The compleat ship-wright plainly and demonstratively teaching the proportions used by experienced ship-wrights according to their custome of building, both geometrically and arithmetically performed : to which by Edmund Bushnell, ship-wright.
         Bushnell, Edmund.
      
       
         
           1664
        
      
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             The compleat ship-wright plainly and demonstratively teaching the proportions used by experienced ship-wrights according to their custome of building, both geometrically and arithmetically performed : to which by Edmund Bushnell, ship-wright.
             Bushnell, Edmund.
          
           [8], 68 p. : ill.
           
             Printed by W. Leybourn for George Hurlock, and are to be sold at his shop ...,
             London :
             1664.
          
           
             Errata: p. [6].
             Advertisements: p. [7]-[8].
             Reproduction of original in Bodleian Library.
          
        
      
    
     
       
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         eng
      
       
         
           Shipbuilding -- Early works to 1800.
        
      
    
     
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           THE
           COMPLEAT
           Ship-Wright
           .
        
         
           Plainly
           and
           Demonstratively
           Teaching
           the
           Proportions
           used
           by
           Experienced
           
             Ship-Wrights
             ,
          
           according
           to
           their
           Custome
           of
           Building
           ;
           both
           
             Geometrically
          
           and
           
             Arithmetically
          
           performed
           .
        
         
           
             To
             which
             is
             added
             ,
          
           Certain
           Propositions
           in
           
             Geometry
             ,
          
           the
           use
           of
           a
           
             Diagonall
             SCALE
             ,
          
           to
           draw
           a
           
             Draught
             ,
          
           with
           the
           Making
           ,
           Graduating
           ,
           or
           Marking
           of
           a
           Bend
           of
           
             Moulds
             ,
          
           and
           ordering
           of
           the
           same
           .
           The
           Extraction
           of
           the
           
             Square
             Root
             ,
          
           with
           a
           
             Table
          
           of
           
             Squares
             .
          
        
         
           Also
           ,
           a
           way
           of
           Rowing
           of
           
             Ships
             ,
          
           by
           heaving
           at
           the
           
             Capstane
             ,
          
           usefull
           in
           any
           
             Ship
          
           becalm'd
           ;
           with
           other
           things
           usefull
           in
           that
           
             ART
             .
          
        
         
           By
           EDMUND
           BUSHNELL
           
             Ship-Wright
             .
          
        
         
           
             LONDON
             ,
          
           Printed
           by
           
             W.
             Leybourn
          
           for
           
             George
             Hurlock
             ,
          
           and
           are
           to
           be
           sold
           at
           his
           Shop
           at
           
             Magnus
          
           Church
           corner
           in
           Thames-Street
           ,
           neer
           
             London-Bridge
             ,
          
           1664.
           
        
      
       
         
         
         
           TO
           THE
           READER
           .
        
         
           
             Friendly
             Reader
             ,
          
        
         
           THe
           Matter
           contained
           in
           this
           
             Treatise
             ,
          
           is
           written
           onely
           for
           the
           good
           and
           profit
           of
           my
           Countrymen
           ,
           who
           are
           still
           in
           that
           capacity
           that
           once
           I
           my self
           was
           ;
           that
           is
           ,
           ignorant
           of
           what
           they
           should
           know
           in
           their
           
             Trades
             ,
          
           and
           desire
           Instruction
           ;
           not
           that
           I
           presume
           to
           teach
           those
           long
           experienced
           
             Ship-Wrights
             ,
          
           whose
           actions
           hath
           declared
           their
           Abilities
           to
           the
           whole
           World
           ,
           in
           their
           Building
           of
           so
           Gallant
           ,
           and
           Serviceable
           a
           Fleet
           of
           Ships
           ,
           as
           at
           present
           his
           
             Majesty
             ,
          
           the
           King
           of
           
             England
             ,
          
           is
           furnished
           withall
           ,
           no
           King
           having
           the
           like
           ,
           either
           for
           Offence
           ,
           or
           Defence
           :
           yet
           their
           knowledge
           they
           desire
           to
           keep
           to
           themselves
           ,
           or
           at
           least
           among
           so
           small
           a
           number
           as
           they
           can
           ;
           for
           although
           some
           of
           them
           have
           many
           Servants
           ,
           and
           by
           Indenture
           
           (
           I
           suppose
           )
           bound
           to
           Teach
           them
           all
           alike
           the
           same
           
             Art
          
           and
           
             Mystery
          
           that
           he
           himself
           useth
           ;
           Yet
           it
           may
           be
           he
           may
           Teach
           some
           one
           ,
           and
           the
           rest
           must
           be
           kept
           ignorant
           ,
           so
           that
           those
           
             Ship
             Wrights
             ,
          
           although
           bred
           by
           such
           knowing
           Men
           ,
           yet
           they
           are
           able
           to
           teach
           their
           Servants
           nothing
           ,
           more
           then
           to
           Hew
           ,
           or
           Dub
           ,
           to
           Fay
           a
           Piece
           when
           it
           is
           Moulded
           to
           his
           place
           assigned
           ,
           or
           the
           like
           :
           but
           if
           occasion
           require
           ,
           that
           the
           greatest
           part
           of
           these
           Men
           ,
           by
           being
           
             Carpenters
          
           of
           Ships
           ,
           or
           the
           like
           ,
           may
           be
           removed
           from
           
             England
          
           to
           
             Virginia
             ,
          
           or
           
             New-England
             ,
          
           or
           the
           like
           Countryes
           ,
           where
           Timber
           is
           plenty
           for
           their
           use
           ,
           yet
           through
           their
           ignorance
           ,
           they
           durst
           not
           undertake
           such
           a
           Work
           :
           For
           their
           sakes
           I
           have
           written
           this
           
             Book
             ,
          
           wherein
           the
           
             Reader
          
           shall
           finde
           instructions
           sufficient
           for
           Moulding
           of
           any
           
             Ship
             ,
          
           or
           
             Vessell
          
           whatever
           ,
           with
           the
           Masting
           of
           them
           ,
           drawing
           of
           
             Draughts
             ,
          
           and
           all
           in
           a
           very
           plain
           and
           exact
           Method
           ,
           which
           I
           am
           confident
           will
           be
           understood
           by
           the
           meanest
           capacities
           ,
           if
           they
           can
           but
           read
           English
           ,
           and
           have
           the
           benefit
           of
           a
           little
           Arithmetick
           as
           Adition
           ,
           Substraction
           ,
           Multiplication
           ,
           Division
           :
           be
           diligent
           ,
           and
           I
           shall
           be
           thereby
           incouraged
           ,
           if
           need
           be
           ,
           to
           help
           thee
           farther
           in
           the
           Art.
           
        
         
           Farewell
           ,
           
             Thy
             Friend
             ,
             Edmund
             Bushnell
             .
          
        
      
       
         
         
           THE
           CONTENTS
           .
        
         
           
             
               Ch.
               I.
            
             OF
             Geometricall
             Problemes
             Page
             1
          
           
             
               Ch.
               II
            
             Of
             your
             SCALE
             Page
             4
          
           
             
               Ch.
               III
            
             Concerning
             the
             drawing
             your
             Draught
             upon
             Paper
             Page
             6
          
           
             
               Ch.
               IV.
            
             Shewing
             ,
             how
             to
             sweep
             out
             the
             Bend
             of
             Moulds
             upon
             a
             Flat
             Page
             9
          
           
             
               Ch.
               V.
            
             The
             Description
             of
             the
             Rising
             Lines
             aftward
             on
             ,
             and
             forward
             on
             ;
             with
             the
             Narrowing
             Lines
             ,
             and
             Lines
             of
             Breadth
             :
             As
             also
             the
             Narrowing
             of
             Lines
             at
             the
             top
             of
             the
             Timbers
             Page
             12
          
           
             
               Ch.
               VI.
            
             Shewing
             the
             Making
             and
             graduating
             ,
             or
             marking
             of
             the
             Bend
             of
             Molds
             Page
             15
          
           
             
               Ch.
               VII
               .
            
             Arithmetically
             shewing
             how
             to
             frame
             the
             body
             of
             a
             Ship
             by
             Segments
             of
             Circles
             :
             being
             a
             true
             way
             to
             examine
             the
             truth
             of
             a
             Bow
             Page
             22
          
           
             
               Ch.
               VIII
               .
            
             How
             to
             Extract
             the
             Square
             Rooot
             Page
             31
          
           
             
               Ch.
               IX
               .
            
             A
             Description
             of
             the
             Table
             of
             Squares
             Page
             39
          
           
             
               Ch.
               X.
            
             Shewing
             ,
             how
             to
             hang
             a
             rising
             line
             by
             severall
             sweeps
             ,
             to
             make
             it
             rounder
             aftward
             ,
             then
             at
             the
             beginning
             of
             of
             the
             same
             Page
             53
          
           
             
             
               Ch.
               XI
               .
            
             Concerning
             Measuring
             of
             Ships
             Page
             59
          
           
             
               Ch.
               XII
               .
            
             Concerning
             the
             Masts
             of
             Ships
             Page
             62
          
           
             
               Ch.
               XIII
               .
            
             Concerning
             Rowing
             of
             Ships
             ,
             when
             they
             are
             becalmed
             .
             Page
             65
          
        
      
       
         
           Advertisement
           .
        
