 in
                 the
                 Moons
                 Motion
                 .
                 The
                 first
                 is
                 Periodical
                 and
                 is
                 to
                 be
                 obtained
                 after
                 the
                 same
                 manner
                 ,
                 as
                 was
                 the
                 excentrick
                 AEquation
                 of
                 the
                 Sun
                 or
                 Earth
                 :
                 in
                 order
                 whereunto
                 ,
                 we
                 will
                 first
                 shew
                 how
                 the
                 place
                 of
                 her
                 Apogaeon
                 and
                 excentricity
                 may
                 be
                 found
                 .
              
               
                 At
                 Bononia
                 in
                 Italy
                 ,
                 whose
                 Longitude
                 is
                 13
                 degrees
                 Eastward
                 from
                 the
                 Meridian
                 of
                 
                   London
                   ,
                   Ricciolus
                
                 and
                 others
                 observed
                 the
                 apparent
                 times
                 of
                 the
                 middle
                 of
                 three
                 lunar
                 Eclipses
                 to
                 be
                 as
                 followeth
                 .
              
               
                 
                   The
                   first
                   1642.
                   
                   April
                   the
                   4.
                   at
                   14
                   hours
                   and
                   4
                   Minutes
                   .
                
                 
                   The
                   second
                   1642
                   ,
                   September
                   27
                   at
                   16
                   hours
                   and
                   46
                   minutes
                   .
                
                 
                   The
                   third
                   1643.
                   
                   September
                   17
                   at
                   7
                   hours
                   and
                   31
                   Minutes
                   .
                
              
               
                 The
                 equal
                 times
                 reduced
                 to
                 the
                 Meridian
                 of
                 London
                 ,
                 with
                 the
                 places
                 of
                 the
                 Sun
                 in
                 these
                 three
                 observations
                 ,
                 according
                 to
                 Mr.
                 Street
                 in
                 the
                 25
                 Page
                 of
                 his
                 
                   Astronomia
                   Carolina
                
                 ,
                 are
                 thus
                 .
              
               
                 
                   Anno
                   Mens
                   .
                   D.
                   h.
                   
                
                 
                   d.
                   
                
                 
                   1642.
                   
                   April
                   4.
                   13.
                   37.
                   
                
                 
                   ♈
                   .
                   25.
                   6.
                   54
                
                 
                   1642.
                   
                   Septemb.
                   27.
                   15.
                   57
                
                 
                   ♎
                   .
                   14.
                   50.
                   09
                
                 
                   1643.
                   
                   Sehtemb
                   .
                   17.
                   6.
                   46
                
                 
                   ♎
                   4.
                   20.
                   20
                
              
               
                 Hence
                 the
                 place
                 of
                 the
                 Moon
                 in
                 the
                 first
                 observation
                 
                 is
                 in
                 ♎
                 25.
                 
                 6′
                 .
                 54.
                 in
                 the
                 second
                 ♈
                 14.
                 50.
                 9.
                 in
                 the
                 third
                 ♓
                 4.
                 20.
                 20.
                 
                 Now
                 then
                 in
                 Fig.
                 10.
                 let
                 the
                 Circle
                 BHDGFE
                 denote
                 the
                 Moons
                 AEquant
                 T
                 the
                 Center
                 of
                 the
                 Earth
                 ,
                 the
                 Semidiameters
                 
                   TD
                   ,
                   TE
                
                 and
                 TF
                 the
                 apparent
                 places
                 of
                 the
                 Moon
                 ,
                 in
                 the
                 first
                 ,
                 second
                 and
                 third
                 observations
                 ,
                 C
                 the
                 Center
                 of
                 the
                 Excentrick
                 ,
                 
                   CD
                   ,
                   CE
                
                 and
                 CF
                 the
                 Lines
                 of
                 middle
                 motion
                 .
              
               
                 
                   From
                   the
                   first
                   observation
                   to
                   the
                   second
                   there
                   are
                
                 
                   176
                   d.
                   2
                   h.
                   20′
                
                 
                   The
                   true
                   motion
                   of
                   the
                   Moon
                   is
                   deg
                   .
                
                 
                   169.
                   43.
                   15″
                
                 
                   The
                   motion
                   of
                   the
                   Apogaeon
                   subtract
                
                 
                   19.
                   37.
                   07
                
              
               
                 
                   The
                   motion
                   of
                   the
                   true
                   Anomaly
                   is
                   the
                   arch
                   DE
                
                 
                   150.
                   06.
                   08
                
                 
                   The
                   motion
                   of
                   the
                   mean
                   Anomaly
                   DCE
                
                 
                   140.
                   42.
                   28
                
              
               
                 
                   From
                   the
                   first
                   observation
                   to
                   the
                   third
                   ,
                   there
                   are
                
                 
                   530
                   d.
                   17
                   h.
                   9.
                   
                
                 
                   The
                   true
                   motion
                   of
                   the
                   Moon
                   is
                   degrees
                
                 
                   159.
                   13.
                   26
                
                 
                   The
                   motion
                   of
                   the
                   Apogaeon
                   subtract
                
                 
                   159.
                   07.
                   32
                
              
               
                 
                 
                   The
                   motion
                   of
                   the
                   true
                   Anomaly
                   is
                   the
                   Arch
                   DF
                
                 
                   100.
                   05.
                   54
                
                 
                   The
                   motion
                   of
                   the
                   mean
                   Anomaly
                   DCF
                
                 
                   93.
                   46.
                   45
                
                 
                   And
                   deducting
                   the
                   Arch
                   DGF
                   from
                   the
                   Arch
                   DFE
                   ,
                   the
                   remainer
                   is
                   the
                   Arch
                   FE
                
                 
                   50.
                   00.
                   14
                
                 
                   And
                   deducting
                   the
                   Angle
                   DCF
                   from
                   the
                   Angle
                   DCE
                   ,
                   the
                   remainer
                   is
                   the
                   Angle
                   FCE
                
                 
                   46.
                   55.
                   43
                
              
               
                 Suppose
                 10.00000000
                 the
                 Logarithm
                 of
                 DC
                 ,
                 continue
                 FC
                 to
                 H
                 ,
                 and
                 with
                 the
                 other
                 right
                 Lines
                 compleat
                 the
                 Diagram
                 .
              
               
                 1.
                 
                 In
                 the
                 Triangle
                 DCH
                 we
                 have
                 given
                 the
                 Angle
                 DCH
                 86.
                 13.
                 15.
                 the
                 complement
                 of
                 DCF
                 93.
                 46.
                 45
                 to
                 a
                 Semicircle
                 .
                 The
                 Angle
                 DHC
                 50.
                 02.
                 57.
                 
                 The
                 half
                 of
                 the
                 Arch
                 DF
                 and
                 the
                 side
                 CD
                 1000000.
                 
                 To
                 find
                 CH.
                 
              
               
                 
                   As
                   the
                   Sine
                   of
                   DHC
                   50.
                   02.
                   57
                
                 
                   9.88456640
                
                 
                   To
                   the
                   Side
                   DC
                   ,
                   so
                   the
                   Sine
                   of
                   HDC
                   43.
                   43.
                   48.
                   
                
                 
                   19.83964197
                
                 
                   To
                   the
                   Side
                   CA
                
                 
                   9.95507557
                
              
               
                 2
                 In
                 the
                 Triangle
                 HCE
                 we
                 have
                 given
                 CH
                 as
                 before
                 ,
                 the
                 Angle
                 CHE
                 25.
                 00.
                 07.
                 
                 The
                 half
                 of
                 the
                 Arch
                 FE
                 ,
                 the
                 Angle
                 HCE
                 133.
                 04.
                 17
                 the
                 complement
                 of
                 FCE
                 ,
                 and
                 by
                 consequence
                 the
                 Angle
                 CEH
                 21.
                 55.
                 36
                 
                 To
                 find
                 the
                 Side
                 CE.
                 
              
               
                 
                 
                   As
                   the
                   Sine
                   of
                   CEH
                   21.
                   55.
                   36
                
                 
                   9.57219707
                
                 
                   To
                   the
                   Side
                   CH
                
                 
                   19.95507557
                
                 
                   So
                   is
                   the
                   Sine
                   of
                   CHE
                   25.
                   00.
                   07
                
                 
                   9.62597986
                
                 
                   To
                   the
                   Sine
                   CE
                
                 
                   
                     
                       19.58105543
                    
                     
                       10.00885836
                    
                  
                
              
               
                 3.
                 
                 In
                 the
                 Triangle
                 DCE
                 ,
                 we
                 have
                 given
                 
                   DC
                   .
                   CE
                
                 and
                 the
                 Angle
                 DCE
                 140.
                 42.
                 28.
                 whose
                 complement
                 39.
                 17.
                 32
                 is
                 the
                 Summ
                 of
                 the
                 Angles
                 ,
                 to
                 find
                 the
                 Angle
                 CED
                 and
                 DE
                 ,
              
               
                 
                   As
                   the
                   greater
                   Side
                   CE
                
                 
                   10.00885836
                
                 
                   Is
                   to
                   the
                   lesser
                   Side
                   DC
                
                 
                   10.00000000
                
                 
                   So
                   is
                   the
                   Radius
                
                 
                   10.00000000
                
                 
                   To
                   the
                   tang
                   .
                   of
                   44.
                   24.
                   54
                
                 
                   19.99114164
                
              
               
                 
                   Which
                   subtracted
                   from
                   45.
                   2
                
                 
                   the
                   remainer
                   is
                   the
                   half
                   .
                
                 
                   Difference
                   of
                   the
                   acute
                   angles
                   35.
                   16.
                   
                
                 
                    
                
              
               
                 
                   As
                   the
                   Radius
                   .
                
                 
                   To
                   the
                   tang
                   .
                   of
                   the
                   com
                   .
                   35.
                   16
                
                 
                   8.01109962
                
                 
                   Is
                   to
                   the
                   tang
                   .
                   of
                   the
                   frac12
                   ;
                   Z.
                   19.
                   38.
                   46
                
                 
                   9.55265735
                
                 
                   To
                   the
                   tang
                   .
                   of
                   frac12
                   ;
                   X.
                   00.
                   12.
                   35
                
                 
                   7.56375697
                
                 
                   Their
                   Sum
                   19.
                   51.
                   21.
                   is
                   the
                   angle
                   —
                   CDE
                   .
                
                 
                    
                
                 
                   Their
                   difference
                   19.
                   26.
                   11.
                   is
                   the
                   angle
                   CED
                   .
                
                 
                    
                
                 
                 
                   As
                   the
                   Sine
                   of
                   CED
                   .
                   19.
                   26.
                   11.
                   
                
                 
                   9.52216126
                
                 
                   Is
                   to
                   the
                   Sine
                   of
                   DCE
                   .
                   140.
                   42.
                   28.
                   
                
                 
                   9.80159290
                
                 
                   So
                   is
                   the
                   Side
                   EC
                   .
                
                 
                   10.00000000
                
                 
                   To
                   the
                   Side
                   DE.
                   
                
                 
                   10.27943164
                
              
               
                 4.
                 
                 In
                 the
                 Isosceles
                 Triangle
                 DTE
                 we
                 have
                 given
                 the
                 Side
                 DE
                 ,
                 the
                 angle
                 DTE
                 150.
                 06.
                 08
                 whose
                 complement
                 29.
                 53.
                 52
                 is
                 the
                 Summ
                 of
                 the
                 other
                 two
                 angles
                 ,
                 the
                 half
                 whereof
                 is
                 the
                 angle
                 TDE
                 14.
                 56.
                 56
                 which
                 being
                 subtracted
                 from
                 the
                 angle
                 CDE
                 .
                 19.
                 51.
                 21
                 the
                 remainer
                 is
                 the
                 angle
                 CDT
                 .
                 4.
                 54.
                 25.
                 
              
               
                 
                   
                     As
                     the
                     Sine
                     of
                  
                   DTE
                   150.
                   06.
                   08
                   
                   Co.
                   ar
                   .
                
                 
                   0.30237482
                
                 
                   Is
                   to
                   the
                   Sine
                   of
                   DET
                   .
                   14.
                   56.
                   56
                
                 
                   9.41154778
                
                 
                   So
                   is
                   the
                   Side
                   DE
                
                 
                   10.27943164
                
                 
                   To
                   the
                   Side
                   DT
                
                 
                   9.99335424
                
              
               
                 5.
                 
                 In
                 the
                 Triangle
                 CDT
                 we
                 have
                 given
                 
                   DC
                   .
                   DT
                
                 and
                 the
                 angle
                 CDT
                 ,
                 to
                 find
                 CTD
                 and
                 CT
                 .
              
               
                 
                   As
                   the
                   Side
                   DT
                
                 
                   9.99335424
                
                 
                   Is
                   to
                   the
                   Side
                   DC
                
                 
                   10.00000000
                
                 
                   So
                   is
                   the
                   Rad.
                   
                
                 
                   10.00000000
                
                 
                   To
                   the
                   tang
                   .
                   of
                   26.
                   18
                
                 
                   10.00664576
                
              
               
                 
                   Deduct
                   45.
                   
                
                 
                   As
                   the
                   Radius
                   .
                
              
               
                 
                 
                   Is
                   to
                   the
                   Sine
                   of
                   the
                   remainer
                   0.
                   26.
                   18.
                   
                
                 
                   7.88368672
                
                 
                   So
                   is
                   the
                   tang
                   .
                   of
                   the
                   frac12
                   ;
                   Z
                   angle
                   87.
                   32.
                   57
                
                 
                   11.36854996
                
                 
                   To
                   the
                   tang
                   .
                   frac12
                   ;
                   X
                   angle
                   10.
                   08.
                   04
                
                 
                   9.25223668
                
                 
                   Their
                   Summ
                   97.
                   41.
                   01
                
                 
                   is
                   the
                   angle
                   CTD
                
              
               
                 
                   As
                   the
                   Sine
                   of
                   
                     CTD
                     .
                     97.
                     41.
                     01.
                     
                     Co.
                     ar
                     .
                  
                
                 
                   0.00391693
                
                 
                   Is
                   to
                   the
                   Side
                   DC
                
                 
                   10.00000000
                
                 
                   So
                   is
                   the
                   Sine
                   of
                   CDT
                   4.
                   54.
                   25
                
                 
                   8.93215746
                
                 
                   To
                   the
                   Side
                   CT
                
                 
                   8.93607439
                
              
               
                 
                    
                
                 
                   s.
                   d.
                   
                
                 
                   The
                   place
                   of
                   the
                   Moon
                   in
                   the
                   first
                   Observation
                
                 
                   6.
                   25.
                   06.
                   54
                
                 
                   The
                   true
                   Anomaly
                   CTD
                   sub
                   .
                
                 
                   3.
                   07.
                   41.
                   01
                
                 
                   The
                   place
                   of
                   the
                   Apogaeon
                
                 
                   3.
                   17.
                   25.
                   53
                
              
               
                 
                   ☽
                   place
                   in
                   the
                   first
                   Observation
                
                 
                   6.
                   25.
                   06.
                   54
                
                 
                   The
                   AEquation
                   CDT
                   Add.
                   
                
                 
                   04.
                   54.
                   25
                
                 
                   The
                   ☽
                   mean
                   Longitude
                
                 
                   7.
                   00.
                   01.
                   19
                
                 
                   From
                   which
                   subtract
                   the
                   place
                   of
                   the
                   Apogeon
                
                 
                   3.
                   27.
                   25.
                   53
                
                 
                   There
                   rests
                   the
                   mean
                   Anomaly
                   BCD
                
                 
                   3.
                   12.
                   35.
                   26
                
              
               
                 And
                 for
                 the
                 excentricity
                 in
                 such
                 parts
                 ,
                 as
                 the
                 Radius
                 of
                 the
                 AEquant
                 is
                 100000
                 the
                 Proportion
                 is
                 .
              
               
                 
                 
                   DT
                
                 
                   9.99335424
                
                 
                   CT
                
                 
                   8.93607439
                
                 
                   100000
                
                 
                   5.00000000
                
                 
                   8764
                
                 
                   3.94272015
                
              
               
                 And
                 this
                 is
                 the
                 Method
                 for
                 finding
                 the
                 place
                 of
                 the
                 Moons
                 Apogaeon
                 and
                 excentricity
                 .
                 And
                 from
                 these
                 and
                 many
                 other
                 Eclipses
                 as
                 well
                 Solar
                 as
                 Lunar
                 ,
                 Mr.
                 Street
                 limits
                 the
                 place
                 of
                 the
                 ☽
                 Apogaeon
                 to
                 be
                 at
                 the
                 time
                 of
                 the
                 first
                 observation
                 21′
                 .
                 04″
                 more
                 ,
                 and
                 the
                 mean
                 Anomaly
                 20.
                 41″
                 less
                 ,
                 and
                 the
                 excentricity
                 8765
                 such
                 parts
                 as
                 the
                 Radius
                 of
                 the
                 AEquant
                 is
                 100000.
                 
              
               
                 And
                 by
                 comparing
                 sundry
                 observations
                 both
                 antient
                 and
                 modern
                 ,
                 he
                 collects
                 the
                 middle
                 motion
                 of
                 the
                 Moon
                 ,
                 from
                 her
                 Apogaeon
                 ,
                 to
                 be
                 in
                 the
                 space
                 of
                 four
                 Julian
                 years
                 or
                 146
                 days
                 ,
                 53
                 revolutions
                 ,
                 0
                 Signes
                 ,
                 7
                 degrees
                 ,
                 56
                 minutes
                 ,
                 45
                 Seconds
                 .
                 And
                 the
                 Apogaeon
                 from
                 the
                 AEquinox
                 5
                 Signes
                 ,
                 12
                 degrees
                 ,
                 46
                 minutes
                 .
                 And
                 hence
                 the
                 daily
                 motion
                 of
                 her
                 mean
                 Anomaly
                 will
                 be
                 found
                 to
                 be
                 13
                 d.
                 03′
                 .
                 53″
                 .
                 57‴
                 .
                 09
                 iv
                 .
                 58
                 v.
                 46
                 vi
                 .
                 Of
                 her
                 Apogaeon
                 0.
                 06.
                 41.
                 04.
                 03.
                 25.
                 33.
                 
              
               
                 And
                 according
                 to
                 these
                 Measures
                 ,
                 if
                 you
                 deduct
                 the
                 motion
                 of
                 the
                 ☽
                 mean
                 Anomaly
                 for
                 1641
                 years
                 April
              
               
                 
                   4.
                   hours
                   13.
                   37′
                   ,
                   viz.
                   
                
                 
                   8.
                   22.
                   02.
                   00.
                   
                
                 
                   from
                
                 
                   3.
                   121.
                   35.
                   26
                
                 
                   The
                   remainer
                   is
                
                 
                   6.
                   201.
                   33.
                   26
                
                 
                   from
                   which
                   abating
                   20′
                   .
                   41″
                   the
                   ☽
                   mean
                   Anom
                   .
                   
                     AEra
                     Chr.
                  
                   6.
                   20.
                   12.
                   45.
                   
                
                 
                    
                
              
               
               
                 
                 
                 
                   In
                   like
                   manner
                   the
                   motion
                   of
                   her
                   Apogaeon
                   for
                   the
                   same
                   time
                   is
                
                 
                   6.
                   05.
                   311.
                   57
                
                 
                   which
                   being
                   deducted
                   from
                
                 
                   3.
                   17.
                   25.
                   57
                
                 
                   The
                   remainer
                   is
                
                 
                   9.
                   11.
                   55.
                   56
                
                 
                   To
                   which
                   if
                   you
                   add
                
                 
                   21.04
                
                 
                   The
                   Sum
                
                 
                   91.
                   121.
                   15200
                
                 
                   is
                   the
                   place
                   of
                   the
                   ☽
                   Apogaeon
                   in
                   the
                   beginning
                   of
                   the
                   Christian
                   AEra
                   .
                
                 
                    
                
              
            
             
               
                 CHAP.
                 XVI
                 .
              
               
                 
                   Of
                   the
                   finding
                   of
                   the
                   place
                   and
                   motion
                   of
                   the
                   Moons
                   Nodes
                   .
                
              
               
                 
                   ANno
                   Christi
                   1652
                   ,
                   March
                
                 28
                 ,
                 hour
                 .
                 22.
                 16′
                 ,
                 the
                 Sun
                 and
                 Moon
                 being
                 in
                 conjunction
                 ,
                 Mr.
                 Street
                 in
                 Page
                 33
                 ,
                 computes
                 the
                 ☽
                 true
                 place
                 in
                 the
                 Meridian
                 of
                 London
                 to
                 be
                 in
                 ♈
                 .
                 19.
                 14.
                 18
                 with
                 latitude
                 North
                 46′
                 .
                 15″
                 .
              
               
                 And
                 
                   Anno
                   Christi
                   1654
                   August
                
                 1.
                 hour
                 .
                 21.
                 
                 19′
                 .
                 30″
                 was
                 the
                 middle
                 of
                 a
                 Solar
                 Eclipse
                 at
                 London
                 .
                 at
                 which
                 time
                 the
                 Moons
                 true
                 place
                 was
                 found
                 to
                 be
                 in
                 ♌
                 18.
                 
                 58′
                 .
                 12″
                 with
                 North
                 Latitude
                 32′
                 .
                 01″
                 .
              
               
                 
                   1654
                   
                     August
                     1.
                     21.
                     
                     19′
                     .
                     30″
                  
                   ☽
                   place
                   ♌
                   18.
                   58.
                   12
                
                 
                   1652
                   March
                   28.
                   22.
                   16.
                   00
                   
                   ☽
                   place
                   ♈
                   19.
                   14.
                   18
                
              
               
                 From
                 the
                 first
                 observation
                 to
                 the
                 second
                 there
                 are
                 27
                 years
                 ,
                 4
                 months
                 ,
                 5
                 days
                 ,
                 23
                 hours
                 03′
                 .
                 30″
                 .
              
               
                 
                 
                   Mean
                   motion
                   of
                   the
                   Nodes
                   in
                   that
                   time
                   ,
                   deg
                   .
                
                 
                   45.
                   19.
                   41
                
                 
                   The
                   true
                   motion
                   of
                   the
                   ☽
                
                 
                   119.
                   43.
                   54
                
                 
                   Their
                   Summ
                   is
                   in
                   Fig.
                   11.
                   
                   The
                   angle
                   DPB
                
                 
                   165.
                   03.
                   35
                
              
               
                 Therefore
                 in
                 the
                 oblique
                 angled
                 Spherical
                 Triangle
                 DPB
                 we
                 have
                 given
                 BP
                 .
                 89.
                 13.
                 45
                 the
                 complement
                 of
                 the
                 Moons
                 Latitude
                 in
                 the
                 first
                 Observation
                 2.
                 
                 PD
                 89.
                 27.
                 50
                 the
                 complement
                 of
                 the
                 Moons
                 Latitude
                 in
                 the
                 second
                 observation
                 ,
                 and
                 the
                 angle
                 DPB
                 165.
                 03.
                 35
                 ,
                 whose
                 complement
                 to
                 a
                 Semicircle
                 is
                 DPF
                 14.
                 56.
                 25.
                 
                 The
                 angle
                 PBD
                 is
                 required
                 .
              
               
                 
                   1.
                   
                   Proportion
                   .
                
                 
                   
                     As
                     the
                     Cotangent
                     of
                     PD
                     89.
                     27.
                     50
                  
                   
                     9.97114485
                  
                   
                     Is
                     to
                     the
                     Radius
                  
                   
                     10.00000000
                  
                   
                     So
                     is
                     the
                     Cosine
                     of
                     DPF
                     14.
                     56.
                     25
                  
                   
                     9.98506483
                  
                   
                     To
                     the
                     tang
                     .
                     of
                     PF
                     89.
                     26.
                     42
                  
                   
                     12.01191998
                  
                   
                     BP
                     89.
                     13.
                     45
                  
                   
                      
                  
                
                 
                   Their
                   Z
                   is
                   FPB
                   178.
                   40.
                   27.
                   whose
                   complement
                   Is
                   the
                   Arch
                   FG
                   1.
                   19.
                   33.
                   
                
              
               
                 
                   2.
                   
                   Proportion
                   .
                
                 
                   
                     As
                     the
                     Sine
                     of
                     
                       FP
                       89.
                       26.
                       42.
                       
                       Co.
                       ar
                       .
                    
                  
                   
                     0.00002037
                  
                   
                     Is
                     to
                     the
                     Cotang
                     .
                     of
                     DPF
                     14.
                     56.
                     25
                  
                   
                     10.57376158
                  
                   
                     So
                     is
                     the
                     Sine
                     of
                     FG
                     1.
                     19.
                     33
                  
                   
                     8.36418419
                  
                   
                     To
                     the
                     Cotang
                     .
                     of
                     FGD
                     85.
                     02.
                     56
                  
                   
                     8.93796614
                  
                   
                     FGD
                     =
                     PBD
                     inquired
                     .
                  
                   
                      
                  
                
                 
                 
                   And
                   in
                   the
                   right
                   angled
                   Spherical
                   Triangle
                   
                     BA
                     ☊
                  
                   right
                   angled
                   at
                   A
                   we
                   have
                   given
                   
                     AB
                     046′
                     .
                     15″
                  
                   the
                   Latitude
                   in
                   the
                   first
                   observation
                   ,
                   and
                   the
                   Angle
                   
                     AB
                     ☊
                     =
                     PBD
                  
                   85.
                   02.
                   56.
                   to
                   find
                   
                     A
                     ☊
                  
                   the
                   Longitude
                   of
                   the
                   Moon
                   from
                   the
                   ascending
                   Node
                   .
                
                 
                   
                     As
                     the
                     Cot.
                     of
                     
                       AB
                       ☊
                    
                     85.
                     02.
                     56
                  
                   
                     8.93796614
                  
                   
                     Is
                     to
                     the
                     Radius
                  
                   
                     10.00000000
                  
                   
                     So
                     is
                     the
                     Sine
                     of
                     
                       AB
                       0
                       .
                       46′
                       .
                       15″
                    
                  
                   
                     8.12882290
                  
                   
                     To
                     the
                     tang
                     .
                     of
                     
                       A
                       ☊
                    
                     8.
                     49.
                     17
                  
                   
                     9.19085676
                  
                
              
               
                 
                   2.
                   
                   To
                   find
                   the
                   Angle
                   A
                   ☊
                   B.
                   
                
                 
                   
                     As
                     the
                     tang
                     .
                     of
                     AB
                     0.
                     46.
                     15
                  
                   
                     8.12886212
                  
                   
                     Is
                     to
                     the
                     Radius
                  
                   
                     10.00000000
                  
                   
                     So
                     is
                     the
                     Sine
                     of
                     
                       A
                       ☊
                       8.
                       49.
                    
                     17
                  
                   
                     9.18569718
                  
                   
                     To
                     the
                     Cotang
                     .
                     of
                     
                       A
                       ☊
                       B
                    
                     5.
                     0.
                     41
                  
                   
                     11.05682506
                  
                
                 
                   
                     The
                     angle
                     of
                     the
                     ☽
                     orbite
                     with
                     the
                     Ecliptick
                  
                   
                      
                  
                   
                     The
                     first
                     observed
                     place
                     of
                     the
                     ☽
                  
                   
                     ♈
                     .
                     19.
                     14.
                     18
                  
                   
                     
                       A
                       ☊
                    
                     Subtract
                  
                   
                     8.
                     49.
                     17
                  
                   
                     There
                     rests
                     the
                     true
                     place
                     of
                     the
                     ☊
                  
                   
                     ♈
                     .
                     10.
                     25.
                     01
                  
                
                 
                   The
                   retrograde
                   motion
                   whereof
                   in
                   4
                   Julian
                   years
                   or
                   2461
                   days
                   ,
                   is
                   by
                   other
                   observations
                   found
                   to
                   be
                   Sign
                   2.
                   deg
                   .
                   17.
                   
                   22′
                   .
                   06″
                   .
                   and
                   therefore
                   the
                   daily
                   motion
                   deg
                   .
                   0.
                   
                   03′
                   .
                   10″
                   .
                   38‴
                   .
                   11
                   iv
                   .
                   35
                   v.
                   
                
                 
                   And
                   the
                   motion
                   thereof
                   for
                   1651
                   years
                   ,
                   
                     March
                     28.
                  
                   h.
                   22.
                   16′
                   ,
                   viz.
                   Sign
                   8.
                   deg
                   .
                   18.
                   
                   26′
                   .
                   58″
                   being
                   added
                   to
                   the
                   place
                   of
                   the
                   Node
                   before
                   found
                   Sig.
                   0.
                   10.
                   25
                   
                   :
                   01.
                   
                   Their
                   Sum
                   is
                   the
                   place
                   thereof
                   in
                   the
                   beginning
                   of
                   the
                   Christian
                   AEra
                   Sign
                   8.
                   deg
                   .
                   28.
                   
                   51′
                   .
                   59″
                   .
                
                 
                 
                   But
                   the
                   Rudolphin
                   Tables
                   as
                   they
                   are
                   corrected
                   by
                   Mr.
                   Horron
                   and
                   reduced
                   to
                   the
                   Meridian
                   of
                   London
                   ,
                   do
                   differ
                   a
                   little
                   from
                   these
                   measures
                   ,
                   for
                   according
                   to
                   these
                   Tables
                   ,
                   the
                   Moons
                   mean
                   motions
                   are
                   .
                
                 
                   
                     AEra
                     Christi
                     .
                  
                   
                     The
                     Moons
                     mean
                     Longitude
                     is
                  
                   
                     Sign
                     .
                     04.
                     deg
                     .
                     02.
                     25.
                     55
                  
                   
                     The
                     Moons
                     Apogaeon
                  
                   
                     Sign
                     .
                     09.
                     deg
                     .
                     13.
                     46.
                     59
                  
                   
                     The
                     Moons
                     mean
                     Anomaly
                  
                   
                     Sign
                     .
                     06.
                     deg
                     .
                     18.
                     38.
                     56
                  
                   
                     The
                     Moons
                     Node
                     Retrograde
                  
                   
                     Sign
                     .
                     08.
                     deg
                     .
                     28.
                     33.
                     16
                  
                
                 
                   And
                   according
                   to
                   these
                   measures
                   ,
                   the
                   Moons
                   mean
                   motions
                   in
                   decimal
                   Numbers
                   are
                   .
                
                 
                   
                     AEra
                     Christi
                     .
                  
                   
                     The
                     Moons
                     mean
                     Longitude
                     ,
                     deg
                     .
                  
                   
                     34.
                     00887.345677
                  
                   
                     The
                     Moons
                     Apogaeon
                     ,
                     deg
                     .
                  
                   
                     78.
                     82862.654320
                  
                   
                     The
                     Moons
                     mean
                     Anomaly
                     ,
                     deg
                     .
                  
                   
                     55.
                     18024.691357
                  
                   
                     The
                     Moons
                     Node
                     Retrograde
                     ,
                     deg
                     .
                  
                   
                     74.
                     69845.679010
                  
                
                 
                 
                   
                   
                   
                     The
                     ☽
                     mean
                     motion
                     for
                     one
                     year
                     .
                  
                   
                     The
                     Moons
                     mean
                     Longitude
                     ,
                     deg
                     .
                  
                   
                     35.
                     94001.
                     44893.
                     1
                  
                   
                     The
                     Moons
                     Apogeaon
                     ,
                     deg
                     .
                  
                   
                     11.
                     29551.
                     126365
                  
                   
                     The
                     Moons
                     mean
                     Anomaly
                     ,
                     deg
                     .
                  
                   
                     24.
                     64450.
                     322566
                  
                   
                     The
                     Moons
                     Node
                     Retrograde
                     ,
                     deg
                     .
                  
                   
                     05.
                     36900.
                     781604
                  
                
                 
                   
                     The
                     ☽
                     mean
                     motion
                     for
                     one
                     day
                     .
                  
                   
                     The
                     Moons
                     mean
                     Longitude
                     ,
                     deg
                  
                   
                     03.
                     66010.
                     962873
                  
                   
                     The
                     Moons
                     Apogaeon
                     ,
                     deg
                     .
                  
                   
                     00.
                     03094.
                     660620
                  
                   
                     The
                     Moons
                     mean
                     Anomaly
                     ,
                     deg
                     .
                  
                   
                     03.
                     62916.
                     302253
                  
                   
                     The
                     Moons
                     Node
                     Retrograde
                     ,
                     deg
                     .
                  
                   
                     00.
                     01470.
                     961045
                  
                
                 
                   And
                   according
                   to
                   these
                   measures
                   are
                   the
                   Tables
                   made
                   shewing
                   the
                   Moons
                   mean
                   Longitude
                   ,
                   Apogaeon
                   ,
                   Anomaly
                   ,
                   and
                   Node
                   retrograde
                   for
                   Years
                   ,
                   Months
                   ,
                   Days
                   and
                   Hours
                   .
                
                 
                   And
                   hence
                   to
                   compute
                   the
                   Moons
                   true
                   place
                   in
                   her
                   Orbit
                   ,
                   I
                   shall
                   make
                   use
                   of
                   the
                   Method
                   ,
                   which
                   Mr.
                   Horron
                   in
                   his
                   Posthumas
                   works
                   lastly
                   published
                   by
                   Mr.
                   Flamsted
                   ,
                   in
                   which
                   from
                   the
                   Rudolphin
                   Tables
                   he
                   sets
                   down
                   these
                   Dimensions
                   .
                
                 
                   
                   
                     The
                     Moons
                     mean
                     Semidiameter
                     deg
                     .
                  
                   
                     00.
                     
                     15′
                     .
                     30″
                  
                   
                     Her
                     mean
                     distance
                     in
                     Semid
                     .
                     of
                     the
                     Earth
                     Deg.
                     
                  
                   
                     11.
                     47.
                     22
                  
                   
                     The
                     half
                     whereof
                     deg
                     .
                     5.
                     53.
                     41.
                     he
                     adds
                     45
                     the
                     whole
                     is
                  
                   
                     deg
                     .
                     50.
                     53.
                     41
                  
                   
                     Whos
                     's
                     Artificial
                     cotangent
                     is
                  
                   
                     9.91000022
                  
                   
                     And
                     the
                     double
                     thereof
                     makes
                     this
                     standing
                     Numb
                     .
                  
                   
                     9.82000044
                  
                
                 
                   
                     
                       
                          
                      
                       
                         Greatest
                         6685.
                         44
                      
                       
                          
                      
                    
                     
                       
                         The
                         Moons
                      
                       
                         Mean
                         5523.
                         69
                      
                       
                         Excentricity
                      
                    
                     
                       
                          
                      
                       
                         Least
                         4361.
                         94
                      
                       
                          
                      
                    
                     
                       
                         And
                         her
                         greatest
                         variation
                         00.
                         
                         36′
                         .
                         27″
                         .
                      
                    
                  
                
                 
                   These
                   things
                   premised
                   his
                   directions
                   for
                   computing
                   the
                   Moons
                   place
                   ,
                   are
                   as
                   followeth
                   .
                
              
            
             
               
                 CHAP.
                 XVII
                 .
              
               
                 
                   How
                   to
                   Calculate
                   the
                   Moons
                   true
                   place
                   in
                   her
                   Orbit
                   .
                
              
               
                 TO
                 the
                 given
                 time
                 find
                 the
                 true
                 place
                 of
                 the
                 Sun
                 ,
                 or
                 his
                 Longitude
                 from
                 the
                 Vernal
                 AEquinox
                 ,
                 as
                 hath
                 been
                 already
                 shewed
                 .
              
               
                 2.
                 
                 From
                 the
                 Tables
                 of
                 the
                 Moons
                 mean
                 motions
                 ,
                 write
                 out
                 the
                 Epocha
                 next
                 before
                 the
                 given
                 time
                 ,
                 and
                 severally
                 under
                 that
                 set
                 the
                 motions
                 ,
                 belonging
                 to
                 the
                 years
                 ,
                 months
                 and
                 days
                 compleat
                 ,
                 and
                 to
                 the
                 hours
                 and
                 scruples
                 current
                 ,
                 every
                 one
                 under
                 his
                 like
                 (
                 only
                 remember
                 that
                 in
                 the
                 Bissextile
                 years
                 ,
                 after
                 the
                 end
                 of
                 February
                 ,
                 the
                 days
                 must
                 be
                 increased
                 by
                 one
                 Unite
                 )
                 then
                 adding
                 them
                 all
                 together
                 ,
                 the
                 Summ
                 shall
                 be
                 
                 the
                 Moons
                 mean
                 motions
                 for
                 the
                 time
                 given
                 :
                 But
                 in
                 her
                 Node
                 Retragrade
                 you
                 must
                 leave
                 out
                 the
                 Radix
                 or
                 first
                 number
                 ,
                 and
                 the
                 Summ
                 of
                 the
                 remainer
                 being
                 deducted
                 from
                 the
                 Radix
                 ,
                 shall
                 be
                 the
                 mean
                 place
                 of
                 her
                 Node
                 required
                 .
              
               
                 3.
                 
                 Deduct
                 the
                 Moons
                 Apogaeon
                 from
                 the
                 ☉
                 true
                 place
                 ,
                 the
                 rest
                 is
                 the
                 annual
                 Augment
                 ,
                 the
                 tangent
                 of
                 whose
                 Complement
                 180
                 or
                 360
                 ,
                 being
                 added
                 to
                 the
                 artificial
                 Number
                 given
                 9.
                 82000044.
                 the
                 Summ
                 shall
                 be
                 the
                 tangent
                 of
                 an
                 Arch
                 ,
                 which
                 being
                 deducted
                 from
                 the
                 said
                 Complement
                 ,
                 giveth
                 the
                 Apogaeon
                 AEquation
                 to
                 be
                 added
                 to
                 the
                 mean
                 Apogaeon
                 ,
                 in
                 the
                 first
                 and
                 third
                 quadrants
                 of
                 the
                 annual
                 Augment
                 ,
                 and
                 Subtracted
                 in
                 the
                 second
                 and
                 fourth
                 ,
                 their
                 Summ
                 or
                 difference
                 is
                 the
                 true
                 Apogaeon
                 .
              
               
                 4.
                 
                 The
                 true
                 Apogaeon
                 being
                 Deducted
                 from
                 the
                 ☽
                 mean
                 Longitude
                 gives
                 the
                 Moons
                 mean
                 Anomaly
                 .
              
               
                 5.
                 
                 Double
                 the
                 annual
                 Augment
                 ,
                 and
                 to
                 the
                 Cosine
                 thereof
                 add
                 the
                 Logarithm
                 of
                 1161.
                 75.
                 the
                 difference
                 between
                 the
                 Moons
                 mean
                 and
                 extream
                 Excentricity
                 ,
                 viz.
                 3.
                 06511268
                 ,
                 the
                 Summ
                 shall
                 be
                 the
                 Logarithm
                 of
                 a
                 number
                 which
                 being
                 added
                 to
                 the
                 mean
                 Excentricity
                 ,
                 if
                 the
                 double
                 annual
                 Augment
                 be
                 in
                 the
                 first
                 or
                 fourth
                 quadrants
                 ;
                 or
                 Subtracted
                 from
                 it
                 ,
                 if
                 in
                 the
                 second
                 or
                 third
                 quadrants
                 ;
                 the
                 Summ
                 or
                 difference
                 shall
                 be
                 the
                 Moons
                 true
                 Excentricity
                 .
              
               
                 6.
                 
                 The
                 Moons
                 true
                 Excentricity
                 being
                 taken
                 for
                 a
                 natural
                 Sine
                 ,
                 the
                 Arch
                 answering
                 thereto
                 shall
                 be
                 the
                 ☽
                 greatest
                 Physical
                 AEquation
                 .
              
               
                 7.
                 
                 To
                 the
                 half
                 of
                 the
                 Moons
                 greatest
                 Physical
                 AEquation
                 add
                 45
                 deg
                 .
                 the
                 cotagent
                 of
                 the
                 Summ
                 is
                 the
                 artificial
                 Logarithm
                 of
                 the
                 Excentrick
                 .
                 
                 To
                 the
                 double
                 whereof
                 if
                 you
                 add
                 the
                 tang
                 .
                 of
                 half
                 the
                 mean
                 Anomaly
                 ,
                 the
                 Summ
                 shall
                 be
                 the
                 tangent
                 of
                 an
                 Arch
                 ,
                 which
                 being
                 added
                 to
                 half
                 the
                 mean
                 Anomaly
                 ,
                 shall
                 give
                 the
                 Excentrick
                 Anomaly
                 .
              
               
                 8.
                 
                 To
                 the
                 Logarithm
                 of
                 the
                 Excentrick
                 ,
                 add
                 the
                 tangent
                 of
                 half
                 the
                 Excentrick
                 Anomaly
                 ,
                 the
                 Summ
                 shall
                 be
                 the
                 tangent
                 of
                 an
                 Arch
                 ,
                 whose
                 double
                 shall
                 be
                 the
                 Coequated
                 Anomaly
                 ,
                 and
                 the
                 difference
                 between
                 this
                 and
                 the
                 mean
                 Anomaly
                 is
                 the
                 terrestrial
                 Equation
                 ,
                 which
                 being
                 added
                 to
                 the
                 Moons
                 mean
                 Longitude
                 ,
                 if
                 the
                 mean
                 Anomaly
                 be
                 in
                 the
                 first
                 Semicircle
                 ,
                 or
                 Subtracted
                 from
                 it
                 ,
                 if
                 in
                 the
                 latter
                 ,
                 the
                 Summ
                 or
                 difference
                 shall
                 be
                 the
                 place
                 of
                 the
                 Moon
                 first
                 Equated
                 .
              
               
                 9.
                 
                 From
                 the
                 place
                 of
                 the
                 Moon
                 first
                 Equated
                 ,
                 Deduct
                 the
                 true
                 place
                 of
                 the
                 Sun
                 ,
                 and
                 double
                 the
                 remainer
                 ,
                 and
                 to
                 the
                 Sine
                 of
                 the
                 double
                 add
                 the
                 Sine
                 of
                 the
                 greatest
                 variation
                 0.
                 36.
                 27
                 ,
                 
                   viz.
                   8.
                
                 02541571
                 ,
                 the
                 Summ
                 shall
                 be
                 the
                 Sine
                 of
                 the
                 true
                 variation
                 ,
                 at
                 that
                 time
                 ,
                 which
                 being
                 added
                 to
                 the
                 Moons
                 place
                 first
                 Equated
                 ,
                 when
                 her
                 single
                 distance
                 from
                 the
                 Sun
                 is
                 in
                 the
                 first
                 or
                 third
                 quadrants
                 ,
                 or
                 Subtracted
                 when
                 in
                 the
                 second
                 or
                 fourth
                 ,
                 the
                 Summ
                 or
                 difference
                 shall
                 be
                 the
                 Moons
                 true
                 place
                 in
                 her
                 Orbit
                 .
              
               
                 Example
                 .
              
               
                 Let
                 the
                 given
                 time
                 be
                 
                   Anno
                   Christi
                   1672.
                   
                   Feb.
                   23.
                
                 h.
                 11.
                 
                 34′
                 .
                 54″
                 at
                 which
                 time
                 the
                 Suns
                 true
                 place
                 is
                 in
                 ♓
                 15.
                 29133
                 and
                 the
                 Moons
                 middle
                 motions
                 are
                 as
                 followeth
                 .
              
               
               
                 
                   
                     
                        
                    
                     
                       ☽
                       Longitude
                    
                     
                       ☽
                       Apogaeon
                    
                     
                       ☊
                       Retrograde
                    
                     
                        
                    
                  
                   
                     
                       1660
                    
                     
                       13.
                       36650.
                       
                    
                     
                       41.
                       78372.
                       
                    
                     
                       55.85177
                    
                     
                        
                    
                  
                   
                     
                       11.
                       
                    
                     
                       02.
                       66032.
                       
                    
                     
                       24.
                       31246.
                       
                    
                     
                       59.08943
                    
                     
                        
                    
                  
                   
                     
                       Ianuary
                       .
                    
                     
                       13.
                       46339.
                       
                    
                     
                       00.95934
                    
                     
                       .45599
                    
                     
                        
                    
                  
                   
                     
                       D.
                       23
                    
                     
                       84.
                       18252.
                       
                    
                     
                       .71177
                    
                     
                       .33832
                    
                     
                        
                    
                  
                   
                     
                       H.
                       11
                    
                     
                       1.
                       67755.
                       
                    
                     
                       .01418
                    
                     
                       .00674
                    
                     
                        
                    
                  
                   
                     
                       34′
                    
                     
                       .08641
                       .
                    
                     
                       .00072
                    
                     
                       .00054
                    
                     
                        
                    
                  
                   
                     
                       54
                    
                     
                       .00228
                       .
                    
                     
                       .00012
                    
                     
                       .00001
                    
                     
                        
                    
                  
                   
                     
                       ☽
                       Longitude
                    
                     
                       15.
                       43897.
                       
                    
                     
                       67.78229
                    
                     
                       59.89082
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       95.96094
                    
                  
                
              
               
                 
                   These
                   Numbers
                   reduced
                   to
                   the
                   Degrees
                   and
                   Parts
                   of
                   the
                   common
                   Circle
                   are
                   for
                   the
                   ☽
                   mean
                   Longitude
                   .
                
                 
                   55.580292
                
                 
                   The
                   ☽
                   Apogaeon
                   .
                
                 
                   244.015956
                
              
               
                 
                   The
                   ☉
                   true
                   place
                   is
                
                 
                   345.29133
                
                 
                   The
                   ☽
                   Apogaeon
                   subtract
                   .
                
                 
                   244.01595
                
              
               
                 
                   The
                   Annual
                   Augment
                   .
                
                 
                   101.27538
                
                 
                   The
                   Complement
                   whereof
                   is
                
                 
                   78.72462
                
              
               
                 
                   The
                   Tang.
                   of
                   deg
                   .
                   78.
                   72462
                
                 
                   10.70033391
                
                 
                   The
                   standing
                   Number
                   .
                
                 
                   9.82000044
                
                 
                   The
                   Tang.
                   of
                   deg
                   .
                   73.
                   20288
                
                 
                   10.52033435
                
                 
                   Their
                   difference
                   .
                   5.
                   52174
                   the
                   Apogaeon
                   Equation
                
                 
                    
                
                 
                   Mean
                   Apogaeon
                   244.
                   01595
                
                 
                    
                
                 
                   Their
                   difference
                   238.
                   49421
                   is
                   the
                   true
                   Apogaeon
                   .
                
                 
                    
                
              
               
               
                 Secondly
                 .
              
               
                 
                   The
                   ☽
                   mean
                   Longitude
                   .
                
                 
                   55.58029
                
                 
                   The
                   true
                   Apogaeon
                   subtract
                   .
                
                 
                   238.49421
                
                 
                   Rests
                   the
                   ☽
                   mean
                   Anom
                   .
                   correct
                   .
                
                 
                   177.08608
                
              
               
                 
                   Or
                   thus
                
                 .
              
               
                 
                   The
                   ☽
                   mean
                   Anomaly
                   in
                   the
                   Tables
                   for
                   the
                   time
                   propounded
                   ,
                   will
                   be
                   found
                   to
                   be
                   67.
                   78221
                   ,
                   which
                   converted
                   into
                   the
                   deg
                   .
                   and
                   parts
                   of
                   the
                   common
                   Circle
                   is
                
                 
                   171.56434
                
                 
                   To
                   which
                   the
                   Apogaeon
                   Equation
                   being
                   added
                
                 
                   5.52174
                
                 
                   Their
                   Sum
                   is
                   the
                   mean
                   Anom
                   .
                   correct
                   .
                
                 
                   177.08608
                
              
               
                 And
                 hence
                 it
                 appears
                 that
                 working
                 by
                 the
                 mean
                 Anomaly
                 instead
                 of
                 the
                 mean
                 Longitude
                 ,
                 the
                 true
                 Apogaeon
                 Equation
                 must
                 be
                 added
                 to
                 the
                 mean
                 Anomaly
                 ,
                 in
                 the
                 second
                 and
                 fourth
                 Quadrants
                 of
                 the
                 ☽
                 Annual
                 Augment
                 ,
                 and
                 subtracted
                 from
                 it
                 in
                 the
                 first
                 and
                 third
                 .
              
               
                 Thirdly
                 .
              
               
                 
                   The
                   Annual
                   Augment
                   .
                   101.
                   27538
                   being
                   doubled
                   is
                   deg
                   .
                   202.
                   55076
                   ,
                   the
                   Cosine
                   of
                   whose
                   excess
                   above
                   180
                   ,
                   that
                   is
                   the
                   Cosine
                   of
                   22.
                   54076
                   is
                
                 
                   9.96545577
                
                 
                   The
                   Logarithm
                   of
                   1161.
                   75
                
                 
                   3.06511268
                
                 
                   The
                   Logarithm
                   of
                   1072.
                   92
                
                 
                   3.03056845
                
                 
                   The
                   ☽
                   mean
                   Excentr
                   .
                   5523.
                   69
                
                 
                    
                
                 
                   Their
                   difference
                   4450.
                   77
                   is
                   the
                   ☽
                   true
                   Excentricity
                   .
                   
                   Which
                   taken
                   as
                   a
                   natural
                   Sine
                   ,
                   the
                   Arch
                   answering
                   thereunto
                   Deg.
                   2.
                   55094
                   is
                   the
                   ☽
                   greatest
                   Physical
                   Equation
                   .
                
                 
                    
                
              
               
                 Fourthly
                 .
              
               
                 
                   To
                   the
                   half
                   of
                   the
                   Physical
                   Equation
                   .
                   deg
                   .
                   01.
                   27547
                   add
                   45
                   degrees
                   ,
                   the
                   Sum
                   is
                   deg
                   .
                   46.
                   27547
                   ,
                   the
                   Cotangent
                   whereof
                   ;
                   
                     viz.
                     9.
                  
                   98080957
                   is
                   the
                   Logarithm
                   of
                   the
                   Excentrick
                   ,
                   the
                   double
                   of
                   which
                   Logarithm
                   is
                
                 
                   9.96161914
                
                 
                   Tangent
                   frac12
                   Anomaly
                   corrected
                   88.
                   54304
                
                 
                   11.59455229
                
                 
                   Tang.
                   of
                   deg
                   .
                   88.
                   40849
                
                 
                   11.55620143
                
                 
                   Their
                   Sum
                   deg
                   .
                   176.
                   95153
                   is
                   the
                   excentrick
                   Anomaly
                   .
                
                 
                    
                
              
               
                 Fifthly
                 .
              
               
                 
                   The
                   Logarithm
                   of
                   the
                   Excentrick
                   is
                
                 
                   9.98080957
                
                 
                   Tang.
                   frac12
                   excent
                   .
                   Anom
                   .
                   88.
                   475765
                
                 
                   11.57505878
                
                 
                   Tangent
                   of
                   deg
                   .
                   88.
                   407268
                
                 
                   11.55586835
                
                 
                   The
                   double
                   whereof
                   176.
                   814536
                
                 
                   is
                   the
                   coequated
                   Anomaly
                   .
                
                 
                   M.
                   Anomaly
                   correct
                   .
                
                 
                   177.086080
                
                 
                   Their
                   difference
                   0.
                   271544
                
                 
                   is
                   the
                   Equation
                   sought
                   to
                
                 
                   be
                   subst
                   .
                   from
                   ☽
                   mean
                   Long.
                   
                
                 
                   55.580292
                
                 
                   The
                   Remainer
                   55.
                   308748
                
                 
                   is
                   the
                   ☽
                   place
                   first
                   Equated
                   .
                
              
               
               
                 Sixthly
                 ,
              
               
                 
                   From
                   the
                   place
                   of
                   the
                   ☽
                   first
                   Equated
                   .
                
                 
                   55.308748
                
                 
                   Deduct
                   the
                   true
                   place
                   of
                   the
                   Sun
                
                 
                   345.291330
                
                 
                   The
                   Remainer
                   is
                   the
                   Distance
                   of
                   the
                   ☽
                   à
                   ☉
                
                 
                   70.017418
                
                 
                   The
                   double
                   whereof
                   is
                   140.
                   034836.
                   
                   The
                   Sine
                   of
                   whose
                   Complement
                   to
                   a
                   Semi-circle
                   ,
                   39.
                   965164
                   is
                
                 
                   9.80775260
                
                 
                   The
                   Sine
                   of
                   the
                   greatest
                   variation
                
                 
                   8.02541571
                
                 
                   The
                   Sine
                   of
                   the
                   true
                   var.
                   0.
                   390206
                
                 
                   7.83316831
                
                 
                   The
                   ☽
                   place
                   first
                   Equa
                   .
                   55.
                   308748
                
                 
                    
                
                 
                   The
                   ☽
                   place
                   in
                   Orbit
                   55.
                   698954
                   that
                   is
                   in
                   Sexagenary
                   Numbers
                   .
                   8.
                   25.
                   41.
                   54.
                   
                
                 
                    
                
              
            
             
               
                 CHAP.
                 XVIII
                 .
              
               
                 
                   To
                   compute
                   the
                   true
                   Latitude
                   of
                   the
                   Moon
                   ,
                   and
                   to
                   reduce
                   her
                   place
                   ,
                   from
                   her
                   Orbit
                   to
                   the
                   Ecliptick
                   .
                
              
               
                 THe
                 greatest
                 Obliquity
                 of
                 the
                 Moon
                 's
                 Orb
                 with
                 the
                 Ecliptick
                 or
                 Angle
                 
                   A
                   ☊
                   B
                   Fig.
                
                 11.
                 is
                 by
                 many
                 Observations
                 confirmed
                 to
                 be
                 5
                 Degrees
                 just
                 ,
                 at
                 the
                 time
                 of
                 the
                 Conjunction
                 or
                 Opposition
                 of
                 the
                 Sun
                 and
                 Moon
                 ,
                 but
                 in
                 her
                 Quarters
                 deg
                 .
                 5.
                 
                 18′
                 .
                 Now
                 then
                 then
                 find
                 her
                 Latitude
                 at
                 all
                 times
                 ,
                 the
                 said
                 Mr.
                 Horrox
                 refers
                 us
                 to
                 
                   pag.
                   87.
                
                 in
                 the
                 Rudolphin
                 Tables
                 ,
                 to
                 find
                 from
                 thence
                 the
                 Equation
                 of
                 the
                 Nodes
                 ,
                 and
                 Inclination
                 
                   limitis
                   menstrui
                
                 ,
                 in
                 this
                 manner
                 .
              
               
                 1.
                 
                 From
                 the
                 mean
                 place
                 of
                 the
                 Node
                 ,
                 deduct
                 
                 the
                 ☉
                 true
                 place
                 ,
                 the
                 Remainer
                 is
                 the
                 distance
                 of
                 the
                 ☉
                 from
                 the
                 ☊
                 .
                 with
                 which
                 entring
                 the
                 said
                 Table
                 ,
                 he
                 finds
                 the
                 Equation
                 of
                 the
                 Node
                 and
                 Inclination
                 
                   limitis
                   menstrui
                
                 ,
                 which
                 being
                 added
                 to
                 or
                 subtracted
                 from
                 the
                 Nodes
                 mean
                 place
                 according
                 to
                 the
                 title
                 ,
                 the
                 Sum
                 or
                 difference
                 is
                 the
                 true
                 place
                 of
                 the
                 Node
                 ,
                 which
                 being
                 deducted
                 from
                 the
                 place
                 of
                 the
                 Moon
                 in
                 her
                 Orb
                 ,
                 the
                 Remainer
                 shall
                 be
                 the
                 Augment
                 of
                 Latitude
                 or
                 Distance
                 of
                 the
                 Moon
                 from
                 the
                 Node
                 ,
                 or
                 Leg
                 A
                 ☊
                 .
              
               
                 2.
                 
                 With
                 the
                 Augment
                 of
                 Latitude
                 ,
                 enter
                 the
                 Table
                 of
                 the
                 Moon
                 's
                 Latitude
                 ,
                 and
                 take
                 thence
                 her
                 Simple
                 and
                 Latitude
                 and
                 Increase
                 answering
                 to
                 it
                 .
                 Then
                 say
                 ,
                 
                   as
                   the
                   whole
                   excess
                   of
                   Latitude
                   18′
                   ,
                   or
                   in
                   Decimals
                   30.
                   is
                   to
                   the
                   Inclination
                   of
                   the
                   Monethly
                   limit
                   :
                   So
                   is
                   the
                   increase
                   of
                   Latitude
                   to
                   the
                   Part
                   Proportional
                
                 ;
                 which
                 being
                 added
                 to
                 the
                 simple
                 Latitude
                 ,
                 will
                 give
                 you
                 the
                 true
                 Latitude
                 of
                 the
                 Moon
                 .
              
               
                 3.
                 
                 With
                 the
                 same
                 Augment
                 of
                 Latitude
                 ,
                 enter
                 the
                 Table
                 of
                 Reduction
                 ,
                 and
                 take
                 thence
                 the
                 Reduction
                 and
                 Inclination
                 answering
                 thereto
                 :
                 Then
                 say
                 again
                 ,
                 
                   as
                   18′
                   .
                   00″
                   .
                   or
                   0.
                   30.
                   is
                   to
                   the
                   Inclination
                   of
                   the
                   Monethly
                   limit
                   :
                   So
                   is
                   the
                   increase
                   of
                   Reduction
                   ,
                   to
                   the
                   Part
                   Proportional
                
                 ;
                 which
                 being
                 added
                 to
                 the
                 simple
                 Reduction
                 ,
                 shall
                 give
                 the
                 true
                 ,
                 to
                 be
                 added
                 to
                 ,
                 or
                 subtracted
                 from
                 the
                 place
                 of
                 the
                 Moon
                 in
                 the
                 Ecliptick
                 .
                 
                   
                     Example
                     .
                     By
                     the
                     former
                     Chapter
                     ,
                     we
                     found
                     the
                     mean
                     motion
                     of
                     the
                     Node
                     to
                     be
                     95.
                     96094
                     ,
                     which
                     reduced
                     to
                     the
                     Degrees
                     and
                     Parts
                     of
                     the
                     common
                     Circle
                     is
                  
                   
                     345.459384
                  
                   
                     And
                     the
                     Suns
                     true
                     place
                     to
                     be
                  
                   
                     345.291334
                  
                   
                     Their
                     difference
                     is
                     the
                     distance
                     ☉
                     à
                     ☊
                  
                   
                     .
                     168050
                  
                
                 
                 with
                 which
                 entring
                 the
                 Table
                 ,
                 Entituled
                 
                   Tabula
                   AEquationis
                   Nodorum
                   Lunae
                
                 .
                 I
                 find
                 the
                 Node
                 to
                 need
                 no
                 Equation
                 ,
                 and
                 the
                 Inclination
                 
                   limitis
                   menstrui
                
                 to
                 be
                 deg
                 .
                 00.
                 30.
                 
              
               
                 
                   The
                   place
                   of
                   the
                   ☽
                   in
                   her
                   Orbit
                
                 
                   55.698954
                
                 
                   The
                   Nodes
                   true
                   place
                   ,
                   subtract
                   .
                
                 
                   345.459384
                
                 
                   The
                   Augment
                   of
                   Latitude
                
                 
                   70.239570
                
              
               
                 
                   2.
                   
                   With
                   this
                   Augment
                   of
                   Latitude
                   I
                   enter
                   the
                   Table
                   shewing
                   the
                   Moons
                   simple
                   Latitude
                   ,
                   and
                   thereby
                   find
                   her
                   simple
                   Latitude
                   to
                   be
                   Degrees
                   .
                   04.
                   70476.
                   
                   North
                   ;
                   And
                   the
                   increase
                
                 
                   00.28234
                
                 
                   And
                   therefore
                   the
                   Moons
                   true
                   Latitude
                   is
                   deg
                   .
                
                 
                   4.98610
                
                 
                   3.
                   
                   With
                   the
                   same
                   Augment
                   of
                   Latitude
                   ,
                   I
                   enter
                   the
                   Table
                   of
                   Reduction
                   ,
                   and
                   thereby
                   find
                   the
                   Reduction
                   to
                   be
                
                 
                   00.06955
                
                 
                   And
                   the
                   increase
                   of
                   Reduction
                   to
                   be
                   deg
                   .
                
                 
                   00.00855
                
                 
                   And
                   therefore
                   the
                   whole
                   Reduction
                   to
                   be
                   sub
                   .
                
                 
                   00.07810
                
                 
                   From
                   the
                   ☽
                   place
                   in
                   her
                   Orbit
                
                 
                   55.69895
                
                 
                   The
                   ☽
                   true
                   place
                   in
                   the
                   Ecliptick
                
                 
                   55.62085
                
                 
                   That
                   is
                   in
                   Sexagenary
                   Numbers
                   .
                
                 
                   8.
                   25.
                   
                   37′
                   .
                   15″
                   .
                
              
            
             
               
               
                 CHAP.
                 XIX
                 .
              
               
                 
                   To
                   find
                   the
                   Mean
                   Conjunction
                   and
                   Opposition
                   of
                   the
                   Sun
                   and
                   Moon
                   .
                
              
               
                 TO
                 this
                 purpose
                 we
                 have
                 here
                 exhibited
                 a
                 Table
                 shewing
                 the
                 Moons
                 mean
                 motion
                 from
                 the
                 Sun
                 ,
                 the
                 construction
                 whereof
                 is
                 this
                 :
                 By
                 the
                 Tables
                 of
                 the
                 Moons
                 mean
                 motions
                 ,
                 her
                 mean
              
               
                 
                   Longitude
                   
                     AEra
                     Christi
                  
                   is
                
                 
                   34.0088734567
                
                 
                   The
                   ☉
                   mean
                   Anomaly
                   .
                
                 
                   56.6997085185
                
                 
                   Praecession
                   of
                   the
                   AEquinox
                   .
                
                 
                   20.4976851851
                
                 
                   Their
                   Sum
                   is
                   the
                   ☉
                   mean
                   longit
                   .
                   
                     AEra
                     a
                     Christi
                  
                   .
                
                 
                   77.4973937036
                
                 
                   Which
                   being
                   deducted
                   from
                   the
                   ☽
                   mean
                   longitude
                   ,
                   the
                   remainer
                   is
                   the
                   Moons
                   mean
                
                 
                   56.8114797531
                
                 
                   distance
                   from
                   the
                   Sun
                   ,
                   in
                   the
                   beginning
                   of
                   the
                   Christian
                   AEra
                   .
                
                 
                    
                
              
               
                 In
                 like
                 manner
                 the
                 Moons
                 mean
                 distance
                 from
                 the
                 Sun
                 in
                 a
                 year
                 or
                 a
                 day
                 is
                 thus
                 found
                 .
              
               
                 
                   ☉
                   Anomaly
                   for
                   a
                   year
                   .
                
                 
                   99.9297857316
                
                 
                   Praecession
                   of
                   the
                   AEquinox
                   .
                
                 
                   0038580246
                
                 
                   Their
                   Sum
                   subtract
                   .
                
                 
                   99.9336437562
                
                 
                   From
                   the
                   ☽
                   mean
                   Longitude
                   .
                
                 
                   35.9400144893
                
                 
                   Moons
                   distance
                   from
                   the
                   ☉
                   .
                
                 
                   36.0063707331
                
              
               
               
                 Moons
                 distance
                 from
                 the
                 Sun
                 in
                 a
                 days
                 time
                 .
              
               
                 
                   ☉
                   mean
                   Anomaly
                   .
                
                 
                   27378.02348
                
                 
                   Praecession
                   of
                   the
                   AEquinox
                   .
                
                 
                   1.05699
                
                 
                   Their
                   Sum
                   subtract
                   .
                
                 
                   27379.08047
                
                 
                   From
                   the
                   ☽
                   mean
                   Longitude
                   .
                
                 
                   03.
                   66010.96287
                
                 
                   ☽
                   Daily
                   motion
                   from
                   the
                   ☉
                   .
                
                 
                   03.
                   38631.88240
                
              
               
                 And
                 according
                 to
                 these
                 measures
                 are
                 the
                 Tables
                 made
                 ,
                 shewing
                 the
                 Moons
                 mean
                 motion
                 from
                 the
                 Sun
                 ,
                 by
                 which
                 the
                 mean
                 conjunction
                 of
                 the
                 ☽
                 and
                 Moon
                 may
                 be
                 thus
                 computed
                 .
              
               
                 To
                 the
                 given
                 year
                 and
                 Month
                 gather
                 the
                 middle
                 motions
                 of
                 the
                 Moon
                 from
                 the
                 Sun
                 ,
                 and
                 take
                 the
                 complement
                 thereof
                 to
                 a
                 whole
                 Circle
                 ,
                 from
                 which
                 subtracting
                 continually
                 the
                 nearest
                 lesser
                 middle
                 motions
                 ,
                 the
                 day
                 ,
                 hour
                 ,
                 and
                 minute
                 enfuing
                 thereto
                 is
                 the
                 mean
                 time
                 of
                 the
                 Conjunction
                 .
              
               
                 Example
                 ,
                 
                   Anno
                   Christi
                
                 1676.
                 
                 I
                 would
                 know
                 the
                 time
                 of
                 the
                 mean
                 Conjunction
                 or
                 New
                 Moon
                 in
                 October
                 .
              
               
                 
                   Epocha
                   1660
                
                 
                   32.697283
                
                 
                   Years
                   Compl.
                   15.
                   
                
                 
                   50.254463
                
                 
                   Septemb.
                   Compl.
                   
                
                 
                   24.465038
                
                 
                   1.
                   day
                   for
                   Leap-year
                   .
                
                 
                   03.386318
                
                 
                   Their
                   Sum
                   is
                   the
                   Moons
                   motion
                   from
                   the
                   ☉
                   .
                
                 
                   10.803102
                
                 
                   Complement
                   to
                   a
                   whole
                   Circle
                   .
                
                 
                   89.196898
                
                 
                   Days
                   26
                   Subtract
                   .
                
                 
                   88.044289
                
                 
                   Hours
                   8.
                   substract
                   .
                
                 
                   
                     
                       1.152609
                    
                     
                       1.128772
                    
                  
                
                 
                   
                   Minutes
                   10
                   Subtract
                   .
                
                 
                   
                     
                       0.023837
                    
                     
                       0.023516
                    
                  
                
                 
                   The
                   Remainer
                   giveth
                   8″
                   .
                
                 
                   .00321
                
              
               
                 Therefore
                 the
                 mean
                 Conjunction
                 in
                 
                   October
                   ,
                   1676.
                
                 was
                 the
                 26
                 day
                 ,
                 10
                 min.
                 8
                 seconds
                 after
                 8
                 at
                 night
                 .
              
               
                 And
                 to
                 find
                 the
                 mean
                 opposition
                 .
                 To
                 the
                 complement
                 of
                 the
                 middle
                 motion
                 ,
                 add
                 a
                 semicircle
                 ,
                 and
                 then
                 subtract
                 the
                 nearest
                 lesser
                 middle
                 motions
                 as
                 before
                 ,
                 the
                 day
                 ,
                 hour
                 ,
                 and
                 minute
                 ensuing
                 thereto
                 ,
                 shall
                 be
                 the
                 mean
                 opposition
                 required
                 .
              
               
                 Example
                 ,
                 
                   Anno
                   Christi
                
                 ,
                 1676.
                 
                 I
                 desire
                 to
                 know
                 the
                 mean
                 opposition
                 in
                 November
                 .
              
               
                 
                   Epocha
                   1660
                
                 
                   32.697283
                
                 
                   Years
                   Compl.
                   15
                
                 
                   50.254463
                
                 
                   October
                   Compl.
                   
                
                 
                   29.440922
                
                 
                   1
                   day
                   for
                   Leap-year
                   .
                
                 
                   03.386318
                
              
               
                 
                   The
                   ☽
                   mean
                   motion
                   from
                   the
                   ☉
                
                 
                   15.778986
                
                 
                   Complement
                   to
                   a
                   whole
                   Circle
                   .
                
                 
                   84.221014
                
                 
                   To
                   which
                   add
                   a
                   Semicircle
                   .
                
                 
                   50.
                   
                
                 
                   The
                   Sum
                   is
                
                 
                   34.221014
                
                 
                   Day
                   10
                   subtract
                   .
                
                 
                   33.863188
                
                 
                   Hours
                   2.
                   
                
                 
                   
                     
                       .357826
                    
                     
                       .282193
                    
                  
                
                 
                   Minutes
                   32.
                   
                
                 
                   
                     
                       .075633
                    
                     
                       .075251
                    
                  
                
                 
                   The
                   Remainer
                   giveth
                   9
                   seconds
                   .
                
                 
                   .000382
                
              
               
               
                 Therefore
                 the
                 Full
                 Moon
                 or
                 mean
                 Opposition
                 of
                 the
                 Sun
                 and
                 Moon
                 was
                 November
                 the
                 10th
                 ,
                 Hours
                 2
                 ,
                 32′
                 09″
                 .
                 The
                 like
                 may
                 be
                 done
                 for
                 any
                 other
                 .
              
               
                 And
                 here
                 I
                 should
                 proceed
                 to
                 shew
                 the
                 manner
                 of
                 finding
                 the
                 true
                 Conjunction
                 or
                 Opposition
                 of
                 the
                 Sun
                 and
                 Moon
                 ,
                 but
                 there
                 being
                 no
                 decimal
                 Canon
                 yet
                 extant
                 ,
                 suitable
                 to
                 the
                 Tables
                 of
                 middle
                 motions
                 here
                 exhibited
                 ,
                 I
                 chuse
                 rather
                 to
                 refer
                 my
                 Reader
                 to
                 Mr.
                 
                 Street's
                 
                   Astronomia
                   Carolina
                
                 ,
                 for
                 instructions
                 in
                 that
                 particular
                 ,
                 and
                 what
                 else
                 shall
                 be
                 found
                 wanting
                 in
                 this
                 Subject
                 .
              
            
          
           
             
             
               AN
               INTRODUCTION
               TO
               Geography
               ,
               OR
               ,
               The
               Fourth
               Part
               of
               COSMOGRAPHY
               .
            
             
               
                 CHAP.
                 I.
                 
              
               
                 
                   Of
                   the
                   Nature
                   and
                   Division
                   of
                   Geography
                   .
                
              
               
                 GEOGRAPHY
                 is
                 a
                 Science
                 concerning
                 the
                 measure
                 and
                 distinction
                 of
                 the
                 Earthly
                 Globe
                 ,
                 as
                 it
                 is
                 a
                 Spherical
                 Body
                 composed
                 of
                 Earth
                 and
                 Water
                 ,
                 for
                 that
                 both
                 these
                 do
                 together
                 make
                 but
                 one
                 Globe
                 .
              
               
               
                 2.
                 
                 And
                 hence
                 the
                 parts
                 of
                 Geography
                 are
                 two
                 ,
                 the
                 one
                 concerns
                 the
                 Earthy
                 part
                 ,
                 and
                 the
                 other
                 the
                 Water
                 .
              
               
                 3.
                 
                 The
                 Earthy
                 part
                 of
                 this
                 Globe
                 is
                 commonly
                 divided
                 into
                 Continents
                 and
                 Islands
                 .
              
               
                 4.
                 
                 A
                 Continent
                 is
                 a
                 great
                 quantity
                 of
                 Land
                 not
                 separated
                 by
                 any
                 Sea
                 from
                 the
                 rest
                 of
                 the
                 World
                 ,
                 as
                 the
                 whole
                 Continent
                 of
                 
                   Europe
                   ,
                   Asia
                
                 ,
                 and
                 Africa
                 ,
                 or
                 the
                 Continents
                 of
                 
                   France
                   ,
                   Spain
                
                 ,
                 and
                 Germany
                 .
              
               
                 5.
                 
                 An
                 Island
                 is
                 a
                 part
                 of
                 Earth
                 environed
                 round
                 about
                 with
                 some
                 Sea
                 or
                 other
                 ;
                 as
                 the
                 Isle
                 of
                 Britain
                 with
                 the
                 Ocean
                 ,
                 the
                 Isle
                 of
                 Sicily
                 with
                 the
                 Mediterranean
                 ,
                 and
                 therefore
                 in
                 Latine
                 it
                 is
                 called
                 Insula
                 ,
                 because
                 it
                 is
                 scituate
                 in
                 Salo
                 ,
                 in
                 the
                 Sea.
                 
              
               
                 6.
                 
                 Both
                 these
                 are
                 subdivided
                 into
                 
                   Peninsula
                   ,
                   Isthmus
                   ,
                   Promontorium
                
                 .
              
               
                 7.
                 
                 
                   Peninsula
                   ,
                   quasi
                   pene
                   insula
                
                 ,
                 is
                 a
                 tract
                 of
                 land
                 which
                 being
                 almost
                 encompassed
                 round
                 by
                 water
                 ,
                 is
                 joyned
                 to
                 the
                 main
                 land
                 by
                 some
                 little
                 part
                 of
                 Earth
                 .
              
               
                 8.
                 
                 Isthmus
                 is
                 that
                 narrow
                 neck
                 of
                 Land
                 which
                 joyneth
                 the
                 Peninsula
                 to
                 the
                 Continent
                 .
              
               
                 9.
                 
                 Promontorium
                 is
                 a
                 high
                 mountain
                 which
                 shooteth
                 it self
                 into
                 the
                 Sea
                 ,
                 the
                 outmost
                 end
                 whereof
                 is
                 called
                 a
                 Cape
                 or
                 Foreland
                 ,
                 as
                 
                   the
                   Cape
                   of
                   Good
                   Hope
                
                 in
                 Africk
                 .
              
               
                 10.
                 
                 The
                 Watry
                 part
                 of
                 this
                 Globe
                 may
                 be
                 also
                 distinguished
                 by
                 diverse
                 Names
                 ,
                 as
                 Seas
                 ,
                 Rivers
                 ,
                 Ponds
                 ,
                 Lakes
                 ,
                 and
                 such
                 like
                 .
              
               
                 11.
                 
                 And
                 this
                 Terrestrial
                 Globe
                 may
                 be
                 measured
                 either
                 in
                 whole
                 ,
                 or
                 in
                 any
                 particular
                 part
                 .
              
               
                 12.
                 
                 The
                 measure
                 of
                 this
                 Earthly
                 Globe
                 in
                 whole
                 ,
                 is
                 either
                 in
                 respect
                 of
                 its
                 circumference
                 ,
                 ●o
                 its
                 bulk
                 and
                 thickness
                 .
              
               
               
                 13.
                 
                 For
                 the
                 measuring
                 of
                 the
                 Earths
                 circumference
                 ,
                 it
                 is
                 supposed
                 to
                 be
                 compassed
                 with
                 a
                 great
                 Circle
                 ,
                 and
                 this
                 Circle
                 in
                 imitation
                 of
                 Astronomers
                 ,
                 is
                 divided
                 into
                 360
                 degrees
                 or
                 parts
                 ,
                 and
                 each
                 degree
                 is
                 supposed
                 to
                 be
                 equal
                 to
                 15
                 common
                 German
                 miles
                 ,
                 or
                 60
                 miles
                 with
                 us
                 in
                 England
                 ,
                 and
                 hence
                 the
                 circumference
                 of
                 the
                 Earth
                 is
                 found
                 ,
                 by
                 multiplying
                 360
                 by
                 15
                 ,
                 to
                 be
                 5400
                 German
                 miles
                 ,
                 or
                 multiplying
                 360
                 by
                 60
                 ,
                 the
                 circumference
                 is
                 21600
                 English
                 miles
                 .
              
               
                 14.
                 
                 The
                 circumference
                 of
                 the
                 Earth
                 being
                 thus
                 obtained
                 ,
                 the
                 Diameter
                 may
                 be
                 found
                 by
                 the
                 common
                 proportion
                 between
                 the
                 Circumference
                 and
                 the
                 Diameter
                 of
                 a
                 Circle
                 ,
                 the
                 which
                 according
                 to
                 Archimedes
                 is
                 as
                 22
                 to
                 7
                 ,
                 or
                 according
                 to
                 
                   Van
                   Culen
                
                 as
                 1
                 to
                 3.
                 14159.
                 and
                 to
                 bring
                 an
                 Unite
                 in
                 the
                 first
                 place
                 .
              
               
                 As
                 the
                 circumference
                 3.
                 14159.
                 is
                 to
                 1
                 the
                 Diameter
                 ,
                 so
                 is
                 1
                 the
                 circumference
                 to
                 318308
                 the
                 Diameter
                 ,
                 which
                 being
                 multiplied
                 by
                 5400
                 ,
                 the
                 Earths
                 Diameter
                 will
                 be
                 found
                 to
                 be
                 1718
                 German
                 miles
                 and
                 8632
                 parts
                 ,
                 but
                 being
                 multiplied
                 by
                 21600
                 ,
                 the
                 Diameter
                 will
                 be
                 6875
                 English
                 miles
                 ,
                 and
                 parts
                 4528.
                 
              
               
                 15.
                 
                 The
                 measure
                 of
                 the
                 Earth
                 being
                 thus
                 found
                 in
                 respect
                 of
                 its
                 whole
                 circumference
                 and
                 Diameter
                 ,
                 that
                 which
                 is
                 next
                 to
                 be
                 considered
                 ,
                 is
                 the
                 distinction
                 of
                 it
                 into
                 convenient
                 spaces
                 .
              
               
                 16.
                 
                 And
                 this
                 is
                 either
                 Primary
                 or
                 Secondary
                 .
              
               
                 17.
                 
                 The
                 Primary
                 distinction
                 of
                 the
                 Earthly
                 Globe
                 into
                 convenient
                 spaces
                 ,
                 is
                 by
                 Circles
                 considered
                 absolutely
                 in
                 themselves
                 ,
                 dividing
                 the
                 Globe
                 into
                 several
                 parts
                 without
                 any
                 reference
                 to
                 one
                 another
                 .
              
               
               
                 Dutch
                 Geographer
                 inclines
                 much
                 to
                 the
                 bringing
                 back
                 the
                 great
                 Meridian
                 to
                 the
                 Fortunate
                 Islands
                 ,
                 more
                 particularly
                 to
                 the
                 Peak
                 a
                 Mountain
                 so
                 called
                 from
                 the
                 sharpness
                 in
                 the
                 top
                 ,
                 in
                 the
                 Isle
                 Teneriff
                 ,
                 which
                 is
                 believed
                 to
                 be
                 the
                 highest
                 Mountain
                 in
                 the
                 World
                 ;
                 therefore
                 the
                 same
                 Iohnson
                 in
                 his
                 greatest
                 Globe
                 of
                 the
                 year
                 1616
                 ,
                 hath
                 drawn
                 the
                 great
                 Meridian
                 in
                 that
                 place
                 ,
                 and
                 it
                 were
                 to
                 be
                 wished
                 ,
                 that
                 this
                 might
                 be
                 made
                 the
                 common
                 and
                 unchangeable
                 practice
                 .
              
               
                 25.
                 
                 The
                 Horizon
                 is
                 a
                 great
                 Circle
                 ,
                 designing
                 so
                 great
                 a
                 Part
                 of
                 the
                 Earth
                 ,
                 as
                 a
                 quick
                 sight
                 can
                 discern
                 in
                 an
                 open
                 field
                 ;
                 it
                 is
                 twofold
                 Rational
                 and
                 Sensible
                 .
              
               
                 26.
                 
                 The
                 Rational
                 Horizon
                 is
                 that
                 which
                 is
                 supposed
                 to
                 pass
                 through
                 the
                 Center
                 of
                 the
                 Earth
                 ,
                 and
                 is
                 represented
                 by
                 the
                 wooden
                 Circle
                 in
                 the
                 Frame
                 ,
                 as
                 well
                 of
                 the
                 Celestial
                 ,
                 as
                 the
                 Terrestrial
                 Globe
                 ,
                 this
                 Rational
                 Horizon
                 belongeth
                 more
                 to
                 Astronomy
                 than
                 Geography
                 .
              
               
                 27.
                 
                 The
                 Sensible
                 Horizon
                 is
                 that
                 before
                 defined
                 ,
                 the
                 use
                 of
                 it
                 is
                 to
                 discern
                 the
                 divers
                 risings
                 and
                 settings
                 of
                 the
                 Stars
                 ,
                 in
                 divers
                 places
                 of
                 the
                 Earth
                 ,
                 and
                 why
                 the
                 days
                 are
                 sometimes
                 longer
                 ,
                 and
                 sometimes
                 shorter
                 .
              
               
                 28.
                 
                 The
                 great
                 but
                 less
                 principal
                 Circle
                 upon
                 the
                 Terrestrial
                 Globe
                 is
                 the
                 Zodiack
                 ,
                 in
                 which
                 the
                 Sun
                 doth
                 always
                 move
                 .
                 This
                 Circle
                 is
                 described
                 upon
                 Globes
                 and
                 Maps
                 for
                 ornament
                 sake
                 ,
                 and
                 to
                 discover
                 under
                 what
                 part
                 of
                 the
                 Zodiack
                 the
                 several
                 Nations
                 lie
                 .
              
               
                 29.
                 
                 The
                 lesser
                 Circles
                 are
                 those
                 which
                 do
                 not
                 divide
                 the
                 Terrestial
                 Globe
                 into
                 two
                 equal
                 ,
                 but
                 into
                 two
                 unequal
                 Parts
                 ,
                 and
                 these
                 by
                 a
                 general
                 name
                 are
                 called
                 Parallels
                 ,
                 or
                 Circles
                 aequidistant
                 
                 from
                 the
                 Equinoctial
                 ;
                 of
                 which
                 as
                 many
                 may
                 be
                 drawn
                 ,
                 as
                 there
                 can
                 Meridians
                 ,
                 namely
                 180
                 if
                 but
                 to
                 each
                 degree
                 ,
                 but
                 they
                 are
                 usually
                 drawn
                 to
                 every
                 ten
                 Degrees
                 in
                 each
                 Quadrant
                 from
                 the
                 AEquator
                 to
                 the
                 Poles
                 .
              
               
                 30.
                 
                 These
                 Parallels
                 are
                 not
                 of
                 the
                 same
                 Magnitude
                 ,
                 but
                 are
                 less
                 and
                 less
                 as
                 they
                 are
                 nearer
                 and
                 nearer
                 to
                 each
                 Pole
                 :
                 and
                 their
                 use
                 is
                 to
                 distinguish
                 the
                 Zones
                 ,
                 Climates
                 and
                 Latitudes
                 of
                 all
                 Countries
                 ,
                 with
                 the
                 length
                 of
                 the
                 Day
                 and
                 Night
                 ▪
                 in
                 any
                 Part
                 of
                 the
                 World.
                 
              
               
                 31.
                 
                 Again
                 ,
                 a
                 Parallel
                 is
                 either
                 named
                 or
                 unnamed
                 .
              
               
                 32.
                 
                 An
                 unnamed
                 Parallel
                 is
                 that
                 which
                 is
                 drawn
                 with
                 small
                 black
                 Circular
                 Lines
                 .
              
               
                 33.
                 
                 A
                 named
                 Parallel
                 is
                 that
                 which
                 is
                 drawn
                 upon
                 the
                 Globe
                 with
                 a
                 more
                 full
                 ruddy
                 and
                 circular
                 Line
                 :
                 such
                 as
                 are
                 the
                 Tropicks
                 of
                 Cancer
                 and
                 Capricorn
                 ,
                 with
                 the
                 Arctick
                 and
                 Antarctick
                 Circles
                 ,
                 of
                 which
                 having
                 spoken
                 before
                 in
                 the
                 general
                 description
                 of
                 the
                 Globe
                 ,
                 there
                 is
                 no
                 need
                 of
                 adding
                 more
                 concerning
                 them
                 now
                 .
              
            
             
               
                 CHAP.
                 II.
                 
              
               
                 
                   Of
                   the
                   Distinction
                   or
                   Dimension
                   of
                   the
                   Earthly
                   Globe
                   by
                   Zones
                   and
                   Climates
                   .
                
              
               
                 HAving
                 shewed
                 the
                 primary
                 distinction
                 of
                 the
                 Globe
                 into
                 convenient
                 spaces
                 by
                 Circles
                 considered
                 absolutely
                 in
                 themselves
                 ,
                 we
                 come
                 now
                 to
                 consider
                 the
                 secondary
                 Dimension
                 or
                 distinction
                 of
                 convenient
                 spaces
                 in
                 the
                 Globe
                 ,
                 by
                 the
                 same
                 Circles
                 compared
                 with
                 one
                 another
                 ,
                 
                 and
                 by
                 the
                 spaces
                 contained
                 between
                 those
                 Circles
                 .
              
               
                 2.
                 
                 This
                 secundary
                 Dimension
                 or
                 Distinction
                 of
                 the
                 terrestial
                 Globe
                 into
                 Parts
                 ,
                 is
                 either
                 a
                 Zone
                 or
                 a
                 Clime
                 .
              
               
                 3.
                 
                 A
                 Zone
                 is
                 a
                 space
                 of
                 the
                 Terrestial
                 Globe
                 included
                 either
                 between
                 two
                 of
                 the
                 lesser
                 nominated
                 Circles
                 ,
                 or
                 between
                 one
                 and
                 either
                 Pole.
                 They
                 are
                 in
                 Number
                 five
                 ,
                 one
                 over
                 hot
                 ,
                 two
                 over
                 cold
                 ,
                 and
                 two
                 temperate
                 .
              
               
                 4.
                 
                 The
                 over
                 hot
                 or
                 Torrid
                 Zone
                 ,
                 is
                 between
                 the
                 two
                 Tropicks
                 ,
                 continually
                 scorched
                 with
                 the
                 presence
                 of
                 the
                 Sun.
                 
              
               
                 5.
                 
                 The
                 two
                 over
                 cold
                 or
                 Frigid
                 Zones
                 ,
                 are
                 scituated
                 between
                 the
                 two
                 polar
                 Circles
                 and
                 the
                 very
                 Poles
                 ,
                 continually
                 wanting
                 the
                 neighbour
                 hood
                 of
                 the
                 Sun.
                 
              
               
                 6.
                 
                 The
                 two
                 temperate
                 Zones
                 ,
                 are
                 one
                 of
                 them
                 between
                 the
                 Tropick
                 of
                 Cancer
                 and
                 the
                 Arctick
                 Circles
                 and
                 the
                 other
                 between
                 the
                 Tropick
                 of
                 Capricorn
                 and
                 the
                 Antarctick
                 Circle
                 ,
                 enjoyning
                 an
                 indifferency
                 between
                 Heat
                 and
                 Cold
                 ;
                 so
                 that
                 the
                 parts
                 next
                 the
                 Torrid
                 Zone
                 are
                 the
                 hotter
                 ,
                 and
                 the
                 parts
                 next
                 the
                 Frigid
                 Zone
                 are
                 the
                 Colder
                 .
              
               
                 7.
                 
                 The
                 Inhabitants
                 of
                 these
                 Zones
                 ,
                 in
                 respect
                 of
                 the
                 diversity
                 of
                 their
                 noon
                 Shadows
                 are
                 divided
                 into
                 three
                 kinds
                 ,
                 
                   Amphiscii
                   ,
                   Heteroscii
                
                 and
                 Periscii
                 .
                 Those
                 that
                 inhabit
                 between
                 the
                 two
                 Tropicks
                 are
                 called
                 Amphiscii
                 ,
                 because
                 that
                 their
                 noon
                 Shadows
                 are
                 diversly
                 cast
                 ,
                 sometimes
                 towards
                 the
                 South
                 as
                 when
                 the
                 Sun
                 is
                 more
                 Northward
                 than
                 their
                 vertical
                 point
                 ,
                 and
                 sometimes
                 towards
                 the
                 North
                 ,
                 as
                 when
                 the
                 Sun
                 declines
                 Southward
                 from
                 the
                 Zenith
                 .
              
               
               
                 Those
                 that
                 live
                 between
                 the
                 Tropick
                 of
                 Cancer
                 and
                 the
                 Arctick
                 Circle
                 or
                 between
                 the
                 Tropick
                 of
                 Capricorn
                 and
                 the
                 Antarctick
                 Circle
                 are
                 ●alled
                 Heteroscii
                 ,
                 because
                 the
                 Shadows
                 at
                 noon
                 are
                 cast
                 one
                 only
                 way
                 ,
                 and
                 that
                 either
                 North
                 or
                 South
                 .
                 They
                 that
                 inhabit
                 Northward
                 of
                 the
                 Tropick
                 of
                 Cancer
                 have
                 their
                 Shadows
                 always
                 towards
                 the
                 North
                 ,
                 and
                 they
                 that
                 inhabit
                 Southward
                 of
                 the
                 Tropick
                 of
                 Capricorn
                 ,
                 have
                 their
                 noon
                 Shadows
                 always
                 towards
                 the
                 South
                 .
              
               
                 Those
                 that
                 inhabit
                 between
                 the
                 Poles
                 and
                 the
                 Arctick
                 or
                 Antarctick
                 Circles
                 are
                 called
                 Periscii
                 ,
                 because
                 that
                 their
                 Gnomons
                 do
                 cast
                 their
                 Shadows
                 circulary
                 ,
                 and
                 the
                 reason
                 hereof
                 is
                 ,
                 for
                 that
                 the
                 Sun
                 is
                 carried
                 round
                 about
                 above
                 their
                 Horizon
                 in
                 his
                 whole
                 diurnal
                 revolution
                 .
              
               
                 8.
                 
                 The
                 next
                 secundary
                 Dimension
                 or
                 distinction
                 of
                 the
                 earthy
                 Globe
                 into
                 convenient
                 parts
                 or
                 spaces
                 ,
                 is
                 by
                 Climes
                 .
              
               
                 9.
                 
                 And
                 a
                 Clime
                 or
                 Climate
                 is
                 a
                 space
                 of
                 Earth
                 conteined
                 between
                 three
                 Paralells
                 ,
                 the
                 middlemo●
                 whereof
                 divideth
                 it
                 into
                 two
                 equal
                 parts
                 ,
                 serving
                 for
                 the
                 setting
                 out
                 the
                 length
                 and
                 shortness
                 of
                 the
                 days
                 in
                 every
                 Country
                 .
              
               
                 10.
                 
                 These
                 Climates
                 and
                 the
                 Parallels
                 by
                 which
                 they
                 are
                 conteined
                 are
                 none
                 of
                 them
                 of
                 equal
                 quantity
                 ,
                 for
                 the
                 first
                 Clime
                 as
                 also
                 the
                 Parallel
                 beginning
                 at
                 the
                 AEquator
                 is
                 larger
                 than
                 the
                 second
                 ,
                 and
                 the
                 second
                 is
                 likewise
                 greater
                 than
                 the
                 third
                 .
              
               
                 11.
                 
                 The
                 Antients
                 reckoned
                 but
                 seven
                 Climates
                 at
                 the
                 first
                 ,
                 to
                 which
                 Number
                 there
                 were
                 afterward
                 added
                 two
                 more
                 ,
                 so
                 that
                 in
                 the
                 first
                 of
                 these
                 Numbers
                 were
                 comprehended
                 fourteen
                 parallels
                 ,
                 but
                 in
                 the
                 latter
                 eighteen
                 .
              
               
               
                 12.
                 
                 Ptolemy
                 accounted
                 the
                 Paralells
                 38
                 each
                 way
                 from
                 the
                 Equator
                 ,
                 that
                 is
                 38
                 towards
                 the
                 North
                 ,
                 and
                 as
                 many
                 towards
                 the
                 South
                 ,
                 24
                 of
                 which
                 he
                 reckoned
                 by
                 the
                 difference
                 of
                 one
                 quarter
                 of
                 an
                 hour
                 ,
                 4
                 by
                 the
                 difference
                 of
                 half
                 an
                 hour
                 ,
                 4
                 by
                 an
                 whole
                 hours
                 difference
                 ,
                 and
                 6
                 by
                 a
                 Months
                 difference
                 ,
                 but
                 now
                 the
                 parallels
                 being
                 reckoned
                 by
                 the
                 difference
                 of
                 a
                 quarter
                 of
                 an
                 hour
                 ,
                 the
                 Climates
                 are
                 24
                 in
                 Number
                 till
                 you
                 come
                 to
                 the
                 Latitude
                 of
                 66
                 degrees
                 31
                 Minutes
                 ,
                 to
                 which
                 are
                 afterwards
                 added
                 6
                 Climates
                 more
                 unto
                 the
                 Pole
                 it self
                 ,
                 where
                 the
                 Artificial
                 day
                 is
                 6
                 Months
                 in
                 length
                 .
              
               
                 13.
                 
                 The
                 distances
                 of
                 all
                 both
                 Climates
                 and
                 Parallels
                 ,
                 together
                 with
                 their
                 Latitudes
                 from
                 the
                 AEquator
                 ,
                 and
                 difference
                 of
                 the
                 quantity
                 of
                 the
                 longest
                 days
                 ,
                 are
                 here
                 fully
                 exprest
                 in
                 the
                 Table
                 following
                 .
              
               
               
                 
                   
                     A
                     Table
                     of
                     the
                     Climates
                     belonging
                     to
                     the
                     three
                     sorts
                     of
                     Inhabitants
                     .
                  
                   
                     
                       Inhabitants
                       belonging
                       to
                       the
                       several
                       Climes
                    
                     
                       Climes
                    
                     
                       Paralells
                    
                     
                       Length
                       of
                       the
                       Day
                    
                     
                       Poles
                       Elevation
                    
                     
                       Bea
                       of
                       the
                       Clime
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       0
                    
                     
                       12.0
                    
                     
                       0.0
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       0
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       4.18
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       1
                    
                     
                       12.15
                    
                     
                       4.18
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       2
                    
                     
                       12.30
                    
                     
                       8.34
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       1
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       8.25
                    
                  
                   
                     
                       Amphiscii
                    
                     
                        
                    
                     
                       3
                    
                     
                       12.45
                    
                     
                       12.43
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       4
                    
                     
                       13.0
                    
                     
                       16.43
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       2
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       7.50
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       5
                    
                     
                       13.15
                    
                     
                       20.33
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       6
                    
                     
                       13.30
                    
                     
                       23.10
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       3
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       7.3
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       7
                    
                     
                       13.45
                    
                     
                       27.36
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       8
                    
                     
                       14.0
                    
                     
                       30.47
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       4
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       6.9
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       9
                    
                     
                       14.15
                    
                     
                       33.45
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       10
                    
                     
                       14.30
                    
                     
                       36.30
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       5
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       5.17
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       11
                    
                     
                       14.45
                    
                     
                       39.02
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       12
                    
                     
                       15.0
                    
                     
                       41.22
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       6
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       4.30
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       13
                    
                     
                       15.15
                    
                     
                       43.32
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       14
                    
                     
                       15.30
                    
                     
                       45.29
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       7
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       3.48
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       15
                    
                     
                       15.45
                    
                     
                       47.20
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       16
                    
                     
                       16.0
                    
                     
                       49.21
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       8
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       3.13
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       17
                    
                     
                       16.15
                    
                     
                       50.13
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       18
                    
                     
                       16.30
                    
                     
                       51.58
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       9
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       2.44
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       19
                    
                     
                       15.45
                    
                     
                       53.17
                    
                     
                        
                    
                  
                
                 
                   
                   
                     
                        
                    
                     
                       Climes
                    
                     
                       Paralells
                    
                     
                       Length
                       of
                       the
                       Days
                    
                     
                       Poles
                       Elevation
                    
                     
                       Breadth
                       of
                       the
                       Clime
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       20
                    
                     
                       17.00
                    
                     
                       54.29
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       10
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       2.17
                    
                  
                   
                     
                       Heteroscii
                    
                     
                        
                    
                     
                       21
                    
                     
                       17.15
                    
                     
                       55.34
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       22
                    
                     
                       17.30
                    
                     
                       56.37
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       11
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       2.0
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       23
                    
                     
                       17.45
                    
                     
                       57.34
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       24
                    
                     
                       18.00
                    
                     
                       58.26
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       12
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       1.40
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       25
                    
                     
                       18.15
                    
                     
                       59.14
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       26
                    
                     
                       18.30
                    
                     
                       59.59
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       13
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       1.26
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       27
                    
                     
                       18.45
                    
                     
                       60.40
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       28
                    
                     
                       19.00
                    
                     
                       61.18
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       14
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       1.13
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       29
                    
                     
                       19.15
                    
                     
                       61.53
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       30
                    
                     
                       19.30
                    
                     
                       62.25
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       15
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       1.0
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       31
                    
                     
                       19.45
                    
                     
                       62.54
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       32
                    
                     
                       20.00
                    
                     
                       63.22
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       16
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       0.52
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       33
                    
                     
                       20.15
                    
                     
                       63.46
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       34
                    
                     
                       20.30
                    
                     
                       64.06
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       17
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       0.44
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       35
                    
                     
                       20.45
                    
                     
                       64.30
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       36
                    
                     
                       21.00
                    
                     
                       64.49
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       18
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       0.36
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       37
                    
                     
                       21.15
                    
                     
                       65.06
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       38
                    
                     
                       21.30
                    
                     
                       65.21
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       19
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       0.29
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       39
                    
                     
                       21.45
                    
                     
                       65.35
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       40
                    
                     
                       22.00
                    
                     
                       65.47
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       20
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       0.22
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       41
                    
                     
                       22.15
                    
                     
                       65.57
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       42
                    
                     
                       22.30
                    
                     
                       66.00
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       21
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       0.17
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       43
                    
                     
                       22.45
                    
                     
                       66.14
                    
                     
                        
                    
                  
                
                 
                   
                     
                       
                    
                     
                       Clime
                    
                     
                       Paralells
                    
                     
                       Length
                       of
                       the
                       Day
                    
                     
                       Poles
                       Elevation
                    
                     
                       Breadth
                       of
                       the
                       Clime
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       44
                    
                     
                       23.00
                    
                     
                       66.20
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       22
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       0.11
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       45
                    
                     
                       23.15
                    
                     
                       66.25
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       46
                    
                     
                       23.30
                    
                     
                       66.28
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       23
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       0.5
                    
                  
                   
                     
                        
                    
                     
                        
                    
                     
                       47
                    
                     
                       23.45
                    
                     
                       66.30
                    
                     
                        
                    
                  
                   
                     
                        
                    
                     
                       24
                    
                     
                       48
                    
                     
                       24.00
                    
                     
                       66.31
                    
                     
                       0.0
                    
                  
                
                 
                   
                     
                       Periscii
                    
                     
                       Here
                       the
                       Climates
                       begin
                       to
                       be
                       accounted
                       by
                       Months
                       ,
                       from
                       66.
                       31
                       where
                       the
                       day
                       is
                       24
                       hours
                       long
                       ;
                       unto
                       the
                       Pole
                       it self
                       ,
                       where
                       it
                       is
                       6
                       Months
                       in
                       length
                       .
                    
                     
                       1
                    
                     
                       67.15
                    
                  
                   
                     
                       2
                    
                     
                       69.30
                    
                  
                   
                     
                       3
                    
                     
                       73.20
                    
                  
                   
                     
                       4
                    
                     
                       78.20
                    
                  
                   
                     
                       5
                    
                     
                       84.0
                    
                  
                   
                     
                       6
                    
                     
                       90.0
                    
                  
                
              
               
               
                 14.
                 
                 Hitherto
                 we
                 have
                 considered
                 the
                 inhabitants
                 of
                 the
                 Earth
                 in
                 respect
                 of
                 the
                 several
                 Zones
                 and
                 Climes
                 into
                 which
                 the
                 whole
                 Globe
                 is
                 divided
                 ;
                 there
                 is
                 yet
                 another
                 distinction
                 behind
                 into
                 which
                 the
                 inhabitants
                 of
                 the
                 Earth
                 are
                 divided
                 in
                 respect
                 of
                 their
                 site
                 and
                 position
                 in
                 reference
                 to
                 one
                 another
                 ,
                 and
                 thus
                 the
                 inhabitants
                 of
                 the
                 Earth
                 are
                 divided
                 into
                 the
                 
                   Perioeci
                   ,
                   Antoec●
                
                 and
                 Antipodes
                 .
              
               
                 15.
                 
                 The
                 Perioeci
                 are
                 such
                 as
                 dwell
                 in
                 the
                 same
                 Parallel
                 on
                 the
                 same
                 side
                 of
                 the
                 AEquator
                 ,
                 how
                 far
                 distant
                 soever
                 they
                 be
                 East
                 and
                 West
                 ,
                 the
                 season
                 of
                 the
                 year
                 and
                 the
                 length
                 of
                 the
                 days
                 being
                 to
                 both
                 alike
                 ,
                 only
                 the
                 midnight
                 of
                 the
                 one
                 is
                 the
                 moon
                 to
                 the
                 other
                 .
              
               
                 16.
                 
                 The
                 Antoeci
                 are
                 such
                 as
                 dwell
                 under
                 the
                 same
                 Meridian
                 and
                 in
                 the
                 same
                 Latitude
                 ,
                 or
                 Parallel
                 distance
                 from
                 the
                 AEquator
                 ,
                 the
                 one
                 Northward
                 and
                 the
                 other
                 Southward
                 ,
                 the
                 days
                 in
                 both
                 places
                 being
                 of
                 the
                 same
                 length
                 ,
                 but
                 differ
                 in
                 the
                 Seasons
                 of
                 the
                 year
                 ,
                 for
                 when
                 it
                 is
                 Summer
                 in
                 the
                 one
                 it
                 is
                 Winter
                 in
                 the
                 other
                 .
              
               
                 17.
                 
                 The
                 Antipodes
                 are
                 such
                 as
                 dwell
                 Feet
                 to
                 Feet
                 ,
                 so
                 as
                 a
                 right
                 Line
                 drawn
                 from
                 the
                 one
                 unto
                 the
                 other
                 ,
                 passeth
                 from
                 North
                 to
                 South
                 through
                 the
                 Center
                 of
                 the
                 World.
                 These
                 are
                 distant
                 180
                 degrees
                 or
                 half
                 the
                 compass
                 of
                 the
                 Earth
                 ,
                 they
                 differ
                 in
                 all
                 things
                 ,
                 as
                 Seasons
                 of
                 the
                 year
                 ,
                 length
                 of
                 days
                 ,
                 rising
                 and
                 setting
                 of
                 the
                 Sun
                 and
                 such
                 like
                 .
                 A
                 matter
                 reckoned
                 so
                 ridiculous
                 and
                 impossible
                 in
                 former
                 times
                 ,
                 that
                 Boniface
                 Arch-Bishop
                 of
                 Mentz
                 seeing
                 a
                 Treatise
                 concerning
                 these
                 Antipodes
                 written
                 by
                 Virgilius
                 Bishop
                 of
                 Salisburg
                 ,
                 and
                 not
                 knowing
                 what
                 damnable
                 Doctrine
                 might
                 be
                 couched
                 under
                 that
                 
                 strange
                 Name
                 ,
                 made
                 complaint
                 first
                 to
                 the
                 Duke
                 of
                 Bohemia
                 ,
                 and
                 after
                 to
                 Pope
                 
                   Zachary
                   Anno
                
                 745
                 by
                 whom
                 the
                 poor
                 Bishop
                 (
                 unfortunate
                 only
                 in
                 being
                 learned
                 in
                 such
                 a
                 time
                 of
                 Ignorance
                 )
                 was
                 condemned
                 of
                 Heresie
                 ,
                 but
                 God
                 hath
                 blest
                 this
                 latter
                 age
                 of
                 the
                 World
                 with
                 more
                 understanding
                 ,
                 whereby
                 we
                 clearly
                 see
                 those
                 things
                 ,
                 which
                 either
                 were
                 unknown
                 ,
                 or
                 but
                 blindly
                 guessed
                 at
                 by
                 the
                 Antients
                 .
              
               
                 18.
                 
                 The
                 second
                 part
                 of
                 the
                 Terrestial
                 Globe
                 is
                 the
                 Water
                 which
                 is
                 commonly
                 divided
                 into
                 these
                 parts
                 ,
                 or
                 distinguished
                 by
                 these
                 Names
                 ,
                 
                   Oceanus
                   ,
                   Mare
                   ,
                   Fretum
                   ,
                   Sinus
                   ,
                   Lacus
                
                 and
                 Flumen
                 .
              
               
                 19.
                 
                 And
                 first
                 Oceanus
                 or
                 the
                 Ocean
                 is
                 that
                 general
                 Collection
                 of
                 all
                 Waters
                 ,
                 which
                 encompasseth
                 the
                 Earth
                 on
                 every
                 side
                 .
              
               
                 20.
                 
                 Mare
                 the
                 Sea
                 ,
                 is
                 a
                 part
                 of
                 the
                 main
                 Ocean
                 ,
                 to
                 which
                 we
                 cannot
                 come
                 but
                 through
                 some
                 Fretum
                 or
                 Strait
                 ,
                 as
                 
                   Mare
                   Mediterraneum
                
                 .
                 And
                 it
                 takes
                 it
                 name
                 first
                 either
                 from
                 the
                 adjacent
                 Shore
                 ,
                 as
                 
                   Mare
                   Adriaticum
                
                 ,
                 from
                 the
                 City
                 of
                 Adria
                 ;
                 or
                 secondly
                 from
                 the
                 first
                 discoverer
                 ,
                 as
                 
                   Mare
                   Magellanicum
                
                 ,
                 from
                 Magellanus
                 who
                 first
                 found
                 it
                 ,
                 or
                 thirdly
                 from
                 some
                 remarkable
                 accident
                 ,
                 as
                 
                   Mare
                   Icarium
                
                 from
                 the
                 drowning
                 of
                 Icarus
                 the
                 Son
                 of
                 Daedalus
                 .
              
               
                 21.
                 
                 Fretum
                 ,
                 a
                 Strait
                 is
                 a
                 part
                 of
                 the
                 Ocean
                 penned
                 within
                 some
                 narrow
                 Bounds
                 ,
                 and
                 opening
                 a
                 way
                 into
                 some
                 Sea
                 ,
                 or
                 out
                 of
                 some
                 Sea
                 into
                 the
                 Ocean
                 ,
                 as
                 the
                 Strait
                 of
                 
                   Hellespont
                   ,
                   Gibralter
                   ,
                   &c.
                
                 
              
               
                 22.
                 
                 Lacus
                 ,
                 a
                 Lake
                 is
                 a
                 great
                 body
                 or
                 collection
                 of
                 Water
                 ,
                 which
                 hath
                 no
                 visible
                 Intercourse
                 with
                 the
                 Sea
                 ,
                 or
                 influx
                 into
                 it
                 ;
                 as
                 the
                 Lake
                 of
                 
                 Thrasymene
                 in
                 Italy
                 ,
                 and
                 
                   Lacus
                   Asphaltites
                
                 ,
                 or
                 the
                 dead
                 Sea
                 in
                 the
                 Land
                 of
                 C●naan
                 .
              
               
                 23.
                 
                 Flumen
                 or
                 Fluvius
                 is
                 a
                 water-course
                 continually
                 running
                 ,
                 (
                 whereby
                 it
                 differs
                 frum
                 Stagnum
                 a
                 standing
                 Pool
                 )
                 issuing
                 from
                 some
                 Spring
                 or
                 Lake
                 ,
                 and
                 emptying
                 it self
                 into
                 some
                 part
                 of
                 the
                 Sea
                 ,
                 or
                 some
                 other
                 great
                 River
                 ,
                 the
                 mouth
                 or
                 outlet
                 of
                 which
                 is
                 called
                 Ostium
                 .
              
               
                 And
                 thus
                 we
                 have
                 gon
                 over
                 those
                 particulars
                 both
                 of
                 Earth
                 and
                 Water
                 ,
                 which
                 appertain
                 to
                 this
                 Science
                 of
                 Geography
                 in
                 the
                 general
                 ;
                 We
                 will
                 now
                 proceed
                 to
                 a
                 more
                 particular
                 Consideration
                 of
                 the
                 several
                 parts
                 into
                 which
                 the
                 Terrestial
                 Globe
                 is
                 commonly
                 divided
                 .
              
            
             
               
                 CHAP.
                 III.
                 
              
               
                 
                   Of
                   Europe
                   .
                
              
               
                 THe
                 Terrestial
                 Globe
                 is
                 divided
                 into
                 two
                 parts
                 ,
                 known
                 or
                 unknown
                 .
              
               
                 2.
                 
                 The
                 unknown
                 or
                 the
                 parts
                 of
                 the
                 World
                 not
                 fully
                 discovered
                 ,
                 are
                 distinguished
                 into
                 North
                 and
                 South
                 ,
                 the
                 unknown
                 parts
                 of
                 the
                 World
                 towards
                 the
                 North
                 ,
                 are
                 those
                 which
                 lie
                 between
                 the
                 North
                 part
                 of
                 Europe
                 or
                 America
                 and
                 the
                 North
                 Pole
                 ;
                 and
                 the
                 unknown
                 parts
                 of
                 the
                 World
                 toward
                 the
                 South
                 ,
                 are
                 those
                 which
                 ly
                 between
                 the
                 South
                 part
                 of
                 America
                 and
                 the
                 South
                 Pole.
                 
              
               
                 3.
                 
                 The
                 known
                 parts
                 of
                 the
                 World
                 were
                 antiently
                 these
                 three
                 ,
                 
                   Europe
                   ,
                   Asia
                
                 and
                 Africk
                 ,
                 to
                 which
                 in
                 latter
                 ages
                 a
                 fourth
                 hath
                 been
                 added
                 which
                 is
                 called
                 America
                 .
              
               
               
                 4.
                 
                 Europe
                 is
                 bounded
                 on
                 the
                 North
                 with
                 the
                 Northern
                 Ocean
                 ,
                 and
                 on
                 the
                 South
                 with
                 the
                 Mediterranean
                 Sea
                 ,
                 on
                 the
                 East
                 with
                 the
                 River
                 Tanais
                 ,
                 and
                 on
                 the
                 West
                 with
                 the
                 Western
                 Ocean
                 ,
                 and
                 is
                 contained
                 between
                 the
                 Tropick
                 of
                 Cancer
                 ,
                 and
                 the
                 Pole
                 Arctick
                 ,
                 or
                 44
                 degrees
                 as
                 most
                 do
                 say
                 ,
                 taking
                 its
                 beginning
                 Southward
                 from
                 Sicily
                 where
                 the
                 Pole
                 is
                 elevated
                 36
                 degrees
                 ,
                 and
                 is
                 thence
                 continued
                 to
                 80
                 degrees
                 of
                 North
                 Latitude
                 ,
                 and
                 so
                 the
                 whole
                 Latitude
                 of
                 Europe
                 is
                 in
                 English
                 miles
                 2640
                 ,
                 but
                 some
                 allow
                 to
                 Europe
                 45
                 degrees
                 of
                 Latitude
                 ,
                 that
                 is
                 in
                 English
                 miles
                 2700.
                 
              
               
                 5.
                 
                 The
                 Longitude
                 of
                 Europe
                 is
                 reckoned
                 from
                 the
                 furthest
                 part
                 of
                 Spain
                 and
                 the
                 Atlantick
                 Ocean
                 ,
                 to
                 the
                 River
                 Tanais
                 ,
                 which
                 some
                 reckon
                 to
                 be
                 60
                 Degrees
                 ,
                 to
                 one
                 of
                 which
                 Degrees
                 passing
                 through
                 the
                 middle
                 of
                 Europe
                 ,
                 they
                 allow
                 fifteen
                 German
                 miles
                 almost
                 ,
                 or
                 sixty
                 English
                 ,
                 and
                 so
                 the
                 Longitude
                 in
                 German
                 miles
                 is
                 900
                 ,
                 in
                 English
                 3600.
                 
              
               
                 6.
                 
                 Europe
                 though
                 the
                 least
                 of
                 all
                 the
                 four
                 Quarters
                 of
                 the
                 World
                 ,
                 is
                 yet
                 of
                 most
                 renown
                 amongst
                 us
                 :
                 First
                 ,
                 because
                 of
                 the
                 temperature
                 of
                 the
                 Air
                 ,
                 and
                 fertility
                 of
                 the
                 Soil
                 :
                 Secondly
                 ,
                 from
                 the
                 study
                 of
                 Arts
                 ,
                 both
                 ingenuous
                 and
                 mechanical
                 :
                 Thirdly
                 ,
                 of
                 the
                 Roman
                 and
                 Greek
                 Monarchies
                 :
                 Fourthly
                 ,
                 from
                 the
                 purity
                 and
                 sincerity
                 of
                 the
                 Christian
                 Faith
                 :
                 Fifthly
                 ,
                 because
                 we
                 dwell
                 in
                 it
                 ,
                 and
                 so
                 give
                 it
                 the
                 first
                 place
                 .
              
               
                 7.
                 
                 Europe
                 may
                 be
                 considered
                 as
                 it
                 stands
                 divided
                 into
                 the
                 Continent
                 and
                 the
                 Islands
                 :
                 the
                 Continent
                 lying
                 all
                 together
                 ,
                 containeth
                 these
                 Countries
                 .
                 1.
                 
                 
                   Spain
                   .
                   2.
                   
                   France
                   .
                   3.
                   
                   Germany
                   .
                   4.
                   
                   Italy
                   ,
                
                 and
                 the
                 
                   Alpes
                   .
                   5.
                   
                   Belgium
                   .
                   6.
                   
                   Denmark
                   ▪
                
                 
                 7.
                 
                 
                   Swethland
                   .
                   8.
                   
                   Russia
                   .
                   9.
                   
                   Poland
                   .
                   10.
                   
                   Hungary
                   .
                   11.
                   
                   Sclavonia
                   ,
                   12.
                   
                   Dacia
                   ,
                
                 and
                 13.
                 
                 Greece
                 .
                 Of
                 each
                 of
                 which
                 I
                 will
                 give
                 some
                 short
                 account
                 ;
                 as
                 also
                 of
                 the
                 chief
                 Islands
                 as
                 they
                 are
                 dispersed
                 ,
                 in
                 the
                 Greek
                 ,
                 AEgaean
                 ,
                 Cretan
                 and
                 Io●ian
                 Seas
                 ,
                 with
                 those
                 in
                 the
                 Adriatick
                 ,
                 Mediterranean
                 ,
                 and
                 in
                 the
                 British
                 and
                 Northern
                 Ocean
                 .
              
               
                 8.
                 
                 Amongst
                 these
                 I
                 give
                 Spain
                 the
                 first
                 place
                 ,
                 as
                 being
                 the
                 most
                 Western
                 Part
                 of
                 all
                 the
                 Continent
                 of
                 Europe
                 environed
                 on
                 all
                 sides
                 with
                 the
                 Sea
                 ,
                 except
                 towards
                 France
                 ;
                 from
                 which
                 it
                 is
                 separated
                 by
                 the
                 Pyrenaean
                 Hills
                 :
                 but
                 more
                 particularly
                 ,
                 it
                 is
                 bounded
                 upon
                 the
                 North
                 with
                 the
                 Cantabrian
                 ,
                 on
                 the
                 West
                 with
                 the
                 Atlantick
                 Ocean
                 ,
                 on
                 the
                 South
                 with
                 the
                 Straits
                 of
                 Gibralter
                 ,
                 on
                 the
                 East
                 with
                 the
                 Mediterranean
                 ,
                 and
                 on
                 the
                 North
                 East
                 with
                 the
                 said
                 Pyren●ean
                 Hills
                 .
                 The
                 Figure
                 of
                 it
                 is
                 compared
                 by
                 Strabo
                 to
                 an
                 Oxes
                 hide
                 spread
                 upon
                 the
                 Ground
                 ;
                 the
                 Neck
                 whereof
                 being
                 that
                 Isthmus
                 which
                 unites
                 it
                 to
                 France
                 .
              
               
                 9.
                 
                 The
                 greatest
                 length
                 hereof
                 ,
                 it
                 reckoned
                 at
                 800
                 miles
                 ,
                 the
                 breadth
                 where
                 it
                 is
                 broadest
                 at
                 500
                 ,
                 the
                 whole
                 Circumforence
                 2480
                 Italian
                 miles
                 :
                 but
                 Mariana
                 measuring
                 the
                 compass
                 of
                 it
                 by
                 the
                 bendings
                 of
                 the
                 Pyrenaean
                 Hills
                 ,
                 and
                 the
                 creeks
                 and
                 windings
                 of
                 the
                 Sea
                 ,
                 makes
                 the
                 full
                 circuit
                 of
                 it
                 to
                 be
                 2816
                 miles
                 of
                 Italian
                 measure
                 .
              
               
                 10.
                 
                 It
                 is
                 situate
                 in
                 the
                 more
                 Southerly
                 Part
                 of
                 the
                 Northern
                 temperate
                 Zone
                 ,
                 and
                 almost
                 in
                 the
                 midst
                 of
                 the
                 fourth
                 and
                 sixth
                 Climates
                 ;
                 the
                 longest
                 day
                 being
                 15
                 hours
                 and
                 a
                 quarter
                 in
                 length
                 in
                 the
                 most
                 Northern
                 Parts
                 hereof
                 :
                 but
                 in
                 the
                 extream
                 South
                 near
                 to
                 Gibralter
                 not
                 above
                 
                 fourteen
                 ,
                 which
                 Situation
                 of
                 this
                 Country
                 ,
                 rendreth
                 the
                 Air
                 here
                 very
                 clear
                 and
                 calm
                 ,
                 seldom
                 obscured
                 with
                 mists
                 and
                 vapours
                 ,
                 and
                 not
                 so
                 much
                 subject
                 to
                 Diseases
                 as
                 the
                 more
                 Northern
                 Regions
                 are
                 .
              
               
                 11.
                 
                 
                   This
                   Continent
                   is
                   subdivided
                   into
                   the
                   Kingdoms
                   of
                
                 Navarr
                 .
                 2.
                 
                 Biscay
                 .
                 3.
                 
                 Guipusco●
                 .
                 4.
                 
                 Lean
                 and
                 Oviodo
                 .
                 5.
                 
                 Gallicia
                 .
                 6.
                 
                 Corduba
                 .
                 7.
                 
                 Granada
                 .
                 8.
                 
                 Murcia
                 .
                 9.
                 
                 Toledo
                 .
                 10.
                 
                 Castile
                 .
                 11.
                 
                 Portugal
                 .
                 12.
                 
                 Valentia
                 .
                 13.
                 
                 Catalonia
                 .
                 14.
                 
                 Majorca
                 .
                 And
                 15.
                 
                 Aragon
                 ;
                 
                   but
                   all
                   of
                   them
                   are
                   now
                   united
                   in
                   the
                   Monarchy
                   of
                
                 Spain
                 .
              
               
                 12.
                 
                 France
                 according
                 to
                 the
                 present
                 dimensions
                 of
                 it
                 ,
                 is
                 bounded
                 on
                 the
                 East
                 with
                 a
                 Branch
                 of
                 the
                 Alpes
                 which
                 divide
                 Dauphine
                 and
                 Piemont
                 ,
                 as
                 also
                 with
                 the
                 Countries
                 of
                 
                   Savoy
                   ,
                   Switzerland
                
                 ,
                 and
                 some
                 Parts
                 of
                 Germany
                 and
                 the
                 Netherlands
                 .
                 On
                 the
                 West
                 with
                 the
                 Aquitanick
                 Ocean
                 ,
                 and
                 a
                 Branch
                 of
                 the
                 Pyrenaean
                 Mountains
                 which
                 divide
                 it
                 from
                 Spain
                 .
                 On
                 the
                 North
                 with
                 the
                 English
                 Ocean
                 ,
                 and
                 some
                 Parts
                 of
                 Belgium
                 ,
                 and
                 on
                 the
                 South
                 with
                 the
                 rest
                 of
                 the
                 Pyrenaean
                 Mountains
                 ,
                 and
                 the
                 Mideterranean
                 .
              
               
                 13.
                 
                 The
                 Figure
                 of
                 it
                 is
                 almost
                 square
                 ,
                 each
                 side
                 of
                 the
                 Quadrature
                 being
                 reckoned
                 600
                 miles
                 in
                 length
                 ,
                 but
                 they
                 that
                 go
                 more
                 exactly
                 to
                 work
                 upon
                 it
                 ,
                 make
                 the
                 length
                 thereof
                 to
                 be
                 660
                 Italian
                 miles
                 ,
                 the
                 breadth
                 570
                 ,
                 the
                 whole
                 Circumference
                 2040.
                 
                 It
                 is
                 seated
                 in
                 the
                 Northern
                 temperate
                 Zone
                 ,
                 between
                 the
                 middle
                 Parallel
                 of
                 the
                 first
                 Clime
                 ,
                 where
                 the
                 longest
                 day
                 is
                 15
                 hours
                 ,
                 and
                 the
                 middle
                 Parallel
                 of
                 the
                 eighth
                 Clime
                 ,
                 where
                 the
                 longest
                 day
                 is
                 16
                 hours
                 and
                 a
                 half
                 .
              
               
                 14.
                 
                 
                   The
                   Principal
                   Provinces
                   in
                   this
                   flourishing
                   
                   Country
                   ,
                   are
                   .
                
                 1.
                 
                 France
                 
                   specially
                   so
                   called
                
                 .
                 2.
                 
                 Champagne
                 .
                 3.
                 
                 Picardy
                 .
                 4.
                 
                 Normandy
                 .
                 5.
                 
                 Bretagne
                 .
                 6.
                 
                 
                   The
                   Estates
                   of
                
                 Angiou
                 .
                 7.
                 
                 La
                 Beausio
                 .
                 8.
                 
                 Nivernois
                 .
                 9.
                 
                 
                   The
                   Dukedom
                   of
                
                 Bourbon
                 .
                 10.
                 
                 Berry
                 .
                 11.
                 
                 Poictou
                 .
                 12.
                 
                 Limosin
                 .
                 13.
                 
                 Piregort
                 .
                 14.
                 
                 Quercu
                 .
                 15.
                 
                 Aquitain
                 .
                 16.
                 
                 Languedoc
                 .
                 17.
                 
                 Provence
                 .
                 18.
                 
                 Daulphine
                 .
                 19.
                 
                 La
                 Bresse
                 .
                 20.
                 
                 Lionnois
                 .
                 21.
                 
                 
                   The
                   Dutchy
                   .
                   22.
                   
                   The
                   County
                   of
                
                 Burgundy
                 .
                 23.
                 
                 
                   The
                   Islands
                   in
                   the
                   Aquitanick
                   and
                   Gallick
                   Ocean
                   :
                   Those
                   of
                   most
                   note
                   are
                   these
                   six
                   .
                
                 1.
                 
                 Oleron
                 .
                 2.
                 
                 Re●
                 .
                 3.
                 
                 Iarsey
                 .
                 4.
                 
                 Gernsey
                 .
                 5.
                 
                 Sarke
                 .
                 6.
                 
                 Aldernay
                 
                   on
                   the
                   shores
                   of
                
                 Normandy
                 ,
                 
                   of
                   which
                   the
                   four
                   last
                   are
                   under
                   the
                   Kings
                   of
                
                 England
                 .
              
               
                 15.
                 
                 Italy
                 once
                 the
                 Empress
                 of
                 the
                 greatest
                 part
                 of
                 the
                 then
                 known
                 World
                 ,
                 is
                 compassed
                 with
                 the
                 Adriatick
                 ,
                 Ionian
                 and
                 Tyrrhenian
                 Seas
                 ,
                 except
                 it
                 be
                 towards
                 France
                 and
                 Germany
                 ,
                 from
                 which
                 it
                 is
                 parted
                 by
                 the
                 Alpes
                 ;
                 so
                 that
                 it
                 is
                 in
                 a
                 manner
                 ,
                 a
                 Peninsula
                 ,
                 or
                 a
                 Demi-Island
                 .
                 But
                 more
                 particularly
                 it
                 hath
                 on
                 the
                 East
                 the
                 lower
                 part
                 of
                 the
                 Adriatick
                 ,
                 and
                 the
                 Ionian
                 Sea
                 ,
                 by
                 which
                 it
                 is
                 divided
                 from
                 Greece
                 ;
                 on
                 the
                 West
                 the
                 River
                 Varus
                 ,
                 and
                 some
                 part
                 of
                 the
                 Alpes
                 ,
                 by
                 which
                 it
                 is
                 parted
                 from
                 France
                 ,
                 on
                 the
                 North
                 in
                 some
                 part
                 the
                 Alpes
                 which
                 divide
                 it
                 from
                 Germany
                 ;
                 and
                 on
                 the
                 other
                 ,
                 part
                 of
                 the
                 Adriatick
                 ,
                 which
                 divides
                 it
                 from
                 Dalmaria
                 ;
                 and
                 on
                 the
                 South
                 the
                 Tyrrhenian
                 and
                 Tuscan
                 Seas
                 ,
                 by
                 which
                 it
                 is
                 separated
                 from
                 the
                 main
                 Land
                 of
                 Africa
                 .
              
               
                 16.
                 