         
           IF
           any
           Gentleman
           ,
           studious
           in
           the
           
             Mathematicks
             ,
          
           have
           ,
           or
           shall
           have
           occasion
           for
           Instruments
           thereunto
           belonging
           ,
           they
           may
           be
           furnished
           with
           all
           sorts
           ,
           usefull
           both
           for
           Sea
           or
           Land
           ,
           either
           in
           Brass
           ,
           or
           Wood
           ,
           by
           
             Walter
             Hayes
             ,
          
           at
           the
           
             Cross-Daggers
          
           in
           
             Moore-Fields
             ,
          
           next
           door
           to
           the
           
             Popes-Head
          
           Tavern
           ;
           where
           they
           may
           have
           all
           sorts
           of
           Maps
           ,
           Globes
           ,
           and
           Mathematicall
           Paper
           ,
           Carpenters
           Rules
           ,
           Post
           and
           Pocket-Dyalls
           for
           any
           Latitude
           ,
           Steel
           Letters
           ,
           Figures
           ,
           Signes
           ,
           Planets
           ,
           or
           Aspects
           ,
           at
           reasonable
           Rates
           .
        
      
       
         
           ERRATA
           .
        
         
           
             
               
                 PAge
                 7
                 ,
              
               
                 Line
                 9
                 ,
              
               
                 Read
                 Halses
              
            
             
               
                 8
              
               
                 16
              
               
                 come
                 not
                 fowl
              
            
             
               
                 8
              
               
                 21
              
               
                 faied
              
            
             
               
                 11
              
               
                 2
              
               
                 at
                 
                   f
                
                 or
                 G
              
            
             
               
                 12
              
               
                 23
              
               
                 afore
              
            
             
               
                 13
              
               
                 2
              
               
                 afore
              
            
             
               
                 13
              
               
                 19
              
               
                 aftward
              
            
             
               
                 14
              
               
                 15
              
               
                 Lo
              
            
             
               
                 14
              
               
                 28
              
               
                 ●
                 /
                 ●
              
            
             
               
                 15
              
               
                 25
              
               
                 dele
                 off
              
            
             
               
                 16
              
               
                 7
              
               
                 Sirmarks
              
            
             
               
                 18
              
               
                 ●
              
               
                 none
                 ,
                 that
              
            
             
               
                 18
              
               
                 11
              
               
                 at
                 the
                 top
              
            
             
               
                 19
              
               
                 2
              
               
                 stick
              
            
             
               
                 20
              
               
                 29
              
               
                 you
                 h●w
                 to
              
            
             
               
                 22
              
               
                 5
              
               
                 make
                 a
              
            
             
               
                 23
              
               
                 3
                 &
                 5
              
               
                 3
                 /
                 5
              
            
             
               
                 54
              
               
                 16
              
               
                 12
                 foot
              
            
             
               
                 57
              
               
                 1
              
               
                 two
                 last
                 numbers
                 .
              
            
          
        
      
       
         
         
           Books
           
             Printed
             and
             Sold
             by
          
           George
           Hurlock
           ,
           
             at
          
           Magnus
           Church-Corner
           
             in
          
           Thames-Street
           ,
           
             neer
          
           London
           Bridge
           .
        
         
           
             SEamans
             Kalender
             ,
          
           or
           
             Ephimerides
          
           of
           the
           Sun
           ,
           Moon
           ,
           and
           certain
           of
           the
           most
           notable
           fixed
           Stars
           ,
           
             &c.
             
          
        
         
           
             Norwoods
          
           Doctrine
           of
           Triangles
           ,
           with
           Logarithmes
           ,
           lately
           printed
           ,
           exactly
           corrected
           ,
           and
           much
           inlarged
           by
           the
           Author
           himself
           .
           
             Norwoods
          
           Epitomy
           ,
           applyed
           to
           plain
           and
           Mercators
           sailing
           
             Norwoods
          
           Sea
           mans
           Practice
           ,
           containing
           a
           Fundamentall
           Probleme
           in
           
             Navigation
             ,
          
           experimentally
           verified
           .
           Safeguard
           of
           Saylors
           ,
           or
           Great
           Rutter
           ,
           by
           
             Ro.
             Norman
             .
          
           Sea
           mans
           secrets
           .
           A
           Table
           of
           Gauging
           all
           manner
           of
           Vessels
           ,
           by
           
             Jo.
             Goodwin
             .
          
           Path-way
           to
           perfect
           sailing
           ,
           by
           
             Richard
             Poltar
             ▪
             Pitiscus
          
           his
           Doctrine
           of
           Triangles
           ,
           with
           Canons
           .
           
             Navigator
          
           by
           
             Cap.
             Charles
             Saltonstal
             ,
          
           newly
           printed
           ,
           with
           additions
           ,
           shewing
           the
           Deceipts
           of
           the
           plain
           Charts
           used
           in
           our
           time
           ,
           and
           a
           way
           to
           prove
           the
           projection
           of
           any
           Plain
           Chart.
           
             Dary's
          
           description
           and
           use
           of
           a
           Vniversall
           Quadrant
           .
           Seamans
           Dictionary
           ,
           or
           the
           Exposition
           and
           Demonstration
           of
           all
           the
           parts
           and
           things
           belonging
           to
           a
           ship
           ▪
           together
           with
           an
           Explanation
           of
           all
           the
           Termes
           and
           Phrases
           used
           in
           the
           practique
           part
           of
           
             Navigation
             ,
          
           by
           Sir
           
             Henry
             Manwarring
             .
          
        
         
           Exact
           Tables
           of
           Naturall
           and
           Artificial
           Sincs
           ,
           Tangents
           ,
           Secants
           and
           Logarithms
           ,
           and
           an
           
             Institution
             Mathematicall
             ,
          
           containing
           their
           constructions
           and
           use
           in
           the
           solution
           of
           all
           Triangles
           Plain
           and
           Spherical
           ,
           and
           the
           application
           thereof
           in
           
             Astronomy
             ,
             Dialling
             ,
          
           and
           
             Navigation
             .
          
        
         
           Seamans
           Glass
           ,
           now
           newly
           published
           ,
           with
           the
           addition
           of
           many
           propositions
           in
           
             Navigation
             ,
             Astronomy
             ,
          
           and
           
             Dialling
             ,
          
           not
           before
           printed
           .
        
         
           The
           Compleat
           Canoneer
           ,
           shewing
           the
           principles
           and
           grounds
           of
           the
           Art
           of
           Gunnery
           ,
           as
           also
           several
           Fire-Works
           for
           Sea
           and
           Land.
           
        
         
           The
           Advancement
           of
           the
           Art
           of
           
             Navigation
             ,
          
           or
           Sea-mans
           Canon
           of
           Triangles
           ,
           shewing
           by
           a
           new
           Canon
           of
           Sines
           ,
           Tangents
           ,
           and
           Secants
           ,
           how
           to
           resolve
           all
           Cases
           of
           right
           lined
           Triangles
           ,
           onely
           by
           looking
           into
           the
           Tables
           ,
           without
           any
           Calculation
           .
           Particularly
           applyed
           to
           all
           the
           three
           kindes
           of
           Sayling
           ,
           
             viz.
          
           by
           the
           Plain
           Chart
           ,
           Mercators
           Chart
           ,
           by
           a
           Great
           Circle
           ;
           and
           to
           the
           Art
           of
           
             Surveying
             .
          
        
         
           
             Trigonometria
             Brittannica
             ,
          
           or
           the
           Doctrine
           of
           Triangles
           ,
           in
           
             folio
             ,
          
           exhibiting
           the
           Logarithms
           of
           all
           numbers
           ,
           from
           one
           to
           a
           hundred
           thousand
           ,
           and
           the
           Sines
           and
           Tangents
           to
           the
           hundred
           part
           of
           a
           Degree
           ,
           with
           Mr.
           
             Gellibrands
          
           Doctrine
           of
           Triangles
           ,
           faithfully
           translated
           from
           the
           Latin
           Copy
           .
        
         
           The
           Sector
           on
           a
           Quadrant
           ,
           containing
           the
           Description
           and
           use
           of
           three
           
           general
           Quadrants
           ,
           accommodated
           for
           the
           ready
           finding
           the
           Hour
           and
           Azimuth
           universally
           in
           the
           equal
           Limbe
           .
        
         
           The
           Compleat
           Modellist
           ,
           shewing
           how
           to
           raise
           the
           Model
           of
           any
           Ship
           or
           Vessel
           ,
           either
           in
           proportion
           ,
           or
           out
           of
           proportion
           ▪
           and
           to
           find
           the
           length
           and
           bigo●ss
           of
           every
           Rope
           ,
           in
           all
           Vessels
           exactly
           ,
           with
           the
           weight
           of
           their
           Anchors
           and
           Cables
           .
        
         
           There
           is
           a
           new
           Book
           ▪
           called
           the
           
             Pilots
             Sea-Mirror
             ,
          
           which
           is
           a
           
             Compendium
          
           of
           the
           largest
           
             Wagoner
             ,
          
           or
           the
           lightning
           
             Sea-Collumbe
             ;
          
           Containing
           all
           Distances
           or
           thwart
           Courses
           of
           the
           
             Eastern
             ,
             Northern
             ,
          
           and
           
             Western
          
           Navigations
           ,
           with
           a
           general
           Tide
           Table
           ,
           for
           every
           day
           ,
           and
           the
           Change
           and
           Full
           of
           the
           Moon
           exactly
           for
           eight
           years
           ,
           also
           Courses
           and
           Distances
           throughout
           the
           Straights
           .
           Printed
           for
           
             George
             Hurlock
             ,
          
           at
           
             Magnus
             Church
             Corner
             ,
          
           by
           
             London
          
           Bridge
           .
        
         
           The
           Saints
           Anchor-hold
           in
           all
           stormes
           and
           Tempests
           ,
           Published
           for
           the
           support
           and
           comfort
           of
           Gods
           people
           in
           all
           times
           of
           Trial
           ,
           by
           
             John
             Davenport
          
           Pastor
           of
           the
           Church
           in
           
             New-Haven
          
           in
           
             New-Ingland
             .
          