                 It
                 containeth
                 in
                 length
                 from
                 
                   Augusta
                   Praetoria
                
                 ,
                 now
                 called
                 Aost
                 ,
                 at
                 the
                 foot
                 of
                 the
                 Alpes
                 ,
                 unto
                 Otranto
                 in
                 the
                 most
                 Eastern
                 Point
                 of
                 the
                 Kingdom
                 of
                 Naples
                 1020
                 miles
                 ;
                 in
                 breadth
                 from
                 
                 the
                 River
                 Varo
                 ,
                 which
                 parts
                 it
                 from
                 Provence
                 ,
                 to
                 the
                 mouth
                 of
                 the
                 River
                 Arsia
                 in
                 Friuli
                 ,
                 where
                 it
                 is
                 broadest
                 ,
                 410
                 miles
                 ;
                 about
                 Otranto
                 ,
                 where
                 it
                 is
                 narrowest
                 not
                 above
                 25
                 miles
                 ;
                 and
                 in
                 the
                 middle
                 parts
                 from
                 the
                 mouth
                 of
                 Peseara
                 in
                 the
                 Adriatick
                 or
                 upper
                 Sea
                 to
                 the
                 mouth
                 of
                 Tiber
                 in
                 the
                 Tuscan
                 or
                 lower
                 Sea
                 ,
                 126
                 miles
                 .
                 The
                 whole
                 compass
                 by
                 Sea
                 reckoning
                 in
                 the
                 windings
                 and
                 turnings
                 of
                 the
                 shore
                 ,
                 comes
                 to
                 3038
                 miles
                 ;
                 which
                 added
                 to
                 the
                 410
                 which
                 it
                 hath
                 by
                 Land
                 ,
                 make
                 up
                 in
                 all
                 3448
                 miles
                 :
                 but
                 if
                 the
                 Coasts
                 on
                 each
                 side
                 be
                 reckoned
                 by
                 a
                 straight
                 Line
                 ,
                 then
                 as
                 Castaldo
                 computes
                 it
                 ,
                 it
                 comes
                 to
                 no
                 more
                 than
                 2550
                 miles
                 .
              
               
                 17.
                 
                 The
                 whole
                 Country
                 lieth
                 under
                 the
                 first
                 and
                 sixth
                 Climates
                 of
                 the
                 Northern
                 temperate
                 Zone
                 ,
                 which
                 it
                 wholly
                 taketh
                 up
                 :
                 so
                 that
                 the
                 longest
                 day
                 in
                 the
                 most
                 Northern
                 Parts
                 is
                 15
                 hours
                 and
                 three
                 first
                 parts
                 of
                 an
                 hour
                 ;
                 the
                 longest
                 in
                 the
                 Southern
                 Parts
                 ,
                 falling
                 short
                 a
                 full
                 hour
                 of
                 that
                 length
                 .
              
               
                 18.
                 
                 Italy
                 as
                 it
                 stands
                 now
                 is
                 divided
                 into
                 the
                 Kingdoms
                 of
                 
                   Naples
                   ,
                   Sicily
                
                 and
                 Sardinia
                 .
                 2.
                 
                 The
                 Land
                 or
                 Patrimony
                 of
                 the
                 Church
                 .
                 3.
                 
                 The
                 great
                 Dukedom
                 of
                 Tuscany
                 .
                 4.
                 
                 The
                 Common-wealths
                 of
                 
                   Venice
                   ,
                   Genoa
                
                 and
                 Luca.
                 5.
                 
                 The
                 Estates
                 of
                 Lombardy
                 ,
                 that
                 is
                 the
                 Dukedoms
                 of
                 1.
                 
                 
                   M●llain
                   .
                   2.
                   
                   Mantua
                   .
                   3.
                   
                   Modena
                   .
                   4.
                   
                   Parma
                   .
                   5.
                   
                   Montferrat
                   ,
                
                 and
                 the
                 Principality
                 of
                 Piedmont
                 .
              
               
                 19.
                 
                 To
                 the
                 Peninsula
                 of
                 Italy
                 belong
                 the
                 Alpes
                 ,
                 aridge
                 of
                 Hills
                 ,
                 wherewith
                 as
                 with
                 a
                 strong
                 and
                 defensible
                 Rampart
                 Italy
                 is
                 assured
                 against
                 France
                 and
                 Germany
                 .
                 They
                 are
                 said
                 to
                 be
                 five
                 days
                 Journey
                 high
                 ,
                 covered
                 continually
                 with
                 Snow
                 ,
                 
                 from
                 the
                 whiteness
                 whereof
                 they
                 took
                 this
                 name
                 ,
                 it
                 doth
                 contain
                 the
                 Dukedom
                 of
                 Savoy
                 ;
                 the
                 Seigniory
                 of
                 Geneva
                 ;
                 the
                 Country
                 of
                 
                   Wallisland
                   ,
                   Switzerland
                
                 and
                 the
                 Grisons
                 .
              
               
                 20.
                 
                 Belgium
                 ,
                 or
                 the
                 Netherlands
                 ,
                 is
                 bounded
                 on
                 the
                 East
                 with
                 
                   Westphalin
                   ,
                   Gulick
                   ,
                   Cleve
                
                 ,
                 and
                 the
                 Land
                 of
                 Triers
                 ,
                 Provinces
                 of
                 the
                 higher
                 Germany
                 ;
                 on
                 the
                 West
                 with
                 the
                 main
                 Ocean
                 ,
                 which
                 divides
                 it
                 from
                 Britain
                 ;
                 on
                 the
                 North
                 with
                 the
                 River
                 Ems
                 ,
                 which
                 parts
                 it
                 from
                 East-Friezeland
                 ;
                 on
                 the
                 South
                 with
                 Picardie
                 and
                 Campagne
                 two
                 French
                 Provinces
                 ;
                 upon
                 the
                 South-East
                 with
                 the
                 Dukedom
                 of
                 Lorrain
                 .
              
               
                 21.
                 
                 It
                 is
                 in
                 compass
                 1000
                 Italian
                 or
                 280
                 German
                 miles
                 ,
                 and
                 is
                 situated
                 in
                 the
                 Northern
                 temperate
                 Zone
                 ,
                 under
                 the
                 seventh
                 ,
                 eighth
                 and
                 ninth
                 Climates
                 :
                 the
                 longest
                 day
                 in
                 the
                 midst
                 of
                 the
                 seventh
                 Climate
                 where
                 it
                 doth
                 begin
                 ,
                 being
                 16
                 hours
                 ,
                 iu
                 the
                 beginning
                 of
                 the
                 ninth
                 Climate
                 increased
                 to
                 16
                 hours
                 3
                 quarters
                 ,
                 or
                 near
                 17
                 hours
                 .
              
               
                 22.
                 
                 It
                 containeth
                 those
                 Provinces
                 which
                 in
                 these
                 later
                 Ages
                 were
                 possessed
                 by
                 the
                 House
                 of
                 Burgundy
                 ,
                 that
                 is
                 the
                 Lordship
                 of
                 West-Friezeland
                 ,
                 given
                 to
                 the
                 Earls
                 of
                 Holland
                 by
                 Charles
                 the
                 Bald
                 ;
                 the
                 Earldom
                 of
                 Zutphen
                 united
                 unto
                 that
                 of
                 Gelder
                 by
                 Earl
                 Otho
                 of
                 Nassau
                 ,
                 and
                 finally
                 the
                 Estate
                 of
                 
                   Groening
                   ,
                   Over-Yssel
                
                 ,
                 and
                 some
                 part
                 of
                 Vtrecht
                 ,
                 by
                 Charles
                 the
                 Fifth
                 .
                 As
                 it
                 stands
                 now
                 divided
                 between
                 the
                 Spaniards
                 and
                 the
                 States
                 it
                 containeth
                 the
                 Provinces
                 of
                 1.
                 
                 
                   Flanders
                   .
                   2.
                   
                   Artois
                   .
                   3.
                   
                   Hainault
                   .
                
                 4.
                 
                 The
                 Bishoprick
                 of
                 
                   Cambray
                   .
                   5.
                   
                   Namur
                   .
                   6.
                   
                   Luxemburg
                   .
                   7.
                   
                   Limbourg
                   .
                   8.
                   
                   Luyckland
                   ,
                
                 or
                 the
                 Bishoprick
                 of
                 
                   Leige
                   .
                   9.
                   
                   Brabant
                   .
                   10.
                   
                   Marquisate
                   .
                   11.
                   
                   Meohlin
                   .
                
                 The
                 rest
                 of
                 the
                 Netherlands
                 
                 which
                 have
                 now
                 for
                 sometime
                 withdrawn
                 their
                 obedience
                 from
                 the
                 Kings
                 of
                 Spain
                 ,
                 are
                 1.
                 
                 
                   Holland
                   .
                   2.
                   
                   Zeland
                   .
                   3.
                   
                   West-Friezeland
                   .
                   4.
                   
                   Vtrecht
                   .
                   5.
                   
                   Over-Yssel
                   .
                   6.
                   
                   Gelderland
                   .
                   7.
                   
                   Zutphen
                   .
                   8.
                   
                   Groening
                   .
                
              
               
                 23.
                 
                 Germany
                 is
                 bounded
                 on
                 the
                 East
                 with
                 
                   Prussia
                   ,
                   Poland
                
                 ,
                 and
                 Hungary
                 ;
                 on
                 the
                 West
                 with
                 
                   France
                   ,
                   Switzerland
                
                 and
                 Belgium
                 ;
                 on
                 the
                 North
                 with
                 the
                 Baltick
                 Seas
                 ,
                 the
                 Ocean
                 ,
                 and
                 some
                 part
                 of
                 Denmark
                 ;
                 on
                 the
                 South
                 with
                 the
                 Alps
                 which
                 part
                 it
                 from
                 Italy
                 .
              
               
                 24.
                 
                 The
                 length
                 from
                 East
                 to
                 West
                 ,
                 that
                 is
                 from
                 the
                 Vistula
                 or
                 Weissel
                 to
                 the
                 Rhine
                 ,
                 is
                 estimated
                 at
                 840
                 Italian
                 miles
                 ,
                 the
                 breadth
                 from
                 North
                 to
                 South
                 ,
                 that
                 is
                 from
                 the
                 Ocean
                 to
                 the
                 Town
                 of
                 Brixen
                 in
                 Tyrol
                 ,
                 740
                 of
                 the
                 same
                 miles
                 .
                 So
                 that
                 the
                 Figure
                 of
                 it
                 being
                 near
                 a
                 Square
                 ,
                 it
                 may
                 take
                 up
                 3160
                 miles
                 in
                 compass
                 ,
                 or
                 thereabouts
                 .
                 Situate
                 in
                 the
                 Northern
                 temperate
                 Zone
                 ,
                 between
                 the
                 middle
                 Parallels
                 of
                 the
                 sixth
                 and
                 tenth
                 Climates
                 ;
                 the
                 longest
                 day
                 in
                 the
                 most
                 Southern
                 Parts
                 being
                 15
                 hours
                 and
                 an
                 half
                 ,
                 and
                 in
                 the
                 most
                 Northern
                 17
                 hours
                 and
                 a
                 quarter
                 .
              
               
                 25.
                 
                 
                   The
                   Principal
                   Parts
                   of
                   this
                   great
                   Continent
                   ,
                   are
                
                 1.
                 
                 Cleveland
                 .
                 2.
                 
                 
                   The
                   Estates
                   of
                   the
                   three
                   spiritual
                   Electors
                   ,
                
                 Colen
                 ,
                 ●●●ntz
                 ,
                 and
                 Triers
                 .
                 3.
                 
                 The
                 Palatinate
                 
                   of
                   the
                
                 Rhine
                 .
                 4.
                 
                 Alsatia
                 .
                 5.
                 
                 Lorrain
                 .
                 6.
                 
                 Suevia
                 or
                 Schwaben
                 .
                 7.
                 
                 Bavaria
                 .
                 8.
                 
                 Austria
                 
                   and
                   its
                   Appendices
                   .
                   9.
                   
                   The
                   Confederation
                   of
                
                 Waderaw
                 .
                 10.
                 
                 Franconia
                 .
                 11.
                 
                 Wirtenberg
                 .
                 12.
                 
                 Baden
                 .
                 13.
                 
                 The
                 Palatinate
                 of
                 Northgoia
                 ,
                 
                   or
                   the
                   Upper
                
                 Palatinate
                 .
                 14.
                 
                 Bohemia
                 
                   and
                   the
                   Incorporate
                   Provinces
                
                 .
                 15.
                 
                 Pomerania
                 .
                 16.
                 
                 Mecklenburg
                 .
                 17.
                 
                 The
                 Marquisate
                 of
                 Brandenburg
                 .
                 
                 18.
                 
                 Saxony
                 ,
                 
                   and
                   the
                   Members
                   of
                   it
                   .
                   19.
                   
                   The
                   Dukedom
                   of
                
                 Brunswick
                 and
                 Lunenburg
                 .
                 20.
                 
                 The
                 Lantgravedom
                 of
                 Hassia
                 .
                 21.
                 
                 Westphalen
                 .
                 22.
                 
                 East-Friezeland
                 .
              
               
                 26.
                 
                 Denmark
                 or
                 Danemark
                 ,
                 reckoning
                 in
                 the
                 Additions
                 of
                 the
                 Dukedom
                 of
                 Holstein
                 ,
                 and
                 the
                 great
                 Continent
                 of
                 Norway
                 ,
                 with
                 the
                 Isles
                 thereof
                 ,
                 now
                 all
                 united
                 and
                 incorporated
                 into
                 one
                 Estate
                 is
                 bounded
                 on
                 the
                 East
                 with
                 the
                 Baltick
                 Sea
                 and
                 some
                 part
                 of
                 Sweden
                 ;
                 on
                 the
                 West
                 with
                 the
                 main
                 Western
                 Ocean
                 ;
                 on
                 the
                 North-East
                 with
                 a
                 part
                 of
                 Sweden
                 ;
                 full
                 North
                 with
                 the
                 main
                 frozen
                 Seas
                 ;
                 and
                 on
                 the
                 South
                 with
                 Germany
                 ,
                 from
                 which
                 it
                 is
                 divided
                 on
                 the
                 South-West
                 by
                 the
                 River
                 Albis
                 ,
                 and
                 on
                 the
                 South-East
                 by
                 the
                 Trave
                 ;
                 a
                 little
                 Isthmus
                 or
                 neck
                 of
                 Land
                 uniting
                 it
                 to
                 the
                 Continent
                 .
              
               
                 27.
                 
                 It
                 lieth
                 partly
                 in
                 the
                 Northern
                 temperate
                 Zone
                 ,
                 and
                 partly
                 within
                 the
                 Arctick
                 Circle
                 ;
                 extending
                 from
                 the
                 middle
                 Parallel
                 of
                 the
                 tenth
                 Clime
                 ,
                 or
                 55
                 degree
                 of
                 Latitude
                 where
                 it
                 joyneth
                 with
                 Germany
                 ,
                 as
                 far
                 as
                 the
                 71
                 degree
                 where
                 it
                 hath
                 no
                 other
                 bound
                 but
                 the
                 frozen
                 Ocean
                 ;
                 by
                 which
                 account
                 the
                 longest
                 day
                 in
                 the
                 most
                 Southern
                 Parts
                 is
                 17
                 hours
                 and
                 a
                 quarter
                 ,
                 but
                 in
                 the
                 Parts
                 extreamly
                 North
                 ,
                 they
                 have
                 no
                 Night
                 for
                 two
                 whole
                 Moneths
                 ,
                 three
                 Weeks
                 ,
                 one
                 Day
                 ,
                 and
                 about
                 seven
                 hours
                 ;
                 as
                 on
                 the
                 other
                 side
                 no
                 day
                 for
                 the
                 like
                 quantity
                 of
                 time
                 ,
                 when
                 the
                 Sun
                 is
                 most
                 remote
                 from
                 them
                 ,
                 in
                 the
                 other
                 Tropick
                 .
              
               
                 28.
                 
                 The
                 whole
                 Body
                 of
                 the
                 Estate
                 consisteth
                 chiefly
                 of
                 three
                 Members
                 .
                 viz.
                 1.
                 
                 The
                 Dukedom
                 
                 of
                 Holstein
                 ;
                 containing
                 
                   Waggerland
                   ,
                   Dilmarsh
                   ,
                   Starmaria
                
                 ,
                 and
                 Holstein
                 ,
                 especially
                 so
                 called
                 .
                 2.
                 
                 The
                 Kingdom
                 of
                 Denmark
                 ;
                 comprehending
                 both
                 Iuitlands
                 ,
                 part
                 of
                 Scandia
                 ,
                 and
                 the
                 Hemodes
                 ,
                 or
                 Baltick
                 Islands
                 .
                 3.
                 
                 The
                 Kingdom
                 of
                 Norway
                 consisting
                 of
                 Norway
                 it self
                 ,
                 and
                 the
                 Islands
                 of
                 the
                 Northern
                 Ocean
                 .
              
               
                 29.
                 
                 Swethland
                 is
                 bounded
                 on
                 the
                 East
                 with
                 Muscovy
                 ,
                 on
                 the
                 West
                 with
                 the
                 Doferine
                 Hills
                 ,
                 which
                 divide
                 it
                 from
                 Norway
                 ;
                 on
                 the
                 North
                 with
                 the
                 great
                 frozen
                 Ocean
                 spoken
                 of
                 before
                 ;
                 on
                 the
                 South
                 with
                 
                   Denmark
                   ,
                   Liefland
                
                 ,
                 and
                 the
                 Baltick
                 Sea.
                 
              
               
                 30.
                 
                 It
                 is
                 situate
                 under
                 the
                 same
                 Parallels
                 and
                 Degrees
                 with
                 Norway
                 ,
                 that
                 is
                 ,
                 from
                 the
                 first
                 Parallel
                 of
                 the
                 12
                 Clime
                 ,
                 where
                 the
                 Pole
                 is
                 elevated
                 58
                 degrees
                 26
                 minutes
                 ,
                 as
                 far
                 as
                 to
                 the
                 71
                 degree
                 of
                 Latitude
                 ,
                 by
                 which
                 account
                 the
                 longest
                 day
                 in
                 the
                 Southern
                 Point
                 is
                 but
                 18
                 hours
                 ,
                 whereas
                 on
                 the
                 farthest
                 North
                 of
                 all
                 the
                 Countrey
                 ,
                 they
                 have
                 no
                 Night
                 for
                 almost
                 three
                 whole
                 Moneths
                 together
                 .
              
               
                 31.
                 
                 The
                 whole
                 Kingdom
                 is
                 divided
                 into
                 two
                 Parts
                 ,
                 the
                 one
                 lying
                 on
                 the
                 East
                 ,
                 the
                 other
                 on
                 the
                 West
                 of
                 the
                 Bay
                 or
                 Gulf
                 of
                 Bodener
                 ,
                 being
                 a
                 large
                 and
                 spacious
                 branch
                 of
                 the
                 Baltick
                 Sea
                 ,
                 extending
                 from
                 the
                 most
                 Southerly
                 Point
                 of
                 Gothland
                 ,
                 as
                 far
                 as
                 to
                 Lapland
                 on
                 the
                 North.
                 According
                 to
                 which
                 Division
                 we
                 have
                 the
                 Provinces
                 of
                 1.
                 
                 
                   Gothland
                   .
                   2.
                   
                   Sweden
                
                 lying
                 on
                 the
                 West
                 side
                 of
                 the
                 Gulph
                 .
                 3.
                 
                 Lapland
                 shutting
                 it
                 up
                 upon
                 the
                 North.
                 4.
                 
                 Bodia
                 or
                 
                   Bodden
                   .
                   5.
                   
                   Finland
                
                 on
                 the
                 East
                 side
                 thereof
                 .
                 6.
                 
                 The
                 Sweedish
                 Islands
                 ,
                 where
                 it
                 mingleth
                 with
                 the
                 rest
                 of
                 the
                 Baltick
                 Seas
                 .
              
               
                 32.
                 
                 Russia
                 is
                 bounded
                 on
                 the
                 East
                 by
                 Tartary
                 ,
                 
                 on
                 the
                 West
                 with
                 Livonia
                 and
                 Finland
                 ,
                 from
                 which
                 it
                 is
                 divided
                 by
                 great
                 mountains
                 and
                 the
                 River
                 Poln
                 ,
                 on
                 the
                 North
                 by
                 the
                 frozen
                 Ocean
                 ,
                 and
                 some
                 part
                 of
                 Lapland
                 ,
                 and
                 on
                 the
                 South
                 by
                 Lituania
                 a
                 Province
                 of
                 the
                 Kingdom
                 of
                 Poland
                 ,
                 and
                 the
                 Crim
                 Tartar
                 inhabiting
                 on
                 the
                 Banks
                 of
                 
                   Palus
                   Maeotis
                
                 ,
                 and
                 the
                 Euxine
                 Sea.
                 It
                 standeth
                 partly
                 in
                 Europe
                 and
                 partly
                 in
                 Asia
                 ,
                 the
                 River
                 Tanais
                 or
                 Don
                 running
                 through
                 it
                 ,
                 the
                 common
                 boundary
                 of
                 those
                 great
                 and
                 noted
                 parts
                 of
                 the
                 world
                 .
              
               
                 33.
                 
                 It
                 is
                 scituate
                 North
                 within
                 the
                 Artick
                 Circle
                 so
                 far
                 ,
                 that
                 the
                 longest
                 day
                 in
                 Summer
                 will
                 be
                 full
                 six
                 months
                 ,
                 whereas
                 the
                 longest
                 day
                 in
                 the
                 southern
                 parts
                 is
                 but
                 16
                 hours
                 and
                 an
                 half
                 .
              
               
                 34.
                 
                 
                   It
                   is
                   divided
                   into
                   the
                   Provinces
                   of
                
                 1.
                 
                 Moscovy
                 
                   specially
                   so
                   called
                
                 .
                 2.
                 
                 Snol●usio
                 ,
                 3.
                 
                 Masaisky
                 ,
                 4.
                 
                 Plesco
                 ,
                 5.
                 
                 Novagrod
                 
                   the
                   great
                
                 ,
                 6.
                 
                 Corelia
                 ,
                 7.
                 
                 Blarmia
                 ,
                 8.
                 
                 Petzora
                 ,
                 9.
                 
                 Condora
                 ,
                 10
                 Obdora
                 ,
                 11.
                 
                 Iugria
                 ,
                 12.
                 
                 Severia
                 ,
                 13.
                 
                 Permia
                 ,
                 14.
                 
                 Rozan
                 ,
                 15.
                 
                 Wiathka
                 ,
                 16.
                 
                 Casau
                 ,
                 17.
                 
                 Astracan
                 ,
                 18.
                 
                 Novogordia
                 inferiour
                 ,
                 10.
                 
                 The
                 Morduits
                 or
                 Mordua
                 ,
                 20.
                 
                 Worotime
                 ,
                 21.
                 
                 Tuba
                 ,
                 22.
                 
                 Wolodomir
                 ,
                 23.
                 
                 Duina
                 ,
                 24.
                 
                   the
                   Russian
                   Islands
                
                 .
              
               
                 35.
                 
                 Poland
                 is
                 bounded
                 on
                 the
                 East
                 with
                 Russia
                 ,
                 and
                 the
                 Crim-Tartar
                 ,
                 from
                 whom
                 it
                 is
                 parted
                 by
                 the
                 River
                 Borysthenes
                 ;
                 on
                 the
                 West
                 with
                 Germany
                 ,
                 on
                 the
                 North
                 with
                 the
                 Baltick
                 Sea
                 and
                 some
                 part
                 of
                 Russia
                 ,
                 on
                 the
                 South
                 with
                 the
                 Carpathian
                 Mountains
                 ,
                 which
                 divide
                 it
                 from
                 
                   Hungary
                   ,
                   Transilvania
                
                 ,
                 and
                 Moldavia
                 .
                 It
                 is
                 of
                 figure
                 round
                 in
                 compass
                 2600
                 miles
                 ,
                 scituate
                 under
                 the
                 8
                 and
                 12
                 Climates
                 ,
                 so
                 that
                 the
                 longest
                 day
                 in
                 the
                 southern
                 parts
                 is
                 but
                 16
                 hours
                 ,
                 and
                 about
                 18
                 
                 hours
                 in
                 the
                 parts
                 most
                 North.
                 
              
               
                 36.
                 
                 
                   The
                   several
                   Provinces
                   of
                   which
                   this
                   Kingdom
                   doth
                   consist
                   ,
                   are
                
                 1.
                 
                 Livonia
                 ,
                 2.
                 
                 Samogitia
                 ,
                 3.
                 
                 Lituania
                 ,
                 4.
                 
                 Volkinia
                 ,
                 5.
                 
                 Podolia
                 ,
                 6.
                 
                 Russia
                 nigra
                 ,
                 7.
                 
                 Massovia
                 ,
                 8.
                 
                 Podlassia
                 ,
                 9.
                 
                 Prussia
                 ,
                 10.
                 
                 Pomerellia
                 ,
                 11.
                 
                 Poland
                 
                   specially
                   so
                   called
                
                 .
              
               
                 37.
                 
                 Hungary
                 is
                 bounded
                 on
                 the
                 East
                 with
                 Transilvania
                 and
                 Walachia
                 ,
                 on
                 the
                 West
                 with
                 
                   Sterria
                   ,
                   Austria
                
                 and
                 Moravia
                 ,
                 on
                 the
                 North
                 with
                 the
                 Carpathian
                 mountains
                 which
                 divide
                 it
                 from
                 Poland
                 ,
                 and
                 on
                 the
                 South
                 with
                 Sclavonia
                 ,
                 and
                 some
                 part
                 of
                 Dacia
                 :
                 it
                 extendeth
                 in
                 length
                 from
                 Presburg
                 along
                 the
                 Danow
                 to
                 the
                 borders
                 of
                 Transilvania
                 ,
                 for
                 the
                 space
                 of
                 300
                 English
                 miles
                 ,
                 and
                 190
                 of
                 the
                 same
                 miles
                 in
                 breadth
                 .
              
               
                 38.
                 
                 It
                 lieth
                 in
                 the
                 Northern
                 temperate
                 Zone
                 ,
                 betwixt
                 the
                 middle
                 parallels
                 of
                 the
                 7
                 and
                 9
                 Climates
                 ,
                 so
                 that
                 the
                 longest
                 Summers
                 day
                 in
                 the
                 Southern
                 parts
                 is
                 but
                 15
                 hours
                 and
                 an
                 half
                 ,
                 and
                 not
                 above
                 16
                 hours
                 in
                 the
                 parts
                 most
                 North.
                 
              
               
                 40.
                 
                 This
                 Country
                 is
                 commonly
                 divided
                 into
                 the
                 upper
                 Hungary
                 and
                 the
                 lower
                 ,
                 the
                 upper
                 lying
                 on
                 the
                 North
                 of
                 the
                 River
                 Danow
                 ,
                 the
                 lower
                 lying
                 on
                 the
                 South
                 of
                 that
                 River
                 ,
                 comprehending
                 all
                 Pannonia
                 inferior
                 and
                 part
                 of
                 Superior
                 ,
                 and
                 is
                 now
                 possessed
                 by
                 the
                 King
                 of
                 Hungary
                 and
                 the
                 Great
                 Turk
                 ,
                 who
                 is
                 Lord
                 of
                 the
                 most
                 part
                 by
                 Arms
                 and
                 Conquest
                 .
              
               
                 04.
                 
                 Sclavonia
                 is
                 bounded
                 on
                 the
                 East
                 with
                 
                   Servia
                   ,
                   Macedonia
                
                 and
                 Epirus
                 ,
                 from
                 which
                 it
                 is
                 parted
                 by
                 the
                 River
                 Drinus
                 ,
                 and
                 a
                 line
                 drawn
                 from
                 thence
                 unto
                 the
                 Adriatick
                 ,
                 on
                 the
                 West
                 with
                 Carniola
                 in
                 Germany
                 ,
                 and
                 Istria
                 in
                 the
                 Seigniory
                 
                 of
                 Venice
                 ,
                 from
                 which
                 last
                 it
                 is
                 divided
                 by
                 the
                 River
                 Arsia
                 ;
                 on
                 the
                 North
                 with
                 Hungary
                 ,
                 on
                 the
                 South
                 with
                 the
                 Adriatick
                 Sea.
                 
              
               
                 41.
                 
                 It
                 is
                 scituate
                 in
                 the
                 Northern
                 temperate
                 Zone
                 ,
                 between
                 the
                 middle
                 Parallels
                 of
                 the
                 sixth
                 and
                 seventh
                 Climates
                 ,
                 so
                 that
                 the
                 longest
                 day
                 in
                 Summer
                 is
                 about
                 15
                 hours
                 and
                 an
                 half
                 .
              
               
                 42.
                 
                 This
                 Country
                 as
                 it
                 came
                 at
                 last
                 to
                 be
                 divided
                 ,
                 between
                 the
                 Kings
                 of
                 Hungary
                 and
                 the
                 State
                 of
                 Venice
                 ;
                 is
                 distinguished
                 into
                 1.
                 
                 
                   Windischland
                   ,
                   2.
                   
                   Croatia
                   ,
                   3.
                   
                   Bosnia
                   ,
                   4.
                   
                   Dalmatia
                   ,
                   5.
                   
                   Liburnia
                
                 or
                 
                   Cantado
                   di
                   Zara
                
                 ,
                 and
                 6.
                 
                 The
                 Sclavonian
                 Islands
                 .
              
               
                 43.
                 
                 Dacia
                 is
                 bounded
                 on
                 the
                 East
                 with
                 the
                 Euxine
                 Sea
                 and
                 some
                 part
                 of
                 Thrace
                 ;
                 on
                 the
                 West
                 with
                 Hungary
                 and
                 Sclavonia
                 ;
                 on
                 the
                 North
                 with
                 Podolia
                 ,
                 and
                 some
                 other
                 members
                 of
                 the
                 Realm
                 of
                 Poland
                 ,
                 on
                 the
                 South
                 with
                 the
                 rest
                 of
                 Thrace
                 and
                 Macedonia
                 .
              
               
                 44.
                 
                 It
                 lieth
                 on
                 both
                 sides
                 of
                 the
                 Danow
                 fronting
                 all
                 along
                 the
                 upper
                 and
                 the
                 lower
                 Hungary
                 ,
                 and
                 some
                 part
                 of
                 Sclavonia
                 ;
                 extended
                 from
                 the
                 7
                 Climate
                 to
                 the
                 10
                 ;
                 so
                 that
                 the
                 longest
                 Summers
                 day
                 in
                 the
                 most
                 northern
                 parts
                 thereof
                 ,
                 is
                 near
                 17
                 hours
                 ,
                 and
                 in
                 the
                 most
                 southern
                 15
                 hours
                 3
                 quarters
                 .
              
               
                 45.
                 
                 The
                 several
                 Provinces
                 comprehended
                 under
                 the
                 name
                 of
                 Dacia
                 ,
                 are
                 1.
                 
                 
                   Transilvania
                   ,
                   2.
                   
                   Moldavia
                   ,
                   3.
                   
                   Walachia
                   ,
                   7.
                   
                   Rascia
                   ,
                   5.
                   
                   Servia
                   ,
                   6.
                   
                   Bulgaria
                   ,
                
                 the
                 first
                 four
                 in
                 old
                 Dacia
                 ,
                 on
                 the
                 North
                 side
                 of
                 the
                 Danow
                 ;
                 the
                 two
                 last
                 in
                 new
                 Dacia
                 ,
                 on
                 the
                 South
                 thereof
                 .
              
               
                 45.
                 
                 Greece
                 in
                 the
                 present
                 Latitude
                 and
                 extent
                 thereof
                 ,
                 is
                 bounded
                 on
                 the
                 East
                 with
                 the
                 
                 Propontick
                 ,
                 Hellespont
                 ,
                 and
                 AEgean
                 Seas
                 ,
                 on
                 the
                 West
                 with
                 the
                 Adriatick
                 ;
                 on
                 the
                 North
                 with
                 Mount
                 Haemus
                 which
                 parteth
                 it
                 from
                 
                   Bulgaria
                   ,
                   Servia
                
                 and
                 some
                 part
                 of
                 Illyricum
                 ;
                 and
                 on
                 the
                 South
                 with
                 the
                 Sea
                 -
                 Ionian
                 ;
                 so
                 that
                 it
                 is
                 in
                 a
                 manner
                 a
                 Peninsula
                 or
                 Demi-Island
                 ,
                 environed
                 on
                 three
                 sides
                 by
                 the
                 Sea
                 ,
                 on
                 the
                 fourth
                 only
                 united
                 to
                 the
                 rest
                 of
                 Europe
                 .
              
               
                 46.
                 
                 It
                 is
                 scituate
                 in
                 the
                 northern
                 temperate
                 Zone
                 ,
                 under
                 the
                 fifth
                 and
                 sixth
                 Climates
                 ,
                 the
                 longest
                 day
                 being
                 15
                 hours
                 .
              
               
                 47.
                 
                 In
                 this
                 Country
                 formerly
                 so
                 famous
                 for
                 learning
                 and
                 government
                 ,
                 the
                 several
                 Provinces
                 are
                 1.
                 
                 
                   Peloponnesus
                   ,
                   2.
                   
                   Achaia
                   ,
                   3.
                   
                   Epirus
                   ,
                   4.
                   
                   Albania
                   ,
                   5.
                   
                   Macedon
                   ,
                   6.
                   
                   Thrace
                   ,
                
                 7.
                 
                 The
                 Islands
                 of
                 the
                 Propontick
                 ;
                 8.
                 
                 AEgean
                 ,
                 and
                 9.
                 
                 The
                 Ionian
                 Seas
                 ,
                 and
                 10.
                 finally
                 the
                 Isle
                 of
                 Crete
                 .
              
               
                 And
                 thus
                 I
                 have
                 given
                 you
                 a
                 brief
                 description
                 of
                 those
                 Countries
                 which
                 are
                 comprehended
                 in
                 the
                 Continent
                 of
                 Europe
                 ;
                 the
                 Islands
                 in
                 this
                 part
                 of
                 the
                 world
                 are
                 many
                 ;
                 I
                 will
                 mention
                 only
                 some
                 few
                 .
                 These
                 two
                 in
                 the
                 British
                 and
                 Northern
                 Ocean
                 ,
                 known
                 by
                 the
                 names
                 of
                 
                   Great
                   Britain
                
                 and
                 Ireland
                 are
                 the
                 most
                 famous
                 ,
                 to
                 which
                 may
                 be
                 added
                 Greenland
                 .
                 In
                 the
                 Mediterranaen
                 Sea
                 you
                 have
                 the
                 Islands
                 of
                 
                   Sicilia
                   ,
                   Sardinia
                   ,
                   Corsica
                
                 and
                 Crete
                 ,
                 which
                 is
                 now
                 called
                 Candia
                 the
                 greater
                 and
                 the
                 less
                 :
                 As
                 for
                 the
                 other
                 Islands
                 belonging
                 to
                 this
                 part
                 of
                 the
                 world
                 ,
                 the
                 Reader
                 may
                 expect
                 a
                 more
                 particular
                 description
                 from
                 them
                 who
                 have
                 or
                 shall
                 write
                 more
                 largely
                 of
                 this
                 subject
                 :
                 This
                 we
                 deem
                 sufficient
                 for
                 our
                 present
                 purpose
                 .
                 Let
                 this
                 then
                 suffice
                 for
                 the
                 description
                 of
                 the
                 first
                 part
                 of
                 the
                 World
                 called
                 Europe
                 .
              
            
             
               
               
                 CHAP.
                 IV.
                 
              
               
                 
                   Of
                   Asia
                   .
                
              
               
                 ASia
                 is
                 bound
                 on
                 the
                 West
                 with
                 the
                 Mediteranean
                 and
                 AEgaean
                 Seas
                 ,
                 the
                 
                   Hellespont
                   ,
                   Propontis
                
                 ,
                 Thracian
                 Bosphorus
                 and
                 the
                 Euxine
                 Sea
                 ,
                 the
                 
                   Palus
                   Maeotis
                
                 ,
                 the
                 Rivers
                 Tanais
                 and
                 Duina
                 ,
                 a
                 Line
                 being
                 drawn
                 from
                 the
                 first
                 of
                 the
                 two
                 said
                 Rivers
                 unto
                 the
                 other
                 ,
                 by
                 all
                 which
                 it
                 is
                 parted
                 from
                 Europe
                 ;
                 on
                 the
                 North
                 it
                 hath
                 the
                 main
                 Scythick
                 Ocean
                 ;
                 but
                 on
                 the
                 East
                 the
                 Indian
                 Ocean
                 ,
                 and
                 
                   Mare
                   del
                   Eur
                
                 by
                 which
                 it
                 is
                 separated
                 from
                 America
                 ;
                 on
                 the
                 South
                 the
                 Mediterranean
                 ,
                 or
                 that
                 part
                 of
                 it
                 ,
                 which
                 is
                 called
                 the
                 Carpathian
                 Sea
                 ,
                 washing
                 the
                 shoars
                 of
                 Anatolia
                 ,
                 and
                 the
                 main
                 Southern
                 Ocean
                 ,
                 passing
                 along
                 the
                 Indian
                 ,
                 Persian
                 and
                 Arabian
                 Coasts
                 :
                 and
                 finally
                 on
                 the
                 south-west
                 ,
                 the
                 red
                 Sea
                 or
                 Bay
                 of
                 Arabia
                 ,
                 by
                 which
                 it
                 is
                 parted
                 from
                 Affrick
                 .
                 Environed
                 on
                 all
                 sides
                 with
                 the
                 Sea
                 ,
                 or
                 some
                 Sea
                 like
                 Rivers
                 ,
                 except
                 a
                 narrow
                 Isthmus
                 in
                 the
                 south-west
                 ,
                 which
                 joyns
                 it
                 to
                 Africk
                 ,
                 and
                 the
                 space
                 of
                 ground
                 (
                 whatsoever
                 it
                 be
                 )
                 between
                 Duina
                 and
                 Tanais
                 ,
                 on
                 the
                 North-west
                 which
                 unites
                 it
                 to
                 Europe
                 .
              
               
                 2.
                 
                 It
                 is
                 situated
                 East
                 and
                 West
                 ,
                 from
                 the
                 52
                 to
                 the
                 169
                 degree
                 of
                 Longitude
                 ;
                 and
                 North
                 and
                 South
                 from
                 the
                 82
                 degree
                 of
                 Latitude
                 to
                 the
                 very
                 AEquator
                 ;
                 some
                 of
                 the
                 Islands
                 only
                 lying
                 on
                 the
                 South
                 of
                 that
                 Circle
                 :
                 so
                 that
                 the
                 longest
                 summers
                 day
                 in
                 the
                 southern
                 parts
                 ,
                 is
                 but
                 twelve
                 hours
                 ,
                 but
                 in
                 the
                 most
                 northern
                 parts
                 hereof
                 almost
                 four
                 whole
                 Months
                 together
                 .
              
               
               
                 3.
                 
                 This
                 Country
                 hath
                 heretofore
                 been
                 had
                 in
                 special
                 honour
                 ;
                 1.
                 
                 For
                 the
                 creation
                 of
                 Man
                 ,
                 who
                 had
                 his
                 first
                 making
                 in
                 this
                 part
                 of
                 the
                 World.
                 2.
                 
                 Because
                 in
                 this
                 part
                 of
                 it
                 stood
                 the
                 Garden
                 of
                 Eden
                 ,
                 which
                 he
                 had
                 for
                 the
                 first
                 place
                 of
                 his
                 habitation
                 .
                 3.
                 
                 Because
                 here
                 flourished
                 the
                 four
                 first
                 great
                 Monarchies
                 of
                 the
                 Assyrians
                 ,
                 Babylonians
                 ,
                 Medes
                 and
                 Persians
                 .
                 4.
                 
                 Because
                 it
                 was
                 the
                 Scene
                 of
                 almost
                 all
                 the
                 memorable
                 Actions
                 which
                 are
                 recorded
                 by
                 the
                 pen-men
                 of
                 the
                 Scriptures
                 .
                 5.
                 
                 Because
                 our
                 Saviour
                 Christ
                 was
                 borne
                 here
                 ,
                 and
                 here
                 wrought
                 his
                 most
                 divine
                 Miracles
                 ,
                 and
                 accomplished
                 the
                 great
                 work
                 of
                 our
                 Redemption
                 .
                 6.
                 
                 And
                 finally
                 ,
                 because
                 from
                 hence
                 all
                 Nations
                 of
                 the
                 World
                 had
                 their
                 first
                 beginning
                 ,
                 on
                 the
                 dispersion
                 which
                 was
                 made
                 by
                 the
                 Sons
                 of
                 Noah
                 after
                 their
                 vain
                 attempt
                 at
                 Babel
                 .
              
               
                 4.
                 
                 This
                 part
                 of
                 the
                 World
                 for
                 the
                 better
                 understanding
                 of
                 the
                 Greek
                 and
                 the
                 Roman
                 Stories
                 and
                 the
                 estate
                 of
                 the
                 Assyrian
                 ,
                 Babylonian
                 and
                 the
                 Persian
                 Monarchies
                 ,
                 to
                 which
                 the
                 holy
                 Scriptures
                 do
                 so
                 much
                 relate
                 ,
                 we
                 shall
                 consider
                 as
                 divided
                 into
                 the
                 Regions
                 of
                 1.
                 
                 
                   Anatolia
                   or
                   Asia
                   minor
                   .
                   2.
                   
                   Cyprus
                   .
                   3.
                   
                   Syria
                   .
                   4.
                   
                   Arabia
                   .
                   5.
                   
                   Chaldea
                   .
                   6.
                   
                   Assyria
                   .
                   7.
                   
                   Mesopotamia
                   .
                   8.
                   
                   Turcomania
                   .
                   9.
                   
                   Media
                   .
                   10.
                   
                   Persia.
                   11.
                   
                   Tartaria
                   .
                   12.
                   
                   China
                   .
                   13.
                   
                   India
                   .
                
                 and
                 14.
                 the
                 Oriental
                 Islands
                 .
              
               
                 
                   Anatolia
                   or
                   Asia
                   minor
                   .
                
                 
                   Anatolia
                   or
                   
                     Asia
                     minor
                  
                   ,
                   is
                   bounded
                   on
                   the
                   East
                   with
                   the
                   River
                   Euphrates
                   ,
                   by
                   which
                   it
                   is
                   parted
                   from
                   the
                   greater
                   Asia
                   ;
                   on
                   the
                   West
                   with
                   the
                   Thracian
                   
                     Bosphorus
                     ,
                     Propontis
                     ,
                     Hellespont
                  
                   ,
                   and
                   
                   the
                   AEgean
                   Sea
                   ,
                   by
                   which
                   it
                   is
                   parted
                   from
                   Europe
                   ;
                   on
                   the
                   North
                   with
                   
                     Pontus
                     Euxinus
                  
                   ,
                   called
                   also
                   the
                   black
                   Sea
                   ,
                   and
                   
                     Mare
                     Maggiore
                  
                   ,
                   and
                   on
                   the
                   South
                   by
                   the
                   Rhodian
                   ,
                   Lydian
                   and
                   Pamphilian
                   Seas
                   ,
                   several
                   parts
                   of
                   the
                   Mediterranean
                   .
                   So
                   that
                   it
                   is
                   a
                   Demi-Island
                   or
                   Peninsula
                   environed
                   on
                   all
                   sides
                   with
                   water
                   ,
                   excepting
                   a
                   small
                   Isthmus
                   or
                   Neck
                   of
                   Land
                   extending
                   from
                   the
                   head
                   of
                   Euphrates
                   to
                   the
                   Euxine
                   Sea
                   ,
                   by
                   which
                   it
                   is
                   joyned
                   to
                   the
                   rest
                   of
                   Asia
                   .
                
                 
                   It
                   reacheth
                   from
                   the
                   51
                   to
                   the
                   72
                   degree
                   of
                   Longitude
                   ,
                   and
                   from
                   the
                   36
                   to
                   the
                   45
                   degree
                   of
                   Latitude
                   ,
                   and
                   lyeth
                   almost
                   in
                   the
                   same
                   position
                   with
                   Italy
                   ,
                   extending
                   from
                   the
                   middle
                   Parallel
                   of
                   the
                   fourth
                   Clime
                   ,
                   to
                   the
                   middle
                   Parallel
                   of
                   the
                   sixth
                   ,
                   so
                   that
                   the
                   longest
                   summers
                   day
                   in
                   the
                   Southern
                   Parts
                   ,
                   is
                   about
                   14
                   hours
                   and
                   a
                   half
                   ;
                   and
                   one
                   hour
                   longer
                   in
                   those
                   parts
                   which
                   lie
                   most
                   towards
                   the
                   North.
                   
                
                 
                   
                     The
                     Provinces
                     into
                     which
                     it
                     was
                     divided
                     before
                     the
                     Roman
                     Conquest
                     were
                  
                   1.
                   
                   Bithynia
                   .
                   2.
                   
                   Pontus
                   .
                   3.
                   
                   Paphlagonia
                   .
                   4.
                   
                   Galatia
                   .
                   5.
                   
                   Cappadocia
                   .
                   6.
                   
                   Armenia
                   Major
                   &
                   Minor.
                   7.
                   
                   Phrygia
                   minor
                   .
                   8.
                   
                   Phrygia
                   major
                   .
                   9.
                   
                   Mysia
                   
                     the
                     greater
                     and
                     the
                     less
                  
                   .
                   10.
                   
                   Asia
                   
                     specially
                     so
                     called
                     ,
                     comprehending
                  
                   AEolis
                   and
                   Ionia
                   .
                   11.
                   
                   Lydia
                   .
                   12.
                   
                   Caria
                   .
                   13.
                   
                   Lycia
                   .
                   14.
                   
                   Lycaonia
                   .
                   15.
                   
                   Pisidia
                   .
                   16.
                   
                   Pamphylia
                   .
                   17.
                   
                   Isauria
                   .
                   18.
                   
                   Cilicia
                   .
                   19.
                   
                   
                     The
                     Province
                     of
                     the
                     Asian
                     Isles
                     ,
                     whereof
                     the
                     most
                     principal
                     are
                  
                   1.
                   
                   Tenedos
                   .
                   2.
                   
                   Chios
                   .
                   3.
                   
                   Samos
                   .
                   4.
                   
                   Choos
                   .
                   5.
                   
                   Icaria
                   .
                   6.
                   
                   Lesbos
                   .
                   7.
                   
                   Patmos
                   .
                   8.
                   
                   Claros
                   .
                   9
                   Carpathos
                   .
                   10.
                   
                   Rhodes
                   .
                
              
               
                 
                 
                   Cyprus
                   .
                
                 
                   Cyprus
                   is
                   situated
                   in
                   the
                   Syrian
                   and
                   Cilician
                   Seas
                   ,
                   extended
                   in
                   length
                   from
                   East
                   to
                   West
                   200
                   miles
                   ,
                   in
                   breadth
                   60
                   the
                   whole
                   compass
                   reckoned
                   550
                   ,
                   distant
                   about
                   60
                   miles
                   from
                   the
                   rocky
                   Shores
                   of
                   Cilicia
                   in
                   
                     Asia
                     minor
                  
                   ,
                   and
                   about
                   one
                   hundred
                   from
                   the
                   main
                   Land
                   of
                   Syria
                   .
                
                 
                   It
                   is
                   situated
                   under
                   the
                   fourth
                   Climate
                   ,
                   so
                   that
                   the
                   longest
                   day
                   in
                   Summer
                   is
                   no
                   more
                   than
                   14
                   hours
                   and
                   a
                   half
                   .
                
                 
                   
                     Divided
                     by
                  
                   Ptolemy
                   
                     into
                     the
                     4
                     provinces
                     of
                  
                   1.
                   
                   Paphia
                   .
                   2.
                   
                   Amathasia
                   .
                   3.
                   
                   Lepathia
                   .
                   4.
                   
                   Salamine
                   .
                
              
               
                 
                   Syria
                   .
                
                 
                   Syria
                   is
                   bounded
                   on
                   the
                   East
                   with
                   the
                   River
                   Euphrates
                   by
                   which
                   it
                   is
                   parted
                   from
                   Mesopotamia
                   ;
                   on
                   the
                   West
                   with
                   the
                   Mediterranean
                   Sea
                   ;
                   on
                   the
                   North
                   with
                   Cilicia
                   and
                   
                     Armenia
                     minor
                  
                   ,
                   parted
                   from
                   the
                   last
                   by
                   mount
                   Taurus
                   ;
                   and
                   on
                   the
                   South
                   with
                   Palestine
                   ,
                   and
                   some
                   parts
                   of
                   Arabia
                   .
                   The
                   length
                   hereof
                   from
                   Mount
                   Taurus
                   to
                   the
                   Edge
                   of
                   Arabia
                   ,
                   is
                   said
                   to
                   be
                   525
                   Miles
                   ;
                   the
                   breadth
                   from
                   the
                   Mediterranean
                   to
                   the
                   River
                   Euphrates
                   470
                   Miles
                   ,
                   drawing
                   somewhat
                   near
                   unto
                   a
                   Square
                   .
                
                 
                   The
                   whole
                   Country
                   was
                   antiently
                   divided
                   into
                   these
                   six
                   parts
                   .
                   1.
                   
                   
                     Phoenicia
                     .
                     2.
                     
                     Palestine
                     .
                     3.
                     
                     Syria
                  
                   specially
                   so
                   called
                   .
                   4.
                   
                   
                     Comagena
                     .
                     5.
                     
                     Palmyrene
                  
                   .
                   and
                   Caelosyria
                   ,
                   or
                   
                     Syria
                     Cava
                  
                   .
                
              
               
                 
                 
                   Arabia
                   .
                
                 
                   Arabia
                   hath
                   on
                   the
                   East
                   Chaldaea
                   and
                   the
                   Bay
                   or
                   Gulf
                   of
                   Persia
                   ;
                   on
                   the
                   West
                   Palestine
                   ,
                   some
                   part
                   of
                   Egypt
                   ,
                   and
                   the
                   whole
                   course
                   of
                   the
                   red
                   Sea
                   ,
                   on
                   the
                   North
                   the
                   River
                   Euphrates
                   with
                   some
                   parts
                   of
                   Syria
                   and
                   Palestine
                   ,
                   and
                   on
                   the
                   South
                   the
                   main
                   southern
                   Ocean
                   .
                   It
                   is
                   in
                   circuit
                   about
                   4000
                   Miles
                   ,
                   but
                   of
                   so
                   unequal
                   and
                   heteregeneous
                   Composition
                   ,
                   that
                   no
                   general
                   Character
                   can
                   be
                   given
                   of
                   it
                   ,
                   and
                   therefore
                   we
                   must
                   look
                   upon
                   it
                   as
                   it
                   stands
                   divided
                   into
                   
                     Arabia
                     Deserta
                     ,
                     2.
                     
                     Arabia
                     Petraea
                     .
                     3.
                     
                     Arabia
                     Felix
                  
                   and
                   4.
                   
                   The
                   Arabick
                   Islands
                   .
                
              
               
                 
                   Chaldea
                   .
                
                 
                   Chaldea
                   is
                   bounded
                   on
                   the
                   East
                   with
                   Susiana
                   a
                   Province
                   of
                   Persia
                   ;
                   on
                   the
                   West
                   with
                   
                     Arabia
                     deserta
                  
                   ;
                   on
                   the
                   North
                   with
                   Mesopotamia
                   ;
                   and
                   on
                   the
                   South
                   with
                   the
                   Persian
                   Bay
                   and
                   the
                   rest
                   of
                   Deserta
                   .
                
              
               
                 
                   Assyria
                   .
                
                 
                   Assyria
                   is
                   bounded
                   on
                   the
                   East
                   with
                   Media
                   ,
                   from
                   which
                   it
                   is
                   parted
                   by
                   the
                   Mountain
                   called
                   Coathras
                   ;
                   on
                   the
                   West
                   with
                   Mesopotamia
                   ,
                   from
                   which
                   it
                   is
                   divided
                   by
                   the
                   River
                   Tygris
                   ;
                   on
                   the
                   South
                   with
                   Susiana
                   ;
                   and
                   on
                   the
                   North
                   with
                   some
                   part
                   of
                   Turcomania
                   ;
                   it
                   was
                   antiently
                   divided
                   into
                   six
                   parts
                   .
                   1.
                   
                   
                     Arraphachitis
                     .
                     2.
                     
                     Adiabene
                     .
                     3.
                     
                     Calacine
                     .
                     4.
                     
                     Aobelites
                     .
                     5.
                     
                     Apolloniates
                     .
                  
                
              
               
                 
                 
                   Mesopotamia
                   .
                
                 
                   Mesopotamia
                   is
                   bounded
                   on
                   the
                   East
                   with
                   the
                   River
                   Tygris
                   by
                   which
                   it
                   is
                   parted
                   from
                   Assyria
                   ;
                   on
                   the
                   West
                   with
                   Euphrates
                   which
                   divides
                   it
                   from
                   Comagena
                   a
                   Province
                   of
                   Syria
                   ;
                   on
                   the
                   North
                   with
                   Mount
                   Taurus
                   ;
                   by
                   which
                   it
                   is
                   separated
                   from
                   
                     Armenia
                     major
                  
                   ;
                   and
                   on
                   the
                   South
                   with
                   Chaldea
                   and
                   
                     Arabia
                     deserta
                  
                   from
                   which
                   last
                   it
                   is
                   parted
                   by
                   the
                   bendings
                   of
                   Euphrates
                   also
                   .
                   It
                   was
                   antiently
                   divided
                   into
                   ,
                   1.
                   
                   
                     Anthemasia
                     .
                     2.
                     
                     Chalcitis
                     .
                     3.
                     
                     Caulanitis
                     .
                     4.
                     
                     Acchabene
                     .
                     5.
                     
                     Ancorabitis
                  
                   and
                   6.
                   
                   Ingine
                   .
                
              
               
                 
                   Turcomania
                   .
                
                 
                   Turcomania
                   is
                   bounded
                   on
                   the
                   East
                   with
                   Media
                   and
                   the
                   Caspian
                   Sea
                   ;
                   on
                   the
                   West
                   with
                   the
                   Euxine
                   Sea
                   ,
                   Cappadocia
                   and
                   
                     Armenia
                     minor
                  
                   ;
                   on
                   the
                   North
                   with
                   Tartary
                   ,
                   and
                   on
                   the
                   South
                   with
                   Mesopotamia
                   and
                   Assyria
                   .
                   A
                   Countrey
                   which
                   consisteth
                   of
                   four
                   Provinces
                   .
                   1.
                   
                   
                     Armenia
                     major
                  
                   or
                   Turcomania
                   properly
                   and
                   specially
                   so
                   called
                   .
                   2.
                   
                   
                     Colchis
                     .
                     3.
                     
                     Iberia
                     .
                     4.
                     
                     Albania
                     .
                  
                
              
               
                 
                   Media
                   .
                
                 
                   Media
                   is
                   bounded
                   on
                   the
                   East
                   with
                   Parthia
                   ,
                   and
                   some
                   part
                   of
                   Otyrcania
                   ,
                   Provinces
                   of
                   the
                   Persian
                   Empire
                   ;
                   on
                   the
                   West
                   with
                   
                     Armenia
                     major
                  
                   ,
                   and
                   some
                   part
                   of
                   Assyria
                   ;
                   on
                   the
                   North
                   with
                   the
                   Caspian
                   Sea
                   and
                   those
                   parts
                   of
                   
                     Armenia
                     major
                  
                   ,
                   which
                   now
                   pass
                   in
                   the
                   account
                   of
                   
                     Iberia
                     ,
                     Georgia
                  
                   ;
                   and
                   on
                   the
                   South
                   with
                   Persia.
                   It
                   is
                   now
                   
                   divided
                   into
                   two
                   Provinces
                   .
                   1.
                   
                   
                     Atropatia
                     .
                     2.
                     
                     Media
                     major
                     .
                  
                
              
               
                 
                   Persia.
                   
                
                 
                   Persia
                   is
                   bounded
                   on
                   the
                   East
                   with
                   India
                   ;
                   on
                   the
                   West
                   with
                   
                     Media
                     ,
                     Assyria
                  
                   ,
                   and
                   Chaldea
                   ;
                   on
                   the
                   North
                   with
                   Tartary
                   ,
                   on
                   the
                   South
                   with
                   the
                   main
                   Ocean
                   .
                
                 
                   
                     It
                     is
                     divided
                     into
                     the
                     particular
                     Provinces
                     of
                  
                   1.
                   
                   Susiana
                   .
                   2.
                   
                   Persis
                   .
                   3.
                   
                   Ormur
                   .
                   4.
                   
                   Carmania
                   .
                   5.
                   
                   Gedrosia
                   .
                   6.
                   
                   Drangiana
                   .
                   7.
                   
                   Arachosia
                   .
                   8.
                   
                   Paropamisus
                   .
                   9.
                   
                   Aria
                   .
                   10.
                   
                   Parthia
                   .
                   11.
                   
                   Hyrcania
                   .
                   12.
                   
                   Margiana
                   and
                   13.
                   
                   Bactria
                   .
                
              
               
                 
                   Tartaria
                   .
                
                 
                   Tartaria
                   is
                   bounded
                   on
                   the
                   East
                   with
                   China
                   ,
                   the
                   Oriental
                   Ocean
                   ,
                   and
                   the
                   Straits
                   of
                   Anian
                   ,
                   by
                   which
                   it
                   is
                   parted
                   from
                   America
                   ,
                   on
                   the
                   West
                   with
                   Russia
                   and
                   Podolia
                   ,
                   a
                   Province
                   of
                   the
                   Realm
                   of
                   Poland
                   ;
                   on
                   the
                   North
                   with
                   the
                   main
                   Scythick
                   or
                   frozen
                   Ocean
                   ;
                   and
                   on
                   the
                   South
                   with
                   part
                   of
                   China
                   ,
                   from
                   which
                   it
                   is
                   separated
                   by
                   a
                   mighty
                   Wall
                   ,
                   some
                   part
                   of
                   India
                   ,
                   the
                   River
                   Oxus
                   parting
                   it
                   from
                   Bactria
                   and
                   Margiana
                   ,
                   two
                   Persian
                   Provinces
                   ;
                   the
                   Caspian
                   Sea
                   which
                   separates
                   it
                   from
                   Media
                   and
                   Hyrcania
                   ;
                   the
                   Caucasian
                   Mountains
                   interposing
                   between
                   it
                   and
                   Turcomania
                   ;
                   and
                   the
                   Euxine
                   Sea
                   which
                   divideth
                   it
                   from
                   Anatolia
                   and
                   Thrace
                   .
                
                 
                   It
                   reacheth
                   from
                   the
                   50
                   degree
                   of
                   Longitude
                   to
                   the
                   195
                   which
                   is
                   145
                   degrees
                   from
                   West
                   to
                   East
                   ;
                   and
                   from
                   the
                   40
                   degree
                   of
                   Northern
                   Latitude
                   ,
                   unto
                   the
                   80
                   ,
                   which
                   is
                   within
                   10
                   degrees
                   
                   of
                   the
                   Pole
                   it self
                   ,
                   By
                   which
                   accompt
                   it
                   lieth
                   from
                   the
                   beginning
                   of
                   the
                   sixth
                   Clime
                   ,
                   where
                   the
                   longest
                   day
                   in
                   Summer
                   is
                   15
                   hours
                   ,
                   till
                   they
                   cease
                   measuring
                   the
                   Climates
                   ,
                   the
                   longest
                   day
                   in
                   the
                   most
                   Northen
                   parts
                   hereof
                   being
                   full
                   six
                   Months
                   ,
                   and
                   in
                   the
                   winter
                   half
                   of
                   the
                   Year
                   ,
                   the
                   night
                   as
                   long
                   .
                
                 
                   
                     It
                     is
                     now
                     divided
                     into
                     these
                     five
                     parts
                     .
                  
                   1.
                   
                   Tartaria
                   Precopensis
                   .
                   2.
                   
                   Asiatica
                   .
                   3.
                   
                   Antiqua
                   .
                   4.
                   
                   Zagathay
                   .
                   5.
                   
                   Cathay
                   .
                
              
               
                 
                   China
                   .
                
                 
                   China
                   is
                   bounded
                   on
                   the
                   North
                   with
                   Altay
                   and
                   the
                   Eastern
                   Tartars
                   ,
                   from
                   which
                   it
                   is
                   separated
                   by
                   a
                   continued
                   Chain
                   of
                   Hills
                   ,
                   part
                   of
                   those
                   of
                   Ararat
                   ,
                   and
                   where
                   that
                   chain
                   is
                   broken
                   off
                   or
                   interrupted
                   ,
                   with
                   a
                   great
                   wall
                   extended
                   400
                   Leagues
                   in
                   length
                   ;
                   on
                   the
                   South
                   partly
                   with
                   
                     Cauchin
                     China
                  
                   a
                   Province
                   of
                   India
                   ,
                   partly
                   with
                   the
                   Ocean
                   ;
                   on
                   the
                   East
                   with
                   the
                   oriental
                   Ocean
                   ,
                   and
                   on
                   the
                   West
                   with
                   part
                   of
                   India
                   and
                   Cathay
                   .
                
                 
                   It
                   reacheth
                   from
                   the
                   130
                   to
                   the
                   160
                   degree
                   of
                   Longitude
                   ,
                   and
                   from
                   the
                   Tropick
                   of
                   Cancer
                   to
                   the
                   53
                   degree
                   of
                   Latitude
                   ;
                   so
                   that
                   it
                   lieth
                   under
                   all
                   the
                   Climes
                   from
                   the
                   third
                   to
                   the
                   ninth
                   inclusively
                   .
                   The
                   longest
                   summers
                   day
                   in
                   the
                   southern
                   parts
                   being
                   13
                   hours
                   and
                   40
                   Minutes
                   increased
                   in
                   the
                   most
                   northern
                   parts
                   to
                   16
                   hours
                   and
                   3
                   quarters
                   .
                
                 
                   
                     It
                     containeth
                     no
                     fewer
                     than
                     15
                     Provinces
                     .
                  
                   1.
                   
                   Canton
                   .
                   2.
                   
                   Foquien
                   .
                   3.
                   
                   Olam
                   .
                   4.
                   
                   Sisnam
                   5.
                   
                   Tolenchia
                   .
                   6.
                   
                   Causay
                   .
                   7.
                   
                   Minchian
                   .
                   8.
                   
                   Ochian
                   .
                   9.
                   
                   Honan
                   .
                   10.
                   
                   Pagnia
                   .
                   11.
                   
                   Taitan
                   .
                   12.
                   
                   Quinchen
                   .
                   13.
                   
                   Chagnian
                   14.
                   
                   Susnan
                   .
                   15.
                   
                   Cunisay
                   .
                   
                   
                     Besides
                     the
                     provinces
                     of
                  
                   Suehuen
                   ,
                   
                     the
                     Island
                     of
                  
                   Chorea
                   
                     and
                     the
                     Island
                     of
                  
                   Cheaxan
                   .
                
              
               
                 
                   India
                   .
                
                 
                   India
                   is
                   bounded
                   on
                   the
                   East
                   with
                   the
                   Oriental
                   Ocean
                   and
                   some
                   part
                   of
                   China
                   ;
                   on
                   the
                   West
                   with
                   the
                   Persian
                   Empire
                   ;
                   on
                   the
                   North
                   with
                   some
                   Branches
                   of
                   Mount
                   Taurus
                   ,
                   which
                   divide
                   it
                   from
                   Tartary
                   ;
                   on
                   the
                   South
                   with
                   the
                   Indian
                   Ocean
                   .
                
                 
                   Extended
                   from
                   106
                   to
                   159
                   degrees
                   of
                   Longitude
                   ,
                   and
                   from
                   the
                   AEquator
                   to
                   the
                   44th
                   degree
                   of
                   Northern
                   Latitude
                   ,
                   by
                   which
                   account
                   it
                   lieth
                   from
                   the
                   beginning
                   of
                   the
                   first
                   to
                   the
                   end
                   of
                   the
                   sixth
                   Clime
                   ,
                   the
                   longest
                   Summers
                   day
                   in
                   the
                   southern
                   Parts
                   being
                   12
                   hours
                   onely
                   ,
                   and
                   in
                   the
                   parts
                   most
                   North
                   15
                   hours
                   and
                   a
                   half
                   .
                
                 
                   The
                   whole
                   Country
                   is
                   divided
                   into
                   two
                   main
                   parts
                   ,
                   
                     India
                     intra
                     Gangem
                  
                   ,
                   and
                   
                     India
                     extra
                     Gangem
                  
                   .
                
              
               
                 
                   The
                   Oriental
                   Islands
                   .
                
                 
                   The
                   Oriental
                   Islands
                   are
                   1.
                   
                   Iapan
                   .
                   2.
                   
                   The
                   Philippine
                   and
                   Isles
                   adjoyning
                   .
                   3.
                   
                   The
                   Islands
                   of
                   Bantam
                   .
                   4.
                   
                   The
                   Moluccoes
                   .
                   5.
                   
                   Those
                   called
                   Sinda
                   or
                   the
                   
                     Celebes
                     .
                     6.
                     
                     Iava
                     .
                     7.
                     
                     Borneo
                     .
                  
                   8.
                   
                   
                     Sumatra
                     .
                     9.
                     
                     Ceilan
                  
                   .
                   and
                   10.
                   others
                   of
                   less
                   note
                   .
                
              
            
             
               
               
                 CHAP.
                 V.
                 
              
               
                 
                   Of
                   Africk
                   .
                
              
               
                 AFrick
                 is
                 bounded
                 on
                 the
                 East
                 by
                 the
                 Red
                 Sea
                 ,
                 and
                 Bay
                 of
                 Arabia
                 ,
                 by
                 which
                 it
                 is
                 parted
                 from
                 Asia
                 ;
                 on
                 the
                 West
                 by
                 the
                 main
                 Atlantick
                 Oceans
                 interposing
                 between
                 it
                 and
                 America
                 ;
                 on
                 the
                 North
                 by
                 the
                 Mediterranean
                 Sea
                 ,
                 which
                 divides
                 it
                 from
                 Europe
                 and
                 Anatolia
                 ;
                 and
                 on
                 the
                 South
                 with
                 the
                 AEthiopick
                 Ocean
                 ,
                 separating
                 it
                 from
                 
                   Terra
                   Australis
                   incognita
                
                 or
                 the
                 southern
                 continent
                 ,
                 parted
                 from
                 all
                 the
                 rest
                 of
                 the
                 World
                 except
                 Asia
                 only
                 ,
                 to
                 which
                 it
                 is
                 joyned
                 by
                 a
                 narrow
                 Isthmus
                 not
                 above
                 60
                 miles
                 in
                 length
                 .
              
               
                 It
                 is
                 situate
                 for
                 the
                 most
                 part
                 under
                 the
                 Torrid
                 Zones
                 ,
                 the
                 AEquator
                 crossing
                 it
                 almost
                 in
                 the
                 midst
                 .
                 It
                 is
                 now
                 commonly
                 divided
                 into
                 these
                 seven
                 parts
                 .
                 1.
                 
                 
                   AEgypt
                   .
                   2.
                   
                   Barbary
                
                 or
                 the
                 Roman
                 Africk
                 .
                 3.
                 
                 
                   Numidia
                   .
                   4.
                   
                   Lybia
                   .
                   5.
                   
                   Terra
                   Nigritarum
                   .
                   6.
                   
                   AEthiopia
                   superior
                   .
                
                 and
                 7.
                 
                 
                   AEthiopia
                   rinferior
                
                 .
              
               
                 
                   AEgypt
                   .
                
                 
                   AEgypt
                   is
                   bounded
                   on
                   the
                   East
                   with
                   Idumea
                   ,
                   and
                   the
                   Bay
                   of
                   Arabia
                   ;
                   on
                   the
                   West
                   with
                   
                     Barbary
                     ,
                     Numidia
                  
                   ,
                   and
                   part
                   of
                   Lybia
                   ;
                   on
                   the
                   North
                   with
                   the
                   Mediterranean
                   Sea
                   ;
                   on
                   the
                   South
                   with
                   
                     AEthiopia
                     superior
                  
                   ,
                   or
                   the
                   Abyssyn
                   Emperor
                   ;
                   it
                   is
                   situate
                   under
                   the
                   second
                   and
                   fifth
                   Climates
                   ,
                   so
                   that
                   the
                   longest
                   day
                   in
                   Summer
                   is
                   but
                   thirteen
                   hours
                   and
                   a
                   half
                   .
                
              
               
                 
                 
                   Barbary
                   .
                
                 
                   Barbary
                   is
                   bounded
                   on
                   the
                   East
                   with
                   Cyrenaica
                   ;
                   on
                   the
                   West
                   with
                   the
                   Atlantick
                   Ocean
                   ;
                   on
                   the
                   North
                   with
                   the
                   Mediterranean
                   Sea
                   ,
                   the
                   Straits
                   of
                   Gibralter
                   and
                   some
                   part
                   of
                   the
                   Atlantick
                   also
                   ;
                   on
                   the
                   South
                   with
                   Mount
                   Atlas
                   ,
                   by
                   which
                   it
                   is
                   separated
                   from
                   
                     Lybia
                     inferior
                  
                   or
                   the
                   Desarts
                   of
                   Lybia
                   .
                
                 
                   It
                   is
                   situated
                   under
                   the
                   third
                   and
                   fourth
                   Climates
                   :
                   so
                   that
                   the
                   longest
                   Summers
                   day
                   in
                   the
                   parts
                   most
                   South
                   ,
                   amounteth
                   to
                   13
                   hours
                   and
                   3
                   quarters
                   ,
                   and
                   in
                   the
                   most
                   northern
                   parts
                   it
                   is
                   14
                   hours
                   and
                   a
                   quarter
                   .
                   This
                   country
                   is
                   now
                   reduced
                   to
                   the
                   Kingdoms
                   of
                   1.
                   
                   
                     Tunis
                     .
                     2.
                     
                     Tremesch
                  
                   or
                   
                     Algiers
                     .
                     3.
                     
                     Fesse
                  
                   and
                   4.
                   
                   Morocco
                   .
                
              
               
                 
                   Numidia
                   .
                
                 
                   Numidia
                   is
                   bounded
                   on
                   the
                   East
                   with
                   Egypt
                   ,
                   on
                   the
                   West
                   with
                   the
                   Atlantick
                   Ocean
                   ;
                   on
                   the
                   North
                   with
                   Mount
                   Atlas
                   ,
                   which
                   parteth
                   it
                   from
                   Barbary
                   and
                   Cyrene
                   ;
                   on
                   the
                   South
                   with
                   
                     Lybia
                     Deserta
                  
                   .
                
              
               
                 
                   Lybia
                   .
                
                 
                   Lybia
                   is
                   either
                   Interior
                   or
                   
                     Deserta
                     ,
                     Libia
                     interior
                  
                   is
                   bounded
                   on
                   the
                   North
                   with
                   Mount
                   Atlas
                   by
                   which
                   it
                   is
                   parted
                   from
                   Barbary
                   and
                   Cyrenaica
                   ;
                   on
                   the
                   East
                   with
                   
                     Lybia
                     Marmarica
                  
                   interposed
                   between
                   it
                   and
                   Egypt
                   ,
                   and
                   part
                   of
                   
                     AEthiopia
                     superior
                  
                   ,
                   or
                   the
                   Habassine
                   Empire
                   ;
                   on
                   the
                   South
                   with
                   
                     AEthiopia
                     inferior
                  
                   ,
                   and
                   the
                   Land
                   of
                   the
                   Negroes
                   ;
                   
                   and
                   on
                   the
                   West
                   with
                   the
                   main
                   Atlantick
                   Ocean
                   .
                
                 
                   
                     Lybia
                     deserta
                  
                   is
                   bounded
                   on
                   the
                   North
                   with
                   Numidia
                   or
                   Biledulgerid
                   ;
                   on
                   the
                   South
                   with
                   the
                   Land
                   of
                   the
                   Negroes
                   ;
                   and
                   on
                   the
                   West
                   with
                   Gulata
                   another
                   Province
                   of
                   the
                   Negroes
                   interposed
                   between
                   it
                   and
                   the
                   Atlantick
                   .
                
              
               
                 
                   Terra
                   Nigritarum
                   .
                
                 
                   
                     Terra
                     Nigritarum
                  
                   or
                   the
                   Land
                   of
                   the
                   Negroes
                   is
                   bounded
                   on
                   the
                   East
                   with
                   
                     AEthiopia
                     Superior
                  
                   ;
                   on
                   the
                   West
                   with
                   the
                   Atlantick
                   Ocean
                   ;
                   on
                   the
                   North
                   with
                   
                     Lybia
                     deserta
                  
                   and
                   on
                   the
                   South
                   with
                   the
                   Ethiopick
                   Ocean
                   ,
                   and
                   part
                   of
                   
                     AEthiopia
                     Inferior
                  
                   .
                
              
               
                 
                   AEthiopia
                   Superior
                   .
                
                 
                   
                     AEthiopia
                     Superior
                  
                   is
                   bounded
                   on
                   the
                   East
                   with
                   the
                   Red
                   Sea
                   and
                   the
                   
                     Sinus
                     Barbaricus
                  
                   ;
                   on
                   the
                   West
                   with
                   
                     Lybia
                     Interior
                  
                   ,
                   the
                   Realm
                   of
                   Nubia
                   in
                   the
                   Land
                   of
                   the
                   Negroes
                   and
                   part
                   of
                   the
                   Kingdoms
                   of
                   Congo
                   in
                   the
                   other
                   AEthiopia
                   ;
                   on
                   the
                   North
                   with
                   Egypt
                   and
                   
                     Lybia
                     Marmarica
                  
                   ,
                   and
                   on
                   the
                   South
                   with
                   the
                   Mountains
                   of
                   the
                   Moon
                   ,
                   by
                   which
                   it
                   is
                   parted
                   from
                   the
                   main
                   Body
                   of
                   
                     AEthiopia
                     Inferior
                  
                   .
                
                 
                   It
                   is
                   situate
                   on
                   both
                   sides
                   of
                   the
                   AEquinoctial
                   ,
                   extending
                   from
                   the
                   South
                   Parallel
                   of
                   seven
                   degrees
                   ,
                   where
                   it
                   meeteth
                   with
                   some
                   part
                   of
                   the
                   other
                   AEthiopia
                   to
                   the
                   Northern
                   end
                   of
                   the
                   Isle
                   of
                   Meroz
                   situated
                   under
                   the
                   fifth
                   Parallel
                   on
                   the
                   North
                   of
                   that
                   Circle
                   .
                
              
               
                 
                 
                   AEthiopia
                   Inferior
                   .
                
                 
                   
                     AEthiopia
                     inferior
                  
                   is
                   bounded
                   on
                   the
                   East
                   with
                   the
                   Red
                   Sea
                   ;
                   on
                   the
                   West
                   with
                   the
                   Ethiopick
                   Ocean
                   ;
                   on
                   the
                   North
                   with
                   
                     Terra
                     Nigritarum
                  
                   ,
                   and
                   the
                   higher
                   AEthiopia
                   ;
                   and
                   on
                   the
                   South
                   where
                   it
                   endeth
                   ,
                   is
                   a
                   point
                   of
                   a
                   Conus
                   ,
                   with
                   the
                   main
                   Ocean
                   parting
                   it
                   from
                   the
                   Southern
                   undiscovered
                   Continent
                   .
                   This
                   in
                   Ptolemyes
                   time
                   went
                   under
                   the
                   name
                   of
                   
                     Terra
                     incognita
                  
                   .
                
              
            
             
               
                 CHAP.
                 IV.
                 
              
               
                 
                   Of
                   America
                   .
                
              
               
                 AMerica
                 the
                 fourth
                 and
                 last
                 part
                 of
                 the
                 World
                 is
                 bounded
                 on
                 the
                 East
                 with
                 the
                 Atlantick
                 Ocean
                 and
                 the
                 Vergivian
                 Seas
                 ,
                 by
                 which
                 it
                 is
                 parted
                 from
                 Europe
                 and
                 Africa
                 ;
                 on
                 the
                 West
                 with
                 the
                 Pacifick
                 Ocean
                 ,
                 which
                 divides
                 it
                 from
                 Asia
                 ;
                 on
                 the
                 South
                 with
                 some
                 part
                 of
                 
                   Terra
                   Australis
                   incognita
                
                 ,
                 from
                 which
                 it
                 is
                 separated
                 by
                 a
                 long
                 ,
                 but
                 narrow
                 Strait
                 ,
                 called
                 the
                 Straits
                 of
                 Magellan
                 ;
                 the
                 North
                 bounds
                 of
                 it
                 hither
                 to
                 not
                 so
                 well
                 discovered
                 ,
                 as
                 that
                 we
                 can
                 certainly
                 affirm
                 it
                 to
                 be
                 Island
                 or
                 Continent
                 .
              
               
                 It
                 is
                 called
                 by
                 some
                 and
                 that
                 most
                 aptly
                 ,
                 The
                 new
                 World
                 ;
                 New
                 for
                 the
                 late
                 discovery
                 ,
                 and
                 World
                 for
                 the
                 vast
                 greatness
                 of
                 it
                 .
                 The
                 whole
                 is
                 naturally
                 divided
                 into
                 two
                 great
                 Peninsules
                 ,
                 whereof
                 that
                 towards
                 the
                 North
                 is
                 called
                 Mexicana
                 .
                 That
                 towards
                 the
                 South
                 hath
                 the
                 name
                 of
                 Peruana
                 :
                 the
                 Isthmus
                 which
                 joyneth
                 these
                 two
                 
                 together
                 is
                 very
                 long
                 ,
                 but
                 narrow
                 in
                 some
                 places
                 not
                 above
                 120
                 miles
                 from
                 Sea
                 to
                 Sea
                 ,
                 in
                 many
                 not
                 above
                 seventeen
                 .
              
               
                 The
                 Northern
                 Peninsula
                 called
                 Mexicana
                 ,
                 may
                 be
                 most
                 properly
                 divided
                 into
                 the
                 Continent
                 and
                 Islands
                 :
                 The
                 Continent
                 again
                 into
                 the
                 several
                 Provinces
                 of
                 1.
                 
                 
                   Estotiland
                   ,
                   2.
                   
                   Nova
                   Francia
                   ,
                   3.
                   
                   Virginia
                   ,
                   4.
                   
                   Florida
                   ,
                   5.
                   
                   California
                   ,
                   6.
                   
                   Nova
                   Gallicia
                   ,
                   7.
                   
                   Nova
                   Hispania
                   ,
                   8.
                   
                   Guntimala
                   .
                
                 The
                 Southern
                 Peninsula
                 called
                 Peruana
                 ,
                 taking
                 in
                 some
                 part
                 of
                 the
                 Isthmus
                 ,
                 hath
                 on
                 the
                 Continent
                 the
                 Provinces
                 of
                 1.
                 
                 
                   Castella
                   Aurea
                   ,
                   2.
                   
                   Nova
                   Granada
                   ,
                   3.
                   
                   Peru
                   ,
                   4.
                   
                   Chile
                   ,
                   5.
                   
                   Paraguay
                   ,
                   6.
                   
                   Brasil
                   ,
                   7.
                   
                   Guiana
                   ,
                
                 and
                 8.
                 
                 Paria
                 .
                 The
                 Islands
                 which
                 belong
                 to
                 both
                 ,
                 are
                 dispersed
                 either
                 in
                 the
                 Southern
                 Ocean
                 called
                 
                   Mare
                   del
                   Zur
                
                 ,
                 where
                 there
                 is
                 not
                 any
                 one
                 of
                 Note
                 but
                 those
                 called
                 
                   Los
                   Ladrones
                
                 and
                 the
                 Islands
                 of
                 Solomon
                 .
                 Or
                 in
                 the
                 Northern
                 Ocean
                 called
                 
                   Mare
                   del
                   Noords
                
                 ,
                 reduced
                 unto
                 the
                 
                   Caribes
                   ,
                   Porto-Rico
                   ,
                   Hispaniola
                   ,
                   Cuba
                
                 and
                 Iamaica
                 .
                 And
                 thus
                 much
                 concerning
                 the
                 real
                 and
                 known
                 parts
                 of
                 the
                 Terrestrial
                 Globe
                 .
              
            
             
               
                 CHAP.
                 XV.
                 
              
               
                 
                   Of
                   the
                   Description
                   of
                   the
                   Terrestrial
                   Globe
                   by
                   Maps
                   Vniversal
                   and
                   Particular
                   .
                
              
               
                 HItherto
                 we
                 have
                 spoken
                 of
                 the
                 true
                 and
                 real
                 Terrestrial
                 Globe
                 ,
                 and
                 of
                 the
                 measure
                 thereof
                 by
                 Circles
                 ,
                 Zones
                 ,
                 and
                 Climates
                 ,
                 as
                 it
                 is
                 usually
                 represented
                 by
                 a
                 Sphere
                 or
                 Globe
                 ;
                 which
                 must
                 be
                 confessed
                 to
                 be
                 the
                 nearest
                 and
                 the
                 most
                 ▪
                 commensurable
                 to
                 nature
                 :
                 Yet
                 it
                 may
                 also
                 be
                 
                 described
                 upon
                 a
                 plain
                 ,
                 in
                 whole
                 or
                 in
                 part
                 many
                 several
                 ways
                 :
                 But
                 those
                 which
                 are
                 most
                 useful
                 and
                 artificial
                 are
                 these
                 two
                 ,
                 by
                 Parallelogram
                 and
                 by
                 Planisphere
                 .
              
               
                 2.
                 
                 The
                 description
                 thereof
                 by
                 Parallelogram
                 is
                 thus
                 ,
                 the
                 Parallelogram
                 is
                 divided
                 in
                 the
                 midst
                 by
                 a
                 line
                 drawn
                 from
                 North
                 to
                 South
                 ,
                 passing
                 by
                 the
                 Azores
                 or
                 Canaries
                 for
                 the
                 great
                 Meridian
                 .
                 Cross
                 to
                 this
                 and
                 at
                 eight
                 Angles
                 ,
                 another
                 line
                 is
                 drawn
                 from
                 East
                 to
                 West
                 for
                 the
                 AEquator
                 ;
                 then
                 two
                 parallels
                 to
                 each
                 to
                 comprehend
                 the
                 figure
                 ,
                 in
                 the
                 squares
                 whereof
                 there
                 are
                 set
                 down
                 four
                 parts
                 of
                 the
                 world
                 rather
                 than
                 the
                 whole
                 :
                 And
                 this
                 way
                 of
                 description
                 though
                 not
                 exact
                 or
                 near
                 to
                 the
                 natural
                 ,
                 hath
                 yet
                 been
                 followed
                 by
                 such
                 as
                 ought
                 still
                 to
                 be
                 accounted
                 excellent
                 ,
                 and
                 is
                 the
                 form
                 of
                 our
                 plain
                 Charts
                 ,
                 and
                 in
                 places
                 near
                 the
                 AEquinoctial
                 may
                 be
                 used
                 without
                 committing
                 any
                 great
                 error
                 ;
                 because
                 the
                 Meridians
                 about
                 the
                 AEquinoctial
                 are
                 equi-distant
                 ,
                 but
                 as
                 they
                 draw
                 up
                 towards
                 the
                 Pole
                 ,
                 they
                 do
                 upon
                 the
                 Globe
                 come
                 nearer
                 and
                 nearer
                 together
                 ,
                 to
                 shew
                 that
                 their
                 distance
                 is
                 proportionably
                 diminished
                 till
                 it
                 come
                 to
                 a
                 concurrence
                 ,
                 and
                 answerably
                 the
                 Parallels
                 as
                 they
                 are
                 deeper
                 in
                 latitude
                 ,
                 so
                 they
                 grow
                 less
                 and
                 less
                 with
                 the
                 Sphere
                 ;
                 so
                 that
                 at
                 60
                 degrees
                 ,
                 the
                 Equinoctial
                 is
                 double
                 to
                 the
                 parallel
                 of
                 Latitude
                 ,
                 and
                 so
                 proportionably
                 of
                 the
                 rest
                 .
              
               
                 3.
                 
                 Hence
                 it
                 followeth
                 ,
                 that
                 if
                 the
                 picture
                 of
                 the
                 earth
                 be
                 drawn
                 upon
                 a
                 Parallelogram
                 ,
                 so
                 that
                 the
                 Meridians
                 be
                 equally
                 distant
                 throughout
                 ,
                 and
                 the
                 Parallels
                 equally
                 extended
                 ,
                 the
                 Parellel
                 of
                 60
                 degrees
                 shall
                 be
                 as
                 great
                 as
                 the
                 line
                 of
                 the
                 AEquator
                 it self
                 is
                 ,
                 and
                 he
                 that
                 coasteth
                 about
                 the
                 world
                 
                 in
                 the
                 latitude
                 of
                 60
                 degrees
                 ,
                 shall
                 have
                 as
                 far
                 to
                 go
                 by
                 this
                 Map
                 ,
                 as
                 he
                 that
                 doth
                 it
                 in
                 the
                 AEquator
                 ,
                 though
                 the
                 way
                 be
                 but
                 half
                 as
                 long
                 .
                 For
                 the
                 longitude
                 of
                 the
                 Earth
                 in
                 the
                 AEquator
                 it self
                 ,
                 is
                 21600
                 ;
                 but
                 in
                 the
                 Parallel
                 of
                 60
                 but
                 10800
                 miles
                 .
                 So
                 two
                 Cities
                 under
                 the
                 same
                 parallel
                 of
                 60
                 ,
                 shall
                 be
                 of
                 equal
                 Longitude
                 to
                 other
                 two
                 under
                 the
                 Line
                 ,
                 and
                 yet
                 the
                 first
                 two
                 shall
                 be
                 but
                 50
                 ,
                 the
                 other
                 two
                 an
                 hundred
                 miles
                 distant
                 .
                 So
                 two
                 Ships
                 departing
                 from
                 the
                 AEquator
                 at
                 60
                 miles
                 distance
                 ,
                 and
                 coming
                 up
                 to
                 the
                 Parallel
                 of
                 60
                 ,
                 shall
                 be
                 thirty
                 miles
                 nearer
                 ,
                 and
                 yet
                 each
                 of
                 them
                 keep
                 the
                 same
                 Meridians
                 and
                 sail
                 by
                 this
                 Card
                 upon
                 the
                 very
                 points
                 of
                 the
                 Compass
                 at
                 which
                 they
                 set
                 forth
                 .
                 This
                 was
                 complained
                 of
                 by
                 
                   Martin
                   Cortez
                
                 and
                 others
                 ,
                 and
                 the
                 learned
                 Mercator
                 considering
                 well
                 of
                 it
                 ,
                 caused
                 the
                 degrees
                 of
                 the
                 Parallel
                 to
                 increase
                 by
                 a
                 proportion
                 towards
                 the
                 Pole.
                 The
                 Mathematical
                 Generation
                 whereof
                 ,
                 Mr.
                 Wright
                 in
                 the
                 second
                 Chapter
                 of
                 his
                 
                   Correction
                   of
                   Errors
                   in
                   Navigation
                
                 ,
                 hath
                 sought
                 by
                 the
                 inscription
                 of
                 a
                 Planisphere
                 into
                 a
                 Concave
                 Cylinder
                 .
                 And
                 this
                 description
                 of
                 the
                 Earth
                 upon
                 a
                 Parallelogram
                 ,
                 may
                 indeed
                 be
                 so
                 ordered
                 by
                 Art
                 ,
                 as
                 to
                 give
                 a
                 true
                 account
                 of
                 the
                 scituation
                 and
                 distance
                 of
                 the
                 parts
                 ,
                 but
                 cannot
                 be
                 fitted
                 to
                 represent
                 the
                 figure
                 of
                 the
                 whole
                 .
              
               
                 4.
                 
                 The
                 description
                 therefore
                 of
                 the
                 whole
                 by
                 Planisphere
                 is
                 much
                 better
                 ,
                 because
                 it
                 represents
                 the
                 face
                 of
                 the
                 Earth
                 upon
                 a
                 plain
                 ,
                 in
                 its
                 own
                 proper
                 Spherical
                 Figure
                 as
                 upon
                 the
                 Globe
                 it self
                 .
                 This
                 description
                 cannot
                 well
                 be
                 contrived
                 upon
                 so
                 few
                 as
                 one
                 Circle
                 or
                 more
                 than
                 two
                 .
              
               
                 Suppose
                 then
                 the
                 Globe
                 to
                 be
                 divided
                 into
                 
                 two
                 equal
                 parts
                 or
                 Hemispheres
                 ,
                 which
                 cannot
                 be
                 done
                 but
                 by
                 a
                 great
                 Circle
                 :
                 And
                 therefore
                 it
                 must
                 be
                 done
                 by
                 the
                 AEquator
                 or
                 Meridian
                 (
                 for
                 the
                 Colure
                 is
                 all
                 one
                 with
                 the
                 Meridian
                 )
                 the
                 Horizon
                 cannot
                 fix
                 ,
                 and
                 the
                 Zodiack
                 hath
                 nothing
                 to
                 do
                 here
                 .
              
               
                 5.
                 
                 Suppose
                 then
                 the
                 Globe
                 to
                 be
                 flatted
                 upon
                 the
                 plain
                 of
                 the
                 AEquator
                 ,
                 and
                 you
                 have
                 the
                 first
                 way
                 of
                 projection
                 dividing
                 the
                 Globe
                 into
                 the
                 North
                 and
                 South
                 Hemispheres
                 .
              
               
                 In
                 this
                 projection
                 the
                 Pole
                 is
                 the
                 Centre
                 ,
                 the
                 AEquator
                 is
                 the
                 Circumference
                 divided
                 into
                 360
                 degrees
                 of
                 Longitude
                 ,
                 the
                 Paralles
                 are
                 whole
                 Circles
                 ,
                 the
                 Meridians
                 are
                 streight
                 lines
                 ,
                 the
                 Parallels
                 are
                 Parallels
                 indeed
                 ,
                 and
                 the
                 Meridians
                 equi-distantly
                 concur
                 ,
                 and
                 therefore
                 all
                 the
                 degrees
                 are
                 equal
                 .
                 After
                 this
                 way
                 of
                 projection
                 ,
                 Ptolemy
                 describes
                 that
                 part
                 of
                 the
                 habitable
                 world
                 which
                 was
                 discovered
                 to
                 his
                 time
                 .
              
               
                 6.
                 
                 Suppose
                 the
                 Globe
                 to
                 be
                 flatted
                 upon
                 the
                 plain
                 of
                 the
                 Meridian
                 ,
                 and
                 you
                 have
                 the
                 other
                 way
                 of
                 projection
                 ;
                 the
                 AEquator
                 here
                 is
                 a
                 streight
                 line
                 ,
                 the
                 great
                 Meridian
                 a
                 whole
                 Circle
                 ,
                 in
                 this
                 Section
                 the
                 Meridians
                 do
                 not
                 equi-distantly
                 concur
                 ,
                 the
                 Parallels
                 are
                 not
                 Parallels
                 indeed
                 ,
                 and
                 therefore
                 the
                 degrees
                 are
                 all
                 unequal
                 .
              
               
                 However
                 ,
                 this
                 latter
                 way
                 is
                 that
                 which
                 is
                 now
                 most
                 and
                 indeed
                 altogether
                 in
                 use
                 .
              
               
                 7.
                 
                 Particular
                 Maps
                 are
                 but
                 limbs
                 of
                 the
                 Globe
                 ,
                 and
                 therefore
                 though
                 they
                 are
                 drawn
                 asunder
                 ,
                 yet
                 are
                 they
                 still
                 to
                 be
                 done
                 with
                 that
                 proportion
                 ,
                 as
                 a
                 remembring
                 eye
                 may
                 suddenly
                 acknowledge
                 ,
                 and
                 joyn
                 them
                 to
                 the
                 whole
                 Body
                 .
              
               
               
                 The
                 Projection
                 is
                 most
                 commonly
                 upon
                 a
                 Parallelogram
                 ,
                 in
                 which
                 the
                 Latitude
                 is
                 to
                 be
                 expressed
                 by
                 Paralles
                 from
                 North
                 to
                 South
                 ,
                 and
                 the
                 Longtitude
                 by
                 Meridians
                 from
                 West
                 to
                 East
                 at
                 10
                 or
                 15
                 degrees
                 distance
                 ,
                 as
                 you
                 please
                 ,
                 and
                 may
                 be
                 drawn
                 either
                 by
                 circle
                 or
                 right
                 Lines
                 ;
                 but
                 if
                 they
                 be
                 right
                 Lines
                 ,
                 the
                 Meridians
                 are
                 not
                 to
                 be
                 drawn
                 parallel
                 ,
                 but
                 inclining
                 and
                 concurring
                 ,
                 to
                 shew
                 the
                 nature
                 of
                 the
                 whole
                 ,
                 whereof
                 they
                 are
                 such
                 parts
                 .
                 For
                 the
                 Graduation
                 ;
                 the
                 degrees
                 of
                 Longitude
                 are
                 most
                 commonly
                 divided
                 upon
                 the
                 North
                 and
                 South
                 sides
                 of
                 the
                 Parallelogram
                 ;
                 the
                 degrees
                 of
                 Latitude
                 upon
                 the
                 East
                 and
                 West
                 sides
                 ,
                 or
                 otherwise
                 upon
                 the
                 most
                 Eastern
                 or
                 Western
                 Meridian
                 of
                 the
                 Map
                 ,
                 within
                 the
                 square
                 .
                 But
                 it
                 hath
                 seemed
                 good
                 to
                 some
                 in
                 these
                 particular
                 descriptions
                 to
                 make
                 no
                 graduation
                 or
                 projection
                 at
                 all
                 ;
                 but
                 to
                 put
                 the
                 matter
                 off
                 to
                 a
                 scale
                 of
                 Miles
                 ,
                 and
                 leave
                 the
                 rest
                 to
                 be
                 believed
                 .
              
               
                 The
                 difference
                 of
                 Miles
                 in
                 several
                 Countries
                 is
                 great
                 ,
                 but
                 it
                 will
                 be
                 enough
                 to
                 know
                 that
                 the
                 Italian
                 and
                 English
                 ,
                 are
                 reckoned
                 for
                 all
                 one
                 ,
                 and
                 four
                 of
                 these
                 do
                 make
                 a
                 German
                 Mile
                 ;
                 two
                 a
                 French
                 League
                 .
                 The
                 Swedish
                 or
                 Danish
                 Mile
                 consisteth
                 of
                 5
                 Miles
                 English
                 and
                 somewhat
                 more
                 .
                 Sixty
                 common
                 English
                 and
                 Italian
                 Miles
                 answer
                 to
                 a
                 degree
                 of
                 a
                 great
                 Circle
                 .
              
               
                 Now
                 as
                 the
                 Miles
                 of
                 several
                 Countries
                 do
                 very
                 much
                 differ
                 ,
                 so
                 those
                 of
                 the
                 same
                 do
                 not
                 very
                 much
                 agree
                 :
                 and
                 therefore
                 the
                 scales
                 are
                 commonly
                 written
                 upon
                 with
                 
                   Magna
                   ,
                   Mediocria
                
                 and
                 Parva
                 ,
                 to
                 shew
                 the
                 difference
                 .
                 In
                 some
                 Maps
                 you
                 shall
                 find
                 the
                 Miles
                 thus
                 hiddenly
                 set
                 down
                 ,
                 and
                 the
                 meaning
                 is
                 ,
                 that
                 you
                 should
                 measure
                 the
                 
                 
                   Milliaria
                   magna
                
                 upon
                 the
                 lowermost
                 Line
                 ,
                 the
                 Parva
                 upon
                 the
                 uppermost
                 ,
                 and
                 the
                 Mediocria
                 upon
                 the
                 middlemost
                 .
              
               
                 
                   Scala
                   Milliarium
                   .
                
                 
                   
                
                 
                   The
                   use
                   of
                   the
                   Scale
                   is
                   for
                   the
                   measuring
                   the
                   distances
                   of
                   places
                   in
                   the
                   Map
                   ,
                   by
                   setting
                   one
                   foot
                   of
                   your
                   Compasses
                   in
                   the
                   little
                   circle
                   representing
                   one
                   place
                   ,
                   and
                   the
                   other
                   foot
                   in
                   the
                   like
                   little
                   circle
                   representing
                   another
                   ,
                   the
                   Compasses
                   kept
                   at
                   that
                   distance
                   being
                   applied
                   to
                   the
                   Scale
                   ,
                   will
                   shew
                   the
                   number
                   of
                   great
                   or
                   middle
                   Miles
                   according
                   as
                   the
                   inhabitants
                   of
                   those
                   places
                   are
                   known
                   to
                   reckon
                   .
                
              
               
                 
                   Soli
                   Deo
                   Gloria
                   .
                
                 
                 
                   
                     
                       A
                       View
                       of
                       the
                       more
                       Notable
                       Epochae
                    
                     
                       
                         Epochae
                         .
                      
                       
                         Years
                         of
                         the
                         Julian
                         Period
                         .
                      
                       
                         Months
                      
                    
                     
                       
                         The
                         Julian
                         Period
                      
                       
                         1
                      
                       
                         Ian.
                         1
                      
                    
                     
                       
                         Creation
                         of
                         the
                         World
                      
                       
                         765
                      
                       
                         Ian.
                         1
                      
                    
                     
                       
                         AEra
                         of
                         the
                         Olympiades
                      
                       
                         3938
                      
                       
                         Iuly
                         8
                      
                    
                     
                       
                         The
                         building
                         of
                         Rome
                      
                       
                         4961
                      
                       
                         Ap.
                         21
                      
                    
                     
                       
                         Epochae
                         of
                         Nabonasser
                      
                       
                         3667
                      
                       
                         Feb.
                         26
                      
                    
                     
                       
                         The
                         beginning
                         of
                         Metons
                         Cyrcle
                         .
                      
                       
                         4281
                      
                       
                         Iune
                         26
                      
                    
                     
                       
                         The
                         beginning
                         of
                         the
                         periods
                         of
                         Calippus
                      
                       
                         4384
                      
                       
                         Iune
                         28
                      
                    
                     
                       
                         The
                         Death
                         of
                         Alexander
                         the
                         great
                      
                       
                         4390
                      
                       
                         No.
                         12
                      
                    
                     
                       
                         AEra
                         of
                         the
                         Caldees
                      
                       
                         4403
                      
                       
                         Oct.
                         15
                      
                    
                     
                       
                         The
                         AEra
                         of
                         Dionysrus
                      
                       
                         4429
                      
                       
                         Mar.
                         25
                      
                    
                  
                   
                     
                       
                         The
                         beginning
                         of
                         the
                         Christian
                         AEra
                         falls
                         in
                         the
                         4713
                         year
                         of
                         the
                         Julian
                         Period
                         .
                      
                       
                         Years
                         of
                         Christ
                      
                       
                         Month
                      
                    
                     
                       
                         The
                         Dioclesian
                         AEra
                      
                       
                         284
                      
                       
                         Aug.
                         29
                      
                    
                     
                       
                         The
                         Turkish
                         AEra
                         or
                         Hegyra
                      
                       
                         622
                      
                       
                         Iuly
                         16
                      
                    
                     
                       
                         The
                         Persian
                         AEra
                         from
                         Iesdagird
                      
                       
                         632
                      
                       
                         Iune
                         16
                      
                    
                     
                       
                         The
                         AEra
                         from
                         the
                         Persian
                         Sultan
                      
                       
                         1079
                      
                       
                         Mar.
                         14
                      
                    
                  
                   
                     
                       Days
                       in
                       the
                       Year
                       of
                    
                     
                       
                         Julian
                         Accompt
                      
                       
                         AEgypt
                         and
                         Persian
                         Accompt
                      
                    
                     
                       
                         1
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         365
                      
                       
                         2
                      
                       
                         5
                      
                       
                         0
                      
                       
                          
                      
                       
                         1
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         365
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                    
                     
                       
                         2
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         730
                      
                       
                         5
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         2
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         730
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                    
                     
                       
                         3
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         1095
                      
                       
                         7
                      
                       
                         5
                      
                       
                         0
                      
                       
                          
                      
                       
                         3
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         1095
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                    
                     
                       
                         4
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         1461
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         4
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         1460
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                    
                     
                       
                         5
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         1826
                      
                       
                         2
                      
                       
                         5
                      
                       
                         0
                      
                       
                          
                      
                       
                         5
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         1825
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                    
                     
                       
                         6
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         2191
                      
                       
                         5
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         6
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         2190
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                    
                     
                       
                         7
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         2556
                      
                       
                         7
                      
                       
                         5
                      
                       
                         0
                      
                       
                          
                      
                       
                         7
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         2555
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                    
                     
                       
                         8
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         2922
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         8
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         2920
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                    
                     
                       
                         9
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         3287
                      
                       
                         2
                      
                       
                         5
                      
                       
                         0
                      
                       
                          
                      
                       
                         9
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         3285
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                    
                     
                       
                         10
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         3652
                      
                       
                         5
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         10
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                       
                          
                      
                       
                         3650
                      
                       
                         0
                      
                       
                         0
                      
                       
                         0
                      
                    
                  
                   
                     
                     
                       
                         Days
                         in
                         Julian
                         Months
                      
                       
                         Days
                         in
                         AEgyptian
                         Months
                      
                       
                         Days
                         in
                         Persian
                         Months
                      
                    
                     
                       
                         Comon
                      
                       
                         Bissex
                      
                       
                         Thoth
                         30
                      
                       
                         Pharvadin
                         30
                      
                    
                     
                       
                         Ianuary
                         31
                      
                       
                         30
                      
                       
                         Paophi
                         60
                      
                       
                         Aripehast
                         60
                      
                    
                     
                       
                         February
                         59
                      
                       
                         60
                      
                       
                         Athyr
                         90
                      
                       
                         Chortat
                         90
                      
                    
                     
                       
                         March
                         90
                      
                       
                         91
                      
                       
                         Chaeae
                         120
                      
                       
                         Tirma
                         120
                      
                    
                     
                       
                         April
                         120
                      
                       
                         121
                      
                       
                         Tybi
                         150
                      
                       
                         Mertat
                         150
                      
                    
                     
                       
                         May
                         151
                      
                       
                         152
                      
                       
                         Michir
                         180
                      
                       
                         Sachriur
                         180
                      
                    
                     
                       
                         Iune
                         181
                      
                       
                         182
                      
                       
                         Phamenoth
                         210
                      
                       
                         Macherma
                         210
                      
                    
                     
                       
                         Iuly
                         212
                      
                       
                         213
                      
                       
                         Pharmuthi
                         ;
                         240
                      
                       
                         Apenina
                         Wahak
                         245
                      
                    
                     
                       
                         August
                         243
                      
                       
                         244
                      
                       
                         Pachon
                         270
                      
                    
                     
                       
                         September
                         273
                      
                       
                         274
                      
                       
                         Payny
                         300
                      
                       
                         Aderma
                         275
                      
                    
                     
                       
                         October
                         304
                      
                       
                         305
                      
                       
                         Ephephi
                         330
                      
                       
                         Dima
                         305
                      
                    
                     
                       
                         November
                         334
                      
                       
                         335
                      
                       
                         Mesori
                         330
                      
                       
                         Pechmam
                         335
                      
                    
                     
                       
                         December
                         365
                      
                       
                         366
                      
                       
                         Epagomena
                         365
                      
                       
                         Aphander
                         365
                      
                    
                  
                   
                     
                       
                         Days
                         in
                         Turkish
                         or
                         Arabical
                         Years
                      
                       
                         Days
                         in
                         Turkish
                         Months
                      
                    
                     
                       
                         1
                      
                       
                         354
                      
                       
                          
                      
                       
                         Muharran
                         30
                      
                    
                     
                       
                         2
                      
                       
                         709
                      
                       
                          
                      
                       
                         Sapher
                         59
                      
                    
                     
                       
                         3
                      
                       
                         .1063
                      
                       
                          
                      
                       
                         Rabie
                         1.
                         89
                      
                    
                     
                       
                         4
                      
                       
                         .1417
                      
                       
                          
                      
                       
                         Rabie
                         2.
                         118
                      
                    
                     
                       
                         5
                      
                       
                         .1772
                      
                       
                          
                      
                       
                         Giumadi
                         1.
                         148
                      
                    
                     
                       
                         6
                      
                       
                         .2126
                      
                       
                          
                      
                       
                         Giumadi
                         2.
                         177
                      
                    
                     
                       
                         7
                      
                       
                         .2480
                      
                       
                          
                      
                       
                         Regeb
                         207
                      
                    
                     
                       
                         8
                      
                       
                         .2835
                      
                       
                          
                      
                       
                         Sahahen
                         236
                      
                    
                     
                       
                         9
                      
                       
                         .3189
                      
                       
                          
                      
                       
                         Ramaddan
                         266
                      
                    
                     
                       
                         10
                      
                       
                         .3543
                      
                       
                          
                      
                       
                         Scheval
                         295
                      
                    
                     
                       
                         11
                      
                       
                         .3898
                      
                       
                          
                      
                       
                         Dulkadati
                         325
                      
                    
                     
                       
                         12
                      
                       
                         .4252
                      
                       
                          
                      
                       
                         Dulhajati
                         Dsilhittsche
                         true
                         354
                      
                    
                     
                       
                         13
                      
                       
                         .4607
                      
                       
                          
                      
                    
                     
                       
                         14
                      
                       
                         .4961
                      
                       
                          
                      
                    
                     
                       
                         15
                      
                       
                         .5315
                      
                       
                          
                      
                       
                         In
                         anno
                         Abundanti
                         355
                      
                    
                     
                       
                         16
                      
                       
                         .5670
                      
                       
                          
                      
                    
                     
                       
                         17
                      
                       
                         .6024
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         18
                      
                       
                         .6378
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         19
                      
                       
                         .6733
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         20
                      
                       
                         .7087
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         21
                      
                       
                          
                      
                       
                         7442
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         22
                      
                       
                          
                      
                       
                         7796
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         23
                      
                       
                          
                      
                       
                         8150
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         24
                      
                       
                          
                      
                       
                         8505
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         25
                      
                       
                          
                      
                       
                         8859
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         26
                      
                       
                          
                      
                       
                         9213
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         27
                      
                       
                          
                      
                       
                         9568
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         28
                      
                       
                          
                      
                       
                         9922
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         29
                      
                       
                          
                      
                       
                         10276
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         30
                      
                       
                         0
                      
                       
                         10631
                      
                       
                         0
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         60
                      
                       
                         0
                      
                       
                         21262
                      
                       
                         0
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         90
                      
                       
                         0
                      
                       
                         31893
                      
                       
                         0
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         120
                      
                       
                         0
                      
                       
                         42524
                      
                       
                         0
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         150
                      
                       
                         0
                      
                       
                         53155
                      
                       
                         0
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         180
                      
                       
                         0
                      
                       
                         63786
                      
                       
                         0
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         210
                      
                       
                         0
                      
                       
                         74417
                      
                       
                         0
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         240
                      
                       
                         0
                      
                       
                         05048
                      
                       
                         0
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         270
                      
                       
                         0
                      
                       
                         95679
                      
                       
                         0
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         300
                      
                       
                         0
                      
                       
                         106310
                      
                       
                         0
                      
                       
                          
                      
                       
                          
                      
                    
                  
                   
                     
                     
                       
                          
                      
                       
                         Ianuary
                      
                       
                         February
                      
                       
                         March
                      
                    
                     
                       
                         1
                      
                       
                         3
                      
                       
                         A
                      
                       
                         Circumcis
                         .
                      
                       
                          
                      
                       
                         D
                      
                       
                         Purificat
                      
                       
                         3
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         2
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                         11
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         3
                      
                       
                         11
                      
                       
                         C
                      
                       
                          
                      
                       
                         19
                      
                       
                         F
                      
                       
                          
                      
                       
                         11
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         4
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                       
                         8
                      
                       
                         G
                      
                       
                          
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         5
                      
                       
                         19
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                       
                         19
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         6
                      
                       
                         8
                      
                       
                         F
                      
                       
                         Epiphany
                      
                       
                         16
                      
                       
                         B
                      
                       
                          
                      
                       
                         8
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         7
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                         5
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         8
                      
                       
                         16
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                       
                         16
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         9
                      
                       
                         5
                      
                       
                         B
                      
                       
                          
                      
                       
                         13
                      
                       
                         E
                      
                       
                          
                      
                       
                         5
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         10
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                         2
                      
                       
                         F
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         11
                      
                       
                         13
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                         13
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         12
                      
                       
                         2
                      
                       
                         E
                      
                       
                          
                      
                       
                         10
                      
                       
                         A
                      
                       
                          
                      
                       
                         2
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         13
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         14
                      
                       
                         10
                      
                       
                         G
                      
                       
                          
                      
                       
                         18
                      
                       
                         C
                      
                       
                          
                      
                       
                         10
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         15
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                       
                         7
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         16
                      
                       
                         18
                      
                       
                         B
                      
                       
                          
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                       
                         18
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         17
                      
                       
                         7
                      
                       
                         C
                      
                       
                          
                      
                       
                         15
                      
                       
                         F
                      
                       
                          
                      
                       
                         7
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         18
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                       
                         4
                      
                       
                         G
                      
                       
                          
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         19
                      
                       
                         15
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                       
                         15
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         20
                      
                       
                         4
                      
                       
                         F
                      
                       
                          
                      
                       
                         12
                      
                       
                         B
                      
                       
                          
                      
                       
                         4
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         21
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                         1
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         22
                      
                       
                         12
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                       
                         12
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         23
                      
                       
                         1
                      
                       
                         B
                      
                       
                          
                      
                       
                         9
                      
                       
                         E
                      
                       
                          
                      
                       
                         1
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         24
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         25
                      
                       
                         9
                      
                       
                         D
                      
                       
                         Conv.
                         S.
                         Paul
                      
                       
                         17
                      
                       
                         G
                      
                       
                         S.
                         Matthias
                      
                       
                         9
                      
                       
                         G
                      
                       
                         Anunc
                         .
                      
                    
                     
                       
                         26
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                       
                         6
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         27
                      
                       
                         17
                      
                       
                         F
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                         17
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         28
                      
                       
                         6
                      
                       
                         G
                      
                       
                          
                      
                       
                         14
                      
                       
                         C
                      
                       
                          
                      
                       
                         6
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         29
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         30
                      
                       
                         14
                      
                       
                         B
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                         14
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         31
                      
                       
                         3
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                         3
                      
                       
                         F
                      
                       
                          
                      
                    
                  
                   
                     
                     
                       
                          
                      
                       
                         April
                      
                       
                         May
                      
                       
                         Iune
                      
                    
                     
                       
                         1
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                         11
                      
                       
                         B
                      
                       
                         Phil.
                         &
                         Jac.
                         
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         2
                      
                       
                         11
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                         19
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         3
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                         19
                      
                       
                         D
                      
                       
                          
                      
                       
                         8
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         4
                      
                       
                         19
                      
                       
                         C
                      
                       
                          
                      
                       
                         8
                      
                       
                         E
                      
                       
                          
                      
                       
                         16
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         5
                      
                       
                         8
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                       
                         5
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         6
                      
                       
                         16
                      
                       
                         E
                      
                       
                          
                      
                       
                         16
                      
                       
                         G
                      
                       
                          
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         7
                      
                       
                         5
                      
                       
                         F
                      
                       
                          
                      
                       
                         5
                      
                       
                         A
                      
                       
                          
                      
                       
                         13
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         8
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                         2
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         9
                      
                       
                         13
                      
                       
                         A
                      
                       
                          
                      
                       
                         14
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         10
                      
                       
                         2
                      
                       
                         B
                      
                       
                          
                      
                       
                         2
                      
                       
                         D
                      
                       
                          
                      
                       
                         10
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         11
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         A
                      
                       
                         S.
                         Barnaby
                      
                    
                     
                       
                         12
                      
                       
                         10
                      
                       
                         D
                      
                       
                          
                      
                       
                         10
                      
                       
                         F
                      
                       
                          
                      
                       
                         18
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         13
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                         7
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         14
                      
                       
                         18
                      
                       
                         F
                      
                       
                          
                      
                       
                         18
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         15
                      
                       
                         7
                      
                       
                         G
                      
                       
                          
                      
                       
                         7
                      
                       
                         B
                      
                       
                          
                      
                       
                         15
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         16
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                         4
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         17
                      
                       
                         15
                      
                       
                         B
                      
                       
                          
                      
                       
                         15
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         18
                      
                       
                         4
                      
                       
                         C
                      
                       
                          
                      
                       
                         4
                      
                       
                         E
                      
                       
                          
                      
                       
                         12
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         19
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                       
                         1
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         20
                      
                       
                         12
                      
                       
                         E
                      
                       
                          
                      
                       
                         12
                      
                       
                         G
                      
                       
                          
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         21
                      
                       
                         1
                      
                       
                         F
                      
                       
                          
                      
                       
                         1
                      
                       
                         A
                      
                       
                          
                      
                       
                         9
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         22
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         23
                      
                       
                         9
                      
                       
                         A
                      
                       
                          
                      
                       
                         9
                      
                       
                         C
                      
                       
                          
                      
                       
                         17
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         24
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                       
                         6
                      
                       
                         G
                      
                       
                         S.
                         John
                         B.
                         
                      
                    
                     
                       
                         25
                      
                       
                         17
                      
                       
                         C
                      
                       
                         Mark
                         Evang.
                         
                      
                       
                         17
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         26
                      
                       
                         6
                      
                       
                         D
                      
                       
                          
                      
                       
                         6
                      
                       
                         F
                      
                       
                          
                      
                       
                         14
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         27
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                         3
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         28
                      
                       
                         14
                      
                       
                         F
                      
                       
                          
                      
                       
                         14
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         29
                      
                       
                         5
                      
                       
                         G
                      
                       
                          
                      
                       
                         3
                      
                       
                         B
                      
                       
                          
                      
                       
                         11
                      
                       
                         E
                      
                       
                         Pet.
                         Ap.
                         
                      
                    
                     
                       
                         30
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         31
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                         11
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                  
                   
                     
                     
                       
                          
                      
                       
                         Iuly
                      
                       
                         August
                      
                       
                         September
                      
                    
                     
                       
                         1
                      
                       
                         19
                      
                       
                         G
                      
                       
                          
                      
                       
                         8
                      
                       
                         C
                      
                       
                          
                      
                       
                         16
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         2
                      
                       
                         8
                      
                       
                         A
                      
                       
                          
                      
                       
                         16
                      
                       
                         D
                      
                       
                          
                      
                       
                         5
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         3
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                         5
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         4
                      
                       
                         16
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                       
                         13
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         5
                      
                       
                         5
                      
                       
                         D
                      
                       
                          
                      
                       
                         13
                      
                       
                         G
                      
                       
                          
                      
                       
                         2
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         6
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                       
                         2
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         7
                      
                       
                         13
                      
                       
                         F
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                         10
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         8
                      
                       
                         2
                      
                       
                         G
                      
                       
                          
                      
                       
                         10
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         9
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                       
                         18
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         10
                      
                       
                         10
                      
                       
                         B
                      
                       
                          
                      
                       
                         18
                      
                       
                         E
                      
                       
                          
                      
                       
                         7
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         11
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                         7
                      
                       
                         F
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         12
                      
                       
                         18
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                         15
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         13
                      
                       
                         7
                      
                       
                         E
                      
                       
                          
                      
                       
                         15
                      
                       
                         A
                      
                       
                          
                      
                       
                         4
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         14
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                       
                         4
                      
                       
                         B
                      
                       
                          
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         15
                      
                       
                         15
                      
                       
                         G
                      
                       
                          
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                         12
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         16
                      
                       
                         4
                      
                       
                         A
                      
                       
                          
                      
                       
                         12
                      
                       
                         D
                      
                       
                          
                      
                       
                         1
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         17
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                         1
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         18
                      
                       
                         12
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                       
                         9
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         19
                      
                       
                         1
                      
                       
                         D
                      
                       
                          
                      
                       
                         9
                      
                       
                         G
                      
                       
                          
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         20
                      
                       
                          
                      
                       
                         E
                      
                       
                         Margaret
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                       
                         17
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         21
                      
                       
                         9
                      
                       
                         F
                      
                       
                          
                      
                       
                         17
                      
                       
                         B
                      
                       
                          
                      
                       
                         6
                      
                       
                         E
                      
                       
                         S.
                         Matth
                      
                    
                     
                       
                         22
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                         6
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         23
                      
                       
                         17
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                       
                         14
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         24
                      
                       
                         6
                      
                       
                         B
                      
                       
                          
                      
                       
                         14
                      
                       
                         E
                      
                       
                         Barthol
                         .
                      
                       
                         3
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         25
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                         3
                      
                       
                         F
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         26
                      
                       
                         14
                      
                       
                         D
                      
                       
                          
                      
                       
                         11
                      
                       
                         G
                      
                       
                          
                      
                       
                         11
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         27
                      
                       
                         3
                      
                       
                         E
                      
                       
                          
                      
                       
                         19
                      
                       
                         A
                      
                       
                          
                      
                       
                         19
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         28
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                         8
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         29
                      
                       
                         11
                      
                       
                         G
                      
                       
                          
                      
                       
                         8
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                         S.
                         Mich.
                         
                      
                    
                     
                       
                         30
                      
                       
                         9
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         31
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                  
                   
                     
                     
                       
                          
                      
                       
                         October
                      
                       
                         November
                      
                       
                         December
                      
                    
                     
                       
                         1
                      
                       
                         16
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                         All
                         Saints
                      
                       
                         13
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         2
                      
                       
                         5
                      
                       
                         B
                      
                       
                          
                      
                       
                         13
                      
                       
                         E
                      
                       
                         All
                         Souls
                      
                       
                         2
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         3
                      
                       
                         13
                      
                       
                         C
                      
                       
                          
                      
                       
                         2
                      
                       
                         F
                      
                       
                          
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         4
                      
                       
                         2
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                         10
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         5
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                       
                         10
                      
                       
                         A
                      
                       
                         P.
                         Conspir
                         .
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         6
                      
                       
                         10
                      
                       
                         F
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                         18
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         7
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                         18
                      
                       
                         C
                      
                       
                          
                      
                       
                         7
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         8
                      
                       
                         18
                      
                       
                         A
                      
                       
                          
                      
                       
                         7
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         9
                      
                       
                         7
                      
                       
                         B
                      
                       
                          
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                       
                         15
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         10
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                         15
                      
                       
                         F
                      
                       
                          
                      
                       
                         4
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         11
                      
                       
                         15
                      
                       
                         D
                      
                       
                          
                      
                       
                         4
                      
                       
                         G
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         12
                      
                       
                         4
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                       
                         12
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         13
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                       
                         12
                      
                       
                         B
                      
                       
                          
                      
                       
                         1
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         14
                      
                       
                         12
                      
                       
                         G
                      
                       
                          
                      
                       
                         1
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                    
                     
                       
                         15
                      
                       
                         13
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                          
                      
                       
                         9
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         16
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                         9
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         17
                      
                       
                         9
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                       
                         17
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         18
                      
                       
                          
                      
                       
                         D
                      
                       
                         Luke
                         Evang.
                         
                      
                       
                         17
                      
                       
                         G
                      
                       
                          
                      
                       
                         6
                      
                       
                         B
                      
                       
                          
                      
                    
                     
                       
                         19
                      
                       
                         17
                      
                       
                         E
                      
                       
                          
                      
                       
                         6
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                    
                     
                       
                         20
                      
                       
                         6
                      
                       
                         F
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                          
                      
                       
                         14
                      
                       
                         D
                      
                       
                          
                      
                    
                     
                       
                         21
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                       
                         14
                      
                       
                         C
                      
                       
                          
                      
                       
                         3
                      
                       
                         E
                      
                       
                         S.
                         Thomas
                      
                    
                     
                       
                         22
                      
                       
                         14
                      
                       
                         A
                      
                       
                          
                      
                       
                         3
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         23
                      
                       
                         3
                      
                       
                         B
                      
                       
                          
                      
                       
                          
                      
                       
                         E
                      
                       
                          
                      
                       
                         11
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         24
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                         11
                      
                       
                         F
                      
                       
                          
                      
                       
                         19
                      
                       
                         A
                      
                       
                          
                      
                    
                     
                       
                         25
                      
                       
                         11
                      
                       
                         D
                      
                       
                          
                      
                       
                         19
                      
                       
                         G
                      
                       
                          
                      
                       
                          
                      
                       
                         B
                      
                       
                         Chri.
                         Nat.
                         