        
         
           There
           will
           shortly
           be
           made
           publick
           a
           Book
           ,
           Intituled
           ,
           The
           
             Mariners
             Compass
             Rectifled
             ,
          
           containing
           ,
           First
           ,
           a
           Table
           shewing
           the
           hour
           of
           the
           day
           ,
           the
           Sun
           being
           upon
           any
           point
           of
           the
           Compass
           .
           Secondly
           ,
           Tables
           of
           the
           Suns
           rising
           and
           setting
           .
           Thirdly
           ,
           Tables
           shewing
           the
           points
           of
           the
           Compass
           ,
           that
           the
           Sun
           and
           Stars
           rise
           and
           set
           with
           .
           Fourthly
           ,
           Tables
           of
           Amplitudes
           ;
           all
           which
           Tables
           are
           Calculated
           from
           the
           Equinoctial
           ,
           to
           60
           degrees
           of
           Latitude
           ,
           with
           Tables
           of
           Latitudes
           and
           Longitudes
           ,
           after
           a
           new
           order
           ,
           with
           the
           description
           and
           use
           of
           all
           those
           Instruments
           that
           are
           in
           use
           in
           the
           
             Art
          
           of
           Navigation
           ,
           either
           for
           
             Operation
          
           or
           
             Observation
             .
          
        
      
    
     
       
         
         
           THE
           COMPLEAT
           Ship-wright
           .
        
         
           
             
               CHAP.
               1.
               
            
             Of
             Geometricall
             Problemes
             .
          
           
             BEfore
             we
             proceed
             to
             draw
             the
             Draught
             of
             any
             Ship
             or
             Vessel
             ,
             it
             will
             be
             necessary
             to
             be
             acquainted
             with
             some
             terms
             in
             
               Geometry
               :
            
             as
             to
             know
             what
             a
             Point
             and
             a
             Line
             meaneth
             ,
             which
             every
             Book
             treating
             of
             Geometry
             plainly
             teacheth
             ,
             and
             therefore
             we
             shall
             passe
             that
             by
             ,
             supposing
             that
             none
             will
             endeavour
             to
             study
             the
             Art
             of
             a
             Ship-wright
             ,
             that
             is
             ignorant
             of
             these
             things
             ;
             and
             therefore
             leaving
             these
             
               Definitions
               ,
            
             I
             will
             proceed
             to
             some
             
               Geometrical
               Problemes
            
             necessary
             to
             this
             Art.
             
          
           
             
             
               
                 PROB.
                 1.
                 
              
               How
               to
               draw
               a
               Parallel
               Line
               .
            
             
               PArallel
               lines
               are
               such
               lines
               as
               are
               equidistant
               one
               from
               another
               in
               all
               parts
               ,
               and
               are
               thus
               drawn
               .
               Draw
               a
               line
               of
               what
               length
               you
               please
               ,
               (
               according
               to
               your
               occasion
               )
               as
               the
               line
               A
               B
               ,
               then
               open
               the
               compasses
               to
               what
               distance
               you
               pleas
               ,
               or
               as
               your
               occasions
               require
               ,
               and
               set
               one
               foot
               of
               the
               compasses
               ▪
               towards
               one
               end
               of
               the
               given
               line
               ,
               as
               at
               A
               ,
               with
               the
               other
               foot
               make
               a
               piece
               of
               an
               arch
               of
               a
               circle
               ,
               over
               or
               under
               the
               given
               line
               ,
               as
               the
               arch
               C
               ,
               keeping
               the
               compasses
               then
               at
               the
               same
               distance
               ,
               make
               such
               another
               arch
               towards
               the
               other
               end
               of
               the
               line
               ,
               setting
               one
               foot
               in
               B
               ,
               and
               with
               the
               other
               describe
               the
               arch
               D
               ,
               then
               laying
               a
               Ruler
               to
               the
               outside
               of
               these
               two
               arches
               ,
               so
               that
               it
               may
               exactly
               touch
               them
               ,
               draw
               the
               line
               C
               D
               ,
               which
               will
               be
               parallel
               to
               the
               given
               line
               A
               B
               ,
               or
               equidistant
               ,
               for
               so
               signifieth
               the
               word
               Parallel
               ,
               to
               be
               of
               equal
               distance
               .
            
             
               
            
          
           
             
               
                 PROBL.
                 2.
                 
              
               How
               to
               erect
               a
               Perpendicular
               ,
               from
               a
               point
               in
               a
               right
               line
               given
               .
            
             
               LEt
               there
               be
               a
               point
               given
               in
               the
               line
               A
               B
               ,
               as
               the
               point
               C
               ,
               whereon
               to
               raise
               a
               perpendicular
               .
            
             
               Set
               one
               foot
               of
               the
               compasses
               in
               the
               given
               point
               C
               ,
               and
               open
               them
               to
               what
               distance
               you
               please
               ,
               as
               to
               the
               point
               E
               ,
               make
               a
               little
               mark
               at
               E
               ,
               and
               keeping
               the
               compasses
               at
               the
               
               same
               distance
               ,
               turn
               them
               about
               ,
               and
               make
               a
               mark
               at
               the
               point
               F
               ,
               in
               the
               line
               A
               B
               :
               Then
               remove
               the
               compasses
               to
               one
               of
               those
               marks
               at
               E
               or
               F
               ,
               and
               seting
               one
               foot
               fast
               therein
               ,
               as
               at
               the
               point
               F
               ,
               open
               the
               other
               foot
               wider
               ,
               and
               therewith
               draw
               a
               small
               arch
               over
               the
               point
               C
               ,
               as
               the
               arch
               D
               ,
               then
               keeping
               the
               compasses
               at
               the
               same
               distance
               ,
               remove
               them
               to
               E
               ,
               and
               seting
               one
               foot
               in
               E
               ,
               with
               the
               other
               foot
               draw
               another
               little
               arch
               ,
               so
               as
               to
               crosse
               the
               former
               arch
               in
               the
               point
               D
               ,
               through
               the
               crossing
               of
               these
               two
               arches
               A
               D
               ,
               draw
               a
               line
               to
               the
               given
               point
               C
               ,
               as
               the
               line
               D
               C
               ,
               which
               shall
               be
               perpendicular
               to
               the
               line
               A
               B.
               
            
             
               Diverse
               other
               wayes
               there
               are
               to
               raise
               a
               perpendicular
               ,
               which
               I
               shall
               leave
               to
               the
               farther
               practice
               of
               such
               as
               desire
               diversity
               of
               wayes
               ,
               and
               proceed
               to
               the
               raising
               of
               a
               Perpendicular
               on
               the
               end
               of
               a
               line
               .
            
             
          
           
             
               
                 PROBL.
                 3.
                 
              
               To
               raise
               a
               Perpendicular
               on
               the
               end
               of
               a
               line
               .
            
             
               DRaw
               a
               line
               at
               pleasure
               ,
               or
               according
               to
               your
               worke
               ,
               as
               the
               line
               A
               B
               :
               On
               the
               end
               thereof
               as
               at
               B
               ,
               set
               one
               foot
               of
               the
               Compasses
               ,
               and
               open
               them
               to
               what
               widenesse
               you
               please
               ,
               as
               to
               C
               ,
               and
               keeping
               fast
               one
               foot
               at
               B
               ,
               pitch
               one
               foot
               by
               adventure
               in
               C
               ,
               then
               keeping
               one
               foot
               of
               the
               compasses
               in
               C
               ,
               and
               at
               the
               same
               distance
               ,
               remove
               the
               foot
               that
               was
               in
               B
               ,
               to
               the
               point
               D
               in
               the
               line
               A
               B
               :
               then
               (
               keeping
               the
               compasses
               stil
               at
               the
               same
               distance
               )
               lay
               a
               ruler
               to
               the
               points
               D
               and
            
             
             
               There
               are
               other
               wayes
               to
               effect
               this
               ,
               which
               I
               shall
               leave
               to
               farther
               practice
               of
               the
               learner
               ,
               this
               being
               the
               properest
               for
               our
               purpose
               .
            
          
           
             
               
                 PROB.
                 4.
                 
              
               From
               a
               Point
               given
               ,
               to
               let
               fall
               a
               Perpendicular
               upon
               a
               Line
               given
               .
            
             
               FRom
               the
               point
               C
               ,
               let
               it
               be
               required
               to
               let
               fall
               a
               perpendicular
               upon
               the
               line
               A
               B
               ,
               proceed
               thus
               :
               Fix
               one
               foot
               of
               the
               compasses
               in
               the
               point
               C
               ,
               and
               open
               them
               to
               a
               greater
               distance
               then
               just
               to
               the
               line
               A
               B
               ,
               and
               make
               with
               the
               same
               extent
               the
               two
               marks
               E
               and
               F
               ,
               in
               the
               given
               line
               A
               B
               ,
               then
               divide
               the
               distance
               betweene
               the
               two
               points
               E
               and
               F
               into
               two
               equall
               parts
               in
               the
               point
               D
               ,
               then
               lay
               a
               Ruler
               to
               the
               given
               point
               C
               ,
               and
               to
               the
               point
               D
               ,
               and
               draw
               the
               line
               C
               D
               ,
               which
               will
               be
               perpendicular
               to
               the
               given
               line
               A
               B.
               
            
             
               
            
          
        
         
           
             
               CHAP.
               II.
            
             Of
             your
             SCALE
             .
          