                      
                    
                     
                       
                         26
                      
                       
                         19
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                       
                         8
                      
                       
                         C
                      
                       
                         S.
                         Steph.
                         
                      
                    
                     
                       
                         27
                      
                       
                          
                      
                       
                         F
                      
                       
                          
                      
                       
                         8
                      
                       
                         B
                      
                       
                          
                      
                       
                          
                      
                       
                         D
                      
                       
                         S.
                         John
                      
                    
                     
                       
                         28
                      
                       
                         8
                      
                       
                         G
                      
                       
                         Sim.
                         &
                         Jude
                      
                       
                          
                      
                       
                         C
                      
                       
                          
                      
                       
                         16
                      
                       
                         E
                      
                       
                         Innocents
                      
                    
                     
                       
                         29
                      
                       
                          
                      
                       
                         A
                      
                       
                          
                      
                       
                         16
                      
                       
                         D
                      
                       
                          
                      
                       
                         5
                      
                       
                         F
                      
                       
                          
                      
                    
                     
                       
                         30
                      
                       
                         16
                      
                       
                         B
                      
                       
                          
                      
                       
                         5
                      
                       
                         E
                      
                       
                         S.
                         Andrew
                      
                       
                          
                      
                       
                         G
                      
                       
                          
                      
                    
                     
                       
                         31
                      
                       
                         5
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                         13
                      
                       
                         A
                      
                       
                         Sylvester
                      
                    
                  
                   
                   
                     
                       
                          
                      
                       
                         Ianuary
                      
                       
                         February
                      
                       
                         March
                      
                    
                     
                       
                         1
                      
                       
                         *
                      
                       
                         A
                      
                       
                         XXIX
                      
                       
                         D
                      
                       
                         *
                      
                       
                         D
                      
                    
                     
                       
                         2
                      
                       
                         XXIX
                      
                       
                         B
                      
                       
                         XXVIII
                      
                       
                         E
                      
                       
                         XXIX
                      
                       
                         E
                      
                    
                     
                       
                         3
                      
                       
                         XXVIII
                      
                       
                         C
                      
                       
                         XXVII
                      
                       
                         F
                      
                       
                         XXVIII
                      
                       
                         F
                      
                    
                     
                       
                         4
                      
                       
                         XXVII
                      
                       
                         D
                      
                       
                         25.
                         XXVI
                      
                       
                         G
                      
                       
                         XXVII
                      
                       
                         G
                      
                    
                     
                       
                         5
                      
                       
                         XXVI
                      
                       
                         E
                      
                       
                         XXV
                         .
                         XXIV
                      
                       
                         A
                      
                       
                         XXVI
                      
                       
                         A
                      
                    
                     
                       
                         6
                      
                       
                         25.
                         XXV
                      
                       
                         F
                      
                       
                         XXIII
                      
                       
                         B
                      
                       
                         25.
                         XXV
                      
                       
                         B
                      
                    
                     
                       
                         7
                      
                       
                         XXIV
                      
                       
                         G
                      
                       
                         XXII
                      
                       
                         C
                      
                       
                         XXIV
                      
                       
                         C
                      
                    
                     
                       
                         8
                      
                       
                         XXIII
                      
                       
                         A
                      
                       
                         XXI
                      
                       
                         D
                      
                       
                         XXIII
                      
                       
                         D
                      
                    
                     
                       
                         9
                      
                       
                         XXII
                      
                       
                         B
                      
                       
                         XX
                      
                       
                         E
                      
                       
                         XXII
                      
                       
                         E
                      
                    
                     
                       
                         10
                      
                       
                         XXI
                      
                       
                         C
                      
                       
                         XIX
                      
                       
                         F
                      
                       
                         XXI
                      
                       
                         F
                      
                    
                     
                       
                         11
                      
                       
                         XX
                      
                       
                         D
                      
                       
                         XVIII
                      
                       
                         G
                      
                       
                         XX
                      
                       
                         G
                      
                    
                     
                       
                         12
                      
                       
                         XIX
                      
                       
                         E
                      
                       
                         XVII
                      
                       
                         A
                      
                       
                         XIX
                      
                       
                         A
                      
                    
                     
                       
                         13
                      
                       
                         XVIII
                      
                       
                         F
                      
                       
                         XVI
                      
                       
                         B
                      
                       
                         XVIII
                      
                       
                         B
                      
                    
                     
                       
                         14
                      
                       
                         XVII
                      
                       
                         G
                      
                       
                         XV
                      
                       
                         C
                      
                       
                         XVII
                      
                       
                         C
                      
                    
                     
                       
                         15
                      
                       
                         XVI
                      
                       
                         A
                      
                       
                         XIV
                      
                       
                         D
                      
                       
                         XVI
                      
                       
                         D
                      
                    
                     
                       
                         16
                      
                       
                         XV
                      
                       
                         B
                      
                       
                         XIII
                      
                       
                         E
                      
                       
                         XV
                      
                       
                         E
                      
                    
                     
                       
                         17
                      
                       
                         XIV
                      
                       
                         C
                      
                       
                         XII
                      
                       
                         F
                      
                       
                         XIV
                      
                       
                         F
                      
                    
                     
                       
                         18
                      
                       
                         XIII
                      
                       
                         D
                      
                       
                         XI
                      
                       
                         G
                      
                       
                         XIII
                      
                       
                         G
                      
                    
                     
                       
                         19
                      
                       
                         XII
                      
                       
                         E
                      
                       
                         X
                      
                       
                         A
                      
                       
                         XII
                      
                       
                         A
                      
                    
                     
                       
                         20
                      
                       
                         XI
                      
                       
                         F
                      
                       
                         IX
                      
                       
                         B
                      
                       
                         XI
                      
                       
                         B
                      
                    
                     
                       
                         21
                      
                       
                         X
                      
                       
                         G
                      
                       
                         VIII
                      
                       
                         C
                      
                       
                         X
                      
                       
                         C
                      
                    
                     
                       
                         22
                      
                       
                         IX
                      
                       
                         A
                      
                       
                         VII
                      
                       
                         D
                      
                       
                         IX
                      
                       
                         D
                      
                    
                     
                       
                         23
                      
                       
                         VIII
                      
                       
                         B
                      
                       
                         VI
                      
                       
                         E
                      
                       
                         VIII
                      
                       
                         E
                      
                    
                     
                       
                         24
                      
                       
                         VII
                      
                       
                         C
                      
                       
                         V
                      
                       
                         F
                      
                       
                         VII
                      
                       
                         F
                      
                    
                     
                       
                         25
                      
                       
                         VI
                      
                       
                         D
                      
                       
                         IV
                      
                       
                         G
                      
                       
                         VI
                      
                       
                         G
                      
                    
                     
                       
                         26
                      
                       
                         V
                      
                       
                         E
                      
                       
                         III
                      
                       
                         A
                      
                       
                         V
                      
                       
                         A
                      
                    
                     
                       
                         27
                      
                       
                         IV
                      
                       
                         F
                      
                       
                         II
                      
                       
                         B
                      
                       
                         IV
                      
                       
                         B
                      
                    
                     
                       
                         28
                      
                       
                         III
                      
                       
                         G
                      
                       
                         I
                      
                       
                         C
                      
                       
                         III
                      
                       
                         C
                      
                    
                     
                       
                         29
                      
                       
                         II
                      
                       
                         A
                      
                       
                          
                      
                       
                          
                      
                       
                         II
                      
                       
                         D
                      
                    
                     
                       
                         30
                      
                       
                         I
                      
                       
                         B
                      
                       
                          
                      
                       
                          
                      
                       
                         I
                      
                       
                         E
                      
                    
                     
                       
                         31
                      
                       
                         *
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         *
                      
                       
                         F
                      
                    
                  
                   
                     
                     
                       
                          
                      
                       
                         April
                      
                       
                         May
                      
                       
                         Iune
                      
                    
                     
                       
                         1
                      
                       
                         XXIX
                      
                       
                         G
                      
                       
                         XXVIII
                      
                       
                         B
                      
                       
                         XXVII
                      
                       
                         E
                      
                    
                     
                       
                         2
                      
                       
                         XXVIII
                      
                       
                         A
                      
                       
                         XXVII
                      
                       
                         C
                      
                       
                         25.
                         XXVI
                      
                       
                         F
                      
                    
                     
                       
                         3
                      
                       
                         XXVII
                      
                       
                         B
                      
                       
                         XXVI
                      
                       
                         D
                      
                       
                         XXV
                         .
                         XXIV
                      
                       
                         G
                      
                    
                     
                       
                         4
                      
                       
                         25.
                         XXVI
                      
                       
                         C
                      
                       
                         25.
                         XXV
                      
                       
                         E
                      
                       
                         XXIII
                      
                       
                         A
                      
                    
                     
                       
                         5
                      
                       
                         XXV
                         .
                         XXIV
                      
                       
                         D
                      
                       
                         XXIV
                      
                       
                         F
                      
                       
                         XXII
                      
                       
                         B
                      
                    
                     
                       
                         6
                      
                       
                         XXIII
                      
                       
                         E
                      
                       
                         XXIII
                      
                       
                         G
                      
                       
                         XXI
                      
                       
                         C
                      
                    
                     
                       
                         7
                      
                       
                         XXII
                      
                       
                         F
                      
                       
                         XXII
                      
                       
                         A
                      
                       
                         XX
                      
                       
                         D
                      
                    
                     
                       
                         8
                      
                       
                         XXI
                      
                       
                         G
                      
                       
                         XXI
                      
                       
                         B
                      
                       
                         XIX
                      
                       
                         E
                      
                    
                     
                       
                         9
                      
                       
                         XX
                      
                       
                         A
                      
                       
                         XX
                      
                       
                         C
                      
                       
                         XVIII
                      
                       
                         F
                      
                    
                     
                       
                         10
                      
                       
                         XIX
                      
                       
                         B
                      
                       
                         XIX
                      
                       
                         D
                      
                       
                         XVII
                      
                       
                         G
                      
                    
                     
                       
                         11
                      
                       
                         XVIII
                      
                       
                         C
                      
                       
                         XVIII
                      
                       
                         E
                      
                       
                         XVI
                      
                       
                         A
                      
                    
                     
                       
                         12
                      
                       
                         XVII
                      
                       
                         D
                      
                       
                         XVII
                      
                       
                         F
                      
                       
                         XV
                      
                       
                         B
                      
                    
                     
                       
                         13
                      
                       
                         XVI
                      
                       
                         E
                      
                       
                         XVI
                      
                       
                         G
                      
                       
                         XIV
                      
                       
                         C
                      
                    
                     
                       
                         14
                      
                       
                         XV
                      
                       
                         F
                      
                       
                         XV
                      
                       
                         A
                      
                       
                         XIII
                      
                       
                         D
                      
                    
                     
                       
                         15
                      
                       
                         XIV
                      
                       
                         G
                      
                       
                         XIV
                      
                       
                         B
                      
                       
                         XII
                      
                       
                         E
                      
                    
                     
                       
                         16
                      
                       
                         XIII
                      
                       
                         A
                      
                       
                         XIII
                      
                       
                         C
                      
                       
                         XI
                      
                       
                         F
                      
                    
                     
                       
                         17
                      
                       
                         XII
                      
                       
                         B
                      
                       
                         XII
                      
                       
                         D
                      
                       
                         X
                      
                       
                         G
                      
                    
                     
                       
                         18
                      
                       
                         XI
                      
                       
                         C
                      
                       
                         XI
                      
                       
                         E
                      
                       
                         IX
                      
                       
                         A
                      
                    
                     
                       
                         19
                      
                       
                         X
                      
                       
                         D
                      
                       
                         X
                      
                       
                         F
                      
                       
                         VIII
                      
                       
                         B
                      
                    
                     
                       
                         20
                      
                       
                         IX
                      
                       
                         E
                      
                       
                         IX
                      
                       
                         G
                      
                       
                         VII
                      
                       
                         C
                      
                    
                     
                       
                         21
                      
                       
                         VIII
                      
                       
                         F
                      
                       
                         VIII
                      
                       
                         A
                      
                       
                         VI
                      
                       
                         D
                      
                    
                     
                       
                         22
                      
                       
                         VII
                      
                       
                         G
                      
                       
                         VII
                      
                       
                         B
                      
                       
                         V
                      
                       
                         E
                      
                    
                     
                       
                         23
                      
                       
                         VI
                      
                       
                         A
                      
                       
                         VI
                      
                       
                         C
                      
                       
                         IV
                      
                       
                         F
                      
                    
                     
                       
                         24
                      
                       
                         V
                      
                       
                         B
                      
                       
                         V
                      
                       
                         D
                      
                       
                         III
                      
                       
                         G
                      
                    
                     
                       
                         25
                      
                       
                         IV
                      
                       
                         C
                      
                       
                         IV
                      
                       
                         E
                      
                       
                         II
                      
                       
                         A
                      
                    
                     
                       
                         26
                      
                       
                         III
                      
                       
                         D
                      
                       
                         III
                      
                       
                         F
                      
                       
                         I
                      
                       
                         B
                      
                    
                     
                       
                         27
                      
                       
                         II
                      
                       
                         E
                      
                       
                         II
                      
                       
                         G
                      
                       
                         *
                      
                       
                         C
                      
                    
                     
                       
                         28
                      
                       
                         I
                      
                       
                         F
                      
                       
                         I
                      
                       
                         A
                      
                       
                         XXIX
                      
                       
                         D
                      
                    
                     
                       
                         29
                      
                       
                         *
                      
                       
                         G
                      
                       
                         *
                      
                       
                         B
                      
                       
                         XXVIII
                      
                       
                         E
                      
                    
                     
                       
                         30
                      
                       
                         XXIX
                      
                       
                         A
                      
                       
                         XXIX
                      
                       
                         C
                      
                       
                         XXVII
                      
                       
                         F
                      
                    
                     
                       
                         31
                      
                       
                          
                      
                       
                          
                      
                       
                         XXVIII
                      
                       
                         D
                      
                       
                          
                      
                       
                          
                      
                    
                  
                   
                     
                     
                       
                          
                      
                       
                         Iuly
                      
                       
                         August
                      
                       
                         September
                      
                    
                     
                       
                         1
                      
                       
                         XXVI
                      
                       
                         G
                      
                       
                         XXV
                         .
                         XXIV
                      
                       
                         C
                      
                       
                         XXIII
                      
                       
                         F
                      
                    
                     
                       
                         2
                      
                       
                         25.
                         XXV
                      
                       
                         A
                      
                       
                         XXIII
                      
                       
                         D
                      
                       
                         XXII
                      
                       
                         G
                      
                    
                     
                       
                         3
                      
                       
                         XXIV
                      
                       
                         B
                      
                       
                         XXII
                      
                       
                         E
                      
                       
                         XXI
                      
                       
                         A
                      
                    
                     
                       
                         4
                      
                       
                         XXIII
                      
                       
                         C
                      
                       
                         XXI
                      
                       
                         F
                      
                       
                         XX
                      
                       
                         B
                      
                    
                     
                       
                         5
                      
                       
                         XXII
                      
                       
                         D
                      
                       
                         XX
                      
                       
                         G
                      
                       
                         XIX
                      
                       
                         C
                      
                    
                     
                       
                         6
                      
                       
                         XXI
                      
                       
                         E
                      
                       
                         XIX
                      
                       
                         A
                      
                       
                         XVIII
                      
                       
                         D
                      
                    
                     
                       
                         7
                      
                       
                         XX
                      
                       
                         F
                      
                       
                         XVIII
                      
                       
                         B
                      
                       
                         XVII
                      
                       
                         E
                      
                    
                     
                       
                         8
                      
                       
                         XIX
                      
                       
                         G
                      
                       
                         XVII
                      
                       
                         C
                      
                       
                         XVI
                      
                       
                         F
                      
                    
                     
                       
                         9
                      
                       
                         XVIII
                      
                       
                         A
                      
                       
                         XVI
                      
                       
                         D
                      
                       
                         XV
                      
                       
                         G
                      
                    
                     
                       
                         10
                      
                       
                         XVII
                      
                       
                         B
                      
                       
                         XV
                      
                       
                         E
                      
                       
                         XIV
                      
                       
                         A
                      
                    
                     
                       
                         11
                      
                       
                         XVI
                      
                       
                         C
                      
                       
                         XIV
                      
                       
                         F
                      
                       
                         XIII
                      
                       
                         B
                      
                    
                     
                       
                         12
                      
                       
                         XV
                      
                       
                         D
                      
                       
                         XIII
                      
                       
                         G
                      
                       
                         XII
                      
                       
                         C
                      
                    
                     
                       
                         13
                      
                       
                         XIV
                      
                       
                         E
                      
                       
                         XII
                      
                       
                         A
                      
                       
                         XI
                      
                       
                         D
                      
                    
                     
                       
                         14
                      
                       
                         XIII
                      
                       
                         F
                      
                       
                         XI
                      
                       
                         B
                      
                       
                         X
                      
                       
                         E
                      
                    
                     
                       
                         15
                      
                       
                         XII
                      
                       
                         G
                      
                       
                         X
                      
                       
                         C
                      
                       
                         IX
                      
                       
                         F
                      
                    
                     
                       
                         16
                      
                       
                         XI
                      
                       
                         A
                      
                       
                         IX
                      
                       
                         D
                      
                       
                         VIII
                      
                       
                         G
                      
                    
                     
                       
                         17
                      
                       
                         X
                      
                       
                         B
                      
                       
                         VIII
                      
                       
                         E
                      
                       
                         VII
                      
                       
                         A
                      
                    
                     
                       
                         18
                      
                       
                         IX
                      
                       
                         C
                      
                       
                         VII
                      
                       
                         F
                      
                       
                         VI
                      
                       
                         B
                      
                    
                     
                       
                         19
                      
                       
                         VIII
                      
                       
                         D
                      
                       
                         VI
                      
                       
                         G
                      
                       
                         V
                      
                       
                         C
                      
                    
                     
                       
                         20
                      
                       
                         VII
                      
                       
                         E
                      
                       
                         V
                      
                       
                         A
                      
                       
                         IV
                      
                       
                         D
                      
                    
                     
                       
                         21
                      
                       
                         VI
                      
                       
                         F
                      
                       
                         IV
                      
                       
                         B
                      
                       
                         III
                      
                       
                         E
                      
                    
                     
                       
                         22
                      
                       
                         V
                      
                       
                         G
                      
                       
                         III
                      
                       
                         C
                      
                       
                         II
                      
                       
                         F
                      
                    
                     
                       
                         23
                      
                       
                         IV
                      
                       
                         A
                      
                       
                         II
                      
                       
                         D
                      
                       
                         I
                      
                       
                         G
                      
                    
                     
                       
                         24
                      
                       
                         III
                      
                       
                         B
                      
                       
                         I
                      
                       
                         E
                      
                       
                         *
                      
                       
                         A
                      
                    
                     
                       
                         25
                      
                       
                         II
                      
                       
                         C
                      
                       
                         *
                      
                       
                         F
                      
                       
                         XXIX
                      
                       
                         B
                      
                    
                     
                       
                         26
                      
                       
                         I
                      
                       
                         D
                      
                       
                         XXIX
                      
                       
                         G
                      
                       
                         XXVIII
                      
                       
                         C
                      
                    
                     
                       
                         27
                      
                       
                         *
                      
                       
                         E
                      
                       
                         XXVIII
                      
                       
                         A
                      
                       
                         XXVII
                      
                       
                         D
                      
                    
                     
                       
                         28
                      
                       
                         XXIX
                      
                       
                         F
                      
                       
                         XXVII
                      
                       
                         B
                      
                       
                         25.
                         XXVI
                      
                       
                         E
                      
                    
                     
                       
                         29
                      
                       
                         XXVIII
                      
                       
                         G
                      
                       
                         XXVI
                      
                       
                         C
                      
                       
                         XXV
                         .
                         XXIV
                      
                       
                         F
                      
                    
                     
                       
                         30
                      
                       
                         XXVII
                      
                       
                         A
                      
                       
                         25.
                         XXV
                      
                       
                         D
                      
                       
                         XXIII
                      
                       
                         G
                      
                    
                     
                       
                         31
                      
                       
                         25.
                         XXVI
                      
                       
                         B
                      
                       
                         XXIV
                      
                       
                         E
                      
                       
                          
                      
                       
                          
                      
                    
                  
                   
                     
                     
                       
                          
                      
                       
                         October
                      
                       
                          
                      
                       
                         November
                      
                       
                          
                      
                       
                         December
                      
                       
                          
                      
                    
                     
                       
                         1
                      
                       
                         XXII
                      
                       
                         A
                      
                       
                         XXI
                      
                       
                         D
                      
                       
                         XX
                      
                       
                         F
                      
                    
                     
                       
                         2
                      
                       
                         XXI
                      
                       
                         B
                      
                       
                         XX
                      
                       
                         E
                      
                       
                         XIX
                      
                       
                         G
                      
                    
                     
                       
                         3
                      
                       
                         XX
                      
                       
                         C
                      
                       
                         XIX
                      
                       
                         F
                      
                       
                         XVIII
                      
                       
                         A
                      
                    
                     
                       
                         4
                      
                       
                         XIX
                      
                       
                         D
                      
                       
                         XVIII
                      
                       
                         G
                      
                       
                         XVII
                      
                       
                         B
                      
                    
                     
                       
                         5
                      
                       
                         XVIII
                      
                       
                         E
                      
                       
                         XVII
                      
                       
                         A
                      
                       
                         XVI
                      
                       
                         C
                      
                    
                     
                       
                         6
                      
                       
                         XVII
                      
                       
                         F
                      
                       
                         XVI
                      
                       
                         B
                      
                       
                         XV
                      
                       
                         D
                      
                    
                     
                       
                         7
                      
                       
                         XVI
                      
                       
                         G
                      
                       
                         XV
                      
                       
                         C
                      
                       
                         XIV
                      
                       
                         E
                      
                    
                     
                       
                         8
                      
                       
                         XV
                      
                       
                         A
                      
                       
                         XIV
                      
                       
                         D
                      
                       
                         XIII
                      
                       
                         F
                      
                    
                     
                       
                         9
                      
                       
                         XIV
                      
                       
                         B
                      
                       
                         XIII
                      
                       
                         E
                      
                       
                         XII
                      
                       
                         G
                      
                    
                     
                       
                         10
                      
                       
                         XIII
                      
                       
                         C
                      
                       
                         XII
                      
                       
                         F
                      
                       
                         XI
                      
                       
                         A
                      
                    
                     
                       
                         11
                      
                       
                         XII
                      
                       
                         D
                      
                       
                         XI
                      
                       
                         G
                      
                       
                         X
                      
                       
                         B
                      
                    
                     
                       
                         12
                      
                       
                         XI
                      
                       
                         E
                      
                       
                         X
                      
                       
                         A
                      
                       
                         IX
                      
                       
                         C
                      
                    
                     
                       
                         13
                      
                       
                         X
                      
                       
                         F
                      
                       
                         IX
                      
                       
                         B
                      
                       
                         VIII
                      
                       
                         D
                      
                    
                     
                       
                         14
                      
                       
                         IX
                      
                       
                         G
                      
                       
                         VIII
                      
                       
                         C
                      
                       
                         VII
                      
                       
                         E
                      
                    
                     
                       
                         15
                      
                       
                         VIII
                      
                       
                         A
                      
                       
                         VII
                      
                       
                         D
                      
                       
                         VI
                      
                       
                         F
                      
                    
                     
                       
                         16
                      
                       
                         VII
                      
                       
                         B
                      
                       
                         VI
                      
                       
                         E
                      
                       
                         V
                      
                       
                         G
                      
                    
                     
                       
                         17
                      
                       
                         VI
                      
                       
                         C
                      
                       
                         V
                      
                       
                         F
                      
                       
                         IV
                      
                       
                         A
                      
                    
                     
                       
                         18
                      
                       
                         V
                      
                       
                         D
                      
                       
                         IV
                      
                       
                         G
                      
                       
                         III
                      
                       
                         B
                      
                    
                     
                       
                         19
                      
                       
                         IV
                      
                       
                         E
                      
                       
                         III
                      
                       
                         A
                      
                       
                         II
                      
                       
                         C
                      
                    
                     
                       
                         20
                      
                       
                         III
                      
                       
                         F
                      
                       
                         II
                      
                       
                         B
                      
                       
                         I
                      
                       
                         D
                      
                    
                     
                       
                         21
                      
                       
                         II
                      
                       
                         G
                      
                       
                         I
                      
                       
                         C
                      
                       
                         *
                      
                       
                         E
                      
                    
                     
                       
                         22
                      
                       
                         I
                      
                       
                         A
                      
                       
                         *
                      
                       
                         D
                      
                       
                         XXIX
                      
                       
                         F
                      
                    
                     
                       
                         23
                      
                       
                         *
                      
                       
                         B
                      
                       
                         XXIX
                      
                       
                         E
                      
                       
                         XXVIII
                      
                       
                         G
                      
                    
                     
                       
                         24
                      
                       
                         XXIX
                      
                       
                         C
                      
                       
                         XXVIII
                      
                       
                         F
                      
                       
                         XXVII
                      
                       
                         A
                      
                    
                     
                       
                         25
                      
                       
                         XXVIII
                      
                       
                         D
                      
                       
                         XXVII
                      
                       
                         G
                      
                       
                         XXVI
                      
                       
                         B
                      
                    
                     
                       
                         26
                      
                       
                         XXVII
                      
                       
                         E
                      
                       
                         25.
                         XXVI
                      
                       
                         A
                      
                       
                         25.
                         XXV
                      
                       
                         C
                      
                    
                     
                       
                         27
                      
                       
                         XXVI
                      
                       
                         F
                      
                       
                         XXV
                         .
                         XXIV
                      
                       
                         B
                      
                       
                         XXIV
                      
                       
                         D
                      
                    
                     
                       
                         28
                      
                       
                         25.
                         XXV
                      
                       
                         G
                      
                       
                         XXIII
                      
                       
                         C
                      
                       
                         XXIII
                      
                       
                         E
                      
                    
                     
                       
                         29
                      
                       
                         XXIV
                      
                       
                         A
                      
                       
                         XXII
                      
                       
                         D
                      
                       
                         XXII
                      
                       
                         F
                      
                    
                     
                       
                         30
                      
                       
                         XXIII
                      
                       
                         B
                      
                       
                         XXI
                      
                       
                         E
                      
                       
                         XXI
                      
                       
                         G
                      
                    
                     
                       
                         31
                      
                       
                         XXII
                      
                       
                         C
                      
                       
                          
                      
                       
                          
                      
                       
                         XX
                      
                       
                         A
                      
                    
                  
                   
                     
                     
                       A
                       Table
                       shewing
                       the
                       Dominical
                       Letter
                       ,
                       Golden
                       Number
                       and
                       Epact
                       ,
                       according
                       to
                       the
                       Julian
                       account
                       for
                       ever
                       ,
                       and
                       in
                       the
                       Gregorian
                       ,
                       till
                       the
                       Year
                       1700.
                       
                    
                     
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         1672
                      
                       
                         1
                      
                       
                         GF
                      
                       
                         CB
                      
                    
                     
                       
                         1673
                      
                       
                         2
                      
                       
                         E
                      
                       
                         A
                      
                    
                     
                       
                         1674
                      
                       
                         3
                      
                       
                         D
                      
                       
                         G
                      
                    
                     
                       
                         1675
                      
                       
                         4
                      
                       
                         C
                      
                       
                         F
                      
                    
                     
                       
                         1676
                      
                       
                         5
                      
                       
                         BA
                      
                       
                         ED
                      
                    
                     
                       
                         1677
                      
                       
                         6
                      
                       
                         G
                      
                       
                         C
                      
                    
                     
                       
                         1678
                      
                       
                         7
                      
                       
                         F
                      
                       
                         B
                      
                    
                     
                       
                         1679
                      
                       
                         8
                      
                       
                         E
                      
                       
                         A
                      
                    
                     
                       
                         1680
                      
                       
                         9
                      
                       
                         DC
                      
                       
                         GF
                      
                    
                     
                       
                         1681
                      
                       
                         10
                      
                       
                         B
                      
                       
                         E
                      
                    
                     
                       
                         1682
                      
                       
                         11
                      
                       
                         A
                      
                       
                         D
                      
                    
                     
                       
                         1683
                      
                       
                         12
                      
                       
                         G
                      
                       
                         C
                      
                    
                     
                       
                         1684
                      
                       
                         13
                      
                       
                         FE
                      
                       
                         BA
                      
                    
                     
                       
                         1685
                      
                       
                         14
                      
                       
                         D
                      
                       
                         G
                      
                    
                     
                       
                         1686
                      
                       
                         15
                      
                       
                         C
                      
                       
                         F
                      
                    
                     
                       
                         1687
                      
                       
                         16
                      
                       
                         B
                      
                       
                         E
                      
                    
                     
                       
                         1688
                      
                       
                         17
                      
                       
                         AG
                      
                       
                         DC
                      
                    
                     
                       
                         1689
                      
                       
                         18
                      
                       
                         F
                      
                       
                         B
                      
                    
                     
                       
                         1690
                      
                       
                         19
                      
                       
                         E
                      
                       
                         A
                      
                    
                     
                       
                         1691
                      
                       
                         20
                      
                       
                         D
                      
                       
                         G
                      
                    
                     
                       
                         1692
                      
                       
                         21
                      
                       
                         CB
                      
                       
                         FE
                      
                    
                     
                       
                         1693
                      
                       
                         22
                      
                       
                         A
                      
                       
                         D
                      
                    
                     
                       
                         1694
                      
                       
                         23
                      
                       
                         G
                      
                       
                         C
                      
                    
                     
                       
                         1695
                      
                       
                         24
                      
                       
                         F
                      
                       
                         B
                      
                    
                     
                       
                         1696
                      
                       
                         25
                      
                       
                         ED
                      
                       
                         AG
                      
                    
                     
                       
                         1697
                      
                       
                         26
                      
                       
                         C
                      
                       
                         F
                      
                    
                     
                       
                         1698
                      
                       
                         27
                      
                       
                         B
                      
                       
                         E
                      
                    
                     
                       
                         1699
                      
                       
                         28
                      
                       
                         A
                      
                       
                         D
                      
                    
                  
                   
                     
                       
                         Year
                      
                       
                         G
                      
                       
                         Julian
                      
                       
                         Gregor
                         .
                      
                    
                     
                       
                          
                      
                       
                         N
                      
                       
                         Epact
                      
                       
                         Epact
                      
                    
                     
                       
                         1672
                      
                       
                         1
                      
                       
                         11
                      
                       
                         1
                      
                    
                     
                       
                         1673
                      
                       
                         2
                      
                       
                         22
                      
                       
                         12
                      
                    
                     
                       
                         1674
                      
                       
                         3
                      
                       
                         3
                      
                       
                         23
                      
                    
                     
                       
                         1675
                      
                       
                         4
                      
                       
                         14
                      
                       
                         4
                      
                    
                     
                       
                         1676
                      
                       
                         5
                      
                       
                         25
                      
                       
                         15
                      
                    
                     
                       
                         1677
                      
                       
                         6
                      
                       
                         6
                      
                       
                         26
                      
                    
                     
                       
                         1678
                      
                       
                         7
                      
                       
                         17
                      
                       
                         7
                      
                    
                     
                       
                         1679
                      
                       
                         8
                      
                       
                         28
                      
                       
                         18
                      
                    
                     
                       
                         1680
                      
                       
                         9
                      
                       
                         9
                      
                       
                         29
                      
                    
                     
                       
                         1681
                      
                       
                         10
                      
                       
                         20
                      
                       
                         10
                      
                    
                     
                       
                         1682
                      
                       
                         11
                      
                       
                         1
                      
                       
                         21
                      
                    
                     
                       
                         1683
                      
                       
                         12
                      
                       
                         12
                      
                       
                         2
                      
                    
                     
                       
                         1684
                      
                       
                         13
                      
                       
                         23
                      
                       
                         13
                      
                    
                     
                       
                         1685
                      
                       
                         14
                      
                       
                         4
                      
                       
                         24
                      
                    
                     
                       
                         1686
                      
                       
                         15
                      
                       
                         15
                      
                       
                         5
                      
                    
                     
                       
                         1687
                      
                       
                         16
                      
                       
                         26
                      
                       
                         16
                      
                    
                     
                       
                         1688
                      
                       
                         17
                      
                       
                         7
                      
                       
                         17
                      
                    
                     
                       
                         1689
                      
                       
                         18
                      
                       
                         18
                      
                       
                         8
                      
                    
                     
                       
                         1690
                      
                       
                         19
                      
                       
                         29
                      
                       
                         19
                      
                    
                  
                
                 
                   
                     The
                     anticipation
                     of
                     the
                     Gregorian
                     Calender
                     .
                  
                   
                     From
                     5
                     October
                     1582
                     D.
                     10
                  
                   
                     From
                     24
                     Feb.
                     1700
                     D.
                     11
                  
                   
                     From
                     24
                     Feb.
                     1800
                     D.
                     12
                  
                   
                     From
                     24
                     Feb.
                     1900
                     D.
                     13
                  
                   
                     From
                     24
                     Feb.
                     2100
                     D.
                     14
                  
                   
                     From
                     24
                     Feb.
                     2200
                     D.
                     15
                  
                   
                     From
                     24
                     Feb.
                     2320
                     D.
                     16
                  
                
                 
                 
                 
                 
                 
                 
                   
                     
                       
                          
                      
                       
                          
                      
                       
                         III
                      
                       
                         IV
                      
                       
                         V
                      
                       
                         VI
                      
                       
                         VII
                      
                       
                         VIII
                      
                    
                     
                       
                         1
                      
                       
                         P
                      
                       
                         *
                      
                       
                         XI
                      
                       
                         XXII
                      
                       
                         III
                      
                       
                         XIV
                      
                       
                         XXV
                      
                    
                     
                       
                         2
                      
                       
                         N
                      
                       
                         XXIX
                      
                       
                         X
                      
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                    
                     
                       
                         3
                      
                       
                         M
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XX
                      
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIII
                      
                    
                     
                       
                         4
                      
                       
                         H
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         *
                      
                       
                         XI
                      
                       
                         XXII
                      
                    
                     
                       
                         5
                      
                       
                         G
                      
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                       
                         X
                      
                       
                         XXI
                      
                    
                     
                       
                         6
                      
                       
                         F
                      
                       
                         XXV
                      
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XX
                      
                    
                     
                       
                         7
                      
                       
                         E
                      
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XIX
                      
                    
                     
                       
                         8
                      
                       
                         D
                      
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XVIII
                      
                    
                     
                       
                         9
                      
                       
                         C
                      
                       
                         XXII
                      
                       
                         III
                      
                       
                         XIV
                      
                       
                         XXV
                      
                       
                         VI
                      
                       
                         XVII
                      
                    
                     
                       
                         10
                      
                       
                         B
                      
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVI
                      
                    
                     
                       
                         11
                      
                       
                         A
                      
                       
                         XX
                      
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XV
                      
                    
                     
                       
                         12
                      
                       
                         u
                      
                       
                         XIX
                      
                       
                         *
                      
                       
                         XI
                      
                       
                         XXII
                      
                       
                         III
                      
                       
                         XIV
                      
                    
                     
                       
                         13
                      
                       
                         t
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                       
                         X
                      
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIII
                      
                    
                     
                       
                         14
                      
                       
                         s
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XX
                      
                       
                         I
                      
                       
                         XII
                      
                    
                     
                       
                         15
                      
                       
                         r
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         *
                      
                       
                         XI
                      
                    
                     
                       
                         16
                      
                       
                         q
                      
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                       
                         X
                      
                    
                     
                       
                         17
                      
                       
                         p
                      
                       
                         XIV
                      
                       
                         XXV
                      
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                    
                     
                       
                         18
                      
                       
                         n
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                    
                     
                       
                         19
                      
                       
                         m
                      
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                    
                     
                       
                         20
                      
                       
                         l
                      
                       
                         XI
                      
                       
                         XXII
                      
                       
                         III
                      
                       
                         XIV
                      
                       
                         XXV
                      
                       
                         VI
                      
                    
                     
                       
                         21
                      
                       
                         k
                      
                       
                         X
                      
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                       
                         V
                      
                    
                     
                       
                         22
                      
                       
                         i
                      
                       
                         IX
                      
                       
                         XX
                      
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         IV
                      
                    
                     
                       
                         23
                      
                       
                         h
                      
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         *
                      
                       
                         XI
                      
                       
                         XXII
                      
                       
                         III
                      
                    
                     
                       
                         24
                      
                       
                         g
                      
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                       
                         X
                      
                       
                         XXI
                      
                       
                         II
                      
                    
                     
                       
                         25
                      
                       
                         f
                      
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XX
                      
                       
                         I
                      
                    
                     
                       
                         26
                      
                       
                         e
                      
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         *
                      
                    
                     
                       
                         27
                      
                       
                         d
                      
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                    
                     
                       
                         28
                      
                       
                         c
                      
                       
                         III
                      
                       
                         XIV
                      
                       
                         XXV
                      
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                    
                     
                       
                         29
                      
                       
                         b
                      
                       
                         II
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                    
                     
                       
                         30
                      
                       
                         a
                      
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVI
                      
                    
                  
                   
                     
                     
                       
                         IX
                      
                       
                         X
                      
                       
                         XI
                      
                       
                         XII
                      
                       
                         XIII
                      
                       
                         XIV
                      
                       
                         XV
                      
                    
                     
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XX
                      
                       
                         I
                      
                       
                         XII
                      
                    
                     
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         *
                      
                       
                         XI
                      
                    
                     
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                       
                          
                      
                    
                     
                       
                         III
                      
                       
                         XIV
                      
                       
                         XXV
                      
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                    
                     
                       
                         II
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                    
                     
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                    
                     
                       
                         *
                      
                       
                         XI
                      
                       
                         XXII
                      
                       
                         III
                      
                       
                         XIV
                      
                       
                         25
                      
                       
                         VI
                      
                    
                     
                       
                         XXIX
                      
                       
                         X
                      
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                       
                         V
                      
                    
                     
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XX
                      
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         IV
                      
                    
                     
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         *
                      
                       
                         XI
                      
                       
                         XXII
                      
                       
                         III
                      
                    
                     
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                       
                         X
                      
                       
                         XXI
                      
                       
                         II
                      
                    
                     
                       
                         XXV
                      
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XX
                      
                       
                         I
                      
                    
                     
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         *
                      
                    
                     
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                    
                     
                       
                         XXII
                      
                       
                         III
                      
                       
                         XIV
                      
                       
                         XXV
                      
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                    
                     
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVI
                      
                    
                     
                       
                         XX
                      
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVII
                      
                    
                     
                       
                         XIX
                      
                       
                         *
                      
                       
                         XI
                      
                       
                         XXII
                      
                       
                         III
                      
                       
                         XIV
                      
                       
                         25
                      
                    
                     
                       
                         XVIII
                      
                       
                         XXIX
                      
                       
                         X
                      
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                    
                     
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XX
                      
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIII
                      
                    
                     
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         *
                      
                       
                         XI
                      
                       
                         XXII
                      
                    
                     
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                       
                         X
                      
                       
                         XXI
                      
                    
                     
                       
                         XIV
                      
                       
                         XV
                      
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XX
                      
                    
                     
                       
                         XIII
                      
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XIX
                      
                    
                     
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XVIII
                      
                    
                     
                       
                         XI
                      
                       
                         XXII
                      
                       
                         III
                      
                       
                         XIV
                      
                       
                         25
                      
                       
                         VI
                      
                       
                         XVII
                      
                    
                     
                       
                         X
                      
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVI
                      
                    
                     
                       
                         IX
                      
                       
                         XX
                      
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XV
                      
                    
                     
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         *
                      
                       
                         XI
                      
                       
                         XXII
                      
                       
                         III
                      
                       
                         XIV
                      
                    
                     
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         XIX
                      
                       
                         X
                      
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIII
                      
                    
                  
                   
                     
                     
                       
                          
                      
                       
                         XVI
                      
                       
                         XVII
                      
                       
                         XVIII
                      
                       
                         XIX
                      
                       
                         I
                      
                       
                         II
                      
                    
                     
                       
                         P
                      
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VIII
                      
                       
                         XIX
                      
                    
                     
                       
                         N
                      
                       
                         XXII
                      
                       
                         III
                      
                       
                         XIV
                      
                       
                         25
                      
                       
                         VII
                      
                       
                         XVIII
                      
                    
                     
                       
                         M
                      
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                       
                         VI
                      
                       
                         XVII
                      
                    
                     
                       
                         H
                      
                       
                         XX
                      
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         V
                      
                       
                         XVI
                      
                    
                     
                       
                         G
                      
                       
                         XIX
                      
                       
                         *
                      
                       
                         XI
                      
                       
                         XXII
                      
                       
                         IV
                      
                       
                         XV
                      
                    
                     
                       
                         F
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                       
                         X
                      
                       
                         XXI
                      
                       
                         III
                      
                       
                         XIV
                      
                    
                     
                       
                         E
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XX
                      
                       
                         II
                      
                       
                         XIII
                      
                    
                     
                       
                         D
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         I
                      
                       
                         XII
                      
                    
                     
                       
                         C
                      
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         *
                      
                       
                         XI
                      
                    
                     
                       
                         B
                      
                       
                         XIV
                      
                       
                         25
                      
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXIX
                      
                       
                         X
                      
                    
                     
                       
                         A
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                    
                     
                       
                         u
                      
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                    
                     
                       
                         t
                      
                       
                         XI
                      
                       
                         XXII
                      
                       
                         III
                      
                       
                         XIV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                    
                     
                       
                         t
                      
                       
                         X
                      
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIII
                      
                       
                         25
                      
                       
                         VI
                      
                    
                     
                       
                         r
                      
                       
                         IX
                      
                       
                         XX
                      
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIV
                      
                       
                         V
                      
                    
                     
                       
                         q
                      
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         *
                      
                       
                         XI
                      
                       
                         XXIII
                      
                       
                         IV
                      
                    
                     
                       
                         p
                      
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                       
                         X
                      
                       
                         XXII
                      
                       
                         III
                      
                    
                     
                       
                         n
                      
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XXI
                      
                       
                         II
                      
                    
                     
                       
                         m
                      
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XX
                      
                       
                         I
                      
                    
                     
                       
                         l
                      
                       
                         IV
                      
                       
                         XV
                      
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XIX
                      
                       
                         *
                      
                    
                     
                       
                         k
                      
                       
                         III
                      
                       
                         XIV
                      
                       
                         25
                      
                       
                         VI
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                    
                     
                       
                         i
                      
                       
                         II
                      
                       
                         XXIII
                      
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                    
                     
                       
                         h
                      
                       
                         I
                      
                       
                         XII
                      
                       
                         XXIII
                      
                       
                         IV
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                    
                     
                       
                         g
                      
                       
                         *
                      
                       
                         XI
                      
                       
                         XXII
                      
                       
                         III
                      
                       
                         XV
                      
                       
                         XXVI
                      
                    
                     
                       
                         f
                      
                       
                         XXIX
                      
                       
                         X
                      
                       
                         XXI
                      
                       
                         II
                      
                       
                         XIV
                      
                       
                         25
                      
                    
                     
                       
                         e
                      
                       
                         XXVIII
                      
                       
                         IX
                      
                       
                         XX
                      
                       
                         I
                      
                       
                         XIII
                      
                       
                         XXIV
                      
                    
                     
                       
                         d
                      
                       
                         XXVII
                      
                       
                         VIII
                      
                       
                         XIX
                      
                       
                         *
                      
                       
                         XII
                      
                       
                         XXIII
                      
                    
                     
                       
                         c
                      
                       
                         XXVI
                      
                       
                         VII
                      
                       
                         XVIII
                      
                       
                         XXIX
                      
                       
                         XI
                      
                       
                         XXII
                      
                    
                     
                       
                         b
                      
                       
                         25
                      
                       
                         VI
                      
                       
                         XVII
                      
                       
                         XXVIII
                      
                       
                         X
                      
                       
                         XXI
                      
                    
                     
                       
                         a
                      
                       
                         XXIV
                      
                       
                         V
                      
                       
                         XVI
                      
                       
                         XXVII
                      
                       
                         IX
                      
                       
                         XX
                      
                    
                  
                   
                     
                     
                       Anni
                       Christi
                       .
                    
                     
                       
                         N
                      
                       
                         I
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         P
                      
                       
                         320
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         P
                      
                       
                         580
                      
                       
                         Biss.
                         
                      
                       
                          
                      
                    
                     
                       
                         a
                      
                       
                         800
                      
                       
                         Biss.
                         
                      
                       
                         C
                      
                    
                     
                       
                         b
                      
                       
                         1100
                      
                       
                         Biss.
                         
                      
                       
                         C
                      
                    
                     
                       
                         c
                      
                       
                         1400
                      
                       
                         Biss.
                         
                      
                       
                         C
                      
                    
                  
                   
                     
                       Detract
                       is
                       decem
                       diebus
                       .
                    
                     
                       
                         D
                      
                       
                         1484
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         D
                      
                       
                         1600
                      
                       
                         Biss.
                         
                      
                       
                          
                      
                    
                     
                       
                         C
                      
                       
                         1700
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         C
                      
                       
                         1800
                      
                       
                          
                      
                       
                         CC
                      
                    
                     
                       
                         B
                      
                       
                         1900
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         B
                      
                       
                         2000
                      
                       
                         Biss.
                         
                      
                       
                          
                      
                    
                     
                       
                         B
                      
                       
                         2100
                      
                       
                          
                      
                       
                         C
                      
                    
                     
                       
                         A
                      
                       
                         2200
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         u
                      
                       
                         2300
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         A
                      
                       
                         2409
                      
                       
                         Biss.
                         
                      
                       
                         C
                      
                    
                     
                       
                         u
                      
                       
                         2500
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         t
                      
                       
                         2600
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         t
                      
                       
                         2700
                      
                       
                          
                      
                       
                         C
                      
                    
                     
                       
                         t
                      
                       
                         2800
                      
                       
                         Biss.
                         
                      
                       
                          
                      
                    
                     
                       
                         s
                      
                       
                         2900
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         s
                      
                       
                         3000
                      
                       
                          
                      
                       
                         C
                      
                    
                     
                       
                         r
                      
                       
                         3100
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         r
                      
                       
                         3200
                      
                       
                         Biss.
                         
                      
                       
                          
                      
                    
                     
                       
                         r
                      
                       
                         3300
                      
                       
                          
                      
                       
                         C
                      
                    
                     
                       
                         q
                      
                       
                         3400
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         p
                      
                       
                         3500
                      
                       
                          
                      
                       
                          
                      
                    
                  
                   
                     
                       Anni
                       Christi
                       .
                    
                     
                       
                         q
                      
                       
                         3600
                      
                       
                         Biss.
                         
                      
                       
                         C
                      
                    
                     
                       
                         p
                      
                       
                         3700
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         n
                      
                       
                         3800
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         n
                      
                       
                         3900
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         n
                      
                       
                         4000
                      
                       
                         Biss.
                         
                      
                       
                         C
                      
                    
                     
                       
                         m
                      
                       
                         4100
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         l
                      
                       
                         4200
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         l
                      
                       
                         4300
                      
                       
                          
                      
                       
                         CC
                      
                    
                     
                       
                         l
                      
                       
                         4400
                      
                       
                         Biss.
                         
                      
                       
                          
                      
                    
                     
                       
                         k
                      
                       
                         4500
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         k
                      
                       
                         4600
                      
                       
                          
                      
                       
                         C
                      
                    
                     
                       
                         i
                      
                       
                         4700
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         i
                      
                       
                         4800
                      
                       
                         Biss.
                         
                      
                       
                          
                      
                    
                     
                       
                         i
                      
                       
                         4900
                      
                       
                          
                      
                       
                         C
                      
                    
                     
                       
                         h
                      
                       
                         5000
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         g
                      
                       
                         5100
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         h
                      
                       
                         5200
                      
                       
                         Biss.
                         
                      
                       
                         C
                      
                    
                     
                       
                         g
                      
                       
                         5300
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         f
                      
                       
                         5400
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         f
                      
                       
                         5500
                      
                       
                          
                      
                       
                         C
                      
                    
                     
                       
                         f
                      
                       
                         5600
                      
                       
                         Biss.
                         
                      
                       
                          
                      
                    
                     
                       
                         e
                      
                       
                         5700
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         e
                      
                       
                         5800
                      
                       
                          
                      
                       
                         C
                      
                    
                     
                       
                         d
                      
                       
                         5900
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         d
                      
                       
                         6000
                      
                       
                         Biss.
                         
                      
                       
                          
                      
                    
                     
                       
                         d
                      
                       
                         6100
                      
                       
                          
                      
                       
                         C
                      
                    
                     
                       
                         c
                      
                       
                         6200
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         b
                      
                       
                         6300
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                         c
                      
                       
                         6400
                      
                       
                         Biss.
                         
                      
                       
                         C
                      
                    
                     
                       
                         b
                      
                       
                         6500
                      
                       
                          
                      
                       
                          
                      
                    
                  
                   
                     
                     
                       A
                       Table
                       shewing
                       the
                       Dominical
                       Letter
                       both
                       in
                       the
                       Julian
                       and
                       the
                       Gregorian
                       account
                       for
                       ever
                       .
                    
                     
                       
                         Cy.
                         ☉
                      
                       
                         1
                      
                       
                         2
                      
                       
                         3
                      
                       
                         4
                      
                       
                         5
                      
                       
                         6
                      
                       
                         7
                      
                    
                     
                       
                         1
                      
                       
                         C
                         B
                      
                       
                         D
                         C
                      
                       
                         E
                         D
                      
                       
                         F
                         E
                      
                       
                         G
                         F
                      
                       
                         A
                         G
                      
                       
                         B
                         A
                      
                    
                     
                       
                         2
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                    
                     
                       
                         3
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                    
                     
                       
                         4
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                    
                     
                       
                         5
                      
                       
                         E
                         D
                      
                       
                         F
                         E
                      
                       
                         G
                         F
                      
                       
                         A
                         G
                      
                       
                         B
                         A
                      
                       
                         C
                         B
                      
                       
                         D
                         C
                      
                    
                     
                       
                         6
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                    
                     
                       
                         7
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                    
                     
                       
                         8
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                    
                     
                       
                         9
                      
                       
                         G
                         F
                      
                       
                         A
                         G
                      
                       
                         B
                         A
                      
                       
                         C
                         B
                      
                       
                         D
                         C
                      
                       
                         E
                         D
                      
                       
                         F
                         E
                      
                    
                     
                       
                         10
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                    
                     
                       
                         11
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                    
                     
                       
                         12
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                    
                     
                       
                         13
                      
                       
                         B
                         A
                      
                       
                         C
                         B
                      
                       
                         D
                         C
                      
                       
                         E
                         D
                      
                       
                         F
                         E
                      
                       
                         G
                         F
                      
                       
                         A
                         G
                      
                    
                     
                       
                         14
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                    
                     
                       
                         15
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                    
                     
                       
                         16
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                    
                     
                       
                         17
                      
                       
                         D
                         C
                      
                       
                         E
                         D
                      
                       
                         F
                         E
                      
                       
                         G
                         F
                      
                       
                         A
                         G
                      
                       
                         B
                         A
                      
                       
                         C
                         B
                      
                    
                     
                       
                         18
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                    
                     
                       
                         19
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                    
                     
                       
                         20
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                    
                     
                       
                         21
                      
                       
                         F
                         E
                      
                       
                         G
                         F
                      
                       
                         A
                         G
                      
                       
                         B
                         A
                      
                       
                         C
                         B
                      
                       
                         D
                         C
                      
                       
                         E
                         D
                      
                    
                     
                       
                         22
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                    
                     
                       
                         23
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                    
                     
                       
                         24
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                    
                     
                       
                         25
                      
                       
                         A
                         G
                      
                       
                         B
                         A
                      
                       
                         C
                         B
                      
                       
                         D
                         C
                      
                       
                         E
                         D
                      
                       
                         F
                         E
                      
                       
                         G
                         F
                      
                    
                     
                       
                         26
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                       
                         E
                      
                    
                     
                       
                         27
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                       
                         D
                      
                    
                     
                       
                         28
                      
                       
                         D
                      
                       
                         E
                      
                       
                         F
                      
                       
                         G
                      
                       
                         A
                      
                       
                         B
                      
                       
                         C
                      
                    
                     
                       
                         Anni
                      
                       
                         1582
                      
                       
                          
                      
                       
                          
                      
                       
                         1900
                      
                       
                          
                      
                       
                          
                      
                       
                         2300
                      
                    
                     
                       
                          
                      
                       
                         1600
                      
                       
                         1700
                      
                       
                         1800
                      
                       
                         2000
                      
                       
                         2100
                      
                       
                         2200
                      
                       
                         2400
                      
                    
                     
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                         2700
                      
                       
                          
                      
                       
                          
                      
                       
                         3100
                      
                       
                          
                      
                    
                     
                       
                         Chr.
                         
                      
                       
                         2500
                      
                       
                         2600
                      
                       
                          
                      
                       
                         2900
                      
                       
                         3000
                      
                       
                          
                      
                       
                          
                      
                    
                     
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                         2800
                      
                       
                          
                      
                       
                          
                      
                       
                         3200
                      
                       
                         3300
                      
                    
                  
                   
                     
                     
                       
                          
                      
                       
                          
                      
                       
                          
                      
                       
                         LXX
                      
                       
                         Ash.
                         
                      
                       
                         East
                         .
                      
                       
                         Asci
                         .
                      
                       
                         Pent.
                         
                      
                       
                         Corp.
                         Christi
                         .
                      
                       
                         Adv.
                         
                      
                    
                     
                       
                         16
                      
                       
                         XXIII
                      
                       
                          
                      
                       
                         Ian.
                         
                      
                       
                         Feb.
                         
                      
                       
                         Mar.
                         
                      
                       
                         Apr.
                         
                      
                       
                         May.
                         
                      
                       
                         May.
                         
                      
                       
                         Nov.
                         
                      
                    
                     
                       
                         5
                      
                       
                         XXII
                      
                       
                         d
                      
                       
                         18
                      
                       
                         4
                      
                       
                         22
                      
                       
                         30
                      
                       
                         10
                      
                       
                         21
                      
                       
                         29
                      
                    
                     
                       
                          
                      
                       
                         XXI
                      
                       
                         e
                      
                       
                         19
                      
                       
                         5
                      
                       
                         23
                      
                       
                         Ma.
                         1
                      
                       
                         11
                      
                       
                         22
                      
                       
                         30
                      
                    
                     
                       
                         13
                      
                       
                         XX
                      
                       
                         f
                      
                       
                         20
                      
                       
                         6
                      
                       
                         24
                      
                       
                         2
                      
                       
                         12
                      
                       
                         23
                      
                       
                         De.
                         1
                      
                    
                     
                       
                         2
                      
                       
                         XIX
                      
                       
                         g
                      
                       
                         21
                      
                       
                         7
                      
                       
                         25
                      
                       
                         3
                      
                       
                         13
                      
                       
                         24
                      
                       
                         2
                      
                    
                     
                       
                          
                      
                       
                         XVIII
                      
                       
                         a
                      
                       
                         22
                      
                       
                         8
                      
                       
                         26
                      
                       
                         4
                      
                       
                         14
                      
                       
                         25
                      
                       
                         3
                      
                    
                     
                       
                         10
                      
                       
                         XVII
                      
                       
                         b
                      
                       
                         23
                      
                       
                         9
                      
                       
                         27
                      
                       
                         5
                      
                       
                         15
                      
                       
                         26
                      
                       
                         No.
                         27
                      
                    
                     
                       
                          
                      
                       
                         XVI
                      
                       
                         c
                      
                       
                         24
                      
                       
                         10
                      
                       
                         28
                      
                       
                         6
                      
                       
                         16
                      
                       
                         27
                      
                       
                         28
                      
                    
                     
                       
                         18
                      
                       
                         XV
                      
                       
                         d
                      
                       
                         25
                      
                       
                         11
                      
                       
                         29
                      
                       
                         7
                      
                       
                         17
                      
                       
                         28
                      
                       
                         29
                      
                    
                     
                       
                         7
                      
                       
                         XIV
                      
                       
                         e
                      
                       
                         26
                      
                       
                         12
                      
                       
                         30
                      
                       
                         8
                      
                       
                         18
                      
                       
                         29
                      
                       
                         30
                      
                    
                     
                       
                          
                      
                       
                         XIII
                      
                       
                         f
                      
                       
                         27
                      
                       
                         13
                      
                       
                         31
                      
                       
                         9
                      
                       
                         19
                      
                       
                         30
                      
                       
                         Dec.
                         1
                      
                    
                     
                       
                         15
                      
                       
                         XII
                      
                       
                         g
                      
                       
                         28
                      
                       
                         14
                      
                       
                         Ap.
                         1
                      
                       
                         10
                      
                       
                         20
                      
                       
                         31
                      
                       
                         2
                      
                    
                     
                       
                         4
                      
                       
                         XI
                      
                       
                         a
                      
                       
                         29
                      
                       
                         15
                      
                       
                         2
                      
                       
                         11
                      
                       
                         21
                      
                       
                         Iun.
                         1
                      
                       
                         3
                      
                    
                     
                       
                          
                      
                       
                         X
                      
                       
                         b
                      
                       
                         30
                      
                       
                         16
                      
                       
                         3
                      
                       
                         12
                      
                       
                         22
                      
                       
                         2
                      
                       
                         No.
                         27
                      
                    
                     
                       
                         12
                      
                       
                         IX
                      
                       
                         c
                      
                       
                         31
                      
                       
                         17
                      
                       
                         4
                      
                       
                         13
                      
                       
                         23
                      
                       
                         3
                      
                       
                         28
                      
                    
                     
                       
                         1
                      
                       
                         VIII
                      
                       
                         d
                      
                       
                         Feb.
                         1
                      
                       
                         18
                      
                       
                         5
                      
                       
                         14
                      
                       
                         24
                      
                       
                         4
                      
                       
                         29
                      
                    
                     
                       
                          
                      
                       
                         VII
                      
                       
                         e
                      
                       
                         2
                      
                       
                         19
                      
                       
                         6
                      
                       
                         15
                      
                       
                         25
                      
                       
                         5
                      
                       
                         30
                      
                    
                     
                       
                          
                      
                       
                         VI
                      
                       
                         f
                      
                       
                         3
                      
                       
                         20
                      
                       
                         7
                      
                       
                         16
                      
                       
                         26
                      
                       
                         6
                      
                       
                         Dec.
                         1
                      
                    
                     
                       
                         9
                      
                       
                         V
                      
                       
                         g
                      
                       
                         4
                      
                       
                         21
                      
                       
                         8
                      
                       
                         17
                      
                       
                         27
                      
                       
                         7
                      
                       
                         2
                      
                    
                     
                       
                         17
                      
                       
                         IV
                      
                       
                         a
                      
                       
                         5
                      
                       
                         22
                      
                       
                         9
                      
                       
                         18
                      
                       
                         28
                      
                       
                         8
                      
                       
                         3
                      
                    
                     
                       
                         6
                      
                       
                         III
                      
                       
                         b
                      
                       
                         6
                      
                       
                         23
                      
                       
                         10
                      
                       
                         19
                      
                       
                         29
                      
                       
                         9
                      
                       
                         No.
                         27
                      
                    
                     
                       
                          
                      
                       
                         II
                      
                       
                         c
                      
                       
                         7
                      
                       
                         24
                      
                       
                         11
                      
                       
                         20
                      
                       
                         30
                      
                       
                         10
                      
                       
                         28
                      
                    
                     
                       
                         14
                      
                       
                         I
                      
                       
                         d
                      
                       
                         8
                      
                       
                         25
                      
                       
                         12
                      
                       
                         21
                      
                       
                         31
                      
                       
                         11
                      
                       
                         29
                      
                    
                     
                       
                         3
                      
                       
                         *
                      
                       
                         e
                      
                       
                         9
                      
                       
                         26
                      
                       
                         13
                      
                       
                         22
                      
                       
                         Iun.
                         1
                      
                       
                         12
                      
                       
                         30
                      
                    
                     
                       
                          
                      
                       
                         XXIX
                      
                       
                         f
                      
                       
                         10
                      
                       
                         27
                      
                       
                         14
                      
                       
                         23
                      
                       
                         2
                      
                       
                         13
                      
                       
                         Dec.
                         1
                      
                    
                     
                       
                         11
                      
                       
                         XXVIII
                      
                       
                         g
                      
                       
                         11
                      
                       
                         28
                      
                       
                         15
                      
                       
                         24
                      
                       
                         3
                      
                       
                         14
                      
                       
                         2
                      
                    
                     
                       
                          
                      
                       
                         XXVII
                      
                       
                         a
                      
                       
                         12
                      
                       
                         Ma.
                         1
                      
                       
                         16
                      
                       
                         25
                      
                       
                         4
                      
                       
                         15
                      
                       
                         3
                      
                    
                     
                       
                         19
                      
                       
                         25.
                         XXVI
                      
                       
                         b
                      
                       
                         13
                      
                       
                         2
                      
                       
                         17
                      
                       
                         26
                      
                       
                         5
                      
                       
                         16
                      
                       
                         No.
                         27
                      
                    
                     
                       
                         8
                      
                       
                         XXV
                         .
                         XXIV
                      
                       
                         c
                      
                       
                         14
                      
                       
                         3
                      
                       
                         18
                      
                       
                         27
                      
                       
                         6
                      
                       
                         17
                      
                       
                         28
                      
                    
                     
                       
                          
                      
                       
                          
                      
                       
                         d
                      
                       
                         15
                      
                       
                         4
                      
                       
                         19
                      
                       
                         28
                      
                       
                         7
                      
                       
                         18
                      
                       
                         29
                      
                    
                     
                       
                          
                      
                       
                          
                      
                       
                         e
                      
                       
                         16
                      
                       
                         5
                      
                       
                         20
                      
                       
                         29
                      
                       
                         8
                      
                       
                         19
                      
                       
                         30
                      
                    
                     
                       
                          
                      
                       
                          
                      
                       
                         f
                      
                       
                         17
                      
                       
                         6
                      
                       
                         21
                      
                       
                         30
                      
                       
                         9
                      
                       
                         20
                      
                       
                         Dec.
                         1
                      
                    
                     
                       
                          
                      
                       
                          
                      
                       
                         g
                      
                       
                         18
                      
                       
                         7
                      
                       
                         22
                      
                       
                         31
                      
                       
                         10
                      
                       
                         21
                      
                       
                         2
                      
                    
                     
                       
                          
                      
                       
                          
                      
                       
                         a
                      
                       
                         19
                      
                       
                         8
                      
                       
                         23
                      
                       
                         Iun.
                         1
                      
                       
                         11
                      
                       
                         22
                      
                       
                         3
                      
                    
                     
                       
                          
                      
                       
                          
                      
                       
                         b
                      
                       
                         20
                      
                       
                         9
                      
                       
                         24
                      
                       
                         2
                      
                       
                         12
                      
                       
                         23
                      
                       
                         No.
                         27
                      
                    
                     
                       
                          
                      
                       
                          
                      
                       
                         c
                      
                       
                         21
                      
                       
                         10
                      
                       
                         25
                      
                       
                         3
                      
                       
                         13
                      
                       
                         24
                      
                       
                         28
                      
                    
                  
                   
                     
                     
                       A
                       Table
                       to
                       convert
                       Sexagenary
                       Degrees
                       and
                       Minutes
                       into
                       Decimals
                       and
                       the
                       contrary
                       .
                    
                     
                       
                         1
                      
                       
                         00
                      
                       
                         37
                      
                       
                         10
                      
                       
                         73
                      
                       
                         20
                      
                       
                         109
                      
                       
                         30
                      
                       
                         145
                      
                       
                         40
                      
                       
                         181
                      
                       
                         50
                      
                    
                     
                       
                         2
                      
                       
                          
                      
                       
                         38
                      
                       
                          
                      
                       
                         74
                      
                       
                          
                      
                       
                         110
                      
                       
                          
                      
                       
                         146
                      
                       
                          
                      
                       
                         182
                      
                       
                          
                      
                    
                     
                       
                         3
                      
                       
                          
                      
                       
                         39
                      
                       
                          
                      
                       
                         75
                      
                       
                          
                      
                       
                         111
                      
                       
                          
                      
                       
                         147
                      
                       
                          
                      
                       
                         183
                      
                       
                          
                      
                    
                     
                       
                         4
                      
                       
                         01
                      
                       
                         40
                      
                       
                         11
                      
                       
                         76
                      
                       
                         21
                      
                       
                         112
                      
                       
                         31
                      
                       
                         148
                      
                       
                         41
                      
                       
                         184
                      
                       
                         51
                      
                    
                     
                       
                         5
                      
                       
                          
                      
                       
                         41
                      
                       
                          
                      
                       
                         77
                      
                       
                          
                      
                       
                         113
                      
                       
                          
                      
                       
                         149
                      
                       
                          
                      
                       
                         185
                      
                       
                          
                      
                    
                     
                       
                         6
                      
                       
                          
                      
                       
                         42
                      
                       
                          
                      
                       
                         78
                      
                       
                          
                      
                       
                         114
                      
                       
                          
                      
                       
                         150
                      
                       
                          
                      
                       
                         186
                      
                       
                          
                      
                    
                     
                       
                         7
                      
                       
                          
                      
                       
                         43
                      
                       
                          
                      
                       
                         79
                      
                       
                          
                      
                       
                         115
                      
                       
                          
                      
                       
                         151
                      
                       
                          
                      
                       
                         187
                      
                       
                          
                      
                    
                     
                       
                         8
                      
                       
                         02
                      
                       
                         44
                      
                       
                         12
                      
                       
                         80
                      
                       
                         22
                      
                       
                         116
                      
                       
                         32
                      
                       
                         152
                      
                       
                         42
                      
                       
                         188
                      
                       
                         52
                      
                    
                     
                       
                         9
                      
                       
                          
                      
                       
                         45
                      
                       
                          
                      
                       
                         81
                      
                       
                          
                      
                       
                         117
                      
                       
                          
                      
                       
                         153
                      
                       
                          
                      
                       
                         189
                      
                       
                          
                      
                    
                     
                       
                         10
                      
                       
                          
                      
                       
                         46
                      
                       
                          
                      
                       
                         82
                      
                       
                          
                      
                       
                         118
                      
                       
                          
                      
                       
                         154
                      
                       
                          
                      
                       
                         190
                      
                       
                          
                      
                    
                     
                       
                         11
                      
                       
                         03
                      
                       
                         47
                      
                       
                         13
                      
                       
                         83
                      
                       
                         23
                      
                       
                         119
                      
                       
                         33
                      
                       
                         155
                      
                       
                         43
                      
                       
                         191
                      
                       
                         53
                      
                    
                     
                       
                         12
                      
                       
                          
                      
                       
                         48
                      
                       
                          
                      
                       
                         84
                      
                       
                          
                      
                       
                         120
                      
                       
                          
                      
                       
                         156
                      
                       
                          
                      
                       
                         192
                      
                       
                          
                      
                    
                     
                       
                         13
                      
                       
                          
                      
                       
                         49
                      
                       
                          
                      
                       
                         85
                      
                       
                          
                      
                       
                         121
                      
                       
                          
                      
                       
                         157
                      
                       
                          
                      
                       
                         193
                      
                       
                          
                      
                    
                     
                       
                         14
                      
                       
                          
                      
                       
                         50
                      
                       
                          
                      
                       
                         86
                      
                       
                          
                      
                       
                         122
                      
                       
                          
                      
                       
                         158
                      
                       
                          
                      
                       
                         194
                      
                       
                          
                      
                    
                     
                       
                         15
                      
                       
                         04
                      
                       
                         51
                      
                       
                         14
                      
                       
                         87
                      
                       
                         24
                      
                       
                         123
                      
                       
                         35
                      
                       
                         159
                      
                       
                         44
                      
                       
                         195
                      
                       
                         54
                      
                    
                     
                       
                         16
                      
                       
                          
                      
                       
                         52
                      
                       
                          
                      
                       
                         88
                      
                       
                          
                      
                       
                         124
                      
                       
                          
                      
                       
                         160
                      
                       
                          
                      
                       
                         196
                      
                       
                          
                      
                    
                     
                       
                         17
                      
                       
                          
                      
                       
                         53
                      
                       
                          
                      
                       
                         89
                      
                       
                          
                      
                       
                         125
                      
                       
                          
                      
                       
                         161
                      
                       
                          
                      
                       
                         197
                      
                       
                          
                      
                    
                     
                       
                         18
                      
                       
                         05
                      
                       
                         54
                      
                       
                         15
                      
                       
                         90
                      
                       
                         25
                      
                       
                         126
                      
                       
                         35
                      
                       
                         162
                      
                       
                         45
                      
                       
                         198
                      
                       
                         55
                      
                    
                     
                       
                         19
                      
                       
                          
                      
                       
                         55
                      
                       
                          
                      
                       
                         91
                      
                       
                          
                      
                       
                         127
                      
                       
                          
                      
                       
                         163
                      
                       
                          
                      
                       
                         199
                      
                       
                          
                      
                    
                     
                       
                         20
                      
                       
                          
                      
                       
                         56
                      
                       
                          
                      
                       
                         92
                      
                       
                          
                      
                       
                         128
                      
                       
                          
                      
                       
                         164
                      
                       
                          
                      
                       
                         200
                      
                       
                          
                      
                    
                     
                       
                         21
                      
                       
                          
                      
                       
                         57
                      
                       
                          
                      
                       
                         93
                      
                       
                          
                      
                       
                         129
                      
                       
                          
                      
                       
                         165
                      
                       
                          
                      
                       
                         201
                      
                       
                          
                      
                    
                     
                       
                         22
                      
                       
                         06
                      
                       
                         58
                      
                       
                         16
                      
                       
                         94
                      
                       
                         26
                      
                       
                         130
                      
                       
                         36
                      
                       
                         166
                      
                       
                         46
                      
                       
                         202
                      
                       
                         56
                      
                    
                     
                       
                         23
                      
                       
                          
                      
                       
                         59
                      
                       
                          
                      
                       
                         95
                      
                       
                          
                      
                       
                         131
                      
                       
                          
                      
                       
                         167
                      
                       
                          
                      
                       
                         203
                      
                       
                          
                      
                    
                     
                       
                         24
                      
                       
                          
                      
                       
                         60
                      
                       
                          
                      
                       
                         96
                      
                       
                          
                      
                       
                         132
                      
                       
                          
                      
                       
                         168
                      
                       
                          
                      
                       
                         204
                      
                       
                          
                      
                    
                     
                       
                         25
                      
                       
                          
                      
                       
                         61
                      
                       
                          
                      
                       
                         97
                      
                       
                          
                      
                       
                         133
                      
                       
                          
                      
                       
                         169
                      
                       
                          
                      
                       
                         205
                      
                       
                          
                      
                    
                     
                       
                         26
                      
                       
                         07
                      
                       
                         62
                      
                       
                         17
                      
                       
                         98
                      
                       
                         27
                      
                       
                         134
                      
                       
                         37
                      
                       
                         170
                      
                       
                         47
                      
                       
                         206
                      
                       
                         57
                      
                    
                     
                       
                         27
                      
                       
                          
                      
                       
                         63
                      
                       
                          
                      
                       
                         99
                      
                       
                          
                      
                       
                         135
                      
                       
                          
                      
                       
                         171
                      
                       
                          
                      
                       
                         207
                      
                       
                          
                      
                    
                     
                       
                         28
                      
                       
                          
                      
                       
                         64
                      
                       
                          
                      
                       
                         100
                      
                       
                          
                      
                       
                         136
                      
                       
                          
                      
                       
                         172
                      
                       
                          
                      
                       
                         208
                      
                       
                          
                      
                    
                     
                       
                         29
                      
                       
                         08
                      
                       
                         65
                      
                       
                         18
                      
                       
                         101
                      
                       
                         28
                      
                       
                         137
                      
                       
                         38
                      
                       
                         173
                      
                       
                         48
                      
                       
                         209
                      
                       
                         58
                      
                    
                     
                       
                         30
                      
                       
                          
                      
                       
                         66
                      
                       
                          
                      
                       
                         102
                      
                       
                          
                      
                       
                         138
                      
                       
                          
                      
                       
                         174
                      
                       
                          
                      
                       
                         210
                      
                       
                          
                      
                    
                     
                       
                         31
                      
                       
                          
                      
                       
                         67
                      
                       
                          
                      
                       
                         103
                      
                       
                          
                      
                       
                         139
                      
                       
                          
                      
                       
                         175
                      
                       
                          
                      
                       
                         211
                      
                       
                          
                      
                    
                     
                       
                         32
                      
                       
                          
                      
                       
                         68
                      
                       
                          
                      
                       
                         104
                      
                       
                          
                      
                       
                         140
                      
                       
                          
                      
                       
                         176
                      
                       
                          
                      
                       
                         212
                      
                       
                          
                      
                    
                     
                       
                         33
                      
                       
                         09
                      
                       
                         69
                      
                       
                         19
                      
                       
                         105
                      
                       
                         29
                      
                       
                         141
                      
                       
                         39
                      
                       
                         177
                      
                       
                         49
                      
                       
                         213
                      
                       
                         59
                      
                    
                     
                       
                         34
                      
                       
                          
                      
                       
                         70
                      
                       
                          
                      
                       
                         106
                      
                       
                          
                      
                       
                         142
                      
                       
                          
                      
                       
                         178
                      
                       
                          
                      
                       
                         214
                      
                       
                          
                      
                    
                     
                       
                         35
                      
                       
                          
                      
                       
                         71
                      
                       
                          
                      
                       
                         107
                      
                       
                          
                      
                       
                         143
                      
                       
                          
                      
                       
                         179
                      
                       
                          
                      
                       
                         215
                      
                       
                          
                      
                    
                     
                       
                         36
                      
                       
                         10
                      
                       
                         72
                      
                       
                         20
                      
                       
                         108
                      
                       
                         30
                      
                       
                         144
                      
                       
                         40
                      
                       
                         180
                      
                       
                         50
                      
                       
                         216
                      
                       
                         60
                      
                    
                     
                       
                         
                         217
                      
                       
                         60
                      
                       
                         253
                      
                       
                         70
                      
                       
                         289
                      
                       
                         80
                      
                       
                         325
                      
                       
                         90
                      
                       
                         277777778
                      
                    
                     
                       
                         218
                      
                       
                          
                      
                       
                         254
                      
                       
                          
                      
                       
                         290
                      
                       
                          
                      
                       
                         326
                      
                       
                          
                      
                       
                         555555555
                      
                    
                     
                       
                         219
                      
                       
                          
                      
                       
                         255
                      
                       
                          
                      
                       
                         291
                      
                       
                          
                      
                       
                         327
                      
                       
                          
                      
                       
                         833333333
                      
                    
                     
                       
                         220
                      
                       
                         61
                      
                       
                         256
                      
                       
                         71
                      
                       
                         292
                      
                       
                         81
                      
                       
                         328
                      
                       
                         91
                      
                       
                         111111111
                      
                    
                     
                       
                         221
                      
                       
                          
                      
                       
                         257
                      
                       
                          
                      
                       
                         293
                      
                       
                          
                      
                       
                         329
                      
                       
                          
                      
                       
                         388888889
                      
                    
                     
                       
                         222
                      
                       
                          
                      
                       
                         258
                      
                       
                          
                      
                       
                         294
                      
                       
                          
                      
                       
                         330
                      
                       
                          
                      
                       
                         666666667
                      
                    
                     
                       
                         223
                      
                       
                          
                      
                       
                         259
                      
                       
                          
                      
                       
                         295
                      
                       
                          
                      
                       
                         331
                      
                       
                          
                      
                       
                         944444444
                      
                    
                     
                       
                         224
                      
                       
                         62
                      
                       
                         260
                      
                       
                         72
                      
                       
                         296
                      
                       
                         82
                      
                       
                         332
                      
                       
                         92
                      
                       
                         222222222
                      
                    
                     
                       
                         225
                      
                       
                          
                      
                       
                         261
                      
                       
                          
                      
                       
                         297
                      
                       
                          
                      
                       
                         333
                      
                       
                          
                      
                       
                         500000000
                      
                    
                     
                       
                         226
                      
                       
                          
                      
                       
                         262
                      
                       
                          
                      
                       
                         298
                      
                       
                          
                      
                       
                         334
                      
                       
                          
                      
                       
                         777777778
                      
                    
                     
                       
                         227
                      
                       
                         63
                      
                       
                         263
                      
                       
                         73
                      
                       
                         299
                      
                       
                         83
                      
                       
                         335
                      
                       
                         93
                      
                       
                         055555555
                      
                    
                     
                       
                         228
                      
                       
                          
                      
                       
                         264
                      
                       
                          
                      
                       
                         300
                      
                       
                          
                      
                       
                         336
                      
                       
                          
                      
                       
                         333333333
                      
                    
                     
                       
                         229
                      
                       
                          
                      
                       
                         265
                      
                       
                          
                      
                       
                         301
                      
                       
                          
                      
                       
                         337
                      
                       
                          
                      
                       
                         511111111
                      
                    
                     
                       
                         230
                      
                       
                          
                      
                       
                         266
                      
                       
                          
                      
                       
                         302
                      
                       
                          
                      
                       
                         338
                      
                       
                          
                      
                       
                         888888889
                      
                    
                     
                       
                         231
                      
                       
                         64
                      
                       
                         267
                      
                       
                         74
                      
                       
                         303
                      
                       
                         84
                      
                       
                         339
                      
                       
                         94
                      
                       
                         166666667
                      
                    
                     
                       
                         232
                      
                       
                          
                      
                       
                         268
                      
                       
                          
                      
                       
                         304
                      
                       
                          
                      
                       
                         340
                      
                       
                          
                      
                       
                         444444444
                      
                    
                     
                       
                         233
                      
                       
                          
                      
                       
                         269
                      
                       
                          
                      
                       
                         305
                      
                       
                          
                      
                       
                         341
                      
                       
                          
                      
                       
                         722222222
                      
                    
                     
                       
                         234
                      
                       
                         65
                      
                       
                         270
                      
                       
                         75
                      
                       
                         306
                      
                       
                         85
                      
                       
                         342
                      
                       
                         95
                      
                       
                         000000000
                      
                    
                     
                       
                         235
                      
                       
                          
                      
                       
                         271
                      
                       
                          
                      
                       
                         307
                      
                       
                          
                      
                       
                         343
                      
                       
                          
                      
                       
                         277777778
                      
                    
                     
                       
                         236
                      
                       
                          
                      
                       
                         272
                      
                       
                          
                      
                       
                         308
                      
                       
                          
                      
                       
                         344
                      
                       
                          
                      
                       
                         555555555
                      
                    
                     
                       
                         237
                      
                       
                          
                      
                       
                         273
                      
                       
                          
                      
                       
                         309
                      
                       
                          
                      
                       
                         345
                      
                       
                          
                      
                       
                         833333333
                      
                    
                     
                       
                         238
                      
                       
                         66
                      
                       
                         274
                      
                       
                         76
                      
                       
                         310
                      
                       
                         86
                      
                       
                         346
                      
                       
                         96
                      
                       
                         111111111
                      
                    
                     
                       
                         239
                      
                       
                          
                      
                       
                         275
                      
                       
                          
                      
                       
                         311
                      
                       
                          
                      
                       
                         347
                      
                       
                          
                      
                       
                         388888889
                      
                    
                     
                       
                         240
                      
                       
                          
                      
                       
                         276
                      
                       
                          
                      
                       
                         312
                      
                       
                          
                      
                       
                         348
                      
                       
                          
                      
                       
                         666666667
                      
                    
                     
                       
                         241
                      
                       
                          
                      
                       
                         277
                      
                       
                          
                      
                       
                         313
                      
                       
                          
                      
                       
                         349
                      
                       
                          
                      
                       
                         944444444
                      
                    
                     
                       
                         242
                      
                       
                         67
                      
                       
                         278
                      
                       
                         77
                      
                       
                         314
                      
                       
                         87
                      
                       
                         350
                      
                       
                         97
                      
                       
                         222222222
                      
                    
                     
                       
                         243
                      
                       
                          
                      
                       
                         279
                      
                       
                          
                      
                       
                         315
                      
                       
                          
                      
                       
                         351
                      
                       
                          
                      
                       
                         500000000
                      
                    
                     
                       
                         244
                      
                       
                          
                      
                       
                         280
                      
                       
                          
                      
                       
                         316
                      
                       
                          
                      
                       
                         352
                      
                       
                          
                      
                       
                         777777778
                      
                    
                     
                       
                         245
                      
                       
                         68
                      
                       
                         281
                      
                       
                         78
                      
                       
                         317
                      
                       
                         88
                      
                       
                         353
                      
                       
                         98
                      
                       
                         055555555
                      
                    
                     
                       
                         246
                      
                       
                          
                      
                       
                         282
                      
                       
                          
                      
                       
                         318
                      
                       
                          
                      
                       
                         354
                      
                       
                          
                      
                       
                         333333333
                      
                    
                     
                       
                         247
                      
                       
                          
                      
                       
                         283
                      
                       
                          
                      
                       
                         319
                      
                       
                          
                      
                       
                         355
                      
                       
                          
                      
                       
                         611111111
                      
                    
                     
                       
                         248
                      
                       
                          
                      
                       
                         284
                      
                       
                          
                      
                       
                         320
                      
                       
                          
                      
                       
                         356
                      
                       
                          
                      
                       
                         888888889
                      
                    
                     
                       
                         249
                      
                       
                         69
                      
                       
                         285
                      
                       
                         79
                      
                       
                         321
                      
                       
                         89
                      
                       
                         357
                      
                       
                         99
                      
                       
                         166666667
                      
                    
                     
                       
                         250
                      
                       
                          
                      
                       
                         286
                      
                       
                          
                      
                       
                         322
                      
                       
                          
                      
                       
                         358
                      
                       
                          
                      
                       
                         444444444
                      
                    
                     
                       
                         251
                      
                       
                          
                      
                       
                         287
                      
                       
                          
                      
                       
                         323
                      
                       
                          
                      
                       
                         359
                      
                       
                          
                      
                       
                         722222222
                      
                    
                     
                       
                         252
                      
                       
                         70
                      
                       
                         288
                      
                       
                         80
                      
                       
                         324
                      
                       
                         90
                      
                       
                         360
                      
                       
                         100
                      
                       
                         000000000
                      
                    
                  
                   
                     
                     
                       A
                       Table
                       to
                       Convert
                       Sexagenary
                       Minutes
                       into
                       Decimals
                       and
                       the
                       contrary
                       .
                    
                     
                       
                          
                      
                       
                         Minutes
                      
                       
                         Seconds
                      
                       
                         Thirds
                      
                    
                     
                       
                         1
                      
                       
                         00462962
                      
                       
                         00007716
                      
                       
                         00000128
                      
                    
                     
                       
                         2
                      
                       
                         00925925
                      
                       
                         15432
                      
                       
                         257
                      
                    
                     
                       
                         3
                      
                       
                         01388889
                      
                       
                         23148
                      
                       
                         385
                      
                    
                     
                       
                         4
                      
                       
                         01851851
                      
                       
                         30864
                      
                       
                         515
                      
                    
                     
                       
                         5
                      
                       
                         02314814
                      
                       
                         00038580
                      
                       
                         00000643
                      
                    
                     
                       
                         6
                      
                       
                         02777778
                      
                       
                         46296
                      
                       
                         771
                      
                    
                     
                       
                         7
                      
                       
                         03240740
                      
                       
                         54012
                      
                       
                         900
                      
                    
                     
                       
                         8
                      
                       
                         03703703
                      
                       
                         61728
                      
                       
                         1028
                      
                    
                     
                       
                         9
                      
                       
                         04166667
                      
                       
                         69444
                      
                       
                         1157
                      
                    
                     
                       
                         10
                      
                       
                         04629629
                      
                       
                         00077160
                      
                       
                         00001286
                      
                    
                     
                       
                         11
                      
                       
                         05092592
                      
                       
                         084876
                      
                       
                         1414
                      
                    
                     
                       
                         12
                      
                       
                         05555555
                      
                       
                         092592
                      
                       
                         1543
                      
                    
                     
                       
                         13
                      
                       
                         06018518
                      
                       
                         100308
                      
                       
                         1671
                      
                    
                     
                       
                         14
                      
                       
                         06481480
                      
                       
                         108024
                      
                       
                         1800
                      
                    
                     
                       
                         15
                      
                       
                         06944444
                      
                       
                         00115740
                      
                       
                         1929
                      
                    
                     
                       
                         16
                      
                       
                         07409407
                      
                       
                         123450
                      
                       
                         2057
                      
                    
                     
                       
                         17
                      
                       
                         07870370
                      
                       
                         131172
                      
                       
                         2186
                      
                    
                     
                       
                         18
                      
                       
                         08333333
                      
                       
                         138889
                      
                       
                         2314
                      
                    
                     
                       
                         19
                      
                       
                         08796296
                      
                       
                         146604
                      
                       
                         2443
                      
                    
                     
                       
                         20
                      
                       
                         09259259
                      
                       
                         00154320
                      
                       
                         2572
                      
                    
                     
                       
                         21
                      
                       
                         00722222
                      
                       
                         162036
                      
                       
                         2700
                      
                    
                     
                       
                         22
                      
                       
                         10185185
                      
                       
                         169752
                      
                       
                         2829
                      
                    
                     
                       
                         23
                      
                       
                         10648148
                      
                       
                         177468
                      
                       
                         2957
                      
                    
                     
                       
                         24
                      
                       
                         11111111
                      
                       
                         185184
                      
                       
                         3086
                      
                    
                     
                       
                         25
                      
                       
                         11574074
                      
                       
                         00192900
                      
                       
                         3215
                      
                    
                     
                       
                         26
                      
                       
                         12037037
                      
                       
                         200616
                      
                       
                         3343
                      
                    
                     
                       
                         27
                      
                       
                         12500000
                      
                       
                         208332
                      
                       
                         3472
                      
                    
                     
                       
                         28
                      
                       
                         12962962
                      
                       
                         216048
                      
                       
                         3600
                      
                    
                     
                       
                         29
                      
                       
                         13425926
                      
                       
                         223764
                      
                       
                         3729
                      
                    
                     
                       
                         30
                      
                       
                         13888889
                      
                       
                         00231481
                      
                       
                         00003858
                      
                    
                     
                       
                         
                         31
                      
                       
                         14351852
                      
                       
                         00239670
                      
                       
                         00003986
                      
                    
                     
                       
                         32
                      
                       
                         14814814
                      
                       
                         246913
                      
                       
                         4115
                      
                    
                     
                       
                         33
                      
                       
                         15277777
                      
                       
                         254629
                      
                       
                         4243
                      
                    
                     
                       
                         34
                      
                       
                         15747040
                      
                       
                         262345
                      
                       
                         4372
                      
                    
                     
                       
                         35
                      
                       
                         16203703
                      
                       
                         270061
                      
                       
                         4581
                      
                    
                     
                       
                         36
                      
                       
                         16666666
                      
                       
                         00277777
                      
                       
                         00004629
                      
                    
                     
                       
                         37
                      
                       
                         17129629
                      
                       
                         285493
                      
                       
                         4758
                      
                    
                     
                       
                         38
                      
                       
                         17592592
                      
                       
                         293209
                      
                       
                         4886
                      
                    
                     
                       
                         39
                      
                       
                         18055555
                      
                       
                         300925
                      
                       
                         5015
                      
                    
                     
                       
                         40
                      
                       
                         18518518
                      
                       
                         308640
                      
                       
                         5144
                      
                    
                     
                       
                         41
                      
                       
                         18981481
                      
                       
                         00316356
                      
                       
                         00005272
                      
                    
                     
                       
                         42
                      
                       
                         19444444
                      
                       
                         324072
                      
                       
                         5401
                      
                    
                     
                       
                         43
                      
                       
                         19907407
                      
                       
                         331788
                      
                       
                         5529
                      
                    
                     
                       
                         44
                      
                       
                         20370370
                      
                       
                         339504
                      
                       
                         5658
                      
                    
                     
                       
                         45
                      
                       
                         20833333
                      
                       
                         347220
                      
                       
                         5787
                      
                    
                     
                       
                         46
                      
                       
                         21296296
                      
                       
                         00354936
                      
                       
                         00005915
                      
                    
                     
                       
                         47
                      
                       
                         21759259
                      
                       
                         362652
                      
                       
                         6044
                      
                    
                     
                       
                         48
                      
                       
                         22222222
                      
                       
                         370●70
                      
                       
                         6172
                      
                    
                     
                       
                         49
                      
                       
                         22685185
                      
                       
                         378084
                      
                       
                         6301
                      
                    
                     
                       
                         50
                      
                       
                         23148148
                      
                       
                         385802
                      
                       
                         6430
                      
                    
                     
                       
                         51
                      
                       
                         23611111
                      
                       
                         00393518
                      
                       
                         00006558
                      
                    
                     
                       
                         52
                      
                       
                         24074074
                      
                       
                         401234
                      
                       
                         6687
                      
                    
                     
                       
                         53
                      
                       
                         24537037
                      
                       
                         408950
                      
                       
                         6815
                      
                    
                     
                       
                         54
                      
                       
                         25000000
                      
                       
                         416666
                      
                       
                         6944
                      
                    
                     
                       
                         55
                      
                       
                         25462963
                      
                       
                         424382
                      
                       
                         7073
                      
                    
                     
                       
                         56
                      
                       
                         25925926
                      
                       
                         00432098
                      
                       
                         00007201
                      
                    
                     
                       
                         57
                      
                       
                         26388888
                      
                       
                         439814
                      
                       
                         7330
                      
                    
                     
                       
                         58
                      
                       
                         26851852
                      
                       
                         447530
                      
                       
                         7458
                      
                    
                     
                       
                         59
                      
                       
                         27314814
                      
                       
                         455256
                      
                       
                         7587
                      
                    
                     
                       
                         60
                      
                       
                         27777777
                      
                       
                         00462962
                      
                       
                         00007716
                      
                    
                  
                   
                     
                     
                       A
                       Table
                       Converting
                       Hours
                       and
                       Minutes
                       into
                       Degrees
                       and
                       Minutes
                       of
                       the
                       AEquator
                       ,
                       and
                       into
                    
                     
                       
                          
                      
                       
                         Hours
                         .
                      
                    
                     
                       
                         1
                      
                       
                         04.16666667
                      
                    
                     
                       
                         2
                      
                       
                         08.33333333
                      
                    
                     
                       
                         3
                      
                       
                         12.5
                      
                    
                     
                       
                         4
                      
                       
                         16.16666667
                      
                    
                     
                       
                         5
                      
                       
                         20.83333333
                      
                    
                     
                       
                         6
                      
                       
                         25.0
                      
                    
                     
                       
                         7
                      
                       
                         29.16666667
                      
                    
                     
                       
                         8
                      
                       
                         33.33333333
                      
                    
                     
                       
                         9
                      
                       
                         37.5
                      
                    
                     
                       
                         10
                      
                       
                         41.66666667
                      
                    
                     
                       
                         11
                      
                       
                         45.83333333
                      
                    
                     
                       
                         12
                      
                       
                         50.
                         
                      
                    
                     
                       
                         13
                      
                       
                         54.16666667
                      
                    
                     
                       
                         14
                      
                       
                         58.33333333
                      
                    
                     
                       
                         15
                      
                       
                         62.5
                      
                    
                     
                       
                         16
                      
                       
                         66.66606667
                      
                    
                     
                       
                         17
                      
                       
                         70.83333333
                      
                    
                     
                       
                         18
                      
                       
                         75.00
                      
                    
                     
                       
                         19
                      
                       
                         79.16660667
                      
                    
                     
                       
                         20
                      
                       
                         83.33333333
                      
                    
                     
                       
                         21
                      
                       
                         87.5
                      
                    
                     
                       
                         22
                      
                       
                         91.66666667
                      
                    
                     
                       
                         23
                      
                       
                         95.83333333
                      
                    
                     
                       
                         24
                      
                       
                         100.00000000
                      
                    
                  
                   
                     
                       
                          
                      
                       
                         Minutes
                      
                    
                     
                       
                         1
                      
                       
                         0.06944444
                      
                    
                     
                       
                         2
                      
                       
                         0.13888888
                      
                    
                     
                       
                         3
                      
                       
                         0.20833333
                      
                    
                     
                       
                         4
                      
                       
                         0.27777777
                      
                    
                     
                       
                         5
                      
                       
                         0.34722222
                      
                    
                     
                       
                         6
                      
                       
                         0.41666666
                      
                    
                     
                       
                         7
                      
                       
                         0.48611111
                      
                    
                     
                       
                         8
                      
                       
                         0.55555555
                      
                    
                     
                       
                         9
                      
                       
                         0.625
                      
                    
                     
                       
                         10
                      
                       
                         0.69444444
                      
                    
                     
                       
                         11
                      
                       
                         0.76388888
                      
                    
                     
                       
                         12
                      
                       
                         0.83333333
                      
                    
                     
                       
                         13
                      
                       
                         0.90277777
                      
                    
                     
                       
                         14
                      
                       
                         0.97222222
                      
                    
                     
                       
                         15
                      
                       
                         1.04166666
                      
                    
                     
                       
                         16
                      
                       
                         1.11111111
                      
                    
                     
                       
                         17
                      
                       
                         1.18055555
                      
                    
                     
                       
                         18
                      
                       
                         1.25
                      
                    
                     
                       
                         19
                      
                       
                         1.31944444
                      
                    
                     
                       
                         20
                      
                       
                         1.38888888
                      
                    
                     
                       
                         21
                      
                       
                         1.45833333
                      
                    
                     
                       
                         22
                      
                       
                         1.52777777
                      
                    
                     
                       
                         23
                      
                       
                         1.59722222
                      
                    
                     
                       
                         24
                      
                       
                         1.66666666
                      
                    
                     
                       
                         25
                      
                       
                         1.73611111
                      
                    
                     
                       
                         26
                      
                       
                         1.80555555
                      
                    
                     
                       
                         27
                      
                       
                         1.875
                      
                    
                     
                       
                         28
                      
                       
                         1.94444444
                      
                    
                     
                       
                         29
                      
                       
                         2.01388888
                      
                    
                     
                       
                         30
                      
                       
                         2.08333333
                      
                    
                  
                   
                     
                     
                       The
                       Decimal
                       parts
                       of
                       a
                       Day
                       and
                       the
                       contrary
                       .
                    
                     
                       
                         Seconds
                      
                       
                          
                      
                       
                         Minutes
                      
                       
                         Seconds
                      
                    
                     
                       
                         .00115740
                      
                       
                         31
                      
                       
                         2.15277777
                      
                       
                         .03587963
                      
                    
                     
                       
                         .00231481
                      
                       
                         32
                      
                       
                         2.22222222
                      
                       
                         .03703704
                      
                    
                     
                       
                         .00347222
                      
                       
                         33
                      
                       
                         2.29166666
                      
                       
                         .03819444
                      
                    
                     
                       
                         .00462962
                      
                       
                         34
                      
                       
                         2.36111111
                      
                       
                         .03935185
                      
                    
                     
                       
                         .00578703
                      
                       
                         35
                      
                       
                         2.43055555
                      
                       
                         .04050926
                      
                    
                     
                       
                         .00694444
                      
                       
                         36
                      
                       
                         2.5
                      
                       
                         .04166666
                      
                    
                     
                       
                         .00810184
                      
                       
                         37
                      
                       
                         2.56944444
                      
                       
                         .04282407
                      
                    
                     
                       
                         .00925925
                      
                       
                         38
                      
                       
                         2.63888888
                      
                       
                         .04398148
                      
                    
                     
                       
                         .01041660
                      
                       
                         39
                      
                       
                         2.70833333
                      
                       
                         .04513888
                      
                    
                     
                       
                         .01157405
                      
                       
                         40
                      
                       
                         2.77777777
                      
                       
                         .04629629
                      
                    
                     
                       
                         .01273148
                      
                       
                         41
                      
                       
                         2.84722222
                      
                       
                         .04745370
                      
                    
                     
                       
                         .01388888
                      
                       
                         42
                      
                       
                         2.91666666
                      
                       
                         .04861111
                      
                    
                     
                       
                         .01504630
                      
                       
                         43
                      
                       
                         2.98611111
                      
                       
                         .
                         0497685●
                      
                    
                     
                       
                         .01620371
                      
                       
                         44
                      
                       
                         3.05555555
                      
                       
                         .05092592
                      
                    
                     
                       
                         .01736111
                      
                       
                         45
                      
                       
                         3.125
                      
                       
                         .05208333
                      
                    
                     
                       
                         .01851853
                      
                       
                         46
                      
                       
                         3.19444444
                      
                       
                         .05324074
                      
                    
                     
                       
                         .01967593
                      
                       
                         47
                      
                       
                         3.26388888
                      
                       
                         .05439814
                      
                    
                     
                       
                         .02083333
                      
                       
                         48
                      
                       
                         3.33333333
                      
                       
                         .05555555
                      
                    
                     
                       
                         .02199074
                      
                       
                         49
                      
                       
                         3.40277777
                      
                       
                         .05671296
                      
                    
                     
                       
                         .02314810
                      
                       
                         50
                      
                       
                         3.47222222
                      
                       
                         .05787037
                      
                    
                     
                       
                         .02430555
                      
                       
                         51
                      
                       
                         3.54166666
                      
                       
                         .05902777
                      
                    
                     
                       
                         .02546295
                      
                       
                         52
                      
                       
                         3.61111111
                      
                       
                         .06018518
                      
                    
                     
                       
                         .02662037
                      
                       
                         53
                      
                       
                         3.68055555
                      
                       
                         .
                         06134●59
                      
                    
                     
                       
                         .02777777
                      
                       
                         54
                      
                       
                         3.75
                      
                       
                         .0625
                      
                    
                     
                       
                         .02893518
                      
                       
                         55
                      
                       
                         3.81944444
                      
                       
                         .06365741
                      
                    
                     
                       
                         .03009259
                      
                       
                         56
                      
                       
                         3.88888888
                      
                       
                         .06481481
                      
                    
                     
                       
                         .03125000
                      
                       
                         57
                      
                       
                         3.95833333
                      
                       
                         .06597222
                      
                    
                     
                       
                         .03240741
                      
                       
                         58
                      
                       
                         4.02777777
                      
                       
                         .06712963
                      
                    
                     
                       
                         .03356482
                      
                       
                         59
                      
                       
                         4.09722222
                      
                       
                         .06828704
                      
                    
                     
                       
                         .03472222
                      
                       
                         60
                      
                       
                         4.16666666
                      
                       
                         .06944444
                      
                    
                  
                   
                     
                     
                       A
                       Catalogue
                       of
                       some
                       of
                       the
                       most
                       eminent
                       Cittes
                       and
                       Towns
                       in
                       England
                       and
                       Ireland
                       wherein
                       is
                       shewed
                       the
                       difference
                       of
                       their
                       Meridian
                       from
                       London
                       ,
                       with
                       the
                       hight
                       of
                       the
                       Pole.
                       
                    
                     
                       
                         Names
                         of
                         Citties
                      
                       
                         Differ
                         .
                         Merid.
                         
                      
                       
                         Hight
                         Pole
                      
                    
                     
                       
                         St.
                         Albons
                      
                       
                         0
                         1
                         s
                      
                       
                         55.55
                      
                    
                     
                       
                         Barwick
                      
                       
                         0
                         6
                         s
                      
                       
                         55.49
                      
                    
                     
                       
                         Bedford
                      
                       
                         0
                         2
                         s
                      
                       
                         52.18
                      
                    
                     
                       
                         Bristol
                      
                       
                         0
                         11
                         s
                      
                       
                         51.32
                      
                    
                     
                       
                         Boston
                      
                       
                         0
                         0
                      
                       
                         53.2
                      
                    
                     
                       
                         Cambridge
                      
                       
                         0
                         1
                         a
                      
                       
                         52.17
                      
                    
                     
                       
                         Canterbury
                      
                       
                         0
                         5
                         a
                      
                       
                         51.27
                      
                    
                     
                       
                         Carlile
                      
                       
                         0
                         10
                         s
                      
                       
                         54.57
                      
                    
                     
                       
                         Chester
                      
                       
                         0
                         11
                         s
                      
                       
                         53.20
                      
                    
                     
                       
                         Coventry
                      
                       
                         0
                         4
                         s
                      
                       
                         52.30
                      
                    
                     
                       
                         Carmarthen
                      
                       
                         0
                         17
                         s
                      
                       
                         52.2
                      
                    
                     
                       
                         Chichester
                      
                       
                         0
                         3
                         s
                      
                       
                         50.56
                      
                    
                     
                       
                         Colchester
                      
                       
                         0
                         5
                         a
                      
                       
                         52.4
                      
                    
                     
                       
                         Darby
                      
                       
                         0
                         5
                         s
                      
                       
                         53.6
                      
                    
                     
                       
                         Dublin
                         in
                         Ireland
                      
                       
                         0
                         26
                         s
                      
                       
                         53.11
                      
                    
                     
                       
                         Duresm●
                      
                       
                         0
                         5
                         s
                      
                       
                         54.45
                      
                    
                     
                       
                         Dartmouth
                      
                       
                         0
                         15
                         s
                      
                       
                         50.32
                      
                    
                     
                       
                         Eely
                      
                       
                         0
                         1
                         a
                      
                       
                         52.20
                      
                    
                     
                       
                         Grantha●
                      
                       
                         0
                         2
                         s
                      
                       
                         52.58
                      
                    
                     
                       
                         Glocester
                      
                       
                         0
                         9
                         s
                      
                       
                         52.00
                      
                    
                     
                       
                         Halefax
                      
                       
                         0
                         6
                         s
                      
                       
                         52.49
                      
                    
                     
                       
                         Hartford
                      
                       
                         0
                         1
                         s
                      
                       
                         52.50
                      
                    
                     
                       
                         Hereford
                      
                       
                         0
                         11
                         s
                      
                       
                         52.14
                      
                    
                     
                       
                         Huntington
                      
                       
                         0
                         1
                         s
                      
                       
                         52.19
                      
                    
                     
                       
                         Hull
                      
                       
                         0
                         1
                         s
                      
                       
                         53.58
                      
                    
                     
                       
                         Lancaster
                      
                       
                         0
                         11
                         s
                      
                       
                         54.08
                      
                    
                     
                       
                         Leicester
                      
                       
                         0
                         4
                         s
                      
                       
                         52.40
                      
                    
                     
                       
                         
                         Lincoln
                      
                       
                         0
                         1
                         s
                      
                       
                         53.12
                      
                    
                     
                       
                         Middle
                         of
                         the
                         Isle
                         of
                         Man
                      
                       
                         0
                         17
                         s
                      
                       
                         54.22
                      
                    
                     
                       
                         Nottingham
                      
                       
                         0
                         4
                         s
                      
                       
                         53.03
                      
                    
                     
                       
                         Newark
                      
                       
                         0
                         3
                         s
                      
                       
                         53.02
                      
                    
                     
                       
                         Newcastle
                      
                       
                         0
                         6
                         s
                      
                       
                         54.58
                      
                    
                     
                       
                         N.
                         Luffingham
                      
                       
                         0
                         3
                         s
                      
                       
                         52.41
                      
                    
                     
                       
                         Norwich
                      
                       
                         0
                         4
                         a
                      
                       
                         52.44
                      
                    
                     
                       
                         Northampton
                      
                       
                         0
                         4
                         s
                      
                       
                         52.18
                      
                    
                     
                       
                         Oxford
                      
                       
                         0
                         5
                         s
                      
                       
                         51.54
                      
                    
                     
                       
                         Okenham
                      
                       
                         0
                         3
                         s
                      
                       
                         52.44
                      
                    
                     
                       
                         Peterborough
                      
                       
                         0
                         2
                         s
                      
                       
                         52.35
                      
                    
                     
                       
                         Richmond
                      
                       
                         0
                         6
                         s
                      
                       
                         54.26
                      
                    
                     
                       
                         Rochester
                      
                       
                         0
                         3
                         a
                      
                       
                         51.28
                      
                    
                     
                       
                         Ross
                      
                       
                         0
                         10
                         s
                      
                       
                         52.07
                      
                    
                     
                       
                         St.
                         Michaels
                         Mount
                         in
                         Cornwal
                      
                       
                         0
                         23
                         s
                      
                       
                         50.38
                      
                    
                     
                       
                         Stafford
                      
                       
                         0
                         8
                         s
                      
                       
                         52.55
                      
                    
                     
                       
                         Stamford
                      
                       
                         0
                         2
                         s
                      
                       
                         52.41
                      
                    
                     
                       
                         Shrewsbury
                      
                       
                         0
                         11
                         s
                      
                       
                         52.48
                      
                    
                     
                       
                         Tredah
                         in
                         Ireland
                      
                       
                         0
                         27
                         s
                      
                       
                         53.28
                      
                    
                     
                       
                         uppingham
                         in
                         Rutland
                      
                       
                         0
                         3
                         s
                      
                       
                         52.40
                      
                    
                     
                       
                         Warwick
                      
                       
                         0
                         6
                         s
                      
                       
                         52.25
                      
                    
                     
                       
                         Winchester
                      
                       
                         0
                         5
                         s
                      
                       
                         50.10
                      
                    
                     
                       
                         Waterford
                         in
                         Ireland
                      
                       
                         0
                         27
                         s
                      
                       
                         52.22
                      
                    
                     
                       
                         Worcester
                      
                       
                         0
                         9
                         s
                      
                       
                         52.20
                      
                    
                     
                       
                         Yarmouth
                         in
                         Suffolk
                      
                       
                         0
                         6
                         a
                      
                       
                         52.45
                      
                    
                     
                       
                         York
                      
                       
                         0
                         4
                         s
                      
                       
                         54.00
                      
                    
                     
                       
                         London
                      
                       
                         0
                         00
                      
                       
                         51.32
                      
                    
                  
                   
                     
                     
                       The
                       Suns
                       mean
                       Longitude
                       and
                       mean
                       Anomaly
                       in
                       AEgyptian
                       Years
                       .
                    
                     
                       
                          
                      
                       
                         ☉
                         Mean
                         Longitude
                      
                       
                         ☉
                         Mean
                         Anomaly
                      
                    
                     
                       
                         1
                      
                       
                         99.9336437563
                      
                       
                         99.9288933116
                      
                    
                     
                       
                         2
                      
                       
                         99.8672875126
                      
                       
                         99.8577866232
                      
                    
                     
                       
                         3
                      
                       
                         99.8009312690
                      
                       
                         99.7866799348
                      
                    
                     
                       
                         4
                      
                       
                         99.7345750253
                      
                       
                         99.7155732465
                      
                    
                     
                       
                         5
                      
                       
                         99.6682187816
                      
                       
                         99.6444665581
                      
                    
                     
                       
                         6
                      
                       
                         99.6018625380
                      
                       
                         99.5733598697
                      
                    
                     
                       
                         7
                      
                       
                         99.5355062943
                      
                       
                         99.5022531814
                      
                    
                     
                       
                         8
                      
                       
                         99.4691500506
                      
                       
                         99.4211464930
                      
                    
                     
                       
                         9
                      
                       
                         99.4027938070
                      
                       
                         99.3600398046
                      
                    
                     
                       
                         10
                      
                       
                         99.3364375633
                      
                       
                         99.2889331162
                      
                    
                     
                       
                         100
                      
                       
                         93.3643756334
                      
                       
                         92.8893311628
                      
                    
                     
                       
                         1000
                      
                       
                         33.6437563341
                      
                       
                         28.8933116289
                      
                    
                  
                   
                     
                       The
                       Suns
                       Mean
                       Anomaly
                       and
                       Praecession
                       of
                       the
                       AEquinox
                       8
                       in
                       .
                       1
                       AEgyptian
                       Years
                       .
                    
                     
                       
                         Year
                         .
                      
                       
                         ☉
                         Mean
                         Anomaly
                      
                       
                         Praecession
                         AEquinox
                         .
                      
                    
                     
                       
                         1
                      
                       
                         99.9297857316
                      
                       
                         00.0038580246
                      
                    
                     
                       
                         2
                      
                       
                         99.8595714632
                      
                       
                         00.0077160493
                      
                    
                     
                       
                         3
                      
                       
                         99.7893571949
                      
                       
                         00.0115740740
                      
                    
                     
                       
                         4
                      
                       
                         99.7191429265
                      
                       
                         00.0154320987
                      
                    
                     
                       
                         5
                      
                       
                         99.6489286582
                      
                       
                         00.0192901234
                      
                    
                     
                       
                         6
                      
                       
                         99.5787143898
                      
                       
                         00.0231481481
                      
                    
                     
                       
                         7
                      
                       
                         66.5085001114
                      
                       
                         00.0270061728
                      
                    
                     
                       
                         8
                      
                       
                         99.2978573164
                      
                       
                         00.0308641975
                      
                    
                     
                       
                         9
                      
                       
                         99.3680715847
                      
                       
                         00.0347222221
                      
                    
                     
                       
                         10
                      
                       
                         99.2978573164
                      
                       
                         00.0385802469
                      
                    
                     
                       
                         100
                      
                       
                         92.9785731642
                      
                       
                         00.3858024691
                      
                    
                     
                       
                         1000
                      
                       
                         99.7857316427
                      
                       
                         03.8580246913
                      
                    
                  
                   
                     
                     
                       The
                       Suns
                       mean
                       Longitude
                       and
                       mean
                       Anomaly
                       in
                       Julian
                       Years
                       .
                    
                     
                       
                          
                      
                       
                         ☉
                         Mean
                         Longitude
                      
                       
                         ☉
                         Mean
                         Anomaly
                      
                    
                     
                       
                         1
                      
                       
                         99.9336437563
                      
                       
                         99.9288933116
                      
                    
                     
                       
                         2
                      
                       
                         99.8672875126
                      
                       
                         99.8577866232
                      
                    
                     
                       
                         3
                      
                       
                         99.8009312689
                      
                       
                         99.7866799348
                      
                    
                     
                       
                         B
                         4
                      
                       
                         00.008365830
                      
                       
                         99.9892901234
                      
                    
                     
                       
                         5
                      
                       
                         99.9420095864
                      
                       
                         99.9181834350
                      
                    
                     
                       
                         6
                      
                       
                         99.875633427
                      
                       
                         99.8470767466
                      
                    
                     
                       
                         7
                      
                       
                         99.8092970990
                      
                       
                         99.7759700583
                      
                    
                     
                       
                         B
                         8
                      
                       
                         00.0167316602
                      
                       
                         99.9785802468
                      
                    
                     
                       
                         9
                      
                       
                         99.9503754165
                      
                       
                         99.9074735584
                      
                    
                     
                       
                         10
                      
                       
                         99.8840191728
                      
                       
                         99.8363668700
                      
                    
                     
                       
                         11
                      
                       
                         99.8176629291
                      
                       
                         99.7652591816
                      
                    
                     
                       
                         B
                         12
                      
                       
                         00.0250974903
                      
                       
                         99.9678703702
                      
                    
                     
                       
                         13
                      
                       
                         99.9587412466
                      
                       
                         99.8967636818
                      
                    
                     
                       
                         14
                      
                       
                         99.8923850029
                      
                       
                         99.8256569934
                      
                    
                     
                       
                         15
                      
                       
                         99.8260287592
                      
                       
                         99.7545503050
                      
                    
                     
                       
                         B
                         16
                      
                       
                         00.0334633205
                      
                       
                         99.9571604936
                      
                    
                     
                       
                         17
                      
                       
                         99.9671070768
                      
                       
                         99.8860548052
                      
                    
                     
                       
                         18
                      
                       
                         99.9007508331
                      
                       
                         99.8149481168
                      
                    
                     
                       
                         19
                      
                       
                         99.8343945894
                      
                       
                         99.7438414284
                      
                    
                     
                       
                         B
                         20
                      
                       
                         00.0418291506
                      
                       
                         99.9164506171
                      
                    
                     
                       
                         40
                      
                       
                         00.0836583012
                      
                       
                         99.8929012342
                      
                    
                     
                       
                         60
                      
                       
                         00.1254874518
                      
                       
                         99.8393518513
                      
                    
                     
                       
                         80
                      
                       
                         00.1673166024
                      
                       
                         99.7858024684
                      
                    
                     
                       
                         100
                      
                       
                         00.2091457530
                      
                       
                         99.
                         73225308●5
                      
                    
                     
                       
                         200
                      
                       
                         00.4182015060
                      
                       
                         99.4645061710
                      
                    
                     
                       
                         300
                      
                       
                         00.6274372590
                      
                       
                         99.1967592565
                      
                    
                     
                       
                         400
                      
                       
                         00.8365830120
                      
                       
                         98.9290123420
                      
                    
                     
                       
                         500
                      
                       
                         01.0457287650
                      
                       
                         98.6612654275
                      
                    
                     
                       
                         600
                      
                       
                         01.2548745180
                      
                       
                         98.3935185130
                      
                    
                     
                       
                         700
                      
                       
                         01.
                         4640●02710
                      
                       
                         98.1257715985
                      
                    
                  
                   
                     
                     
                       The
                       ☉
                       mean
                       Longitude
                       and
                       Anomaly
                    
                     
                       
                         AEra
                      
                       
                         ☉
                         mean
                         Longitude
                      
                       
                         ☉
                         mean
                         Anomaly
                      
                    
                     
                       
                         Chr.
                         
                      
                       
                         77.
                         22400.86419
                      
                       
                         58.
                         24289.56790
                      
                    
                     
                       
                         1600
                      
                       
                         80.
                         54891.97529
                      
                       
                         53.
                         95880.62961
                      
                    
                     
                       
                         1620
                      
                       
                         80.
                         59074.89035
                      
                       
                         53.
                         90525.69132
                      
                    
                     
                       
                         1640
                      
                       
                         80.
                         63257.80541
                      
                       
                         53.
                         85170.75303
                      
                    
                     
                       
                         1660
                      
                       
                         80.
                         67440.72047
                      
                       
                         53.
                         79815.81474
                      
                    
                     
                       
                         1680
                      
                       
                         80.
                         71623.63553
                      
                       
                         53.
                         74460.87645
                      
                    
                     
                       
                         1700
                      
                       
                         80.
                         75806.55059
                      
                       
                         53.
                         69105.93816
                      
                    
                     
                       
                         1720
                      
                       
                         80.
                         79989.46665
                      
                       
                         53.
                         63750.99987
                      
                    
                     
                       
                         1740
                      
                       
                         80.
                         84172.38171
                      
                       
                         53.
                         58396.06158
                      
                    
                     
                       
                         1760
                      
                       
                         80.
                         88265.29677
                      
                       
                         53.
                         53041.12329
                      
                    
                     
                       
                          
                      
                       
                         ☉
                         mean
                         Lon.
                         in
                         Mon.
                         
                      
                       
                         ☉
                         mean
                         Ano.
                         in
                         Mo.
                         
                      
                    
                     
                       
                         Ianu.
                         
                      
                       
                         08.
                         48751.49488
                      
                       
                         08.
                         48711.14867
                      
                    
                     
                       
                         Febr.
                         
                      
                       
                         16.
                         15365.74832
                      
                       
                         16.
                         15288.96037
                      
                    
                     
                       
                         Mar.
                         
                      
                       
                         24.
                         64117.24320
                      
                       
                         24.
                         64000.10904
                      
                    
                     
                       
                         April
                      
                       
                         32.
                         85489.65760
                      
                       
                         32.
                         85333.47872
                      
                    
                     
                       
                         May
                      
                       
                         41.
                         34241.15248
                      
                       
                         41.
                         34044.62739
                      
                    
                     
                       
                         Iune
                      
                       
                         49.
                         55613.56688
                      
                       
                         49.
                         55377.99708
                      
                    
                     
                       
                         Iuly
                      
                       
                         58.
                         04365.06176
                      
                       
                         58.
                         04089.14575
                      
                    
                     
                       
                         Aug.
                         
                      
                       
                         66.
                         53116.55664
                      
                       
                         66.
                         52800.29442
                      
                    
                     
                       
                         Sept.
                         
                      
                       
                         74.
                         74488.97104
                      
                       
                         74.
                         74133.66410
                      
                    
                     
                       
                         Octo.
                         
                      
                       
                         83.
                         23240.46592
                      
                       
                         85.
                         22844.81277
                      
                    
                     
                       
                         Nov.
                         
                      
                       
                         91.
                         44612.88032
                      
                       
                         91.
                         44178.18245
                      
                    
                     
                       
                         Dec.
                         
                      
                       
                         99.
                         93364.37563
                      
                       
                         99.
                         92889.33116
                      
                    
                  
                
                 
                   In
                   Anno
                   ●issentili
                   ;
                   post
                   Februarium
                   adde
                   unum
                   diem
                   &
                   unius
                   dies
                   motum
                   .
                
                 
                 
                   
                     
                       The
                       Suns
                       mean
                       Longitude
                       and
                       mean
                       Anomaly
                       in
                       Days
                       .
                    
                     
                       
                          
                      
                       
                         ☉
                         mean
                         Longitude
                      
                       
                         ☉
                         mean
                         Anomaly
                      
                    
                     
                       
                         1
                      
                       
                         0.2737908048
                      
                       
                         0.2737777898
                      
                    
                     
                       
                         2
                      
                       
                         0.5475816096
                      
                       
                         0.5475555796
                      
                    
                     
                       
                         3
                      
                       
                         0.8213724144
                      
                       
                         0.8213333694
                      
                    
                     
                       
                         4
                      
                       
                         1.0951632192
                      
                       
                         1.0951111592
                      
                    
                     
                       
                         5
                      
                       
                         1
                         .
                         3●89540240
                      
                       
                         1.3688889490
                      
                    
                     
                       
                         6
                      
                       
                         1.6427448288
                      
                       
                         1.6426667388
                      
                    
                     
                       
                         7
                      
                       
                         1.9165356336
                      
                       
                         1.9164445286
                      
                    
                     
                       
                         8
                      
                       
                         2.1903264384
                      
                       
                         2.1902223184
                      
                    
                     
                       
                         9
                      
                       
                         2.4641172432
                      
                       
                         2.4640001082
                      
                    
                     
                       
                         10
                      
                       
                         2.7379080480
                      
                       
                         2.7377778980
                      
                    
                     
                       
                         11
                      
                       
                         3.0116988528
                      
                       
                         3.0115556878
                      
                    
                     
                       
                         12
                      
                       
                         3.2854896576
                      
                       
                         3.2853334776
                      
                    
                     
                       
                         13
                      
                       
                         3.5592804624
                      
                       
                         3.5591112674
                      
                    
                     
                       
                         14
                      
                       
                         3.8330712672
                      
                       
                         3.8328890572
                      
                    
                     
                       
                         15
                      
                       
                         4.1068620720
                      
                       
                         4.1066668470
                      
                    
                     
                       
                         16
                      
                       
                         4.3806428768
                      
                       
                         4.3804446368
                      
                    
                     
                       
                         17
                      
                       
                         4.6544436816
                      
                       
                         4.6542224266
                      
                    
                     
                       
                         18
                      
                       
                         4.9282344864
                      
                       
                         4.9280002164
                      
                    
                     
                       
                         19
                      
                       
                         5.2020252912
                      
                       
                         5.2077780062
                      
                    
                     
                       
                         20
                      
                       
                         5.4758160960
                      
                       
                         5.4755557960
                      
                    
                     
                       
                         21
                      
                       
                         5.7496069008
                      
                       
                         5.7493335858
                      
                    
                     
                       
                         22
                      
                       
                         6.0233977056
                      
                       
                         6.0231113756
                      
                    
                     
                       
                         23
                      
                       
                         6.2971885104
                      
                       
                         6.2968891654
                      
                    
                     
                       
                         24
                      
                       
                         6.5709793152
                      
                       
                         6.5706669552
                      
                    
                     
                       
                         25
                      
                       
                         6.8447701200
                      
                       
                         6.8444447450
                      
                    
                     
                       
                         26
                      
                       
                         7.1185609248
                      
                       
                         7.1182225348
                      
                    
                     
                       
                         27
                      
                       
                         7.3923517296
                      
                       
                         7.3920003246
                      
                    
                     
                       
                         28
                      
                       
                         7.6661425344
                      
                       
                         7.6957781144
                      
                    
                     
                       
                         29
                      
                       
                         7.9399333392
                      
                       
                         7.9395559042
                      
                    
                     
                       
                         30
                      
                       
                         8.2137241440
                      
                       
                         8.2133336940
                      
                    
                     
                       
                         31
                      
                       
                         8.4875149488
                      
                       
                         8.4871114838
                      
                    
                  
                
                 
                 
                   
                     
                       The
                       Suns
                       mean
                       Longitude
                       and
                       mean
                       Anomaly
                       in
                       Days
                    
                     
                       
                          
                      
                       
                         ☉
                         Mean
                         Longitude
                      
                       
                         ☉
                         Mean
                         Anomaly
                         .
                      
                    
                     
                       
                         1
                      
                       
                         0.0114079502
                      
                       
                         0.0114074079
                      
                    
                     
                       
                         2
                      
                       
                         0.0228159004
                      
                       
                         0.0228148158
                      
                    
                     
                       
                         3
                      
                       
                         0.0342238506
                      
                       
                         0.0342222237
                      
                    
                     
                       
                         4
                      
                       
                         0.0456318008
                      
                       
                         0.0456296316
                      
                    
                     
                       
                         5
                      
                       
                         0.0570397510
                      
                       
                         0.0570370395
                      
                    
                     
                       
                         6
                      
                       
                         0.0684477012
                      
                       
                         0.0684444474
                      
                    
                     
                       
                         7
                      
                       
                         0.0798556514
                      
                       
                         0.0798518553
                      
                    
                     
                       
                         8
                      
                       
                         0.0912636016
                      
                       
                         0.0912592632
                      
                    
                     
                       
                         9
                      
                       
                         0.1026715518
                      
                       
                         0.1026666711
                      
                    
                     
                       
                         10
                      
                       
                         0.1140795020
                      
                       
                         0.1140740790
                      
                    
                     
                       
                         11
                      
                       
                         0.1254874522
                      
                       
                         0.1254814869
                      
                    
                     
                       
                         12
                      
                       
                         0.1368954024
                      
                       
                         0.1368888948
                      
                    
                     
                       
                         13
                      
                       
                         0.1483033526
                      
                       
                         0.1482963027
                      
                    
                     
                       
                         14
                      
                       
                         0.1597113028
                      
                       
                         0.1597037106
                      
                    
                     
                       
                         15
                      
                       
                         0.1711192530
                      
                       
                         0.1711111185
                      
                    
                     
                       
                         16
                      
                       
                         0.1825272032
                      
                       
                         0.1825185264
                      
                    
                     
                       
                         17
                      
                       
                         0.1939351534
                      
                       
                         0.1939259343
                      
                    
                     
                       
                         18
                      
                       
                         0.2053431036
                      
                       
                         0.2053333422
                      
                    
                     
                       
                         19
                      
                       
                         0.2167510538
                      
                       
                         0.2167407501
                      
                    
                     
                       
                         20
                      
                       
                         0.2281590040
                      
                       
                         0.2281481580
                      
                    
                     
                       
                         21
                      
                       
                         0.2395669542
                      
                       
                         0.2395555659
                      
                    
                     
                       
                         22
                      
                       
                         0.2509749044
                      
                       
                         0.2509629738
                      
                    
                     
                       
                         23
                      
                       
                         0.2623828546
                      
                       
                         0.2623703817
                      
                    
                     
                       
                         24
                      
                       
                         0.2737777048
                      
                       
                         0.2737777896
                      
                    
                  
                
                 
                 
                   
                     
                       The
                       Suns
                       mean
                       Anomaly
                       and
                       Praecession
                       of
                       the
                       AEquinox
                       .
                    
                     
                       
                         AEra
                      
                       
                         ☉
                         Anomaly
                         .
                      
                       
                         Praecess
                         .
                         AEquinox
                      
                    
                     
                       
                         Chr.
                         
                      
                       
                         56.
                         69976.85185
                      
                       
                         20.
                         49768.51851
                      
                    
                     
                       
                         1600
                      
                       
                         53.
                         87323.10751
                      
                       
                         26.
                         67052.46907
                      
                    
                     
                       
                         1620
                      
                       
                         53.
                         83789.15687
                      
                       
                         26.
                         74768.51845
                      
                    
                     
                       
                         1640
                      
                       
                         53.
                         80255.20623
                      
                       
                         26.
                         82484.56783
                      
                    
                     
                       
                         1660
                      
                       
                         53.
                         76721.25559
                      
                       
                         26.
                         90200.61721
                      
                    
                     
                       
                         1680
                      
                       
                         53.
                         73187.30495
                      
                       
                         26.
                         97916.66659
                      
                    
                     
                       
                         1700
                      
                       
                         53.69653
                         ▪
                         35431
                      
                       
                         27.
                         05632.71597
                      
                    
                     
                       
                         1720
                      
                       
                         53.
                         66119.40367
                      
                       
                         27.
                         13348.76535
                      
                    
                     
                       
                         1740
                      
                       
                         53.
                         65585.45303
                      
                       
                         27.
                         21064.81473
                      
                    
                     
                       
                         1760
                      
                       
                         53.
                         59051.50230
                      
                       
                         27.
                         28780.86411
                      
                    
                     
                       
                          
                      
                       
                         ☉
                         Anomaly
                         in
                         Months
                      
                       
                         Praecess
                         .
                         AEquinox
                         in
                         Months
                      
                    
                     
                       
                         Ianu
                      
                       
                         08.
                         48718.72813
                      
                       
                         0.
                         00032.76678
                      
                    
                     
                       
                         Febr.
                         
                      
                       
                         16.
                         15303.38579
                      
                       
                         0.
                         00062.36258
                      
                    
                     
                       
                         Mar.
                         
                      
                       
                         24.
                         64022.11392
                      
                       
                         0.
                         00095.12937
                      
                    
                     
                       
                         April
                      
                       
                         32.
                         85362.81857
                      
                       
                         0.
                         00126.83916
                      
                    
                     
                       
                         May
                      
                       
                         41.
                         34081.54670
                      
                       
                         0.
                         00159.60594
                      
                    
                     
                       
                         Iune
                      
                       
                         49.
                         55422.25134
                      
                       
                         0.
                         00191.31573
                      
                    
                     
                       
                         Iuly
                      
                       
                         58.
                         04140.97947
                      
                       
                         0.
                         00224.08251
                      
                    
                     
                       
                         Aug.
                         
                      
                       
                         66.
                         52859.70760
                      
                       
                         0.
                         00256.84929
                      
                    
                     
                       
                         Sept.
                         
                      
                       
                         74.
                         74200.41225
                      
                       
                         0.
                         00288.55908
                      
                    
                     
                       
                         Octo.
                         
                      
                       
                         83.
                         22919.14038
                      
                       
                         0.
                         00321.32587
                      
                    
                     
                       
                         Nov.
                         
                      
                       
                         91.
                         44259.84502
                      
                       
                         0.
                         00353.03566
                      
                    
                     
                       
                         Dec.
                         
                      
                       
                         99.
                         92978.57315
                      
                       
                         0.
                         00385.80244
                      
                    
                  
                
                 
                 
                   
                     
                       The
                       ☉
                       mean
                       Anomaly
                       ,
                       and
                       Praecession
                       of
                       the
                       AEquinox
                       in
                       Julian
                       Years
                       .
                    
                     
                       
                          
                      
                       
                         ☉
                         mean
                         Anomaly
                      
                       
                         Praecess
                         .
                         AEquinox
                      
                    
                     
                       
                         1
                      
                       
                         99.9297857316
                      
                       
                         00.0038580246
                      
                    
                     
                       
                         2
                      
                       
                         99.8595714612
                      
                       
                         00.0077160493
                      
                    
                     
                       
                         3
                      
                       
                         99.7893571949
                      
                       
                         00.0115740740
                      
                    
                     
                       
                         B
                         4
                      
                       
                         99.9929231686
                      
                       
                         00.0154320987
                      
                    
                     
                       
                         5
                      
                       
                         99.9227089002
                      
                       
                         00.0192901233
                      
                    
                     
                       
                         6
                      
                       
                         99.8524946318
                      
                       
                         00.0231481479
                      
                    
                     
                       
                         7
                      
                       
                         99.7822803634
                      
                       
                         00.0270061725
                      
                    
                     
                       
                         B
                         8
                      
                       
                         99.9858463372
                      
                       
                         00.0308641974
                      
                    
                     
                       
                         9
                      
                       
                         99.9156320688
                      
                       
                         00.0347222220
                      
                    
                     
                       
                         10
                      
                       
                         99.8454178004
                      
                       
                         00.0385802466
                      
                    
                     
                       
                         11
                      
                       
                         99.7752035321
                      
                       
                         00.0424382714
                      
                    
                     
                       
                         B
                         12
                      
                       
                         99.9787695058
                      
                       
                         00.0462962961
                      
                    
                     
                       
                         13
                      
                       
                         99.9085552374
                      
                       
                         00.0501543207
                      
                    
                     
                       
                         14
                      
                       
                         99.8383409690
                      
                       
                         00.0540123453
                      
                    
                     
                       
                         15
                      
                       
                         99.7681266066
                      
                       
                         00.0578703699
                      
                    
                     
                       
                         B
                         16
                      
                       
                         99.9716926744
                      
                       
                         00.0617283948
                      
                    
                     
                       
                         17
                      
                       
                         99.9014784060
                      
                       
                         00.0655864194
                      
                    
                     
                       
                         18
                      
                       
                         99.8312647376
                      
                       
                         00.0694444440
                      
                    
                     
                       
                         19
                      
                       
                         99.7610498692
                      
                       
                         00.0733024686
                      
                    
                     
                       
                         B
                         20
                      
                       
                         99.9646158434
                      
                       
                         00.0771604938
                      
                    
                     
                       
                         40
                      
                       
                         99.9292306868
                      
                       
                         00.1543209876
                      
                    
                     
                       
                         60
                      
                       
                         99.8938465302
                      
                       
                         00.2314814814
                      
                    
                     
                       
                         80
                      
                       
                         99.8584623736
                      
                       
                         00.3086419752
                      
                    
                     
                       
                         100
                      
                       
                         99.8270782170
                      
                       
                         00.3858024690
                      
                    
                     
                       
                         200
                      
                       
                         99.6461564340
                      
                       
                         00.7716049380
                      
                    
                     
                       
                         300
                      
                       
                         99.4692346510
                      
                       
                         01.1574074070
                      
                    
                     
                       
                         400
                      
                       
                         99.2923128680
                      
                       
                         01.5432098760
                      
                    
                     
                       
                         500
                      
                       
                         99.1153910850
                      
                       
                         01.9290123450
                      
                    
                     
                       
                         600
                      
                       
                         98.9384693020
                      
                       
                         02.3148148140
                      
                    
                     
                       
                         700
                      
                       
                         98.7615475190
                      
                       
                         02.7006172830
                      
                    
                  
                
                 
                 
                   
                     
                       The
                       Suns
                       mean
                       Anomaly
                       and
                       Praec
                       .
                       of
                       the
                       AEqui
                       .
                       in
                       Days
                       .
                    