           
             BEing
             perfect
             in
             the
             raising
             and
             letting
             fall
             of
             perpendiculars
             ,
             and
             in
             the
             drawing
             of
             Parallel
             lines
             ,
             you
             may
             proceed
             to
             draught
             :
             but
             first
             I
             will
             unfold
             unto
             
             
             you
             the
             use
             of
             a
             Diagonall
             Scale
             of
             Inches
             and
             Feet
             ,
             whose
             use
             is
             to
             represent
             a
             foot
             measure
             ,
             or
             a
             Rule
             so
             small
             ,
             that
             a
             Ship
             of
             100
             foot
             by
             the
             Keel
             ,
             may
             be
             demonstrated
             on
             a
             common
             sheet
             of
             paper
             ,
             really
             and
             truly
             to
             be
             so
             many
             foot
             long
             ,
             and
             so
             many
             foot
             broad
             ,
             of
             such
             a
             depth
             ,
             and
             of
             such
             a
             height
             between
             the
             Decks
             .
             And
             therein
             ,
             the
             first
             thing
             to
             be
             considered
             is
             ,
             the
             length
             of
             the
             platform
             ,
             and
             of
             the
             Vessel
             you
             intend
             to
             demonstrate
             ,
             to
             the
             end
             you
             may
             make
             your
             Scale
             as
             large
             as
             you
             can
             ,
             because
             the
             larger
             the
             Scale
             is
             ,
             the
             larger
             will
             the
             draught
             be
             ,
             and
             so
             the
             measure
             of
             the
             demonstration
             will
             be
             the
             larger
             ,
             and
             more
             easie
             to
             unfold
             .
             The
             Scale
             adjoyning
             consisteth
             (
             as
             you
             see
             )
             of
             12
             feet
             in
             all
             ,
             11
             thereof
             are
             marked
             with
             figures
             downwards
             ,
             beginning
             at
             1
             ,
             2
             ,
             3
             ,
             4
             and
             so
             to
             11
             :
             the
             first
             at
             the
             top
             is
             sub-divided
             into
             inches
             by
             diagonal
             lines
             ,
             as
             the
             distance
             between
             the
             first
             line
             of
             the
             Scale
             and
             the
             first
             diagonal
             line
             is
             one
             inch
             ,
             the
             second
             is
             2
             ,
             and
             the
             third
             3
             inches
             ,
             and
             so
             to
             Six
             .
             The
             way
             to
             demonstrate
             the
             Scale
             ,
             you
             see
             ,
             is
             very
             easie
             :
             Draw
             Seven
             lines
             parallel
             to
             each
             other
             ,
             and
             of
             what
             length
             you
             please
             ,
             to
             retain
             what
             number
             of
             Feet
             you
             please
             ,
             then
             beginning
             at
             the
             top
             ,
             set
             off
             with
             the
             compasses
             
             the
             length
             of
             your
             Feet
             both
             allow
             and
             aloft
             ,
             then
             draw
             lines
             thwart
             the
             parallel
             lines
             ,
             to
             every
             foot
             of
             the
             Scale
             ,
             and
             set
             numbers
             to
             them
             ,
             beginning
             at
             the
             second
             foot
             1
             ,
             and
             to
             the
             third
             2
             ,
             to
             the
             fourth
             3
             ,
             and
             so
             forward
             ,
             leaving
             the
             first
             Foot
             to
             be
             divided
             into
             Inches
             by
             the
             Diagonall
             lines
             ,
             as
             you
             see
             in
             the
             foregoing
             Scale
             .
          
        
         
           
             
               CHAP.
               III.
            
             Concerning
             the
             drawing
             your
             Draught
             upon
             Paper
             .
          
           
             HAving
             fitted
             your
             Scale
             ready
             ,
             draw
             a
             line
             to
             represent
             the
             Keele
             of
             the
             Ship
             ,
             as
             you
             see
             in
             the
             draught
             following
             of
             60
             foot
             long
             by
             the
             Keele
             ,
             and
             20
             foot
             broad
             :
             the
             streight
             line
             that
             representeth
             the
             Keele
             is
             marked
             with
             A
             B.
             Then
             draw
             a
             line
             underneath
             of
             equall
             length
             to
             signifie
             the
             bottome
             of
             the
             Keele
             .
             Then
             next
             you
             may
             proceed
             to
             the
             Stern-post
             ,
             as
             the
             line
             A
             C
             will
             signifie
             the
             foreside
             or
             the
             inside
             thereof
             ,
             racking
             the
             one
             quarter
             of
             his
             length
             aft
             ,
             and
             for
             the
             length
             of
             the
             Stern-post
             it
             must
             be
             directed
             to
             the
             built
             of
             the
             Ship
             ,
             as
             whether
             she
             be
             to
             be
             a
             deep
             Ship
             or
             a
             shallow
             Ship
             ,
             so
             that
             the
             draught
             of
             the
             water
             ought
             to
             be
             respected
             first
             ,
             and
             then
             the
             lying
             of
             the
             Ports
             for
             the
             convenience
             of
             Ordnance
             ,
             for
             that
             the
             upper
             transome
             of
             the
             Buttock
             ,
             commonly
             is
             just
             under
             the
             Gun-Room
             ports
             ,
             to
             the
             upper
             edge
             of
             the
             said
             transome
             we
             understand
             the
             length
             of
             the
             Stern-post
             ,
             although
             if
             the
             Stern-post
             were
             continued
             to
             the
             height
             of
             the
             Tiller
             ,
             and
             another
             Transome
             fard
             there
             for
             the
             Tiller
             to
             run
             on
             ,
             it
             would
             steady
             the
             quarters
             of
             the
             Vessel
             very
             much
             ,
             and
             do
             good
             service
             .
          
           
           
             The
             Stern-post
             being
             drawn
             ,
             we
             may
             proceed
             to
             draw
             the
             Stem
             ,
             which
             in
             the
             following
             Draught
             is
             not
             so
             much
             racked
             as
             was
             the
             old
             proportion
             of
             
               England
               ,
            
             which
             was
             the
             whole
             breadth
             of
             the
             Ship
             ,
             for
             then
             it
             should
             be
             20
             foot
             ,
             but
             it
             is
             no
             more
             then
             15
             foot
             ,
             just
             ¾
             of
             the
             breadth
             ,
             for
             too
             much
             racke
             with
             the
             Stem
             doth
             a
             great
             deale
             of
             damage
             to
             any
             Ship
             ,
             if
             we
             consider
             that
             in
             this
             small
             Vessel
             ,
             had
             we
             given
             5
             foot
             more
             Racke
             ,
             all
             the
             weight
             of
             the
             Ships
             Head
             ,
             and
             Boltspreet
             ,
             Foremast
             ,
             Manger
             ,
             Halsps
             ,
             Brest-hooks
             aloft
             ,
             had
             been
             so
             much
             farther
             forward
             ,
             where
             there
             would
             have
             been
             want
             of
             Bodie
             to
             lift
             it
             ,
             so
             that
             it
             must
             of
             necessity
             be
             detriment
             to
             the
             Vessel
             when
             she
             saileth
             against
             a
             head
             sea
             ,
             and
             a
             great
             strain
             to
             her
             .
             Now
             it
             will
             be
             very
             good
             to
             spend
             as
             much
             of
             this
             racke
             as
             we
             can
             under
             the
             water
             ,
             for
             it
             will
             help
             the
             Ship
             to
             keepe
             a
             good
             Winde
             ,
             by
             giving
             her
             something
             more
             Body
             in
             the
             water
             .
          
           
             Next
             draw
             the
             Water-line
             ,
             in
             the
             following
             draught
             signified
             by
             the
             pricked
             line
             ;
             it
             is
             drawn
             to
             9
             foot
             height
             afore
             ,
             and
             to
             10
             foot
             height
             abaft
             from
             the
             upper
             edge
             of
             the
             Keele
             ,
             and
             higher
             abaft
             then
             afore
             ,
             for
             the
             most
             Ships
             saile
             by
             the
             Sterne
             ,
             and
             also
             for
             that
             the
             Guns
             should
             lie
             something
             higher
             abaft
             then
             afore
             from
             the
             water
             .
          
           
             Then
             proceed
             to
             hanging
             of
             the
             Waals
             ,
             and
             here
             you
             see
             the
             lower
             Waalle
             drawne
             from
             the
             head
             of
             the
             Sterne-post
             ,
             to
             signifie
             that
             it
             should
             lie
             against
             the
             end
             of
             the
             Transome
             ,
             that
             the
             Transome
             Knees
             might
             be
             bolted
             to
             the
             Waals
             without
             board
             to
             one
             foot
             and
             an
             halfe
             under
             the
             Water-line
             ,
             a
             little
             before
             the
             middle
             of
             the
             Water
             line
             ,
             and
             at
             9
             foot
             high
             on
             the
             Stem
             ,
             and
             the
             next
             Waale
             parallel
             to
             the
             lower
             Waale
             ,
             one
             foot
             and
             an
             half
             asunder
             ,
             so
             that
             the
             upper
             Waale
             will
             lie
             just
             at
             the
             waters
             edge
             ,
             in
             the
             mid-ships
             ,
             the
             upper
             edge
             of
             the
             Gun-deck
             will
             lie
             one
             foot
             aboye
             the
             water
             line
             abaft
             ,
             and
             halfe
             a
             foot
             above
             water
             on
             the
             Stem
             ;
             
             so
             then
             letting
             the
             lower
             sell
             of
             the
             Ports
             be
             two
             foot
             from
             the
             Gun-decks
             ▪
             the
             lower
             edge
             of
             the
             Ports
             wil
             be
             three
             foot
             from
             the
             water
             abaft
             ,
             and
             two
             foot
             and
             an
             halfe
             afore
             ,
             in
             the
             middle
             of
             the
             Gun-deck
             2
             foot
             9
             inches
             ,
             sufficient
             for
             so
             small
             a
             Vessel
             ,
             a
             greater
             Vessel
             would
             require
             to
             have
             the
             Guns
             something
             farther
             from
             the
             water
             ,
             then
             if
             another
             Waale
             be
             required
             ,
             first
             set
             off
             the
             Ports
             in
             their
             places
             ,
             that
             the
             Waale
             may
             ly
             above
             the
             Ports
             ,
             or
             else
             he
             would
             be
             cut
             with
             the
             ports
             in
             pieces
             ,
             the
             upper
             Deck
             with
             height
             respecting
             the
             bignesse
             of
             the
             Ship
             ,
             having
             respect
             to
             not
             over
             building
             small
             Ships
             ,
             to
             damage
             their
             bearing
             of
             Sail.
             
          
           
             Then
             for
             the
             Head
             ,
             the
             length
             of
             the
             Knee
             would
             be
             two
             thirds
             of
             the
             breadth
             ,
             so
             then
             the
             Knee
             of
             the
             Head
             in
             this
             Draught
             will
             be
             12
             foot
             8
             inches
             long
             ,
             and
             for
             his
             place
             ,
             as
             low
             as
             conveniently
             he
             can
             ,
             provided
             that
             the
             Rails
             of
             the
             Head
             ,
             fall
             not
             fowl
             of
             the
             ha●shols
             ,
             because
             that
             in
             placing
             of
             the
             Knee
             low
             ,
             giveth
             room
             to
             round
             the
             Head
             ,
             and
             steeve
             it
             to
             content
             :
             The
             place
             of
             the
             Knee
             will
             be
             at
             ,
             or
             very
             neer
             ,
             the
             upper
             Waal
             ,
             the
             upper
             edge
             of
             the
             Knee
             against
             the
             upper
             edge
             of
             the
             uper
             harping
             ,
             which
             will
             be
             very
             well
             for
             the
             lower
             Cheeks
             of
             the
             head
             to
             be
             faced
             against
             ,
             for
             by
             that
             means
             they
             wil
             be
             clear
             of
             any
             Seame
             to
             avoid
             Leakings
             ,
             and
             will
             very
             well
             bolt
             the
             end
             of
             the
             harping
             ,
             if
             a
             Brest-hook
             be
             fastned
             also
             within
             board
             against
             them
             ,
             will
             very
             well
             fasten
             all
             together
             .
          
           
             Then
             for
             the
             steeving
             of
             him
             ,
             and
             rounding
             the
             Knee
             ,
             a
             regard
             must
             be
             had
             to
             the
             lying
             of
             the
             Boltspreet
             ,
             leaving
             room
             enough
             for
             the
             Lyon
             and
             Scrowl
             under
             the
             Boltsprit
             .
             Then
             ▪
             for
             the
             rounding
             of
             the
             Rails
             ,
             round
             them
             most
             at
             the
             after
             ends
             .
          
           
             For
             the
             heights
             between
             Decks
             and
             Steeridge
             ,
             Cabine
             ,
             Fore-Castle
             ,
             those
             heights
             are
             commonly
             mentioned
             in
             contract
             by
             the
             Master
             or
             Owners
             building
             .
          
           
             
               Place
               this
               Draught
               at
               Page
               8
            
             cross-section of a ship's hull
          
        
         
           
           
             
               CHAP.
               IV.
            
             Shewing
             ,
             how
             to
             sweepe
             out
             the
             Bend
             of
             Moulds
             upon
             a
             Flat
             .
          
           
             FIrst
             ,
             draw
             a
             line
             ,
             as
             the
             line
             AB
             ,
             then
             in
             the
             middle
             thereof
             ,
             as
             at
             the
             point
             C
             ,
             raise
             a
             perpendicular
             ,
             as
             is
             the
             line
             CM
             ,
             perpendicular
             to
             the
             line
             AB
             ;
             then
             set
             off
             the
             halfe
             breadth
             ,
             on
             either
             side
             ,
             at
             the
             Points
             AB
             ,
             and
             draw
             the
             two
             lines
             IA
             ,
             and
             KB
             ,
             parallels
             to
             CD
             ,
             signifying
             the
             breadth
             of
             the
             Vessell
             20
             foot
             ;
             then
             draw
             the
             two
             lines
             EF
             ,
             and
             HG
             ,
             signifying
             the
             breadth
             of
             the
             Floare
             thwart
             Ships
             ,
             8
             Foot
             ,
             more
             then
             one
             third
             part
             of
             the
             breadth
             ,
             which
             was
             formerly
             an
             old
             Proportion
             ;
             so
             that
             according
             to
             that
             it
             should
             have
             been
             but
             6
             Foot
             8
             Inches
             .
          
           
             Herein
             any
             may
             do
             as
             they
             please
             ,
             give
             more
             or
             less
             ;
             my
             judgment
             is
             ,
             rather
             more
             then
             less
             :
             for
             ,
             that
             it
             maketh
             a
             Vessell
             to
             carry
             more
             in
             Burden
             ,
             and
             I
             conceive
             it
             may
             ,
             if
             it
             be
             well
             ended
             forward
             ,
             it
             will
             not
             damage
             the
             Sayling
             :
             I
             also
             think
             ,
             it
             doth
             stiffen
             a
             Vessell
             on
             this
             account
             .
             Our
             
               English
            
             Vessells
             have
             been
             used
             to
             have
             their
             breadth
             lying
             at
             the
             height
             of
             the
             Halfe
             Breadth
             ,
             then
             observing
             1
             /
             3
             breadth
             for
             the
             length
             of
             the
             Floare
             Thwart
             Ships
             ,
             it
             maketh
             the
             Vessells
             Body
             to
             be
             very
             neare
             a
             Circle
             ,
             as
             is
             a
             Cask
             ,
             which
             causeth
             such
             Vessells
             to
             be
             easie
             to
             slew
             in
             the
             Water
             ;
             yet
             I
             would
             not
             exceed
             neither
             ,
             or
             run
             into
             extreams
             herein
             ,
             but
             if
             I
             were
             to
             make
             a
             Vessell
             stiff
             ,
             I
             would
             that
             
             the
             Halfe
             Breadth
             be
             more
             then
             the
             draught
             of
             Water
             ,
             which
             causeth
             that
             the
             Body
             be
             stronger
             in
             the
             Water
             ,
             and
             will
             not
             Slew
             so
             easily
             .
             Now
             to
             sweep
             out
             the
             Sides
             under
             Water
             ,
             I
             draw
             the
             
               Diagonall
            
             lines
             DA
             ,
             
             and
             DB
             ;
             then
             I
             divide
             the
             
               Diagonall
            
             lines
             into
             9
             parts
             ,
             and
             set
             off
             2
             of
             them
             from
             the
             Corners
             A
             and
             B
             ,
             to
             the
             points
             
               e
               ,
            
             then
             I
             set
             off
             the
             Dead
             Rising
             ,
             which
             is
             4
             Inches
             ,
             one
             Inch
             to
             a
             Foot
             ,
             for
             halfe
             the
             breadth
             represented
             in
             the
             Figure
             above
             ,
             by
             the
             little
             line
             parallel
             to
             FG
             :
             from
             which
             Dead
             Rising
             ,
             take
             with
             the
             Compasses
             the
             Distance
             that
             will
             draw
             a
             piece
             of
             an
             Arch
             from
             ●
             to
             ●
             ,
             and
             so
             as
             one
             foot
             of
             the
             Compasses
             
             stand
             in
             the
             line
             EF
             ,
             and
             exactly
             touch
             the
             points
             at
             the
             Dead-Rising
             ,
             at
             
               f
            
             or
             
               g
               ,
            
             and
             touch
             also
             the
             points
             e
             ,
             over
             which
             point
             falls
             at
             ⊙
             ,
             in
             EF
             ,
             or
             ⊙
             in
             HG
             ,
             wherewith
             I
             describe
             the
             Arch
             e
             F
             ,
             or
             e
             G
             ,
             which
             is
             by
             the
             Scale
             in
             the
             Draught
             4
             Foot
             8
             Inches
             :
             then
             for
             the
             other
             part
             of
             the
             Side
             upwards
             ,
             seek
             for
             a
             Point
             in
             the
             breadth
             line
             IK
             ,
             at
             which
             ,
             if
             one
             foot
             of
             the
             Compasses
             be
             set
             ,
             and
             the
             other
             foot
             opened
             to
             the
             Extreame
             Breadth
             ,
             will
             also
             draw
             ,
             or
             signifie
             an
             Arch
             to
             meet
             with
             the
             other
             Lower
             Arch
             ,
             on
             the
             
               Diagonall
            
             line
             at
             
               e
               ,
            
             which
             is
             at
             the
             points
             ⊙
             and
             ⊙
             ;
             thus
             the
             point
             ⊙
             ,
             between
             D
             and
             K
             ,
             neere
             H
             ,
             Sweepeth
             the
             contrary
             Side
             I
             
               e
               ,
            
             and
             so
             the
             point
             ⊙
             ,
             between
             DI
             ,
             neere
             E
             ,
             Sweepeth
             the
             contrary
             side
             at
             K
             ,
             extend
             the
             same
             Sweepe
             also
             above
             the
             Breadth
             line
             above
             Water
             3
             or
             4
             Foot
             ,
             the
             length
             of
             this
             Sweepe
             is
             12
             Foot
             9
             Inches
             :
             then
             set
             off
             the
             Tumbling
             Home
             ,
             at
             the
             Height
             of
             the
             two
             first
             Haanses
             ,
             at
             the
             Maine
             Mast
             and
             Foarcastle
             ,
             2
             foot
             of
             a
             side
             ;
             then
             draw
             a
             line
             from
             the
             said
             2
             Foot
             of
             Narrowing
             ,
             at
             the
             points
             
               o
               v
               ,
            
             till
             it
             break
             off
             on
             the
             back
             of
             the
             Sweep
             ,
             on
             either
             side
             .
             This
             kinde
             of
             Demonstration
             I
             conceive
             most
             suitable
             to
             our
             following
             discourse
             of
             
               Arithmeticall
            
             Work
             ,
             I
             could
             have
             cited
             other
             wayes
             ,
             but
             I
             Judge
             this
             way
             sufficient
             .
          