                     
                       
                         D
                      
                       
                         ☉
                         Anomaly
                      
                       
                         Praecess
                         .
                         AEquinox
                      
                    
                     
                       
                         1
                      
                       
                         0.2737802348
                      
                       
                         0.0000105699
                      
                    
                     
                       
                         2
                      
                       
                         0.5475604697
                      
                       
                         0.0000211398
                      
                    
                     
                       
                         3
                      
                       
                         0.8213407046
                      
                       
                         0.0000317097
                      
                    
                     
                       
                         4
                      
                       
                         1.0951209395
                      
                       
                         0.0000422797
                      
                    
                     
                       
                         5
                      
                       
                         1.3689011744
                      
                       
                         0.0000528496
                      
                    
                     
                       
                         6
                      
                       
                         1.6426814092
                      
                       
                         0.0000634195
                      
                    
                     
                       
                         7
                      
                       
                         1.9164616441
                      
                       
                         0.0000739894
                      
                    
                     
                       
                         8
                      
                       
                         2.1902418790
                      
                       
                         0.0000845593
                      
                    
                     
                       
                         9
                      
                       
                         2.4640221139
                      
                       
                         0.0000951292
                      
                    
                     
                       
                         10
                      
                       
                         2.7378023488
                      
                       
                         0.0001056993
                      
                    
                     
                       
                         11
                      
                       
                         3.0115825836
                      
                       
                         0.0001162692
                      
                    
                     
                       
                         12
                      
                       
                         3.2853628184
                      
                       
                         0.0001268391
                      
                    
                     
                       
                         13
                      
                       
                         3.5591430532
                      
                       
                         0.0001374090
                      
                    
                     
                       
                         14
                      
                       
                         3.8329232880
                      
                       
                         0.0001479789
                      
                    
                     
                       
                         15
                      
                       
                         4.1067035228
                      
                       
                         0.0001585488
                      
                    
                     
                       
                         16
                      
                       
                         4.3804837576
                      
                       
                         0.0001691187
                      
                    
                     
                       
                         17
                      
                       
                         4.6542639924
                      
                       
                         0.0001796886
                      
                    
                     
                       
                         18
                      
                       
                         4.9280442272
                      
                       
                         0.0001902585
                      
                    
                     
                       
                         19
                      
                       
                         4.2018244620
                      
                       
                         0.0002008284
                      
                    
                     
                       
                         20
                      
                       
                         5.4756046976
                      
                       
                         0.0002113986
                      
                    
                     
                       
                         21
                      
                       
                         5.7493849324
                      
                       
                         0.0002219685
                      
                    
                     
                       
                         22
                      
                       
                         6.0231651672
                      
                       
                         0.0002325384
                      
                    
                     
                       
                         23
                      
                       
                         6.2969454020
                      
                       
                         0.0002431083
                      
                    
                     
                       
                         24
                      
                       
                         6.5707256368
                      
                       
                         0.0002536782
                      
                    
                     
                       
                         25
                      
                       
                         6.8445058716
                      
                       
                         0.0002642481
                      
                    
                     
                       
                         26
                      
                       
                         7.1182861064
                      
                       
                         0.0002748180
                      
                    
                     
                       
                         27
                      
                       
                         7.3920663412
                      
                       
                         0.0002853879
                      
                    
                     
                       
                         28
                      
                       
                         7.6658455766
                      
                       
                         0.0002959580
                      
                    
                     
                       
                         29
                      
                       
                         7.9396258115
                      
                       
                         0.0003065279
                      
                    
                     
                       
                         30
                      
                       
                         8.2134070464
                      
                       
                         0.0003170979
                      
                    
                     
                       
                         31
                      
                       
                         8.4871872813
                      
                       
                         0.0003276678
                      
                    
                  
                
                 
                 
                   
                     
                       The
                       Suns
                       mean
                       Anomaly
                       and
                       Praec
                       .
                       of
                       the
                       AEqui
                       .
                       in
                       Hours
                    
                     
                       
                         D
                      
                       
                         ☉
                         mean
                         Anomaly
                      
                       
                         Praecess
                         .
                         AEquinox
                      
                    
                     
                       
                         1
                      
                       
                         0.0114075097
                      
                       
                         0.0000004404
                      
                    
                     
                       
                         2
                      
                       
                         0.0228150195
                      
                       
                         08808
                      
                    
                     
                       
                         3
                      
                       
                         0.0342225293
                      
                       
                         13212
                      
                    
                     
                       
                         4
                      
                       
                         0.0456300391
                      
                       
                         17616
                      
                    
                     
                       
                         5
                      
                       
                         0.0570375489
                      
                       
                         22020
                      
                    
                     
                       
                         6
                      
                       
                         0.0684450587
                      
                       
                         0.0000026424
                      
                    
                     
                       
                         7
                      
                       
                         0.0798525684
                      
                       
                         30828
                      
                    
                     
                       
                         8
                      
                       
                         0.0912600782
                      
                       
                         35232
                      
                    
                     
                       
                         9
                      
                       
                         0.1026675881
                      
                       
                         39636
                      
                    
                     
                       
                         10
                      
                       
                         0.1140750978
                      
                       
                         44041
                      
                    
                     
                       
                         11
                      
                       
                         0.1254826075
                      
                       
                         0.0000048445
                      
                    
                     
                       
                         12
                      
                       
                         0.1368901174
                      
                       
                         0.0000052849
                      
                    
                     
                       
                         13
                      
                       
                         0.1482976271
                      
                       
                         57253
                      
                    
                     
                       
                         14
                      
                       
                         0.1597051368
                      
                       
                         61657
                      
                    
                     
                       
                         15
                      
                       
                         0.1711126465
                      
                       
                         66061
                      
                    
                     
                       
                         16
                      
                       
                         0.1825201562
                      
                       
                         70465
                      
                    
                     
                       
                         17
                      
                       
                         0.1939276659
                      
                       
                         74869
                      
                    
                     
                       
                         18
                      
                       
                         0.2053351761
                      
                       
                         0.0000079272
                      
                    
                     
                       
                         19
                      
                       
                         0.2167426858
                      
                       
                         83677
                      
                    
                     
                       
                         20
                      
                       
                         0.2281501955
                      
                       
                         88081
                      
                    
                     
                       
                         21
                      
                       
                         0.2395577052
                      
                       
                         92485
                      
                    
                     
                       
                         22
                      
                       
                         0.2509652149
                      
                       
                         96889
                      
                    
                     
                       
                         23
                      
                       
                         0.2623727246
                      
                       
                         101293
                      
                    
                     
                       
                         24
                      
                       
                         0.2737802348
                      
                       
                         0.0000105698
                      
                    
                  
                
              
            
          
           
             
             
               THE
               TABLES
               OF
               THE
               MOONS
               MEAN
               MOTIONS
               .
            
             
             
               
                 
                   The
                   Moons
                   mean
                   Longitude
                   and
                   Apogeon
                
                 
                   
                     AEra
                  
                   
                     ☽
                     Mean
                     Longitude
                  
                   
                     ☽
                     Apogaeon
                  
                
                 
                   
                     Chr.
                     
                  
                   
                     34.0088734567
                  
                   
                     78.8286265432
                  
                
                 
                   
                     1600
                  
                   
                     02.0644290122
                  
                   
                     63.5892746911
                  
                
                 
                   
                     1620
                  
                   
                     39.1651134566
                  
                   
                     89.6540895059
                  
                
                 
                   
                     1640
                  
                   
                     76.2658079010
                  
                   
                     15.7189033207
                  
                
                 
                   
                     1660
                  
                   
                     13.3665023454
                  
                   
                     41.7837191355
                  
                
                 
                   
                     1680
                  
                   
                     50.4671967898
                  
                   
                     67.6485339503
                  
                
                 
                   
                     1700
                  
                   
                     87.5675912342
                  
                   
                     93.9133487651
                  
                
                 
                   
                     1620
                  
                   
                     29.6685801230
                  
                   
                     19.9781635799
                  
                
                 
                   
                     1740
                  
                   
                     61.7692801230
                  
                   
                     46.0429783947
                  
                
                 
                   
                     1760
                  
                   
                     98.8699745674
                  
                   
                     72.1077932095
                  
                
                 
                   
                      
                  
                   
                     ☽
                     Mean
                     Long.
                     in
                     Mon.
                     
                  
                   
                     ☽
                     Apogaeon
                     in
                     Mont.
                     
                  
                
                 
                   
                     Ianu.
                     
                  
                   
                     13.4633984897
                  
                   
                     00.9593447922
                  
                
                 
                   
                     Febr.
                     
                  
                   
                     15.9464670933
                  
                   
                     01.8258497658
                  
                
                 
                   
                     Mar.
                     
                  
                   
                     29.4098665830
                  
                   
                     02.7851945580
                  
                
                 
                   
                     April
                  
                   
                     39.2131554440
                  
                   
                     03.7135927440
                  
                
                 
                   
                     May.
                     
                  
                   
                     52.6765539337
                  
                   
                     04.6729375362
                  
                
                 
                   
                     Iune
                  
                   
                     62.4798427947
                  
                   
                     05.6013357222
                  
                
                 
                   
                     Iuly
                  
                   
                     75.9432412844
                  
                   
                     06.5606805144
                  
                
                 
                   
                     Aug.
                     
                  
                   
                     89.4066397741
                  
                   
                     07.5200253066
                  
                
                 
                   
                     Sept.
                     
                  
                   
                     99.2099286451
                  
                   
                     08.4484234926
                  
                
                 
                   
                     Octo.
                     
                  
                   
                     12.6733271348
                  
                   
                     09.4077682848
                  
                
                 
                   
                     Nov.
                     
                  
                   
                     22.4766159958
                  
                   
                     10.3361664708
                  
                
                 
                   
                     Dec.
                     
                  
                   
                     35.9400144893
                  
                   
                     11.2955112636
                  
                
              
            
             
             
               
                 
                   The
                   Moons
                   mean
                   Anomaly
                   and
                   Node
                   Retrograde
                
                 
                   
                     AEra
                  
                   
                     ☽
                     Mean
                     Anomaly
                  
                   
                     ☽
                     Node
                     Retrograde
                  
                
                 
                   
                     Chr.
                     
                  
                   
                     55.1802469135
                  
                   
                     74.6984567901
                  
                
                 
                   
                     1600
                  
                   
                     38.4751543211
                  
                   
                     78.2198302468
                  
                
                 
                   
                     1620
                  
                   
                     49.5110239507
                  
                   
                     70.7638117283
                  
                
                 
                   
                     1640
                  
                   
                     60.5469035803
                  
                   
                     63.3077932098
                  
                
                 
                   
                     1660
                  
                   
                     71.5827832099
                  
                   
                     55.8517746913
                  
                
                 
                   
                     1680
                  
                   
                     82.6186628395
                  
                   
                     48.3957561728
                  
                
                 
                   
                     1700
                  
                   
                     93.6545424691
                  
                   
                     40.9397376543
                  
                
                 
                   
                     1720
                  
                   
                     04.6904220987
                  
                   
                     33.4837191358
                  
                
                 
                   
                     1740
                  
                   
                     15.7263017283
                  
                   
                     26.0277006173
                  
                
                 
                   
                     1760
                  
                   
                     26.7621813579
                  
                   
                     18.5716820988
                  
                
                 
                   
                      
                  
                   
                     ☽
                     Mean
                     Ano.
                     in
                     Mon.
                     
                  
                   
                     Node
                     Ret.
                     in
                     Mont.
                     
                  
                
                 
                   
                     Ianu.
                     
                  
                   
                     12.5040536975
                  
                   
                     00.4559979224
                  
                
                 
                   
                     Febr.
                     
                  
                   
                     14.7206183275
                  
                   
                     00.8678670136
                  
                
                 
                   
                     Mar.
                     
                  
                   
                     27.2246720250
                  
                   
                     01.3238649360
                  
                
                 
                   
                     April
                  
                   
                     35.4995627000
                  
                   
                     01.7651532480
                  
                
                 
                   
                     May.
                     
                  
                   
                     48.0036163975
                  
                   
                     02.2211511704
                  
                
                 
                   
                     Iune
                  
                   
                     56.8785070725
                  
                   
                     02.6624394824
                  
                
                 
                   
                     Iuly
                  
                   
                     69.3825607700
                  
                   
                     03.1184374048
                  
                
                 
                   
                     Aug.
                     
                  
                   
                     81.8866144675
                  
                   
                     03.5744353272
                  
                
                 
                   
                     Sept.
                     
                  
                   
                     90.7615051425
                  
                   
                     04.0157236392
                  
                
                 
                   
                     Octo.
                     
                  
                   
                     03.2655588400
                  
                   
                     04.4717215616
                  
                
                 
                   
                     Nov.
                     
                  
                   
                     12.1404495150
                  
                   
                     04.9130098736
                  
                
                 
                   
                     Dec.
                     
                  
                   
                     24.6445032256
                  
                   
                     05.3690078260
                  
                
              
               
                 
                 
                   The
                   Moons
                   mean
                   Motions
                   in
                   Julian
                   Years
                   .
                
                 
                   
                      
                  
                   
                     ☽
                     Mean
                     Longitude
                  
                   
                     ☽
                     Apogaeon
                  
                
                 
                   
                     1
                  
                   
                     35.9400144893
                  
                   
                     11.2955112636
                  
                
                 
                   
                     2
                  
                   
                     71.8800289786
                  
                   
                     22.5910225272
                  
                
                 
                   
                     3
                  
                   
                     07.8200434679
                  
                   
                     33.8865337908
                  
                
                 
                   
                     B
                     4
                  
                   
                     47.4201388888
                  
                   
                     45.2129629629
                  
                
                 
                   
                     5
                  
                   
                     83.3601533781
                  
                   
                     56.5084742265
                  
                
                 
                   
                     6
                  
                   
                     19.3001678674
                  
                   
                     67.8039854901
                  
                
                 
                   
                     7
                  
                   
                     55.2401823567
                  
                   
                     79.0994967537
                  
                
                 
                   
                     B
                     8
                  
                   
                     94.8402777777
                  
                   
                     90.4259259258
                  
                
                 
                   
                     9
                  
                   
                     30.7802922670
                  
                   
                     01●7214371894
                  
                
                 
                   
                     10
                  
                   
                     66.7203067563
                  
                   
                     13.0169484530
                  
                
                 
                   
                     11
                  
                   
                     02.6603212456
                  
                   
                     24.3124597166
                  
                
                 
                   
                     B
                     12
                  
                   
                     42.2604166666
                  
                   
                     35.6388888888
                  
                
                 
                   
                     13
                  
                   
                     78.
                     ●004311559
                  
                   
                     46.9344001524
                  
                
                 
                   
                     14
                  
                   
                     14.1404456652
                  
                   
                     58
                     .
                     2299114●60
                  
                
                 
                   
                     15
                  
                   
                     50.0804601545
                  
                   
                     69.
                     ●2●4226706
                  
                
                 
                   
                     B
                     16
                  
                   
                     89.6805555555
                  
                   
                     80.8518518518
                  
                
                 
                   
                     17
                  
                   
                     25.6205700448
                  
                   
                     91.1473631154
                  
                
                 
                   
                     18
                  
                   
                     61.5605845341
                  
                   
                     02.4428743790
                  
                
                 
                   
                     19
                  
                   
                     97.5005990234
                  
                   
                     13.7383856426
                  
                
                 
                   
                     B
                     20
                  
                   
                     37.1006944404
                  
                   
                     26
                     .
                     0648●48148
                  
                
                 
                   
                     40
                  
                   
                     74.2013888888
                  
                   
                     52.1296296296
                  
                
                 
                   
                     60
                  
                   
                     11.3020833333
                  
                   
                     78.1944444444
                  
                
                 
                   
                     80
                  
                   
                     48.4027777777
                  
                   
                     04.2592592592
                  
                
                 
                   
                     100
                  
                   
                     85.5034722222
                  
                   
                     30.3240740740
                  
                
                 
                   
                     200
                  
                   
                     71.0069444444
                  
                   
                     60
                     .
                     648●●81●81
                  
                
                 
                   
                     300
                  
                   
                     56.5104166666
                  
                   
                     90.9722222222
                  
                
                 
                   
                     400
                  
                   
                     42.0138888888
                  
                   
                     21.2962962962
                  
                
                 
                   
                     500
                  
                   
                     27
                     .
                     517361111●
                  
                   
                     51.6003703700
                  
                
                 
                   
                     600
                  
                   
                     13.0208333333
                  
                   
                     91.9444444442
                  
                
                 
                   
                     700
                  
                   
                     98.5243055555
                  
                   
                     12.2685185182
                  
                
              
            
             
             
               
                 
                   The
                   Moons
                   mean
                   Motions
                   in
                   Julian
                   Years
                
                 
                   
                      
                  
                   
                     ☽
                     Mean
                     Anomaly
                  
                   
                     ☽
                     Nodes
                     Retrograde
                  
                
                 
                   
                     1
                  
                   
                     24.6445032256
                  
                   
                     05.3690078260
                  
                
                 
                   
                     2
                  
                   
                     49.2890064512
                  
                   
                     10.7380156520
                  
                
                 
                   
                     3
                  
                   
                     73.9335096768
                  
                   
                     16.1070234780
                  
                
                 
                   
                     B
                     4
                  
                   
                     02.2071759259
                  
                   
                     21.4912037037
                  
                
                 
                   
                     5
                  
                   
                     26.8516791515
                  
                   
                     26.7602115297
                  
                
                 
                   
                     6
                  
                   
                     5●
                     .
                     4951823771
                  
                   
                     32.1292193557
                  
                
                 
                   
                     7
                  
                   
                     76.1396856027
                  
                   
                     37.4982271817
                  
                
                 
                   
                     B
                     8
                  
                   
                     04.4143518518
                  
                   
                     42.9824074074
                  
                
                 
                   
                     9
                  
                   
                     29.0588550774
                  
                   
                     48.3514152334
                  
                
                 
                   
                     10
                  
                   
                     53.7033583030
                  
                   
                     53.7204230594
                  
                
                 
                   
                     11
                  
                   
                     78.3478615286
                  
                   
                     59.0894308854
                  
                
                 
                   
                     B
                     12
                  
                   
                     06.6215277777
                  
                   
                     64.4736111111
                  
                
                 
                   
                     13
                  
                   
                     37.2660310033
                  
                   
                     69.8426189371
                  
                
                 
                   
                     14
                  
                   
                     55.9105342289
                  
                   
                     74.2116267631
                  
                
                 
                   
                     15
                  
                   
                     80.5550374545
                  
                   
                     79.5806345891
                  
                
                 
                   
                     B
                     16
                  
                   
                     08.8287037037
                  
                   
                     85.9648148148
                  
                
                 
                   
                     17
                  
                   
                     33.4732069293
                  
                   
                     91.3338226408
                  
                
                 
                   
                     18
                  
                   
                     58.1177101549
                  
                   
                     96.7028304668
                  
                
                 
                   
                     19
                  
                   
                     82.
                     ●622133805
                  
                   
                     02.0718382928
                  
                
                 
                   
                     B
                     20
                  
                   
                     11
                     .
                     0●58796●97
                  
                   
                     07.4560185185
                  
                
                 
                   
                     40
                  
                   
                     22.0717592594
                  
                   
                     14.9120370370
                  
                
                 
                   
                     60
                  
                   
                     33.1076388891
                  
                   
                     22.3680555555
                  
                
                 
                   
                     80
                  
                   
                     44.1435185188
                  
                   
                     29.8040740740
                  
                
                 
                   
                     100
                  
                   
                     55.1793981487
                  
                   
                     37.2800925925
                  
                
                 
                   
                     200
                  
                   
                     10.3587062074
                  
                   
                     74.5601851850
                  
                
                 
                   
                     300
                  
                   
                     65.5381944461
                  
                   
                     11.8402777775
                  
                
                 
                   
                     400
                  
                   
                     20.7175925948
                  
                   
                     49.1203703700
                  
                
                 
                   
                     500
                  
                   
                     75.8969907435
                  
                   
                     86.4004629629
                  
                
                 
                   
                     600
                  
                   
                     31.0763888922
                  
                   
                     23.6805555555
                  
                
                 
                   
                     700
                  
                   
                     86.2557870409
                  
                   
                     60.9606481480
                  
                
              
            
             
             
               
                 
                   The
                   Moons
                   mean
                   Motions
                   in
                   Days
                   .
                
                 
                   
                     Days
                  
                   
                     ☽
                     Mean
                     Longitude
                  
                   
                     ☽
                     Apogaeon
                  
                
                 
                   
                     1
                  
                   
                     03.6601096287
                  
                   
                     00.0309466062
                  
                
                 
                   
                     2
                  
                   
                     07.3202192574
                  
                   
                     00.0618932124
                  
                
                 
                   
                     3
                  
                   
                     10.9803288861
                  
                   
                     00.0928398186
                  
                
                 
                   
                     4
                  
                   
                     14.6404385148
                  
                   
                     00.1237864248
                  
                
                 
                   
                     5
                  
                   
                     18.3005481435
                  
                   
                     00.1547330310
                  
                
                 
                   
                     6
                  
                   
                     21.9606577722
                  
                   
                     00.1856796372
                  
                
                 
                   
                     7
                  
                   
                     25.6207674009
                  
                   
                     00.2166262434
                  
                
                 
                   
                     8
                  
                   
                     29.2808770296
                  
                   
                     00.2475728496
                  
                
                 
                   
                     9
                  
                   
                     32.9409866583
                  
                   
                     00.2785194558
                  
                
                 
                   
                     10
                  
                   
                     36.6010962870
                  
                   
                     00.3094660620
                  
                
                 
                   
                     11
                  
                   
                     40.2612059157
                  
                   
                     00.3404126682
                  
                
                 
                   
                     12
                  
                   
                     43.9213155444
                  
                   
                     00.3713592744
                  
                
                 
                   
                     13
                  
                   
                     47.5814251731
                  
                   
                     00.4023058806
                  
                
                 
                   
                     14
                  
                   
                     51.2415348018
                  
                   
                     00.4332524868
                  
                
                 
                   
                     15
                  
                   
                     54.9016444305
                  
                   
                     00.4641990930
                  
                
                 
                   
                     16
                  
                   
                     58.5617540592
                  
                   
                     00.4951456992
                  
                
                 
                   
                     17
                  
                   
                     62.2218636879
                  
                   
                     00.5260923054
                  
                
                 
                   
                     18
                  
                   
                     65.8819733166
                  
                   
                     00.5570389116
                  
                
                 
                   
                     19
                  
                   
                     69.5420829453
                  
                   
                     00.5879855178
                  
                
                 
                   
                     20
                  
                   
                     73.2021925740
                  
                   
                     00.6189321240
                  
                
                 
                   
                     21
                  
                   
                     76.8623022037
                  
                   
                     00.6498787302
                  
                
                 
                   
                     22
                  
                   
                     80.5224118314
                  
                   
                     00.6808233364
                  
                
                 
                   
                     23
                  
                   
                     84.1825214601
                  
                   
                     00.7117719426
                  
                
                 
                   
                     24
                  
                   
                     87.8426310898
                  
                   
                     00.7427185488
                  
                
                 
                   
                     25
                  
                   
                     91.5027407175
                  
                   
                     00.7736651550
                  
                
                 
                   
                     26
                  
                   
                     95.1628503462
                  
                   
                     00.8046117612
                  
                
                 
                   
                     27
                  
                   
                     98.8229599749
                  
                   
                     00.8355583674
                  
                
                 
                   
                     28
                  
                   
                     02.4830696036
                  
                   
                     00.8665049736
                  
                
                 
                   
                     29
                  
                   
                     06.1431792323
                  
                   
                     00.8974515798
                  
                
                 
                   
                     30
                  
                   
                     09.8032888610
                  
                   
                     00.9283981860
                  
                
                 
                   
                     31
                  
                   
                     13.4633984897
                  
                   
                     00.9593447922
                  
                
              
            
             
             
               
                 
                   The
                   Moons
                   mean
                   Motions
                   in
                   Days
                   .
                
                 
                   
                     Days
                  
                   
                     ☽
                     Mean
                     Anomaly
                  
                   
                     ☽
                     Node
                     Retrograde
                  
                
                 
                   
                     1
                  
                   
                     03.6291630225
                  
                   
                     00.0147096104
                  
                
                 
                   
                     2
                  
                   
                     07.2583260450
                  
                   
                     00.0294192208
                  
                
                 
                   
                     3
                  
                   
                     10.8874890675
                  
                   
                     00.0441288312
                  
                
                 
                   
                     4
                  
                   
                     14.5166520900
                  
                   
                     00.0588384416
                  
                
                 
                   
                     5
                  
                   
                     18.1458151125
                  
                   
                     00.0735480520
                  
                
                 
                   
                     6
                  
                   
                     21.7749781350
                  
                   
                     00.0882576624
                  
                
                 
                   
                     7
                  
                   
                     25.4041411575
                  
                   
                     00.1029672728
                  
                
                 
                   
                     8
                  
                   
                     29.0333041800
                  
                   
                     00.1176768832
                  
                
                 
                   
                     9
                  
                   
                     32.6624672025
                  
                   
                     00.1323864936
                  
                
                 
                   
                     10
                  
                   
                     36.2916302250
                  
                   
                     00.1470961040
                  
                
                 
                   
                     11
                  
                   
                     39.9207932475
                  
                   
                     00.1618057144
                  
                
                 
                   
                     12
                  
                   
                     43.5499562700
                  
                   
                     00.1765153248
                  
                
                 
                   
                     13
                  
                   
                     47.1791192925
                  
                   
                     00.1912249352
                  
                
                 
                   
                     14
                  
                   
                     50.8082823150
                  
                   
                     00
                     .
                     20●9345456
                  
                
                 
                   
                     15
                  
                   
                     54.4374453375
                  
                   
                     00.2206441560
                  
                
                 
                   
                     16
                  
                   
                     58.0666083600
                  
                   
                     00.2353537664
                  
                
                 
                   
                     17
                  
                   
                     61.6957713825
                  
                   
                     00.2500633768
                  
                
                 
                   
                     18
                  
                   
                     65.3249344050
                  
                   
                     00.2647729872
                  
                
                 
                   
                     19
                  
                   
                     68.9540974275
                  
                   
                     00.2794825976
                  
                
                 
                   
                     20
                  
                   
                     72.5832604500
                  
                   
                     00.2941922080
                  
                
                 
                   
                     21
                  
                   
                     76.2124234725
                  
                   
                     00.3089018184
                  
                
                 
                   
                     22
                  
                   
                     79.8415864950
                  
                   
                     00.3236114288
                  
                
                 
                   
                     23
                  
                   
                     83.4707495175
                  
                   
                     00.3383210392
                  
                
                 
                   
                     24
                  
                   
                     87.0999125400
                  
                   
                     00.3530306496
                  
                
                 
                   
                     25
                  
                   
                     90.7290755625
                  
                   
                     00.3677402600
                  
                
                 
                   
                     26
                  
                   
                     94.3582385850
                  
                   
                     00.3824498704
                  
                
                 
                   
                     27
                  
                   
                     97.9874016075
                  
                   
                     00.3971594808
                  
                
                 
                   
                     28
                  
                   
                     01.6165646300
                  
                   
                     00.4118690912
                  
                
                 
                   
                     29
                  
                   
                     05.2457276525
                  
                   
                     00.4265787016
                  
                
                 
                   
                     30
                  
                   
                     08.8748906750
                  
                   
                     00.4412883120
                  
                
                 
                   
                     31
                  
                   
                     12.5040536975
                  
                   
                     00.4559979224
                  
                
              
            
             
             
               
                 
                   The
                   Moons
                   mean
                   Motions
                   in
                   Hours
                   .
                
                 
                   
                     Hours
                  
                   
                     ☽
                     Mean
                     Longitude
                  
                   
                     ☽
                     Apogaeon
                  
                
                 
                   
                     1
                  
                   
                     00.1525045678
                  
                   
                     00.0012894419
                  
                
                 
                   
                     2
                  
                   
                     00.3050091357
                  
                   
                     00.0025788838
                  
                
                 
                   
                     3
                  
                   
                     00.4575137035
                  
                   
                     00.0038683257
                  
                
                 
                   
                     4
                  
                   
                     00.6100182713
                  
                   
                     00.0041577676
                  
                
                 
                   
                     5
                  
                   
                     00.
                     ●625228391
                  
                   
                     00.0064172095
                  
                
                 
                   
                     6
                  
                   
                     00.9150274071
                  
                   
                     00.0077366515
                  
                
                 
                   
                     7
                  
                   
                     01.0675319749
                  
                   
                     00.0090260934
                  
                
                 
                   
                     8
                  
                   
                     01.2200365427
                  
                   
                     00.0103155353
                  
                
                 
                   
                     9
                  
                   
                     01.3725411105
                  
                   
                     00.0116049772
                  
                
                 
                   
                     10
                  
                   
                     01.5250456786
                  
                   
                     00.0128044192
                  
                
                 
                   
                     11
                  
                   
                     01.6775502464
                  
                   
                     00.0141838611
                  
                
                 
                   
                     12
                  
                   
                     01.8300548143
                  
                   
                     00.0154733031
                  
                
                 
                   
                     13
                  
                   
                     01.9825593821
                  
                   
                     00.0167627450
                  
                
                 
                   
                     14
                  
                   
                     02.1350639499
                  
                   
                     00.0180521869
                  
                
                 
                   
                     15
                  
                   
                     02.2875685177
                  
                   
                     00.0193416288
                  
                
                 
                   
                     16
                  
                   
                     02.4400730855
                  
                   
                     00.0206310707
                  
                
                 
                   
                     17
                  
                   
                     02.5925776533
                  
                   
                     00.0219205126
                  
                
                 
                   
                     18
                  
                   
                     02.7450822211
                  
                   
                     00.0232099545
                  
                
                 
                   
                     19
                  
                   
                     02.8975867891
                  
                   
                     00.0244993964
                  
                
                 
                   
                     20
                  
                   
                     03
                     .
                     0500●13560
                  
                   
                     00.0257888384
                  
                
                 
                   
                     21
                  
                   
                     03.2025959250
                  
                   
                     00.0270782803
                  
                
                 
                   
                     22
                  
                   
                     03.3551004928
                  
                   
                     00.0283677222
                  
                
                 
                   
                     23
                  
                   
                     03.5076050607
                  
                   
                     00.0296571642
                  
                
                 
                   
                     24
                  
                   
                     03.6601096285
                  
                   
                     00.0309466061
                  
                
              
            
             
             
               
                 
                   The
                   Moons
                   mean
                   Motions
                   in
                   Hours
                   .
                
                 
                   
                     Hours
                  
                   
                     ☽
                     Mean
                     Anomaly
                  
                   
                     ☽
                     Node
                     Retrograde
                  
                
                 
                   
                     1
                  
                   
                     00.1512151259
                  
                   
                     00.0006129004
                  
                
                 
                   
                     2
                  
                   
                     00.3024302518
                  
                   
                     00.0012258008
                  
                
                 
                   
                     3
                  
                   
                     00.4536453778
                  
                   
                     00.0018387013
                  
                
                 
                   
                     4
                  
                   
                     00.6048605037
                  
                   
                     00.0024516017
                  
                
                 
                   
                     5
                  
                   
                     00.7560756296
                  
                   
                     00.0030645021
                  
                
                 
                   
                     6
                  
                   
                     00.9072907556
                  
                   
                     00.0036774026
                  
                
                 
                   
                     7
                  
                   
                     01.0585058815
                  
                   
                     00.0042903030
                  
                
                 
                   
                     8
                  
                   
                     01.2097210074
                  
                   
                     00.0049032034
                  
                
                 
                   
                     9
                  
                   
                     01.3609361333
                  
                   
                     00.0055161038
                  
                
                 
                   
                     10
                  
                   
                     01.5121512593
                  
                   
                     00.0061290043
                  
                
                 
                   
                     11
                  
                   
                     01.6633663852
                  
                   
                     00.0067419047
                  
                
                 
                   
                     12
                  
                   
                     01.8145815112
                  
                   
                     00.0073548052
                  
                
                 
                   
                     13
                  
                   
                     01.9657066371
                  
                   
                     00.0079677056
                  
                
                 
                   
                     14
                  
                   
                     01.1170117630
                  
                   
                     00.0085806060
                  
                
                 
                   
                     15
                  
                   
                     02.2682068889
                  
                   
                     00.0091935064
                  
                
                 
                   
                     16
                  
                   
                     02.4194420148
                  
                   
                     00
                     .
                     009●064068
                  
                
                 
                   
                     17
                  
                   
                     02.5706571407
                  
                   
                     00
                     .
                     0●04193072
                  
                
                 
                   
                     18
                  
                   
                     02.7218722666
                  
                   
                     00.0110722076
                  
                
                 
                   
                     19
                  
                   
                     02.8730873926
                  
                   
                     00.0116451081
                  
                
                 
                   
                     20
                  
                   
                     03
                     .
                     9243025●85
                  
                   
                     00.0122580085
                  
                
                 
                   
                     21
                  
                   
                     03.1755176445
                  
                   
                     00.0128709090
                  
                
                 
                   
                     22
                  
                   
                     03.3267327704
                  
                   
                     00.0134838004
                  
                
                 
                   
                     23
                  
                   
                     03.4779478964
                  
                   
                     00.0140967099
                  
                
                 
                   
                     24
                  
                   
                     03.6291630223
                  
                   
                     00.0147096103
                  
                
              
            
             
             
               
                 
                   The
                   Moons
                   mean
                   Motions
                   in
                   Minutes
                   of
                   an
                   Hour
                
                 
                   
                     M.
                     
                  
                   
                     ☽
                     M.
                     Long.
                     
                  
                   
                     ☽
                     Apog
                     .
                  
                   
                     ☽
                     M.
                     Au.
                     
                  
                   
                     ●
                     Retrog
                     .
                  
                
                 
                   
                     1
                  
                   
                     .0025414
                  
                   
                     .0000214
                  
                   
                     .0025202
                  
                   
                     .0000102
                  
                
                 
                   
                     2
                  
                   
                     .0050828
                  
                   
                     .0000429
                  
                   
                     .0050405
                  
                   
                     .0000204
                  
                
                 
                   
                     3
                  
                   
                     .0076242
                  
                   
                     .0000643
                  
                   
                     .0075607
                  
                   
                     .0000306
                  
                
                 
                   
                     4
                  
                   
                     .0101656
                  
                   
                     .0000859
                  
                   
                     .0100810
                  
                   
                     .0000408
                  
                
                 
                   
                     5
                  
                   
                     .0127070
                  
                   
                     .0001074
                  
                   
                     .0126012
                  
                   
                     .0000510
                  
                
                 
                   
                     6
                  
                   
                     .0152484
                  
                   
                     .0001288
                  
                   
                     .0151214
                  
                   
                     .0000612
                  
                
                 
                   
                     7
                  
                   
                     .0177898
                  
                   
                     .0001502
                  
                   
                     .0176416
                  
                   
                     .0000714
                  
                
                 
                   
                     8
                  
                   
                     .0203312
                  
                   
                     .0001716
                  
                   
                     .0201618
                  
                   
                     .0000816
                  
                
                 
                   
                     9
                  
                   
                     .0228726
                  
                   
                     .0001930
                  
                   
                     .0226820
                  
                   
                     .0000918
                  
                
                 
                   
                     10
                  
                   
                     .0254141
                  
                   
                     .0002149
                  
                   
                     .0252025
                  
                   
                     .0001021
                  
                
                 
                   
                     11
                  
                   
                     .0279555
                  
                   
                     .0002363
                  
                   
                     .0277227
                  
                   
                     .0001123
                  
                
                 
                   
                     12
                  
                   
                     .0304969
                  
                   
                     .0002577
                  
                   
                     .0302429
                  
                   
                     .0001225
                  
                
                 
                   
                     13
                  
                   
                     .0330383
                  
                   
                     .0002791
                  
                   
                     .0327631
                  
                   
                     .0001327
                  
                
                 
                   
                     14
                  
                   
                     .0355797
                  
                   
                     .0003004
                  
                   
                     .0352833
                  
                   
                     .0001429
                  
                
                 
                   
                     15
                  
                   
                     .0381211
                  
                   
                     .0003218
                  
                   
                     .0378035
                  
                   
                     .0001531
                  
                
                 
                   
                     16
                  
                   
                     .0406624
                  
                   
                     .0003432
                  
                   
                     .0403237
                  
                   
                     .0001633
                  
                
                 
                   
                     17
                  
                   
                     .0432038
                  
                   
                     .0003646
                  
                   
                     .0428439
                  
                   
                     .0001735
                  
                
                 
                   
                     18
                  
                   
                     .0457452
                  
                   
                     .0003860
                  
                   
                     .0453641
                  
                   
                     .0001837
                  
                
                 
                   
                     19
                  
                   
                     .0482867
                  
                   
                     .0004079
                  
                   
                     .0478843
                  
                   
                     .0001939
                  
                
                 
                   
                     20
                  
                   
                     .0508284
                  
                   
                     .0004298
                  
                   
                     .0504045
                  
                   
                     .0002041
                  
                
                 
                   
                     21
                  
                   
                     .0533696
                  
                   
                     .0004512
                  
                   
                     .0529247
                  
                   
                     .0002143
                  
                
                 
                   
                     22
                  
                   
                     .0559110
                  
                   
                     .0004726
                  
                   
                     .0554449
                  
                   
                     .0002245
                  
                
                 
                   
                     23
                  
                   
                     .0584524
                  
                   
                     .0004940
                  
                   
                     .0579651
                  
                   
                     .0002347
                  
                
                 
                   
                     24
                  
                   
                     .0609938
                  
                   
                     .0005154
                  
                   
                     .0604853
                  
                   
                     .0002442
                  
                
                 
                   
                     25
                  
                   
                     .0635352
                  
                   
                     .0005368
                  
                   
                     .0630055
                  
                   
                     .0002544
                  
                
                 
                   
                     26
                  
                   
                     .0660766
                  
                   
                     .0005582
                  
                   
                     .0655257
                  
                   
                     .0002642
                  
                
                 
                   
                     27
                  
                   
                     .0686180
                  
                   
                     .0005795
                  
                   
                     .0680459
                  
                   
                     .0002744
                  
                
                 
                   
                     28
                  
                   
                     .0711594
                  
                   
                     .0006008
                  
                   
                     .0705661
                  
                   
                     .0002846
                  
                
                 
                   
                     29
                  
                   
                     .0737008
                  
                   
                     .0006222
                  
                   
                     .0730863
                  
                   
                     .0092948
                  
                
                 
                   
                     30
                  
                   
                     .0762422
                  
                   
                     .0006437
                  
                   
                     .0756075
                  
                   
                     .0003064
                  
                
              
            
             
             
               
                 
                   The
                   Moons
                   mean
                   Motions
                   in
                   Seconds
                   .
                
                 
                   
                      
                  
                   
                     ☽
                     M.
                     Long.
                     
                  
                   
                     ☽
                     Apog
                     .
                  
                   
                     ☽
                     M.
                     Au.
                     
                  
                   
                     ☊
                     Retrog
                     .
                  
                
                 
                   
                     1
                  
                   
                     0000423
                  
                   
                     0000003
                  
                   
                     0000420
                  
                   
                     0000002
                  
                
                 
                   
                     2
                  
                   
                     0000847
                  
                   
                     0000007
                  
                   
                     0000840
                  
                   
                     0000003
                  
                
                 
                   
                     3
                  
                   
                     0001270
                  
                   
                     0000010
                  
                   
                     0001260
                  
                   
                     0000005
                  
                
                 
                   
                     4
                  
                   
                     0001693
                  
                   
                     0000013
                  
                   
                     0001680
                  
                   
                     0000006
                  
                
                 
                   
                     5
                  
                   
                     0002116
                  
                   
                     0000016
                  
                   
                     0002100
                  
                   
                     0000009
                  
                
                 
                   
                     6
                  
                   
                     0002539
                  
                   
                     0000019
                  
                   
                     0002520
                  
                   
                     0000010
                  
                
                 
                   
                     7
                  
                   
                     0002969
                  
                   
                     0000022
                  
                   
                     0002940
                  
                   
                     0000012
                  
                
                 
                   
                     8
                  
                   
                     0003392
                  
                   
                     0000025
                  
                   
                     0003360
                  
                   
                     0000013
                  
                
                 
                   
                     9
                  
                   
                     0003815
                  
                   
                     0000028
                  
                   
                     0003780
                  
                   
                     0000015
                  
                
                 
                   
                     10
                  
                   
                     0004275
                  
                   
                     0000035
                  
                   
                     0004200
                  
                   
                     0000017
                  
                
                 
                   
                     11
                  
                   
                     0004658
                  
                   
                     0000038
                  
                   
                     0004620
                  
                   
                     0000019
                  
                
                 
                   
                     12
                  
                   
                     0005078
                  
                   
                     0000041
                  
                   
                     0005040
                  
                   
                     0000020
                  
                
                 
                   
                     13
                  
                   
                     0005504
                  
                   
                     0000044
                  
                   
                     0005460
                  
                   
                     0000022
                  
                
                 
                   
                     14
                  
                   
                     0005930
                  
                   
                     0000047
                  
                   
                     0005880
                  
                   
                     0000023
                  
                
                 
                   
                     15
                  
                   
                     0006357
                  
                   
                     0000050
                  
                   
                     0006300
                  
                   
                     0000025
                  
                
                 
                   
                     16
                  
                   
                     0006784
                  
                   
                     0000053
                  
                   
                     0006720
                  
                   
                     0000027
                  
                
                 
                   
                     17
                  
                   
                     0007207
                  
                   
                     0000056
                  
                   
                     0007140
                  
                   
                     0000028
                  
                
                 
                   
                     18
                  
                   
                     0007630
                  
                   
                     0000059
                  
                   
                     0007560
                  
                   
                     0000029
                  
                
                 
                   
                     19
                  
                   
                     0008050
                  
                   
                     0000062
                  
                   
                     0007980
                  
                   
                     0000031
                  
                
                 
                   
                     20
                  
                   
                     0008470
                  
                   
                     0000065
                  
                   
                     0008400
                  
                   
                     0000033
                  
                
                 
                   
                     21
                  
                   
                     0008893
                  
                   
                     0000068
                  
                   
                     0008820
                  
                   
                     0000035
                  
                
                 
                   
                     22
                  
                   
                     0009316
                  
                   
                     0000071
                  
                   
                     0009240
                  
                   
                     0000036
                  
                
                 
                   
                     23
                  
                   
                     0009736
                  
                   
                     0000074
                  
                   
                     0009660
                  
                   
                     0000038
                  
                
                 
                   
                     24
                  
                   
                     0010156
                  
                   
                     0000077
                  
                   
                     0010080
                  
                   
                     0000039
                  
                
                 
                   
                     25
                  
                   
                     0010582
                  
                   
                     0000080
                  
                   
                     0010500
                  
                   
                     0000041
                  
                
                 
                   
                     26
                  
                   
                     0011008
                  
                   
                     0000083
                  
                   
                     0010920
                  
                   
                     0000043
                  
                
                 
                   
                     27
                  
                   
                     0011434
                  
                   
                     0000086
                  
                   
                     0011340
                  
                   
                     0000044
                  
                
                 
                   
                     28
                  
                   
                     0011860
                  
                   
                     0000089
                  
                   
                     0011760
                  
                   
                     0000047
                  
                
                 
                   
                     29
                  
                   
                     0012287
                  
                   
                     0000092
                  
                   
                     0012180
                  
                   
                     0000049
                  
                
                 
                   
                     30
                  
                   
                     0012714
                  
                   
                     0000095
                  
                   
                     0012600
                  
                   
                     0000051
                  
                
              
            
             
             
               
                 
                   
                     ☉
                  
                   
                     Sig.
                     o.
                     &
                     .
                     6
                  
                   
                     1
                     &
                     7
                  
                   
                     2
                     &
                     8
                  
                   
                     ☉
                  
                
                 
                   
                     a
                  
                   
                     AEqu.
                     ☊
                  
                   
                     Inclin
                     .
                  
                   
                     AEqu.
                     ☊
                  
                   
                     Inclin
                     .
                  
                   
                     AEqu.
                     ☊
                  
                   
                     Inclin
                     .
                  
                   
                     a
                  
                
                 
                   
                     ☊
                  
                   
                     Addi
                  
                   
                     limetis
                  
                   
                     Addi
                  
                   
                     limitis
                  
                   
                     Addi
                  
                   
                     limitis
                  
                   
                     ☊
                  
                
                 
                   
                     0
                  
                   
                     0.00000
                  
                   
                     30000
                  
                   
                     1.06500
                  
                   
                     20000
                  
                   
                     1.08500
                  
                   
                     15000
                  
                   
                     30
                  
                
                 
                   
                     1
                  
                   
                     0.00000
                  
                   
                     30000
                  
                   
                     1.12888
                  
                   
                     25722
                  
                   
                     1.01888
                  
                   
                     14527
                  
                   
                     29
                  
                
                 
                   
                     2
                  
                   
                     0.00055
                  
                   
                     30000
                  
                   
                     1.19277
                  
                   
                     25472
                  
                   
                     0.95305
                  
                   
                     14055
                  
                   
                     28
                  
                
                 
                   
                     3
                  
                   
                     0.00194
                  
                   
                     29972
                  
                   
                     1.25222
                  
                   
                     25166
                  
                   
                     0.88666
                  
                   
                     13583
                  
                   
                     27
                  
                
                 
                   
                     4
                  
                   
                     0
                     .
                     0041●
                  
                   
                     29944
                  
                   
                     1.30833
                  
                   
                     24888
                  
                   
                     0.82055
                  
                   
                     13138
                  
                   
                     26
                  
                
                 
                   
                     5
                  
                   
                     0.00888
                  
                   
                     29888
                  
                   
                     1.36166
                  
                   
                     24583
                  
                   
                     0.55333
                  
                   
                     12666
                  
                   
                     25
                  
                
                 
                   
                     6
                  
                   
                     0.01472
                  
                   
                     29833
                  
                   
                     1.41055
                  
                   
                     24277
                  
                   
                     0.68694
                  
                   
                     12194
                  
                   
                     24
                  
                
                 
                   
                     7
                  
                   
                     0.02305
                  
                   
                     29777
                  
                   
                     1.45666
                  
                   
                     23972
                  
                   
                     0.62416
                  
                   
                     11●22
                  
                   
                     23
                  
                
                 
                   
                     8
                  
                   
                     0.02416
                  
                   
                     29722
                  
                   
                     1.49916
                  
                   
                     23638
                  
                   
                     0.56444
                  
                   
                     11250
                  
                   
                     22
                  
                
                 
                   
                     9
                  
                   
                     0.04805
                  
                   
                     29638
                  
                   
                     1.53666
                  
                   
                     23305
                  
                   
                     0.50555
                  
                   
                     10750
                  
                   
                     21
                  
                
                 
                   
                     10
                  
                   
                     0.06500
                  
                   
                     29555
                  
                   
                     1.58000
                  
                   
                     22972
                  
                   
                     0.44666
                  
                   
                     10250
                  
                   
                     20
                  
                
                 
                   
                     11
                  
                   
                     0.08555
                  
                   
                     29444
                  
                   
                     1.60027
                  
                   
                     22638
                  
                   
                     0.38888
                  
                   
                     09750
                  
                   
                     19
                  
                
                 
                   
                     12
                  
                   
                     0.10944
                  
                   
                     29361
                  
                   
                     1.62527
                  
                   
                     22277
                  
                   
                     0.34000
                  
                   
                     09250
                  
                   
                     18
                  
                
                 
                   
                     13
                  
                   
                     0.13666
                  
                   
                     29250
                  
                   
                     1.64472
                  
                   
                     219●6
                  
                   
                     0.28972
                  
                   
                     08750
                  
                   
                     17
                  
                
                 
                   
                     14
                  
                   
                     0.16833
                  
                   
                     29111
                  
                   
                     1.65771
                  
                   
                     21●55
                  
                   
                     0.25083
                  
                   
                     08250
                  
                   
                     16
                  
                
                 
                   
                     15
                  
                   
                     0.20250
                  
                   
                     28972
                  
                   
                     1.66277
                  
                   
                     21222
                  
                   
                     0.20972
                  
                   
                     07750
                  
                   
                     15
                  
                
                 
                   
                     16
                  
                   
                     0
                     .
                     2411●
                  
                   
                     28833
                  
                   
                     1.65805
                  
                   
                     20833
                  
                   
                     0.17388
                  
                   
                     07250
                  
                   
                     14
                  
                
                 
                   
                     17
                  
                   
                     0.27472
                  
                   
                     28667
                  
                   
                     1.64527
                  
                   
                     20444
                  
                   
                     0.14138
                  
                   
                     06750
                  
                   
                     13
                  
                
                 
                   
                     18
                  
                   
                     0.
                     ●2944
                  
                   
                     28567
                  
                   
                     1.62638
                  
                   
                     20055
                  
                   
                     0.11305
                  
                   
                     06250
                  
                   
                     12
                  
                
                 
                   
                     19
                  
                   
                     0.37916
                  
                   
                     28361
                  
                   
                     1.60194
                  
                   
                     19666
                  
                   
                     0.08805
                  
                   
                     05722
                  
                   
                     11
                  
                
                 
                   
                     20
                  
                   
                     0.43277
                  
                   
                     28194
                  
                   
                     1.58222
                  
                   
                     19279
                  
                   
                     0.06722
                  
                   
                     05222
                  
                   
                     10
                  
                
                 
                   
                     21
                  
                   
                     0.48888
                  
                   
                     18027
                  
                   
                     1.53972
                  
                   
                     18861
                  
                   
                     0.04916
                  
                   
                     04694
                  
                   
                     9
                  
                
                 
                   
                     22
                  
                   
                     0.54833
                  
                   
                     27833
                  
                   
                     1.50333
                  
                   
                     18444
                  
                   
                     0.03416
                  
                   
                     04166
                  
                   
                     8
                  
                
                 
                   
                     23
                  
                   
                     0.60694
                  
                   
                     27611
                  
                   
                     1.46222
                  
                   
                     18027
                  
                   
                     0.02333
                  
                   
                     03638
                  
                   
                     7
                  
                
                 
                   
                     24
                  
                   
                     0.66833
                  
                   
                     27416
                  
                   
                     1.41799
                  
                   
                     17614
                  
                   
                     0.01500
                  
                   
                     03138
                  
                   
                     6
                  
                
                 
                   
                     25
                  
                   
                     0.73555
                  
                   
                     27104
                  
                   
                     1.37027
                  
                   
                     17194
                  
                   
                     0.00888
                  
                   
                     02611
                  
                   
                     5
                  
                
                 
                   
                     26
                  
                   
                     0.79805
                  
                   
                     26972
                  
                   
                     1
                     .
                     3186●
                  
                   
                     14750
                  
                   
                     0.00416
                  
                   
                     02083
                  
                   
                     4
                  
                
                 
                   
                     27
                  
                   
                     0
                     .
                     8641●
                  
                   
                     26722
                  
                   
                     1.26527
                  
                   
                     16333
                  
                   
                     0
                     .
                     001●4
                  
                   
                     01555
                  
                   
                     3
                  
                
                 
                   
                     28
                  
                   
                     0.93083
                  
                   
                     26500
                  
                   
                     1.20833
                  
                   
                     15888
                  
                   
                     0.00055
                  
                   
                     01027
                  
                   
                     2
                  
                
                 
                   
                     29
                  
                   
                     0.99611
                  
                   
                     26250
                  
                   
                     1.14750
                  
                   
                     15444
                  
                   
                     0.00000
                  
                   
                     ●0527
                  
                   
                     1
                  
                
                 
                   
                     30
                  
                   
                     1.06500
                  
                   
                     26600
                  
                   
                     1.08500
                  
                   
                     14000
                  
                   
                     0.00000
                  
                   
                     00000
                  
                   
                     0
                  
                
                 
                   
                      
                  
                   
                     Sntract
                  
                   
                      
                  
                   
                     Subtract
                     .
                  
                   
                      
                  
                   
                     Subtract
                     .
                  
                   
                      
                  
                   
                      
                  
                
                 
                   
                      
                  
                   
                     Sig.
                     5.
                     
                     &
                     11
                  
                   
                     4
                     &
                     10
                  
                   
                     3
                     &
                     9
                  
                   
                      
                  
                
              
            
             
             
               
                 
                   
                     Aug.
                     
                  
                   
                     Sig.
                     o.
                     N.
                     
                  
                   
                     Incr.
                     
                  
                   
                     1.
                     North
                  
                   
                     Incr.
                     
                  
                   
                     2.
                     North
                  
                   
                     I
                     ncr
                     .
                  
                   
                      
                  
                
                 
                   
                      
                  
                   
                     Sig.
                     6.
                     
                     S.
                     
                  
                   
                      
                  
                   
                     7.
                     South
                  
                   
                      
                  
                   
                     8.
                     South
                  
                   
                      
                  
                   
                      
                  
                
                 
                   
                     Lat.
                     
                  
                   
                      
                  
                   
                     or
                     Exc.
                     
                  
                   
                      
                  
                   
                     or
                     Exc.
                     
                  
                   
                      
                  
                   
                     or
                     Exc.
                     
                  
                   
                      
                  
                
                 
                   
                      
                  
                   
                     Latit
                     .
                  
                   
                      
                  
                   
                     Latit
                     .
                  
                   
                      
                  
                   
                     Latit
                     .
                  
                   
                      
                  
                   
                      
                  
                
                 
                   
                     0
                  
                   
                     0.00000
                  
                   
                     00000
                  
                   
                     2.49750
                  
                   
                     15000
                  
                   
                     4.32888
                  
                   
                     26000
                  
                   
                     30
                  
                
                 
                   
                     1
                  
                   
                     0.08722
                  
                   
                     00527
                  
                   
                     2.57277
                  
                   
                     15444
                  
                   
                     4.37166
                  
                   
                     26250
                  
                   
                     29
                  
                
                 
                   
                     2
                  
                   
                     0.17444
                  
                   
                     01027
                  
                   
                     2.64722
                  
                   
                     15888
                  
                   
                     4.41361
                  
                   
                     26500
                  
                   
                     28
                  
                
                 
                   
                     3
                  
                   
                     0.26166
                  
                   
                     01555
                  
                   
                     2.72083
                  
                   
                     16333
                  
                   
                     4.45388
                  
                   
                     26722
                  
                   
                     27
                  
                
                 
                   
                     4
                  
                   
                     0.34861
                  
                   
                     02083
                  
                   
                     2.79361
                  
                   
                     16416
                  
                   
                     4.49277
                  
                   
                     26972
                  
                   
                     26
                  
                
                 
                   
                     5
                  
                   
                     0.43555
                  
                   
                     02611
                  
                   
                     2.86555
                  
                   
                     17194
                  
                   
                     4.53055
                  
                   
                     27194
                  
                   
                     25
                  
                
                 
                   
                     6
                  
                   
                     0.52222
                  
                   
                     03138
                  
                   
                     2.93638
                  
                   
                     17611
                  
                   
                     4.56666
                  
                   
                     27416
                  
                   
                     24
                  
                
                 
                   
                     7
                  
                   
                     0.60888
                  
                   
                     03638
                  
                   
                     3.00666
                  
                   
                     18027
                  
                   
                     4.60166
                  
                   
                     27611
                  
                   
                     23
                  
                
                 
                   
                     8
                  
                   
                     0.69527
                  
                   
                     04166
                  
                   
                     3.
                     ●7583
                  
                   
                     18444
                  
                   
                     4.63500
                  
                   
                     27833
                  
                   
                     22
                  
                
                 
                   
                     9
                  
                   
                     0.78138
                  
                   
                     04694
                  
                   
                     3.14416
                  
                   
                     18861
                  
                   
                     4.66722
                  
                   
                     28027
                  
                   
                     21
                  
                
                 
                   
                     10
                  
                   
                     0.86722
                  
                   
                     05222
                  
                   
                     3.21166
                  
                   
                     19277
                  
                   
                     4.69777
                  
                   
                     28194
                  
                   
                     20
                  
                
                 
                   
                     11
                  
                   
                     0.95277
                  
                   
                     05722
                  
                   
                     3.27805
                  
                   
                     19666
                  
                   
                     4.72694
                  
                   
                     28361
                  
                   
                     19
                  
                
                 
                   
                     12
                  
                   
                     1.03833
                  
                   
                     06250
                  
                   
                     3.34333
                  
                   
                     20055
                  
                   
                     4.75472
                  
                   
                     28527
                  
                   
                     18
                  
                
                 
                   
                     13
                  
                   
                     1.12333
                  
                   
                     06750
                  
                   
                     3.41055
                  
                   
                     20444
                  
                   
                     4.78111
                  
                   
                     28666
                  
                   
                     17
                  
                
                 
                   
                     14
                  
                   
                     1.10805
                  
                   
                     07250
                  
                   
                     3.47111
                  
                   
                     20833
                  
                   
                     4.80583
                  
                   
                     28833
                  
                   
                     16
                  
                
                 
                   
                     15
                  
                   
                     1.29250
                  
                   
                     07750
                  
                   
                     3.53333
                  
                   
                     21222
                  
                   
                     4.82916
                  
                   
                     28972
                  
                   
                     15
                  
                
                 
                   
                     16
                  
                   
                     1.37666
                  
                   
                     08250
                  
                   
                     3.59444
                  
                   
                     21555
                  
                   
                     4.85111
                  
                   
                     29111
                  
                   
                     14
                  
                
                 
                   
                     17
                  
                   
                     1.46027
                  
                   
                     08750
                  
                   
                     3.65472
                  
                   
                     21916
                  
                   
                     4.87166
                  
                   
                     29250
                  
                   
                     13
                  
                
                 
                   
                     18
                  
                   
                     1.54333
                  
                   
                     09250
                  
                   
                     3.71361
                  
                   
                     22277
                  
                   
                     4.89055
                  
                   
                     29361
                  
                   
                     12
                  
                
                 
                   
                     19
                  
                   
                     1.62611
                  
                   
                     09750
                  
                   
                     3.77138
                  
                   
                     22638
                  
                   
                     4.90777
                  
                   
                     29444
                  
                   
                     11
                  
                
                 
                   
                     20
                  
                   
                     1.70805
                  
                   
                     10250
                  
                   
                     3.82833
                  
                   
                     22972
                  
                   
                     4.92388
                  
                   
                     29555
                  
                   
                     10
                  
                
                 
                   
                     21
                  
                   
                     1.78972
                  
                   
                     10750
                  
                   
                     3.88388
                  
                   
                     23305
                  
                   
                     4.93833
                  
                   
                     29638
                  
                   
                     9
                  
                
                 
                   
                     22
                  
                   
                     1.87111
                  
                   
                     11250
                  
                   
                     3.93805
                  
                   
                     23638
                  
                   
                     4.95111
                  
                   
                     29722
                  
                   
                     8
                  
                
                 
                   
                     23
                  
                   
                     1.95166
                  
                   
                     11722
                  
                   
                     3.99138
                  
                   
                     23972
                  
                   
                     4.96250
                  
                   
                     29777
                  
                   
                     7
                  
                
                 
                   
                     24
                  
                   
                     2.03166
                  
                   
                     12194
                  
                   
                     4.04333
                  
                   
                     24277
                  
                   
                     4.97250
                  
                   
                     29833
                  
                   
                     6
                  
                
                 
                   
                     25
                  
                   
                     2.11083
                  
                   
                     12666
                  
                   
                     4.29416
                  
                   
                     24583
                  
                   
                     4.98083
                  
                   
                     29888
                  
                   
                     5
                  
                
                 
                   
                     26
                  
                   
                     2.18972
                  
                   
                     13138
                  
                   
                     4.14361
                  
                   
                     24888
                  
                   
                     4.98777
                  
                   
                     29944
                  
                   
                     4
                  
                
                 
                   
                     27
                  
                   
                     2.26777
                  
                   
                     13583
                  
                   
                     4.19166
                  
                   
                     25166
                  
                   
                     4.99301
                  
                   
                     29972
                  
                   
                     3
                  
                
                 
                   
                     28
                  
                   
                     2.34500
                  
                   
                     14055
                  
                   
                     4.23861
                  
                   
                     25472
                  
                   
                     4.99694
                  
                   
                     29972
                  
                   
                     2
                  
                
                 
                   
                     29
                  
                   
                     2.42166
                  
                   
                     14527
                  
                   
                     4.28444
                  
                   
                     25722
                  
                   
                     4.99916
                  
                   
                     18000
                  
                   
                     1
                  
                
                 
                   
                     30
                  
                   
                     2.49750
                  
                   
                     15000
                  
                   
                     4.32888
                  
                   
                     26000
                  
                   
                     5.00000
                  
                   
                     18000
                  
                   
                     0
                  
                
                 
                   
                      
                  
                   
                     Sig.
                     11.
                     