        
         
           
           
             
               CHAP.
               V.
            
             The
             Description
             of
             the
             Rising
             Lines
             aftward
             on
             ,
             and
             forward
             on
             ;
             with
             the
             Narrowing
             Lines
             ,
             and
             Lines
             of
             Breadth
             :
             As
             also
             the
             Narrowing
             Lines
             at
             the
             top
             of
             the
             Timbers
             .
          
           
             DRaw
             a
             Hanging
             line
             on
             the
             Draught
             ,
             from
             the
             Keele
             ,
             from
             the
             middle
             of
             the
             Keele
             to
             the
             height
             of
             the
             Water
             line
             ,
             on
             the
             Post
             which
             will
             be
             the
             Rising
             line
             ,
             as
             the
             line
             DE
             ;
             this
             line
             DE
             is
             supposed
             to
             be
             sweept
             ,
             or
             drawn
             by
             a
             
               Semidiameter
            
             of
             a
             Circle
             ,
             extended
             on
             a
             Perpendicular
             raised
             at
             the
             point
             E
             ,
             for
             if
             it
             be
             shorter
             then
             such
             a
             
               Semidiameter
            
             of
             the
             true
             Circle
             ,
             it
             will
             make
             a
             fuller
             line
             then
             it
             should
             be
             ,
             and
             so
             must
             not
             be
             so
             long
             ,
             or
             else
             it
             will
             make
             a
             breach
             at
             the
             beginning
             of
             the
             line
             ;
             this
             ,
             if
             the
             Centre
             be
             supposed
             to
             be
             Abaft
             such
             a
             Perpendicular
             ,
             that
             should
             draw
             a
             Rising
             line
             Abaft
             ,
             I
             say
             ,
             that
             it
             will
             shorten
             the
             Rising
             line
             ,
             and
             make
             it
             fuller
             then
             it
             should
             be
             ;
             or
             then
             if
             it
             be
             farther
             forward
             ,
             it
             will
             be
             straighter
             then
             a
             Circle
             ,
             and
             also
             be
             a
             breach
             at
             the
             beginning
             of
             the
             Rising
             line
             ;
             therefore
             it
             should
             be
             a
             Circle
             ,
             I
             say
             ,
             whose
             
               Semidiameter
            
             will
             be
             on
             the
             Perpendicular
             line
             ,
             at
             the
             beginning
             of
             any
             such
             Rising
             line
             ,
             on
             the
             Heele
             ,
             either
             Afoare
             ,
             or
             
             Abaft
             ,
             and
             the
             like
             ought
             to
             be
             for
             all
             other
             crooked
             lines
             ,
             as
             the
             narrowing
             lines
             Abaft
             ,
             or
             Afoare
             ,
             or
             at
             the
             Narrowing
             of
             the
             Floare
             ,
             or
             other
             Circular
             lines
             ,
             as
             Hanging
             of
             Waals
             ,
             and
             the
             like
             ;
             the
             way
             whereof
             I
             shall
             describe
             ,
             to
             finde
             the
             lengths
             of
             all
             such
             Sweeps
             by
             Arithmetick
             ;
             as
             also
             the
             true
             Rising
             ,
             Narrowing
             of
             any
             Timber
             ,
             according
             to
             exact
             peeces
             of
             Circles
             ,
             very
             usefull
             for
             the
             setting
             of
             Bows
             ,
             to
             trie
             whether
             they
             hang
             to
             a
             true
             Sweepe
             or
             no
             :
             I
             shall
             demonstrate
             it
             ,
             I
             say
             ,
             in
             the
             following
             discourse
             ,
             and
             in
             this
             place
             end
             what
             I
             intend
             to
             say
             .
             For
             Demonstration
             then
             ,
             At
             ¾
             of
             the
             Keele
             forward
             I
             draw
             a
             Rising
             line
             forward
             to
             the
             height
             of
             the
             Water
             line
             ,
             forward
             on
             the
             Stemm
             ,
             as
             you
             see
             the
             line
             
               op
               ;
            
             and
             the
             little
             line
             ,
             between
             these
             two
             lines
             ,
             parallel
             to
             the
             inside
             of
             the
             Keele
             ,
             marked
             
               Eo
               ,
            
             is
             the
             dead
             rising
             4
             inches
             high
             ,
             as
             in
             the
             bend
             of
             Moulds
             it
             is
             parallel
             to
             FG
             ,
             the
             height
             of
             the
             breadth
             from
             the
             Mid-Ship
             forward
             is
             the
             lower
             Edge
             of
             the
             upper
             Waale
             ;
             but
             afterward
             on
             it
             is
             the
             pricked
             line
             ,
             between
             the
             Water
             line
             and
             the
             lower
             Waale
             ,
             on
             the
             Post
             ,
             which
             runneth
             forward
             to
             the
             edge
             of
             the
             Waale
             ,
             and
             hath
             Figures
             set
             to
             it
             ,
             to
             signifie
             the
             places
             of
             the
             Timbers
             marked
             1
             ,
             2
             ,
             3
             ,
             4
             ,
             5
             ,
             to
             15
             ;
             as
             you
             see
             answers
             to
             the
             Figures
             on
             the
             Keele
             :
             and
             the
             Letters
             set
             to
             forward
             on
             ,
             signifie
             the
             places
             of
             the
             Timbers
             forward
             ,
             marked
             ABCD
             to
             L
             ,
             in
             the
             middle
             of
             the
             Vessel
             :
             the
             places
             marked
             with
             a
             Cipher
             signifie
             the
             Flats
             ,
             which
             have
             onely
             Dead
             rising
             ,
             although
             they
             ought
             to
             have
             ,
             some
             of
             them
             ,
             something
             more
             Dead
             rising
             then
             each
             other
             ;
             and
             those
             that
             have
             least
             ,
             to
             be
             placed
             in
             the
             middle
             of
             the
             rest
             ,
             that
             so
             there
             be
             no
             Clings
             in
             the
             Buldge
             ,
             but
             that
             it
             have
             also
             a
             little
             Hanging
             
             in
             it
             ,
             it
             will
             seeme
             the
             fairer
             :
             Then
             I
             draw
             a
             straight
             line
             ,
             parallel
             to
             the
             bottome
             of
             the
             Keele
             ,
             as
             is
             the
             line
             FG
             ,
             parallel
             to
             the
             line
             AB
             ,
             the
             Keele
             ,
             and
             distant
             10
             foot
             by
             the
             Scale
             ,
             which
             is
             the
             halfe
             breadth
             of
             the
             Vessell
             ;
             for
             this
             line
             signifieth
             a
             line
             stretched
             from
             the
             middle
             of
             the
             Sterne-Post
             to
             the
             middle
             of
             the
             Stem
             ,
             called
             by
             
               Ship-wrightes
               ,
            
             a
             Ram-line
             :
             Parallel
             to
             this
             Middle
             line
             I
             draw
             another
             line
             straight
             ,
             marked
             
               nm
               ,
            
             and
             is
             4
             foot
             asunder
             from
             the
             Middle
             line
             ,
             to
             signifie
             the
             halfe
             length
             of
             the
             Floare
             thwartships
             ,
             as
             in
             the
             Bend
             of
             Moulds
             EF
             is
             distant
             from
             DC
             4
             Foote
             :
             then
             I
             draw
             a
             Crooked
             line
             Abaft
             ,
             within
             this
             line
             
               nm
               ,
            
             to
             signifie
             the
             narrowing
             of
             the
             Floare
             ,
             to
             bring
             ,
             or
             forme
             the
             Vessels
             way
             Abast
             ,
             as
             you
             see
             the
             line
             
               ik
               ;
            
             Abaft
             and
             Afoare
             it
             is
             represented
             by
             the
             line
             
               lo
               :
            
             then
             here
             in
             this
             Draught
             I
             draw
             a
             Sweepe
             ,
             or
             a
             piece
             of
             a
             Circle
             ,
             from
             the
             point
             G
             ,
             the
             marke
             of
             the
             Timber
             G
             ,
             on
             the
             Keele
             ,
             to
             the
             halfe
             breadth
             of
             the
             Stemm
             ,
             to
             the
             point
             G
             on
             the
             Stemm
             ,
             signifying
             the
             Sweep
             of
             the
             Harping
             ,
             and
             is
             Sweept
             by
             the
             breadth
             of
             the
             Vessell
             20
             Foot
             ;
             the
             piece
             of
             the
             Pricked
             Circle
             Abaft
             at
             the
             Starne
             ,
             which
             is
             drawn
             by
             a
             Centre
             on
             the
             line
             FG
             ,
             is
             the
             length
             of
             the
             Transom
             thwart
             the
             Starne
             ,
             as
             is
             the
             Arch
             FS
             ,
             the
             length
             whereof
             is
             8
             Foot
             ,
             which
             doubled
             is
             16
             Foot
             ,
             for
             the
             whole
             length
             :
             which
             is
             ⅘
             of
             the
             breadth
             20
             Foot
             ,
             the
             length
             of
             the
             Sweepe
             that
             sweepeth
             it
             is
             the
             length
             of
             the
             Starnpost
             to
             the
             bottome
             of
             the
             Keele
             14
             Foot
             ⅓
             ,
             then
             the
             Crooked
             line
             ,
             from
             the
             end
             of
             the
             Transom
             ,
             or
             from
             the
             point
             S
             ,
             and
             toucheth
             the
             Keele
             at
             the
             point
             
               p
               :
            
             this
             Arch
             
               Sp
               ,
            
             is
             the
             narrowing
             line
             Abaft
             at
             the
             breadth
             ,
             and
             the
             Crooked
             pricked
             line
             within
             the
             Keele
             ,
             marked
             with
             TR
             ,
             is
             a
             
             Rising
             line
             ,
             to
             order
             a
             hollow
             Moulde
             by
             the
             Timbers
             ,
             are
             placed
             at
             2
             Foot
             Timber
             and
             Roome
             ,
             as
             you
             may
             see
             by
             the
             Scale
             ,
             the
             line
             drawne
             from
             the
             Poope
             to
             the
             Foar-Castle
             ,
             marked
             by
             the
             letters
             VW
             ,
             is
             a
             line
             signifying
             the
             breadth
             of
             the
             Vessell
             ,
             at
             the
             top
             of
             the
             side
             ,
             from
             the
             top
             of
             the
             Poope
             to
             the
             Fore-Castle
             ,
             the
             top
             of
             the
             Poop
             is
             in
             breadth
             10
             Foot
             ,
             halfe
             the
             breadth
             at
             the
             beame
             ;
             the
             use
             of
             this
             line
             is
             in
             ordering
             of
             the
             Moulds
             ,
             to
             stedy
             the
             Head
             of
             the
             Top-Timber
             Mould
             ,
             to
             find
             his
             breadth
             aloft
             .
          
        
         
           
             
               CHAP.
               VI.
            
             Shewing
             the
             Making
             and
             graduating
             ,
             or
             marking
             of
             the
             Bend
             of
             Molds
             .
          
           
             REpaire
             to
             some
             House
             that
             hath
             some
             Roome
             or
             other
             broad
             enough
             to
             demonstrate
             the
             breadth
             of
             the
             Vessell
             ,
             and
             height
             enough
             for
             the
             top
             of
             the
             Poope
             in
             the
             length
             of
             the
             Roome
             ;
             or
             else
             if
             you
             cannot
             finde
             such
             a
             Roome
             convenient
             ,
             lay
             boards
             together
             ,
             or
             planks
             ,
             that
             may
             be
             large
             enough
             for
             your
             business
             ,
             as
             in
             the
             following
             
               Scheame
            
             you
             see
             ;
             First
             ,
             a
             long
             square
             made
             for
             the
             breadth
             of
             the
             Vessell
             ,
             as
             in
             the
             following
             Figure
             IABK
             :
             then
             make
             the
             Moulds
             by
             their
             Sweepes
             ,
             and
             make
             Sirmarks
             to
             them
             for
             the
             laying
             of
             them
             together
             in
             their
             true
             places
             ,
             off
             first
             the
             Mould
             ,
             for
             the
             Floare
             being
             made
             ,
             you
             may
             make
             a
             Sirmarke
             by
             the
             line
             EF
             ,
             on
             the
             head
             of
             the
             
             Floare
             Mould
             ,
             and
             another
             on
             the
             foot
             of
             the
             Navill
             Timber
             Mould
             ,
             at
             the
             same
             place
             ,
             to
             signifie
             ,
             that
             those
             two
             marks
             put
             together
             ,
             they
             are
             in
             their
             true
             places
             ,
             and
             will
             compare
             so
             when
             any
             Timbers
             are
             Molded
             by
             them
             :
             those
             Sirmarks
             must
             also
             be
             marked
             off
             on
             the
             Timbers
             ,
             and
             so
             in
             putting
             the
             Timbers
             up
             in
             the
             frame
             ,
             a
             regard
             being
             had
             to
             compare
             Sirmarks
             with
             Hirmarks
             ,
             each
             Timber
             will
             finde
             his
             own
             place
             ,
             and
             come
             to
             his
             own
             breadth
             ,
             and
             give
             the
             Vessell
             that
             forme
             assigned
             her
             by
             your
             
               Draught
               ,
            
             if
             it
             be
             wrought
             by
             it
             ,
             and
             so
             for
             all
             the
             other
             Moulds
             .
          
           
             In
             making
             your
             Moulds
             ,
             that
             they
             may
             be
             smaller
             and
             smaller
             upwards
             ,
             and
             not
             all
             of
             a
             bigness
             ,
             you
             may
             measure
             the
             depth
             of
             the
             Side
             in
             the
             Mid
             Ships
             Circular
             ,
             as
             it
             goeth
             from
             the
             Keele
             to
             the
             top
             of
             the
             Side
             ,
             as
             here
             the
             Side
             ,
             as
             it
             Roundeth
             ,
             is
             26
             foot
             ,
             and
             in
             depth
             at
             the
             Rounheads
             ,
             or
             at
             the
             end
             of
             the
             Floare
             ,
             is
             one
             Foot
             ,
             as
             
               m
               m
               ;
            
             and
             at
             the
             other
             end
             ,
             at
             the
             head
             of
             the
             Timber
             is
             but
             halfe
             a
             Foot
             ,
             as
             at
             
               n
               n
               ,
            
             so
             then
             drawing
             two
             lines
             ,
             as
             the
             lines
             
               n
               m
               ,
            
             represents
             the
             diminishing
             of
             the
             Moulds
             in
             thickness
             upwards
             ,
             as
             those
             two
             lines
             representeth
             ;
             as
             if
             you
             would
             finde
             the
             thickness
             of
             the
             Timbers
             at
             the
             breadth
             ,
             take
             your
             2
             Foot
             Rule
             ,
             and
             measure
             the
             length
             from
             the
             end
             of
             the
             Floare
             at
             the
             point
             F
             to
             I
             ,
             at
             the
             breadth
             in
             the
             crooked
             body
             ,
             and
             it
             is
             11
             Foot
             9
             Inches
             ,
             signified
             at
             the
             Sirmarks
             there
             ,
             those
             two
             lines
             shew
             the
             thickness
             to
             be
             9
             Inches
             ;
             and
             so
             thick
             ought
             the
             Moulds
             to
             be
             at
             the
             breadth
             of
             the
             Vessell
             .
          
           
           
             Now
             I
             have
             briefly
             touched
             the
             Demonstration
             of
             a
             
               Ship
               ,
            
             by
             Projection
             ,
             I
             shall
             now
             come
             to
             an
             
               Arithmeticall
            
             way
             ,
             farr
             surpassing
             any
             Demonstration
             for
             exactness
             .
          
        
         
           
             
               CHAP.
               VII
               .
            
             Arithmetically
             shewing
             how
             to
             frame
             the
             body
             of
             a
             
               Ship
            
             by
             Segments
             of
             Circles
             :
             being
             a
             true
             way
             to
             examine
             the
             truth
             of
             a
             Bow.
             
          
           
             LEt
             A
             B
             represent
             the
             length
             of
             a
             Rising
             line
             12
             foot
             long
             ,
             or
             144
             inches
             ,
             the
             height
             whereof
             let
             be
             B
             C
             ,
             5
             foot
             ,
             or
             60
             inches
             ,
             to
             finde
             the
             side
             D
             E
             ,
             or
             D
             A
             ,
             the
             radius
             of
             the
             circle
             A
             C
             ,
             whereto
             A
             D
             is
             the
             Semidiameter
             ;
             multiply
             the
             side
             A
             B
             144
             inches
             in
             it self
             ,
             and
             so
             cometh
             20736
             ,
             which
             sum
             divide
          
           
             
               
                 
                   144
                
              
               
                 
                   144
                
              
               
                 
                   576
                
              
               
                 
                   576
                
              
               
                 
                   144
                
              
               
                 
                   20736
                
              
            
             
             by
             the
             side
             B
             C
             ,
             the
             height
             of
             the
             rising
             60
             inches
             ,
             and
             so
             cometh
             345
             ,
             and
             3●6
             /
             60
             ,
             which
             is
             abreviated
             3
             ;
             unto
             this
             345
             ●
             /
             ●
             must
             be
             added
             again
             the
             height
             of
             the
             Rising
             ,
             the
             side
             B
             
               e
               ,
            
             60
             ,
             which
             make
             405
             
               3
            
             of
             an
             inch
             ,
             which
             is
             the
             whole
             Diameter
             of
             the
             Circle
             ,
             the
             half
             whereof
             is
             202
             1
             /
             ●
             inches
             ,
             and
             something
             more
             ,
             near
             ●
             /
             4
             ,
             therefore
             we
             will
             avoide
             the
             fraction
             ,
             and
             account
             it
             203
             ▪
             inches
             ,
             or
             16
             foot
             11
             inches
             ,
             which
             is
             the
             length
             of
             the
             Sweep
             ,
             or
             the
             side
             D
             E
             ,
             and
             so
             in
             all
             other
             Sweeps
             given
             whatsoever
             ;
             the
             Rule
             is
             generall
             ,
             and
             holds
             true
             in
             all
             things
             :
             as
             to
             finde
             the
             Sweepe
             at
             once
             ,
             that
             will
             round
             any
             Beame
             ,
             or
             other
             piece
             of
             Timber
             that
             is
             to
             be
             Sweept
             ;
             remembring
             ,
             that
             if
             it
             be
             a
             Beame
             ,
             you
             are
             to
             finde
             the
             Sweepe
             you
             take
             but
             the
             half
             of
             his
             length
             .
          