                     S.
                     
                  
                   
                      
                  
                   
                     Sig.
                     19.
                     
                     S.
                     
                  
                   
                      
                  
                   
                     9.
                     South
                  
                   
                      
                  
                   
                      
                  
                
                 
                   
                      
                  
                   
                     Sig.
                     5.
                     
                     N.
                     
                  
                   
                      
                  
                   
                     4
                     N.
                     
                  
                   
                      
                  
                   
                     3.
                     North
                  
                   
                      
                  
                   
                      
                  
                
              
               
                 
                 
                   A
                   Table
                   of
                   the
                   Moons
                   Red.
                   to
                   the
                   El.
                   Subt
                
                 
                   
                     As
                     Lat.
                     
                  
                   
                     Sig.
                     0.6
                  
                   
                      
                  
                   
                     S.
                     1.7
                  
                   
                      
                  
                   
                     S.
                     2.8
                  
                   
                      
                  
                   
                     As.
                     Lat.
                     
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                     Incr.
                     
                  
                   
                      
                  
                   
                     Incr.
                     
                  
                   
                      
                  
                   
                     Incr.
                     
                  
                   
                      
                  
                
                 
                   
                      
                  
                   
                     Red.
                     
                  
                   
                      
                  
                   
                     Red.
                     
                  
                   
                      
                  
                   
                     Red.
                     
                  
                   
                      
                  
                   
                      
                  
                
                 
                   
                     0
                  
                   
                     .00000
                  
                   
                     00000
                  
                   
                     09444
                  
                   
                     01166
                  
                   
                     09472
                  
                   
                     01166
                  
                   
                     30
                  
                
                 
                   
                     1
                  
                   
                     .00388
                  
                   
                     00055
                  
                   
                     09638
                  
                   
                     01194
                  
                   
                     09277
                  
                   
                     01138
                  
                   
                     29
                  
                
                 
                   
                     2
                  
                   
                     .00750
                  
                   
                     00111
                  
                   
                     09805
                  
                   
                     01222
                  
                   
                     09055
                  
                   
                     01111
                  
                   
                     28
                  
                
                 
                   
                     3
                  
                   
                     .01138
                  
                   
                     00166
                  
                   
                     09972
                  
                   
                     01250
                  
                   
                     08833
                  
                   
                     01083
                  
                   
                     27
                  
                
                 
                   
                     4
                  
                   
                     .01527
                  
                   
                     00222
                  
                   
                     10111
                  
                   
                     01277
                  
                   
                     08611
                  
                   
                     01055
                  
                   
                     26
                  
                
                 
                   
                     5
                  
                   
                     .01888
                  
                   
                     00250
                  
                   
                     10250
                  
                   
                     01277
                  
                   
                     08388
                  
                   
                     01027
                  
                   
                     25
                  
                
                 
                   
                     6
                  
                   
                     .02277
                  
                   
                     00305
                  
                   
                     10388
                  
                   
                     01277
                  
                   
                     08138
                  
                   
                     01000
                  
                   
                     24
                  
                
                 
                   
                     7
                  
                   
                     .02638
                  
                   
                     00333
                  
                   
                     10500
                  
                   
                     01305
                  
                   
                     07861
                  
                   
                     00972
                  
                   
                     23
                  
                
                 
                   
                     8
                  
                   
                     .03000
                  
                   
                     00361
                  
                   
                     10583
                  
                   
                     01305
                  
                   
                     07611
                  
                   
                     00944
                  
                   
                     22
                  
                
                 
                   
                     9
                  
                   
                     .03361
                  
                   
                     00416
                  
                   
                     10666
                  
                   
                     01305
                  
                   
                     07305
                  
                   
                     00916
                  
                   
                     21
                  
                
                 
                   
                     10
                  
                   
                     .03722
                  
                   
                     00472
                  
                   
                     10750
                  
                   
                     01333
                  
                   
                     07027
                  
                   
                     00861
                  
                   
                     20
                  
                
                 
                   
                     11
                  
                   
                     .04083
                  
                   
                     00527
                  
                   
                     10805
                  
                   
                     01333
                  
                   
                     06722
                  
                   
                     00833
                  
                   
                     19
                  
                
                 
                   
                     12
                  
                   
                     .04444
                  
                   
                     00555
                  
                   
                     10861
                  
                   
                     01333
                  
                   
                     06416
                  
                   
                     00805
                  
                   
                     18
                  
                
                 
                   
                     13
                  
                   
                     .04777
                  
                   
                     00611
                  
                   
                     10888
                  
                   
                     01333
                  
                   
                     06111
                  
                   
                     00777
                  
                   
                     17
                  
                
                 
                   
                     14
                  
                   
                     .05111
                  
                   
                     00638
                  
                   
                     10916
                  
                   
                     01361
                  
                   
                     05805
                  
                   
                     00722
                  
                   
                     16
                  
                
                 
                   
                     15
                  
                   
                     .05444
                  
                   
                     00666
                  
                   
                     10916
                  
                   
                     01361
                  
                   
                     05472
                  
                   
                     00666
                  
                   
                     15
                  
                
                 
                   
                     16
                  
                   
                     .05777
                  
                   
                     00722
                  
                   
                     10916
                  
                   
                     01361
                  
                   
                     05138
                  
                   
                     00638
                  
                   
                     14
                  
                
                 
                   
                     17
                  
                   
                     .06111
                  
                   
                     00777
                  
                   
                     10862
                  
                   
                     01361
                  
                   
                     04805
                  
                   
                     00611
                  
                   
                     13
                  
                
                 
                   
                     18
                  
                   
                     .06416
                  
                   
                     00805
                  
                   
                     10861
                  
                   
                     01361
                  
                   
                     04444
                  
                   
                     00555
                  
                   
                     12
                  
                
                 
                   
                     19
                  
                   
                     .06722
                  
                   
                     00833
                  
                   
                     10805
                  
                   
                     0133●
                  
                   
                     04111
                  
                   
                     00527
                  
                   
                     11
                  
                
                 
                   
                     20
                  
                   
                     .07000
                  
                   
                     00861
                  
                   
                     10750
                  
                   
                     01333
                  
                   
                     03750
                  
                   
                     00472
                  
                   
                     10
                  
                
                 
                   
                     21
                  
                   
                     .07305
                  
                   
                     00916
                  
                   
                     10694
                  
                   
                     01305
                  
                   
                     03388
                  
                   
                     00416
                  
                   
                     9
                  
                
                 
                   
                     22
                  
                   
                     .07583
                  
                   
                     00944
                  
                   
                     10611
                  
                   
                     01305
                  
                   
                     03027
                  
                   
                     00361
                  
                   
                     8
                  
                
                 
                   
                     23
                  
                   
                     .07888
                  
                   
                     00972
                  
                   
                     10500
                  
                   
                     01305
                  
                   
                     02092
                  
                   
                     00333
                  
                   
                     7
                  
                
                 
                   
                     24
                  
                   
                     .08111
                  
                   
                     01000
                  
                   
                     10388
                  
                   
                     01277
                  
                   
                     02611
                  
                   
                     00305
                  
                   
                     6
                  
                
                 
                   
                     25
                  
                   
                     .08361
                  
                   
                     01027
                  
                   
                     10277
                  
                   
                     01277
                  
                   
                     02222
                  
                   
                     00250
                  
                   
                     5
                  
                
                 
                   
                     26
                  
                   
                     .08583
                  
                   
                     01055
                  
                   
                     10138
                  
                   
                     01277
                  
                   
                     01527
                  
                   
                     00222
                  
                   
                     4
                  
                
                 
                   
                     27
                  
                   
                     .08823
                  
                   
                     01083
                  
                   
                     10000
                  
                   
                     01250
                  
                   
                     01138
                  
                   
                     00166
                  
                   
                     ●3
                  
                
                 
                   
                     28
                  
                   
                     .09055
                  
                   
                     01111
                  
                   
                     09833
                  
                   
                     01222
                  
                   
                     00750
                  
                   
                     00111
                  
                   
                     2
                  
                
                 
                   
                     29
                  
                   
                     .09250
                  
                   
                     01138
                  
                   
                     09638
                  
                   
                     01194
                  
                   
                     00388
                  
                   
                     00055
                  
                   
                     1
                  
                
                 
                   
                     30
                  
                   
                     .09444
                  
                   
                     01166
                  
                   
                     09472
                  
                   
                     01166
                  
                   
                     00000
                  
                   
                     00006
                  
                   
                     0
                  
                
                 
                   
                      
                  
                   
                     11.5
                  
                   
                      
                  
                   
                     10.4
                  
                   
                      
                  
                   
                     9.3
                  
                   
                      
                  
                   
                      
                  
                
              
            
             
             
               
                 
                   A
                   Table
                   shewing
                   the
                   mean
                   Motion
                   of
                   the
                   Moon
                   from
                   the
                   Sun
                   in
                   Years
                   and
                   Months
                   .
                
                 
                   
                     AEra
                  
                   
                     ☽
                     à
                     ☉
                     in
                     Years
                  
                   
                      
                  
                   
                     ☽
                     à
                     ☉
                     in
                     Years
                  
                
                 
                   
                     Chr.
                     
                  
                   
                     56.8114797531
                  
                   
                     1
                  
                   
                     36.0063707331
                  
                
                 
                   
                     1600
                  
                   
                     21.5206732464
                  
                   
                     2
                  
                   
                     72
                     .
                     012741466●
                  
                
                 
                   
                     1620
                  
                   
                     58.5795367034
                  
                   
                     3
                  
                   
                     08.0191121993
                  
                
                 
                   
                     1640
                  
                   
                     95.6384101604
                  
                   
                     4
                  
                   
                     47.4117836215
                  
                
                 
                   
                     1660
                  
                   
                     32.6972836174
                  
                   
                     5
                  
                   
                     83.4181543546
                  
                
                 
                   
                     1680
                  
                   
                     69.7561560744
                  
                   
                     6
                  
                   
                     19.4245250877
                  
                
                 
                   
                     1700
                  
                   
                     06.8150305314
                  
                   
                     7
                  
                   
                     55.4308958208
                  
                
                 
                   
                     1720
                  
                   
                     43.8739039884
                  
                   
                     8
                  
                   
                     94.8235672430
                  
                
                 
                   
                     1740
                  
                   
                     80.9027774454
                  
                   
                     9
                  
                   
                     40.8298379761
                  
                
                 
                   
                     1760
                  
                   
                     17.9916509024
                  
                   
                     10
                  
                   
                     76.8362087092
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                     11
                  
                   
                     02.8426794423
                  
                
                 
                   
                      
                  
                   
                     Motion
                     of
                     the
                  
                   
                     12
                  
                   
                     42.2353508645
                  
                
                 
                   
                      
                  
                   
                     Moon
                     from
                     the
                  
                   
                     13
                  
                   
                     78.2417215976
                  
                
                 
                   
                      
                  
                   
                     Sun
                     in
                     Months
                     .
                  
                   
                     14
                  
                   
                     14.2480923307
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                     15
                  
                   
                     50.2544630638
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                     16
                  
                   
                     89.6471344860
                  
                
                 
                   
                     Ian.
                     
                  
                   
                     04.9758835440
                  
                   
                     17
                  
                   
                     25.6535052191
                  
                
                 
                   
                     Feb.
                     
                  
                   
                     99.7928106160
                  
                   
                     18
                  
                   
                     61.6598759522
                  
                
                 
                   
                     Mar.
                     
                  
                   
                     04.7686941600
                  
                   
                     19
                  
                   
                     97.6662466853
                  
                
                 
                   
                     April
                  
                   
                     06.3582588800
                  
                   
                     20
                  
                   
                     37.0589181075
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                   
                     74.1178362150
                  
                
                 
                   
                     May
                  
                   
                     11.3341424240
                  
                   
                     60
                  
                   
                     11.1767543225
                  
                
                 
                   
                     Iune
                  
                   
                     12.9237071440
                  
                   
                     80
                  
                   
                     48.2356724300
                  
                
                 
                   
                     Iuly
                  
                   
                     17.8995906880
                  
                   
                     100
                  
                   
                     85.2945905375
                  
                
                 
                   
                     Aug.
                     
                  
                   
                     22.8754742320
                  
                   
                     200
                  
                   
                     70.5891810750
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                     300
                  
                   
                     55.8837716125
                  
                
                 
                   
                     Sept.
                     
                  
                   
                     24.4650389520
                  
                   
                     400
                  
                   
                     41.1783621500
                  
                
                 
                   
                     Octo.
                     
                  
                   
                     29.4409224960
                  
                   
                     500
                  
                   
                     26.4729526875
                  
                
                 
                   
                     Nov.
                     
                  
                   
                     31.0304872160
                  
                   
                     600
                  
                   
                     11.7675432250
                  
                
                 
                   
                     Dec.
                     
                  
                   
                     36.0063707331
                  
                   
                     700
                  
                   
                     97.0621337625
                  
                
              
            
             
             
               
                 
                   A
                   Table
                   shewing
                   the
                   mean
                   Motion
                   of
                   the
                   Moon
                   from
                   the
                   Sun
                   in
                   Days
                   and
                   Hours
                   .
                
                 
                   
                      
                  
                   
                     ☽
                     à
                     ☉
                     in
                     Days
                     .
                  
                   
                      
                  
                   
                     ☽
                     à
                     ☉
                     in
                     Hours
                     .
                  
                
                 
                   
                     1
                  
                   
                     03.3863188240
                  
                   
                     1
                  
                   
                     00.1410966176
                  
                
                 
                   
                     2
                  
                   
                     06.7726376480
                  
                   
                     2
                  
                   
                     00.2821932352
                  
                
                 
                   
                     3
                  
                   
                     10.1589564720
                  
                   
                     3
                  
                   
                     00.4232898530
                  
                
                 
                   
                     4
                  
                   
                     13.5452752960
                  
                   
                     4
                  
                   
                     00.5643864706
                  
                
                 
                   
                     5
                  
                   
                     16.9315941200
                  
                   
                     5
                  
                   
                     00.7054830882
                  
                
                 
                   
                     6
                  
                   
                     20.3179129440
                  
                   
                     6
                  
                   
                     00.8465797060
                  
                
                 
                   
                     7
                  
                   
                     23.7042317680
                  
                   
                     7
                  
                   
                     00.
                     ●876763236
                  
                
                 
                   
                     8
                  
                   
                     27.0905505920
                  
                   
                     8
                  
                   
                     01.1287729412
                  
                
                 
                   
                     9
                  
                   
                     30.4768694160
                  
                   
                     9
                  
                   
                     01.2698695588
                  
                
                 
                   
                     10
                  
                   
                     33.8631882400
                  
                   
                     10
                  
                   
                     01.4109661766
                  
                
                 
                   
                     11
                  
                   
                     37.2495070640
                  
                   
                     11
                  
                   
                     01.5520627942
                  
                
                 
                   
                     12
                  
                   
                     47.6358258880
                  
                   
                     12
                  
                   
                     01.6931594120
                  
                
                 
                   
                     13
                  
                   
                     44.0221447720
                  
                   
                     13
                  
                   
                     01.8342560296
                  
                
                 
                   
                     14
                  
                   
                     47.4084635360
                  
                   
                     14
                  
                   
                     01.9753526472
                  
                
                 
                   
                     15
                  
                   
                     50.
                     ●947823600
                  
                   
                     15
                  
                   
                     0●
                     .
                     1164492648
                  
                
                 
                   
                     16
                  
                   
                     54.1811011840
                  
                   
                     16
                  
                   
                     02.2575458824
                  
                
                 
                   
                     17
                  
                   
                     57.5674200080
                  
                   
                     17
                  
                   
                     02.3986425000
                  
                
                 
                   
                     18
                  
                   
                     60.9537388320
                  
                   
                     18
                  
                   
                     02.5397391176
                  
                
                 
                   
                     19
                  
                   
                     64.3400576560
                  
                   
                     19
                  
                   
                     02.6808357354
                  
                
                 
                   
                     20
                  
                   
                     67.7263764800
                  
                   
                     20
                  
                   
                     02.8219323520
                  
                
                 
                   
                     21
                  
                   
                     71.1126953040
                  
                   
                     21
                  
                   
                     02.9630289708
                  
                
                 
                   
                     22
                  
                   
                     74.4990141280
                  
                   
                     22
                  
                   
                     03.1041255884
                  
                
                 
                   
                     23
                  
                   
                     77.8853329520
                  
                   
                     23
                  
                   
                     03.2452222062
                  
                
                 
                   
                     24
                  
                   
                     81.2716517760
                  
                   
                     24
                  
                   
                     03.3863188240
                  
                
                 
                   
                     25
                  
                   
                     84.6579706000
                  
                   
                      
                  
                   
                      
                  
                
                 
                   
                     26
                  
                   
                     88.0442804240
                  
                   
                      
                  
                   
                      
                  
                
                 
                   
                     27
                  
                   
                     91
                     4306082480
                  
                   
                      
                  
                   
                      
                  
                
                 
                   
                     28
                  
                   
                     94.8169270720
                  
                   
                      
                  
                   
                      
                  
                
                 
                   
                     29
                  
                   
                     98.2032458960
                  
                   
                      
                  
                   
                      
                  
                
                 
                   
                     30
                  
                   
                     01.5895647200
                  
                   
                      
                  
                   
                      
                  
                
                 
                   
                     31
                  
                   
                     04.9758835440
                  
                   
                      
                  
                   
                      
                  
                
              
            
             
             
               
                 
                   A
                   Table
                   shewing
                   the
                   mean
                   Motion
                   of
                   the
                   Moon
                   from
                   the
                   Sun
                   in
                   Minutes
                   .
                
                 
                   
                      
                  
                   
                     ☽
                     à
                     ☉
                     in
                     Minutes
                     .
                  
                
                 
                   
                     1
                  
                   
                     00.0023516102
                  
                
                 
                   
                     2
                  
                   
                     00.0047032205
                  
                
                 
                   
                     3
                  
                   
                     00.0070548308
                  
                
                 
                   
                     4
                  
                   
                     00
                     .
                     00●4064411
                  
                
                 
                   
                     5
                  
                   
                     00.0117580513
                  
                
                 
                   
                     6
                  
                   
                     00.0141096617
                  
                
                 
                   
                     7
                  
                   
                     00.0164612719
                  
                
                 
                   
                     8
                  
                   
                     00.0188128822
                  
                
                 
                   
                     9
                  
                   
                     00.0211644924
                  
                
                 
                   
                     10
                  
                   
                     00.0235161029
                  
                
                 
                   
                     11
                  
                   
                     00.0258677131
                  
                
                 
                   
                     12
                  
                   
                     00.0262193233
                  
                
                 
                   
                     13
                  
                   
                     00.0305709335
                  
                
                 
                   
                     14
                  
                   
                     00.0329225437
                  
                
                 
                   
                     15
                  
                   
                     00.0352741539
                  
                
                 
                   
                     16
                  
                   
                     00.0376257644
                  
                
                 
                   
                     17
                  
                   
                     00.0399773746
                  
                
                 
                   
                     18
                  
                   
                     00.0423289848
                  
                
                 
                   
                     19
                  
                   
                     00
                     .
                     044680●950
                  
                
                 
                   
                     20
                  
                   
                     00.0170322052
                  
                
                 
                   
                     21
                  
                   
                     00.0493838154
                  
                
                 
                   
                     22
                  
                   
                     00.0517354256
                  
                
                 
                   
                     23
                  
                   
                     00
                     .
                     0540870●58
                  
                
                 
                   
                     24
                  
                   
                     00.0564386460
                  
                
                 
                   
                     25
                  
                   
                     00.0587902562
                  
                
                 
                   
                     26
                  
                   
                     00.0611418664
                  
                
                 
                   
                     27
                  
                   
                     00.0634934766
                  
                
                 
                   
                     28
                  
                   
                     00.0658450868
                  
                
                 
                   
                     29
                  
                   
                     00.0681966970
                  
                
                 
                   
                     30
                  
                   
                     00.0705483080
                  
                
                 
                   
                      
                  
                   
                     ☽
                     à
                     ☉
                     in
                     Minutes
                     .
                  
                
                 
                   
                     31
                  
                   
                     00.0728999183
                  
                
                 
                   
                     32
                  
                   
                     00.0752515088
                  
                
                 
                   
                     33
                  
                   
                     00.0776031390
                  
                
                 
                   
                     34
                  
                   
                     00.0799547492
                  
                
                 
                   
                     35
                  
                   
                     00.0823063594
                  
                
                 
                   
                     36
                  
                   
                     00.0846579696
                  
                
                 
                   
                     37
                  
                   
                     00.0870095798
                  
                
                 
                   
                     38
                  
                   
                     00.0893611900
                  
                
                 
                   
                     39
                  
                   
                     00.0917128002
                  
                
                 
                   
                     40
                  
                   
                     00.0940644104
                  
                
                 
                   
                     41
                  
                   
                     00.0964160206
                  
                
                 
                   
                     42
                  
                   
                     00.0997676308
                  
                
                 
                   
                     43
                  
                   
                     00.1011192410
                  
                
                 
                   
                     44
                  
                   
                     00.1034708512
                  
                
                 
                   
                     45
                  
                   
                     00.1058224614
                  
                
                 
                   
                     46
                  
                   
                     00.1081740716
                  
                
                 
                   
                     47
                  
                   
                     00.1105256818
                  
                
                 
                   
                     48
                  
                   
                     00.1128772920
                  
                
                 
                   
                     49
                  
                   
                     00.1152289022
                  
                
                 
                   
                     50
                  
                   
                     00.1175805124
                  
                
                 
                   
                     51
                  
                   
                     00.1199321226
                  
                
                 
                   
                     52
                  
                   
                     00.1222837328
                  
                
                 
                   
                     53
                  
                   
                     00.1246353430
                  
                
                 
                   
                     54
                  
                   
                     00.1269869532
                  
                
                 
                   
                     55
                  
                   
                     00.1293385634
                  
                
                 
                   
                     56
                  
                   
                     00.1316901736
                  
                
                 
                   
                     57
                  
                   
                     00.1340417838
                  
                
                 
                   
                     58
                  
                   
                     00.1363933940
                  
                
                 
                   
                     59
                  
                   
                     00.1387450050
                  
                
                 
                   
                     60
                  
                   
                     00.1410966152
                  
                
              
            
             
             
               
                 
                   A
                   Table
                   shewing
                   the
                   mean
                   Motion
                   of
                   the
                   Moon
                   from
                   the
                   Sun
                   in
                   Seconds
                   .
                
                 
                   
                      
                  
                   
                     ☽
                     à
                     ☉
                     in
                     Seconds
                  
                
                 
                   
                     1
                  
                   
                     00.0000391935
                  
                
                 
                   
                     2
                  
                   
                     00.0000783870
                  
                
                 
                   
                     3
                  
                   
                     00.0001175805
                  
                
                 
                   
                     4
                  
                   
                     00.0001567740
                  
                
                 
                   
                     5
                  
                   
                     00.0001959675
                  
                
                 
                   
                     6
                  
                   
                     00.0002351610
                  
                
                 
                   
                     7
                  
                   
                     00.0002743545
                  
                
                 
                   
                     8
                  
                   
                     00.0003135480
                  
                
                 
                   
                     9
                  
                   
                     00.0003527415
                  
                
                 
                   
                     10
                  
                   
                     60.0003919350
                  
                
                 
                   
                     11
                  
                   
                     00.0004811285
                  
                
                 
                   
                     12
                  
                   
                     00.0004703220
                  
                
                 
                   
                     13
                  
                   
                     00.0005995155
                  
                
                 
                   
                     14
                  
                   
                     00.0005487090
                  
                
                 
                   
                     15
                  
                   
                     00.0005879025
                  
                
                 
                   
                     16
                  
                   
                     00
                     .
                     00●6270960
                  
                
                 
                   
                     17
                  
                   
                     00.0006662895
                  
                
                 
                   
                     18
                  
                   
                     00.0007954830
                  
                
                 
                   
                     19
                  
                   
                     00.0007446765
                  
                
                 
                   
                     20
                  
                   
                     00.0007838700
                  
                
                 
                   
                     21
                  
                   
                     00.0008230635
                  
                
                 
                   
                     22
                  
                   
                     00.0008622570
                  
                
                 
                   
                     23
                  
                   
                     00.0009014505
                  
                
                 
                   
                     24
                  
                   
                     00.0009406440
                  
                
                 
                   
                     25
                  
                   
                     00
                     .
                     0009798●75
                  
                
                 
                   
                     26
                  
                   
                     00.0010190310
                  
                
                 
                   
                     27
                  
                   
                     00.0010582245
                  
                
                 
                   
                     28
                  
                   
                     00.0010974180
                  
                
                 
                   
                     29
                  
                   
                     00.0011366115
                  
                
                 
                   
                     30
                  
                   
                     00.0011758050
                  
                
                 
                   
                      
                  
                   
                     ☽
                     à
                     ☉
                     in
                     Seconds
                  
                
                 
                   
                     31
                  
                   
                     00.0012149985
                  
                
                 
                   
                     32
                  
                   
                     00.0012541920
                  
                
                 
                   
                     33
                  
                   
                     00.0012933855
                  
                
                 
                   
                     34
                  
                   
                     00.0013325790
                  
                
                 
                   
                     35
                  
                   
                     00.0013717725
                  
                
                 
                   
                     36
                  
                   
                     00.0014109660
                  
                
                 
                   
                     37
                  
                   
                     00.0014501595
                  
                
                 
                   
                     38
                  
                   
                     00.0014893530
                  
                
                 
                   
                     39
                  
                   
                     00.0015285465
                  
                
                 
                   
                     40
                  
                   
                     00.0015677400
                  
                
                 
                   
                     41
                  
                   
                     00.0016069335
                  
                
                 
                   
                     42
                  
                   
                     00.0016461270
                  
                
                 
                   
                     43
                  
                   
                     00.0016853205
                  
                
                 
                   
                     44
                  
                   
                     00.0017245140
                  
                
                 
                   
                     45
                  
                   
                     00.0917637075
                  
                
                 
                   
                     46
                  
                   
                     00.0018029010
                  
                
                 
                   
                     47
                  
                   
                     00.0018420945
                  
                
                 
                   
                     48
                  
                   
                     00.0018812880
                  
                
                 
                   
                     49
                  
                   
                     00.0019204815
                  
                
                 
                   
                     50
                  
                   
                     00.0019596750
                  
                
                 
                   
                     51
                  
                   
                     00
                     0019988685
                  
                
                 
                   
                     52
                  
                   
                     00.0020380620
                  
                
                 
                   
                     53
                  
                   
                     00.0020772555
                  
                
                 
                   
                     54
                  
                   
                     00.0021164490
                  
                
                 
                   
                     55
                  
                   
                     00.0021556425
                  
                
                 
                   
                     56
                  
                   
                     00.0021948360
                  
                
                 
                   
                     57
                  
                   
                     00.0022340295
                  
                
                 
                   
                     58
                  
                   
                     00.0022732230
                  
                
                 
                   
                     59
                  
                   
                     00.0023124165
                  
                
                 
                   
                     60
                  
                   
                     00.0023516100
                  
                
              
            
             
             
               
                 
                   A
                   Catalogue
                   of
                   some
                   of
                   the
                   most
                   notable
                   fixed
                   Stars
                   according
                   to
                   the
                   observations
                   of
                   Tycho
                   Brahe
                   ,
                   and
                   by
                   him
                   rectified
                   to
                   the
                   beginning
                   of
                   the
                   Year
                   of
                   Mans
                   Redemption
                   ,
                   1601.
                   
                
                 
                   
                     The
                     Names
                     of
                     the
                     Stars
                  
                   
                     Longit.
                     
                  
                   
                     Latit
                     .
                  
                
                 
                   
                     The
                     first
                     Star
                     of
                     Aries
                     .
                  
                   
                     07.671
                     ♈
                  
                   
                     7.
                     8.
                     
                     N
                     4
                  
                
                 
                   
                     The
                     bright
                     Star
                     in
                     the
                     top
                     of
                     the
                     head
                     of
                     Aries
                     .
                  
                   
                     00.583
                     ♉
                  
                   
                     9.
                     57.
                     
                     N
                     3
                  
                
                 
                   
                     The
                     South
                     Eye
                     of
                     Taurus
                     .
                  
                   
                     01.169
                     ●
                  
                   
                     5.
                     31.
                     
                     S
                     1
                  
                
                 
                   
                     The
                     North
                     Eye
                     of
                     Taurus
                     .
                  
                   
                     00.801
                     ●
                  
                   
                     5.
                     31.
                     
                     S
                     1
                  
                
                 
                   
                     The
                     bright
                     Star
                     of
                     the
                     Pleiades
                     .
                  
                   
                     06.620
                     ♉
                  
                   
                     2.
                     6.
                     
                     S
                     3
                  
                
                 
                   
                     The
                     higher
                     head
                     of
                     Gemini
                     .
                  
                   
                     04.078
                     ●
                  
                   
                     4.
                     11.
                     
                     N
                     5
                  
                
                 
                   
                     The
                     lower
                     head
                     of
                     Gemini
                     .
                  
                   
                     04.921
                     ♋
                  
                   
                     10.
                     2.
                     
                     N
                     2
                  
                
                 
                   
                     The
                     bright
                     foot
                     of
                     Gemini
                     .
                  
                   
                     01.069
                     ♋
                  
                   
                     6.
                     38.
                     
                     N
                     2
                  
                
                 
                   
                     In
                     the
                     South
                     Arm
                     of
                     Cancer
                     .
                  
                   
                     02.238
                     ♌
                  
                   
                     6.
                     48.
                     
                     S
                     2
                  
                
                 
                   
                     The
                     bright
                     Star
                     in
                     the
                     neck
                     of
                     Leo.
                     
                  
                   
                     06.662
                     ♌
                  
                   
                     5.
                     8.
                     
                     S
                     3
                  
                
                 
                   
                     The
                     heart
                     of
                     Leo.
                     
                  
                   
                     06.745
                     ♌
                  
                   
                     ●
                     .
                     47
                     .
                     N
                     2
                  
                
                 
                   
                     In
                     the
                     extream
                     of
                     the
                     tail
                     of
                     Leo.
                     
                  
                   
                     04.458
                     ♍
                  
                   
                     0.
                     26.
                     
                     N
                     1
                  
                
                 
                   
                     In
                     Virgo's
                     Wing
                     ;
                     Vindemiatrix
                     .
                  
                   
                     01.217
                     ♎
                  
                   
                     12.
                     18.
                     
                     N
                     1
                  
                
                 
                   
                     Virgins
                     Spike
                     .
                  
                   
                     05.074
                     ♎
                  
                   
                     16.
                     15.
                     
                     N
                     3
                  
                
                 
                   
                     South
                     Ballance
                     .
                  
                   
                     02.643
                     ♏
                  
                   
                     1.
                     59.
                     
                     S
                     1
                  
                
                 
                   
                     North
                     Ballance
                     .
                  
                   
                     03.833
                     ♏
                  
                   
                     0.
                     26.
                     
                     N
                     2
                  
                
                 
                   
                     The
                     highest
                     in
                     the
                     Forehead
                     of
                     Scorpio
                     .
                  
                   
                     07.388
                     ♏
                  
                   
                     8.
                     35.
                     
                     N
                     2
                  
                
                 
                   
                     The
                     Scorpions
                     heart
                     .
                  
                   
                     01.171
                     ●
                  
                   
                     1.
                     05.
                     
                     N
                     3
                  
                
                 
                   
                     Former
                     of
                     the
                     3
                     in
                     the
                     head
                     of
                     Sagittarius
                     .
                  
                   
                     02.203
                     ●
                  
                   
                     4.
                     27.
                     
                     S
                     1
                  
                
                 
                   
                     Northern
                     in
                     the
                     former
                     horn
                     of
                     Capricorn
                     .
                  
                   
                     07.861
                     ●
                  
                   
                     1.
                     24.
                     
                     N
                     4
                  
                
                 
                   
                     The
                     left
                     Shoulder
                     of
                     Aquarius
                     .
                  
                   
                     04.949
                     ♒
                  
                   
                     7.
                     22.
                     
                     N
                     3
                  
                
                 
                   
                     In
                     the
                     mouth
                     of
                     the
                     South
                     Fish.
                     
                  
                   
                     03.620
                     ♓
                  
                   
                     8.
                     42.
                     
                     N
                     3
                  
                
                 
                   
                     The
                     Polar
                     Star
                     or
                     last
                     Star
                     in
                     the
                     ●ail
                     of
                     the
                     lesser
                     Bear.
                     
                  
                   
                      
                  
                   
                     9.
                     4.
                     
                     N
                     5
                  
                
                 
                   
                      
                  
                   
                     06.400
                     ●
                  
                   
                     66.
                     02.
                     
                     N
                     2
                  
                
                 
                   
                     
                     The
                     last
                     Star
                     in
                     the
                     tail
                     of
                     the
                     great
                     Bear
                     ,
                  
                   
                     05.888
                     ♍
                  
                   
                     54.
                     25.
                     
                     N
                     2
                  
                
                 
                   
                     The
                     Tongu●
                     of
                     the
                     Dragon
                     .
                  
                   
                     05.259
                     ♍
                  
                   
                     76.
                     17.
                     
                     N
                     4
                  
                
                 
                   
                     Arcturus
                     in
                     the
                     skirt
                     of
                     his
                     Garment
                     .
                  
                   
                     05.181
                     ♎
                  
                   
                     31.
                     2.
                     
                     N
                     1
                  
                
                 
                   
                     The
                     bright
                     Star
                     of
                     the
                     North
                     Crown
                     .
                  
                   
                     01.845
                     ♏
                  
                   
                     44.
                     23.
                     
                     N
                     2
                  
                
                 
                   
                     The
                     Head
                     of
                     
                       Hercules
                       ▪
                    
                  
                   
                     02.921
                     ●
                  
                   
                     37.
                     23.
                     
                     N
                     ●
                  
                
                 
                   
                     The
                     bright
                     S●●r
                     of
                     the
                     H●rp
                     .
                  
                   
                     0●
                     .
                     699
                     ●
                  
                   
                     61.
                     47.
                     
                     N
                     ●
                  
                
                 
                   
                     The
                     Head
                     of
                     Medusa
                     .
                  
                   
                     05.727
                     ♉
                  
                   
                     22.
                     22.
                     
                     N
                     3
                  
                
                 
                   
                     The
                     bright
                     Star
                     in
                     the
                     Goa●s
                     left
                     Shoulder
                     .
                  
                   
                     04.518
                     ♊
                  
                   
                     22.
                     50.
                     
                     N
                     1
                  
                
                 
                   
                     The
                     middle
                     of
                     the
                     Serp●nts
                     Neck
                     .
                  
                   
                     04.583
                     ♍
                  
                   
                     25.
                     35.
                     
                     N
                     2
                  
                
                 
                   
                     The
                     bright
                     Star
                     in
                     the
                     ●agles
                     Shoulder
                     .
                  
                   
                     07.264
                     ♑
                  
                   
                     29.
                     21.
                     
                     N
                     2
                  
                
                 
                   
                     The
                     bright
                     Star
                     in
                     the
                     〈◊〉
                     Tail.
                     
                  
                   
                     02.370
                     ♒
                  
                   
                     29.
                     8.
                     
                     N
                     3
                  
                
                 
                   
                     The
                     mouth
                     of
                     Pegas●s
                     .
                  
                   
                     07
                     .
                     3●4
                     ♒
                  
                   
                     22.
                     7.
                     
                     N
                     3
                  
                
                 
                   
                     The
                     head
                     of
                     And●omeda
                     .
                  
                   
                     0●
                     .
                     4●0
                     ♈
                  
                   
                     ●5
                     .
                     42.
                     
                     N
                     2
                  
                
                 
                   
                     In
                     the
                     top
                     of
                     the
                     Triangle
                     .
                  
                   
                     00.366
                     ♉
                  
                   
                     16.
                     49.
                     
                     N
                     4
                  
                
                 
                   
                     In
                     the
                     Snout
                     of
                     the
                     Whale
                     .
                  
                   
                     02.643
                     ♉
                  
                   
                     7.
                     50.
                     S
                  
                
                 
                   
                     The
                     bright
                     Star
                     in
                     the
                     Whales
                     Tail.
                     
                  
                   
                     07.481
                     ♓
                  
                   
                     20.
                     47.
                     
                     S
                     2
                  
                
                 
                   
                     Bright
                     Shoulder
                     of
                     Orion
                     .
                  
                   
                     06.444
                     ♊
                  
                   
                     16.06
                     S
                     2
                  
                
                 
                   
                     Middlemost
                     in
                     the
                     belt
                     of
                     Orion
                     .
                  
                   
                     04.972
                     ♊
                  
                   
                     24.
                     33.
                     
                     S
                     2
                  
                
                 
                   
                     The
                     last
                     in
                     the
                     tail
                     of
                     the
                     Har●
                     .
                  
                   
                     0●
                     .
                     324
                     ♊
                  
                   
                     38.
                     26.
                     
                     S
                     4
                  
                
                 
                   
                     The
                     great
                     Dogs
                     mouth
                     Sirius
                     .
                  
                   
                     02.386
                     ●
                  
                   
                     38.
                     30.
                     
                     S
                     1
                  
                
                 
                   
                     The
                     lesser
                     Dog
                     Procyon
                     .
                  
                   
                     05.641
                     ●
                  
                   
                     1●
                     .
                     57
                     .
                     S
                     2
                  
                
                 
                   
                     In
                     the
                     top
                     of
                     the
                     Ships
                     Stern
                     .
                  
                   
                     01.636
                     ♌
                  
                   
                     43.
                     18.
                     
                     S
                     3
                  
                
                 
                   
                     Brightest
                     in
                     Hydra's
                     Heart
                     .
                  
                   
                     06.044
                     ♌
                  
                   
                     22.
                     24.
                     
                     S
                     1
                  
                
              
            
             
               FINIS
            
          
        
         
           
             
             
               THE
               CONTENTS
               OF
               THE
               First
               Part
               ,
               CONTAINING
               The
               Practical
               Geometry
               or
               the
               Art
               of
               Surveying
               .
            
             
               
                 CHapter
                 1.
                 
                 Of
                 the
                 Definition
                 and
                 Division
                 of
                 Geometry
                 .
              
               
                 Chap.
                 2.
                 
                 Of
                 Figures
                 in
                 the
                 General
                 ,
                 more
                 particularly
                 of
                 a
                 Circle
                 and
                 the
                 Affections
                 thereof
                 .
              
               
                 Chap.
                 3.
                 
                 Of
                 Triangles
                 .
              
               
                 Chap.
                 4.
                 
                 Of
                 Quadrangular
                 and
                 Multangular
                 Figures
                 .
              
               
                 Chap.
                 5.
                 
                 Solid
                 Bodies
                 .
              
               
                 
                 Chap.
                 6.
                 
                 Of
                 the
                 measuring
                 of
                 Lines
                 both
                 Right
                 and
                 Circular
              
               
                 Chap.
                 7.
                 
                 Of
                 the
                 measuring
                 of
                 a
                 Circle
                 .
              
               
                 Chap.
                 8.
                 
                 Of
                 the
                 measuring
                 of
                 plain
                 Triangles
                 .
              
               
                 Chap.
                 9.
                 
                 Of
                 the
                 measuring
                 of
                 Heights
                 and
                 Distances
                 .
              
               
                 Chap.
                 10.
                 
                 Of
                 the
                 taking
                 of
                 Distances
                 .
              
               
                 Chap.
                 11.
                 
                 How
                 to
                 take
                 the
                 Plot
                 of
                 a
                 Field
                 at
                 one
                 Station
                 ,
                 &c.
                 
              
               
                 Chap.
                 12.
                 
                 How
                 to
                 take
                 the
                 Plot
                 of
                 a
                 Wood
                 ,
                 Park
                 ,
                 or
                 other
                 Champian
                 Plane
                 ,
                 &c.
                 
              
               
                 Chap.
                 13.
                 
                 The
                 Plot
                 of
                 a
                 Field
                 being
                 taken
                 by
                 an
                 Instrument
                 ,
                 how
                 to
                 compute
                 the
                 Content
                 thereof
                 in
                 Acres
                 ,
                 Roods
                 ,
                 and
                 Perches
                 .
              
               
                 Chap.
                 14.
                 
                 How
                 to
                 take
                 the
                 Plot
                 of
                 mountainous
                 and
                 uneven
                 Ground
                 ,
                 &c.
                 
              
               
                 Chap.
                 15.
                 
                 To
                 reduce
                 Statute
                 measure
                 
                 into
                 Customary
                 ,
                 and
                 the
                 contrary
                 .
              
               
                 
                   Chap.
                   16
                   ▪
                
                 Of
                 the
                 measuring
                 of
                 solid
                 Bodies
                 .
              
            
             
               
                 Tables
                 .
              
               
                 A
                 Table
                 of
                 Squares
                 .
                 Page
                 .
                 99
              
               
                 A
                 Table
                 for
                 the
                 Gauging
                 of
                 Wine
                 Vessels
                 .
                 114
              
               
                 A
                 Table
                 for
                 the
                 Gauging
                 of
                 Beer
                 and
                 Ale
                 Vessels
                 .
                 120
              
               
                 A
                 Table
                 shewing
                 the
                 third
                 part
                 of
                 the
                 Areas
                 of
                 Circles
                 ,
                 in
                 Foot
                 measure
                 and
                 Deoimal
                 parts
                 of
                 a
                 Foot.
                 132
              
               
                 A
                 Table
                 shewing
                 the
                 third
                 part
                 of
                 the
                 Area
                 of
                 any
                 Circle
                 in
                 Foot
                 measure
                 ,
                 not
                 exceeding
                 10
                 f.
                 circumf
                 .
                 136
              
               
                 A
                 Table
                 for
                 the
                 speedy
                 finding
                 of
                 the
                 length
                 or
                 Circumference
                 answering
                 to
                 any
                 Arch
                 in
                 Degrees
                 and
                 Decimal
                 parts
                 .
                 151
              
               
                 A
                 Common
                 Divisor
                 for
                 the
                 speedy
                 
                 converting
                 of
                 the
                 Table
                 ,
                 shewing
                 the
                 Areas
                 of
                 the
                 Segments
                 of
                 a
                 Circle
                 whose
                 Diameter
                 is
                 2
                 &c.
                 154
              
               
                 A
                 Table
                 shewing
                 the
                 Ordinates
                 ,
                 Arches
                 ,
                 and
                 A
                 rea●
                 of
                 the
                 Segments
                 of
                 a
                 Circle
                 ,
                 whose
                 Diameter
                 is
                 〈◊〉
                 &c.
                 156
              
            
          
           
             
             
               The
               Contents
               of
               the
               Second
               Part
               of
               this
               Treatise
               ,
               of
               the
               Doctrine
               of
               the
               PRIMUM
               MOBILE
               .
            
             
               
                 CHap.
                 1.
                 
                 Of
                 the
                 General
                 Subject
                 of
                 Astronomy
                 .
              
               
                 Chap.
                 2.
                 
                 Of
                 the
                 Distinctions
                 and
                 Affections
                 of
                 Spherical
                 Lines
                 and
                 Arches
                 .
              
               
                 Chap.
                 3.
                 
                 Of
                 the
                 kind
                 and
                 parts
                 of
                 Spherical
                 Triangles
                 ,
                 and
                 how
                 to
                 project
                 the
                 same
                 upon
                 the
                 Plane
                 of
                 the
                 Meridian
                 .
              
               
                 Chap.
                 4.
                 
                 Of
                 the
                 solution
                 of
                 Spherical
                 Triangles
                 .
              
               
                 Chap.
                 5.
                 
                 Of
                 such
                 Spherical
                 Problems
                 as
                 are
                 of
                 most
                 general
                 Vse
                 in
                 the
                 Doctrine
                 of
                 the
                 
                   Primum
                   Mobile
                   ,
                   &c.
                
                 
              
            
          
           
             
             
               The
               Contents
               of
               the
               Third
               Part
               of
               this
               Treatise
               being
               an
               Account
               of
               the
               Civil
               Year
               with
               the
               reason
               of
               the
               difference
               between
               the
               Julian
               and
               Gregorian
               Calendars
               ,
               and
               the
               manner
               of
               Computing
               the
               Places
               of
               the
               Sun
               and
               Moon
               .
            
             
               
                 CHap.
                 1.
                 
                 Of
                 the
                 Year
                 Civil
                 and
                 Astronomical
                 .
              
               
                 Chap.
                 2.
                 
                 Of
                 the
                 Cycle
                 of
                 the
                 Moon
                 ,
                 what
                 it
                 is
                 ,
                 how
                 placed
                 in
                 the
                 Calendar
                 ,
                 and
                 to
                 what
                 purpose
                 .
              
               
                 Chap.
                 3.
                 
                 Of
                 the
                 use
                 of
                 the
                 Golden
                 Number
                 in
                 finding
                 the
                 Feast
                 of
                 Easter
                 .
              
               
                 Chap.
                 4.
                 
                 Of
                 the
                 Reformation
                 of
                 the
                 
                 Calendar
                 by
                 Pope
                 Gregory
                 the
                 Thirteenth
                 ,
                 &c.
                 
              
               
                 Chap.
                 5.
                 
                 Of
                 the
                 Moons
                 mean
                 Motion
                 and
                 how
                 the
                 Anticipation
                 of
                 the
                 New
                 Moons
                 may
                 be
                 discovered
                 by
                 the
                 Ep●●●ts
                 .
              
               
                 Chap.
                 6.
                 
                 To
                 find
                 the
                 Dominical
                 Letter
                 and
                 Feast
                 of
                 Easter
                 according
                 to
                 the
                 Gregorian
                 Account
                 .
              
               
                 Chap.
                 7.
                 
                 How
                 to
                 reduce
                 Sexagenary
                 Numbers
                 into
                 Decimals
                 ,
                 and
                 the
                 contrary
                 .
              
               
                 Chap.
                 8.
                 
                 Of
                 the
                 difference
                 of
                 Meridians
                 .
              
               
                 Chap.
                 9.
                 
                 Of
                 the
                 Theory
                 of
                 the
                 Suns
                 or
                 Earths
                 motion
                 .
              
               
                 
                   Chap
                   ▪
                
                 10.
                 
                 Of
                 the
                 finding
                 of
                 the
                 Suns
                 Apogaeon
                 ,
                 quantity
                 of
                 Excentricity
                 and
                 middle
                 Motion
                 .
              
               
                 Chap.
                 11.
                 
                 Of
                 the
                 quantity
                 of
                 the
                 tropical
                 and
                 sydereal
                 Year
                 .
              
               
                 Chap.
                 12.
                 
                 Of
                 the
                 Suns
                 mean
                 Motion
                 otherwise
                 stated
                 .
              
               
                 
                 Chap.
                 13.
                 
                 How
                 to
                 calculate
                 the
                 Suns
                 true
                 place
                 by
                 either
                 of
                 the
                 Tables
                 of
                 〈◊〉
                 middle
                 Motion
                 .
                 I
                 〈…〉
              
               
                 Chap.
                 14.
                 
                 To
                 find
                 the
                 place
                 of
                 the
                 fixed
                 Stars
                 .
              
               
                 Chap.
                 15.
                 
                 Of
                 the
                 Theory
                 of
                 the
                 Moon
                 and
                 the
                 finding
                 the
                 place
                 of
                 her
                 Apogaeon
                 ,
                 quantity
                 of
                 Excentricity
                 ,
                 and
                 middle
                 motion
                 .
              
               
                 Chap.
                 16.
                 
                 Of
                 the
                 finding
                 of
                 the
                 place
                 and
                 motion
                 of
                 the
                 Moons
                 Nodes
                 .
              
               
                 Chap.
                 17.
                 
                 How
                 to
                 calculate
                 the
                 Moons
                 true
                 place
                 in
                 her
                 Orbs.
                 
              
               
                 Chap.
                 18.
                 
                 To
                 compute
                 the
                 true
                 Latitude
                 of
                 the
                 Moon
                 ,
                 and
                 to
                 reduce
                 her
                 place
                 from
                 her
                 Orbit
                 to
                 the
                 Ecliptick
                 .
              
               
                 Chap.
                 19.
                 
                 To
                 find
                 the
                 mean
                 Conjunctions
                 and
                 Opposition
                 of
                 the
                 Sun
                 and
                 Moon
                 ▪
              
            
          
           
             
             
               The
               Fourth
               Part
               ,
               or
               an
               Introduction
               to
               Geography
               .
            
             
               
                 CHap.
                 1.
                 
                 Of
                 the
                 Nature
                 and
                 Division
                 of
                 Geography
                 .
              
               
                 Chap.
                 2.
                 
                 Of
                 the
                 Distinction
                 or
                 Dimension
                 of
                 the
                 Earthly
                 Globe
                 by
                 Zones
                 and
                 Climates
                 .
              
               
                 Chap.
                 3.
                 
                 Of
                 Europe
                 .
              
               
                 Chap.
                 4.
                 
                 Of
                 Asia
                 .
              
               
                 Chap.
                 5.
                 
                 Of
                 Africk
                 .
              
               
                 Chap.
                 6.
                 
                 Of
                 America
                 .
              
               
                 Chap.
                 7.
                 
                 Of
                 the
                 description
                 of
                 the
                 Terrestrial
                 Globe
                 ,
                 by
                 Maps
                 Vniversal
                 and
                 Particular
                 .
              
            
             
               
                 A
                 Table
                 of
                 the
                 view
                 of
                 the
                 most
                 notable
                 Epochas
                 .
              
               
                 
                   The
                   Iulian
                   Calendar
                   .
                   Page
                   .
                   461
                
                 
                   The
                   Gregorian
                   Calendar
                   .
                   466
                
                 
                   
                   A
                   Table
                   to
                   convert
                   Sexagenary
                   Degrees
                   and
                   Minutes
                   into
                   Decimals
                   and
                   the
                   contrary
                   .
                   476
                
                 
                   A
                   Table
                   converting
                   hours
                   and
                   minutes
                   into
                   degrees
                   and
                   minutes
                   of
                   the
                   AEquator
                   .
                   480
                
                 
                   A
                   Table
                   of
                   the
                   Longitudes
                   and
                   Latitudes
                   of
                   some
                   of
                   the
                   most
                   eminent
                   Cities
                   and
                   Towns
                   in
                   England
                   and
                   Ireland
                   .
                   482
                
                 
                   A
                   Table
                   of
                   the
                   Suns
                   mean
                   Longitude
                   and
                   Anomaly
                   in
                   both
                   AEgyptian
                   and
                   Iulian
                   Years
                   ,
                   Months
                   ,
                   Days
                   ,
                   Hours
                   and
                   Minutes
                   .
                   484
                
                 
                   Tables
                   of
                   the
                   Moons
                   mean
                   motion
                   .
                   493
                
                 
                   A
                   Catalogue
                   of
                   some
                   of
                   the
                   most
                   notable
                   fixed
                   Stars
                   ,
                   according
                   to
                   the
                   observation
                   of
                   
                     Tycho
                     Brahe
                  
                   ,
                   rectified
                   to
                   the
                   year
                   1601.
                   511
                
              
            
          
           
             
             
               Books
               Printed
               for
               and
               sold
               by
               Thomas
               Passinger
               at
               the
               Three
               Bibles
               on
               the
               middle
               of
               London-Bridge
               .
            
             
               THe
               Elements
               of
               the
               Mathematical
               Art
               ,
               commonly
               called
               Algebra
               ,
               expounded
               in
               four
               Books
               by
               
                 Iohn
                 Kersey
              
               ,
               in
               two
               Vol.
               fol.
               A
               mirror
               or
               Looking-glass
               for
               Saints
               and
               Sinners
               ,
               shewing
               the
               Justice
               of
               God
               on
               the
               one
               ,
               and
               his
               Mercy
               towards
               the
               other
               ,
               set
               forth
               in
               some
               thousands
               of
               Examples
               by
               
                 Sam.
                 Clark
              
               ,
               in
               two
               Vol.
               fol.
               
            
             
               The
               Mariners
               Magazine
               by
               Capt.
               
                 Sam.
                 Sturmy
                 ,
                 fol.
              
               
            
             
               Military
               and
               Maritime
               Discipline
               in
               three
               Books
               ,
               by
               Capt.
               
                 Tho.
                 Kent
                 ,
                 fol.
              
               
            
             
               Dr.
               
               Cudworth's
               universal
               Systeme
               .
            
             
               The
               Triumphs
               of
               Gods
               Revenge
               against
               the
               Crying
               and
               Execrable
               sin
               of
               wilful
               and
               premeditated
               Murther
               ,
               by
               
                 Iohn
                 Reynolds
                 ,
                 fol.
              
               
            
             
               Royal
               and
               Practical
               Chymistry
               by
               
                 Oswaldus
                 Crollius
              
               and
               
                 Iohn
                 Hartman
              
               ,
               faithfully
               rendred
               into
               English
               ,
               fol.
               
            
             
               Practical
               Navigation
               by
               
                 Iohn
                 Seller
                 .
                 Quarto
              
               .
            
             
               The
               History
               of
               the
               Church
               of
               Great
               Britain
               from
               the
               Birth
               of
               our
               Saviour
               until
               the
               Year
               of
               our
               Lord
               1667.
               quarto
               .
            
             
               The
               Ecclesiastical
               History
               of
               France
               from
               the
               first
               plantation
               of
               Christianity
               there
               unto
               this
               time
               ,
               quarto
               .
            
             
               The
               book
               of
               Architecture
               by
               
                 Andrea
                 Palladio
                 ,
                 quarto
              
               .
            
             
             
               The
               mirror
               of
               Architecture
               or
               the
               ground
               Rules
               of
               the
               Art
               of
               Building
               ,
               by
               
                 Vincent
                 Scammozi
                 quarto
              
               .
            
             
               Trigonometry
               ,
               on
               the
               Doctrine
               of
               Triangles
               ,
               by
               
                 Rich.
                 Norwood
                 ,
                 quarto
              
               .
            
             
               
               Markham's
               Master-piece
               Revived
               ,
               containing
               all
               knowledge
               belonging
               to
               the
               Smith
               ,
               Farrier
               ,
               or
               Horse-Leach
               ,
               touching
               the
               curing
               of
               all
               Diseases
               in
               Horses
               ,
               quarto
               .
            
             
               
                 Collins
                 Sector
              
               on
               a
               Quadrant
               ,
               quarto
               .
            
             
               The
               famous
               History
               of
               the
               destruction
               of
               Troy
               ,
               in
               three
               books
               ,
               quarto
               .
            
             
               Safeguard
               of
               Sailers
               ,
               quarto
               .
            
             
               
               Norwood's
               Seamans
               Companion
               ,
               quarto
               .
            
             
               Geometrical
               Seaman
               ,
               quarto
               .
            
             
               A
               plain
               and
               familiar
               Exposition
               of
               the
               Ten
               Commandments
               ,
               by
               
                 Iohn
                 Dod
                 ,
                 quarto
              
               .
            
             
               The
               Mariners
               new
               Calendar
               ,
               quarto
               .
            
             
               The
               Seamans
               Calendar
               ,
               quarto
               .
            
             
               The
               Seamans
               Practice
               ,
               quarto
               .
            
             
               The
               honour
               of
               Chivalry
               do
               the
               famous
               and
               delectable
               History
               of
               
                 Don
                 Belianus
                 of
              
               Greece
               ,
               quarto
               .
            
             
               The
               History
               
                 of
                 Amadis
                 de
                 Gaul
              
               ,
               the
               fifth
               part
               ,
               quarto
               .
            
             
               The
               Seamans
               Dictionary
               ,
               quarto
               .
            
             
               The
               complete
               Canonier
               ,
               quarto
               .
            
             
               Seamans
               Glass
               ,
               quarto
               .
            
             
               Complete
               Shipwright
               ,
               quarto
               .
            
             
               The
               History
               of
               Valentine
               and
               
                 Orson
                 ,
                 quarto
              
               .
            
             
               The
               Complete
               Modellist
               ,
               quarto
               .
            
             
               The
               Boat-swains
               Art
               ,
               quarto
               .
            
             
               Pilots
               Sea-mirror
               ,
               quarto
               .
            
             
               The
               famous
               History
               of
               Montelion
               Knight
               of
               the
               Oracle
               ,
               quarto
               .
            
             
               The
               History
               of
               Palladine
               of
               
                 England
                 ,
                 quarto
              
               .
            
             
             
               The
               History
               of
               Cleocretron
               and
               
                 Clori●ma
                 ,
                 quarto
              
               .
            
             
               The
               Arralgnment
               of
               lower
               ,
               idle
               ,
               froward
               and
               unconstant
               Women
               ,
               quarto
               .
            
             
               The
               pleasant
               History
               of
               Iack
               of
               
                 Newb●●y
                 ,
                 quarto
              
            
             
               Philips
               Mathematical
               Manual
               ,
               Octavo
               .
            
             
               A
               prospect
               of
               Heaven
               ,
               or
               a
               Treatise
               of
               the
               happiness
               of
               the
               Saints
               in
               Glory
               ,
               oct
               .
            
             
               Etymologicunt
               parvum
               ,
               oct
               .
            
             
               Thesaurus
               Astrologiae
               ,
               
                 or
                 an
                 Astrological
                 Treasury
                 by
              
               Iohn
               Gadbury
               ,
               oct
               .
            
             
               Gellibrand
               '
               
                 s
                 Epitome
              
               ,
               oct
               .
            
             
               The
               English
               Academy
               or
               a
               brief
               Introduction
               to
               the
               seven
               Liberal
               Arts
               ,
               by
               
                 Iohn
                 Newton
              
               ,
               D.
               D.
               oct
               .
            
             
               The
               best
               exercise
               for
               Christians
               in
               the
               worst
               times
               ,
               by
               
                 I.
                 H.
                 oct
              
               .
            
             
               A
               seasonable
               discourse
               of
               the
               right
               use
               and
               abuse
               of
               Reason
               in
               matters
               of
               Religion
               ,
               oct
               .
            
             
               The
               Mariners
               Compass
               rectified
               ,
               oct
               .
            
             
               Norwood
               '
               
                 s
                 Epitome
              
               ,
               oct
               .
            
             
               Chymical
               Essays
               by
               
                 Iohn
                 Beguinus
                 ,
                 oct
              
               .
            
             
               A
               spiritual
               Antidote
               against
               sinful
               Contagions
               ,
               by
               
                 Tho.
                 Doolittle
                 ,
                 oct
              
               .
            
             
               
                 Monastieon
                 Fevershamiense
              
               ;
               or
               a
               description
               of
               the
               Abby
               of
               
                 Feversham
                 ,
                 oct
              
               .
            
             
               Scarborough
               '
               
                 s
                 Spaw
              
               ,
               oct
               .
            
             
               French
               Schoolmaster
               ,
               oct
               .
            
             
               
                 The
                 Poems
                 of
              
               Ben.
               Iohnson
               ,
               junior
               ,
               oct
               .
            
             
               A
               book
               of
               Knowledge
               in
               three
               parts
               ,
               oct
               .
            
             
               The
               Book
               of
               Palmestry
               ,
               oct
               .
            
             
               Farnaby
               '
               
                 s
                 Epigramms
              
               ,
               oct
               .
            
             
               The
               Huswifes
               Companion
               ,
               and
               the
               Husbandmans
               Guide
               ,
               oct
               .
            
             
               Jovial
               Garland
               ,
               oct
               .
            
             
               Cocker
               '
               
                 s
                 Arithmetick
              
               ,
               twelves
               .
            
             
               The
               Path
               Way
               to
               Health
               ,
               twelves
               .
            
             
               Hall
               '
               
                 s
                 Soliloquies
              
               ,
               twelves
               .
            
             
             
               The
               Complete
               Servant
               Maid
               ,
               or
               the
               young
               Maidens
               Tutor
               ,
               twelves
               .
            
             
               
               Newton's
               Introduction
               to
               the
               Art
               of
               Logick
               ,
               twelves
               .
            
             
               
               Newton's
               Introduction
               to
               the
               Art
               of
               Rhetorick
               ,
               twelves
               .
            
             
               The
               Anatomy
               of
               Popery
               ,
               or
               a
               Catalogue
               of
               Popish
               errors
               in
               Doctrine
               and
               corruptions
               in
               Worship
               ,
               twelves
               .
            
             
               The
               famous
               History
               of
               the
               five
               wise
               Philosophers
               ,
               containing
               the
               Life
               of
               Iehosophat
               the
               Hermit
               .
               twelves
               ,
            
             
               The
               exact
               Constable
               with
               his
               Original
               and
               Power
               in
               all
               cases
               belonging
               to
               his
               Office
               ,
               twelves
               .
            
             
               The
               Complete
               Academy
               or
               a
               Nursery
               of
               Complements
               ,
               twelves
               .
            
             
               Heart
               salve
               for
               a
               wounded
               Soul
               ,
               and
               Eye
               salve
               for
               a
               blind
               World
               ,
               by
               
                 Tho.
                 Calvert
                 .
                 twelves
              
               .
            
             
               Pilgrims
               Port
               ,
               or
               the
               weary
               mans
               rest
               in
               the
               Grave
               ,
               twelves
               .
            
             
               Christian
               Devotion
               or
               a
               manual
               of
               Prayers
               ,
               twelves
               .
            
             
               The
               Mariners
               divine
               Mate
               ,
               twelves
               .
            
             
               At
               Cherry
               Garden
               Stairs
               on
               Rotherhith
               Wall
               ,
               are
               taught
               these
               Mathematical
               Sciences
               ,
               viz.
               Arithmetick
               ,
               Algebra
               ,
               Geometry
               ,
               Trigonometry
               ,
               Surveying
               ,
               Navigation
               ,
               Dyalling
               ,
               Astronomy
               ,
               Gauging
               ,
               Gunnery
               and
               Fortification
               :
               The
               use
               of
               the
               Globes
               ,
               and
               other
               Mathematical
               Instruments
               ,
               the
               projection
               of
               the
               Sphere
               on
               any
               circle
               ,
               &c.
               
               He
               maketh
               and
               selleth
               all
               sorts
               of
               Mathematical
               Instruments
               in
               Wood
               and
               Brass
               ,
               for
               Sea
               and
               Land
               ,
               with
               Books
               to
               shew
               the
               use
               of
               them
               :
               Where
               you
               may
               have
               all
               sorts
               of
               Maps
               ,
               Plats
               ,
               Sea-Charts
               ,
               in
               Plain
               and
               Mercator
               ,
               on
               reasonable
               Terms
               .
            
             
               
                 By
                 Iames
                 Atkinson
                 .
              
            
             
               FINIS
               .