           
             
               
                 
                   23
                   (
                   3
                
              
               
                 
                   20736
                   (
                   345
                
              
               
                 
                   6000
                
              
               
                 
                   66
                
              
            
          
           
             
               Example
               ,
            
             As
             if
             the
             Beame
             be
             30
             foot
             in
             length
             ,
             and
             to
             round
             one
             foot
             ,
             you
             must
             Work
             by
             15
             ,
             the
             halfe
             length
             of
             the
             Beame
             ;
             and
             turne
             15
             foot
             into
             inches
             ,
             by
             multiplying
             15
             by
             12
             ,
             so
             cometh
             180
             inches
             :
             remember
             the
             length
             of
             the
             Rising
             line
             ,
             if
             it
             be
             to
             finde
             the
             Sweepe
             ,
             it
             must
             be
             multiplied
             by
             it selfe
             ,
             or
             the
             halfe
             length
             of
             the
             Timber
             must
             be
             Multiplied
             in
             it selfe
             ,
             as
             180
             by
             180
             ,
             so
             cometh
             32400
             ,
             which
             must
             be
             divided
             by
             12
             the
             rounding
             ,
             cometh
             in
             the
             quotient
             2700
             ,
             to
             which
             must
             be
             added
             the
             12
             again
             ,
             the
             rounding
             of
             the
             piece
             ,
             and
             so
             it
             is
             2712
             the
             whole
             Circle
             ,
             the
             halfe
             of
             this
             2712
             is
             1356
             for
             the
             length
             of
             the
             Sweep
             ,
             and
             so
             in
             all
             other
             matters
             where
             the
             Sweepe
             is
             required
             :
             This
             I
             read
             in
             Mr.
             
               Gunters
            
             Book
             ,
             where
             he
             calls
             it
             the
             halfe
             Chord
             ,
             being
             given
             ,
             and
             the
             Versed
             fine
             ,
             to
             finde
             the
             
               Diameter
               ,
            
             and
             
               Semidiameter
            
             of
             the
             circle
             thereto
             belonging
             :
          
           
           
             
               
                 Example
              
               in
               the
               
                 Draught
              
               foregoing
               .
            
             
               Where
               the
               length
               of
               the
               Rising
               line
               is
               from
               the
               point
               E
               ,
               to
               the
               point
               
                 i
                 ,
              
               32
               foot
               ;
               and
               half
               the
               height
               thereof
               is
               the
               line
               D
               
                 i
                 ,
              
               10
               foot
               :
               turne
               both
               Summs
               into
               inches
               ,
               as
               32
               foot
               multiplyed
               by
               12
               produceth
               ,
               adding
               the
               ½
               foot
               6
               inches
               ,
               390
               inches
               length
               for
               the
               Rising
               line
               :
               then
               turn
               the
               height
               of
               the
               Rising
               into
               inches
               ,
               as
               10
               foot
               multiplied
               by
               12
               ,
               produceth
               120
               inches
               ,
               from
               which
               4
               inches
               must
               be
               substracted
               ,
               because
               of
               the
               dead
               Rising
               is
               4
               inches
               ,
               so
               then
               the
               height
               is
               116
               inches
               :
               Now
               multiply
               the
               length
               390
               inches
               by
               it self
               ,
               390
               maketh
               152100.
               
            
             
               
                 
                   
                     390
                  
                
                 
                   
                     390
                  
                
                 
                   
                     000
                  
                
                 
                   
                     3510
                  
                
                 
                   
                     1170
                  
                
                 
                   
                     152100
                  
                
              
            
             
               This
               Multiplication
               of
               the
               summ
               152100
               ,
               must
               be
               divided
               by
               116
               inches
               ,
               the
               height
               of
               the
               Rising
               ,
               and
               so
               cometh
               in
               the
               quotient
               of
               the
               devision
               1311
               inches
               ;
               unto
               this
               1311
               inches
               ,
               must
               be
               added
               the
               116
               inches
               ,
               the
               height
               of
               the
               Rising
               116
               /
               1427
               ,
               and
               it
               maketh
               1427
               ,
               which
               is
               the
               whole
            
             
               
                 
                   
                     112
                  
                
                 
                   
                     3323
                  
                
                 
                   
                     46344
                  
                
                 
                   
                     152100
                     (
                     1311
                  
                
                 
                   
                     116666
                  
                
                 
                   
                     0111
                  
                
                 
                   
                     11
                  
                
              
               
               Circle
               :
               divide
               it
               by
               2
               ,
               to
               finde
               the
               half
               of
               it
               ,
               so
               have
               you
               in
               the
               quotient
               713
               inches
               ½
               inch
               for
               the
               length
               of
               the
               Sweep
               ,
               which
               divided
               by
               12
               ,
               to
               bring
               it
               into
               feet
               ,
               maketh
               59
               feet
               ,
               5
               inches
               and
               a
               halfe
               ,
               and
               so
               for
               all
               other
               Circular
               lines
               whatever
               ,
               when
               the
               length
               is
               known
               ,
               and
               the
               rounding
               of
               them
               also
               known
               ;
               as
               for
               the
               hanging
               of
               Waals
               ,
               the
               height
               of
               them
               known
               in
               the
               Midships
               from
               the
               Keele
               ,
               substracted
               from
               the
               height
               ,
               at
               the
               Post
               ,
               and
               that
               will
               be
               the
               hanging
               of
               them
               ,
               which
               is
               the
               same
               with
               the
               height
               of
               the
               Rising
               line
               on
               the
               Post
               ,
               in
               the
               
                 Arithmeticall
              
               Work
               ,
               and
               is
               the
               same
               with
               the
               Versed
               sine
               in
               
                 Geometry
                 ;
              
               these
               I
               think
               Examples
               sufficient
               ,
               to
               signifie
               the
               Construction
               of
               this
               way
               of
               Working
               by
               Sweepes
               .
            
             
               
                 
                   
                     1
                  
                
                 
                   
                     1427
                     (
                     713
                  
                
                 
                   
                     222
                  
                
              
            
             
               It
               followeth
               now
               that
               I
               shew
               the
               manner
               of
               finding
               the
               Risings
               of
               Timbers
               by
               
                 Arithmetick
              
               also
               .
            
          
           
             
               To
               finde
               the
               Rising
               of
               the
               line
               
                 F
                 E
                 ,
              
               in
               the
               Figure
               foregoing
               .
            
             
               The
               Sweepe
               being
               first
               found
               to
               be
               as
               before
               203
               inches
               ,
               as
               the
               side
               D
               E
               signifieth
               ,
               then
               there
               is
               known
               the
               side
               E
               G
               ,
               108
               inches
               ;
               now
               these
               two
               sides
               being
               given
               ,
               we
               are
               to
               finde
               the
               third
               side
               D
               G
               ,
               so
               here
               is
               made
               a
               right
               Angled
               Triangle
               ,
               two
               sides
               thereof
               are
               given
               to
               finde
               a
               third
               ,
               which
               to
               do
               ,
               proceed
               thus
               ;
               Multiply
               the
               two
               sides
               given
               by
               themselves
               ,
               and
               substract
               the
               Multiplication
               of
               the
               shortest
               side
               ,
               from
               the
               Multiplication
               made
               of
               the
               other
               sides
               ,
               and
               extract
               the
               square
               Root
               of
               the
               remainder
               ,
               so
               have
               you
               the
               third
               side
               sought
               for
               .
            
             
               
                 
                   Example
                
                 in
                 the
                 following
                 
                   Triangle
                   .
                
              
            
             
               Having
               the
               side
               D
               C
               ,
               12
               foot
               ,
               which
               is
               144
               inches
               ▪
               and
               the
               side
               A
               C
               ,
               10
               foot
               ,
               otherwise
               120
               inches
               ;
               to
               finde
               the
               side
               D
               A
               ,
               multiply
               the
               sides
               given
               ,
               in
               themselves
               ,
               which
               is
               called
               squaring
               of
               them
               :
               as
               ,
               multiply
               the
               side
               D
               C
               ,
               144
               inches
               ,
               by
               144
               inches
               ,
               so
               cometh
               20736.
               
               Then
               multiply
               the
               other
               side
               A
               C
               120
               also
               by
               it self
               ,
               so
               cometh
               in
               the
               quotient
               14400
               ,
               which
               must
               be
               substracted
               from
               the
               other
               Multiplication
               ,
               as
               you
               see
               ,
               so
               cometh
               in
               the
               quotient
               6336
               ,
               from
               which
               the
               greatest
               square
               must
               be
               extracted
               ,
               called
               extraction
               of
               the
               square
               root
               ,
            
             
               
                 
                   
                     144
                  
                
                 
                   
                     144
                  
                
                 
                   
                     576
                  
                
                 
                   
                     576
                  
                
                 
                   
                     144
                  
                
                 
                   
                     20736
                  
                
                 
                   
                     120
                  
                
                 
                   
                     120
                  
                
                 
                   
                     000
                  
                
                 
                   
                     240
                  
                
                 
                   
                     120
                  
                
                 
                   
                     14400
                  
                
                 
                   
                     20736
                  
                
                 
                   
                     14400
                  
                
                 
                   
                     6336
                  
                
              
               
               which
               is
               79
               inches
               ,
               and
               almost
               another
               by
               the
               Fraction
               ,
               that
               is
               6
               foot
               ,
               and
               very
               near
               8
               inches
               .
            
             
               
                 
                   
                     1
                  
                
                 
                   
                     595
                  
                
                 
                   
                     147
                  
                
                 
                   
                     6●3●
                     (
                     79
                  
                
                 
                   
                     14
                  
                
              
            
             
               
                 Note
                 ,
              
               These
               Demonstrations
               ,
               this
               and
               the
               former
               ,
               are
               laid
               down
               by
               the
               first
               Scale
               ,
               made
               to
               shew
               the
               Demonstration
               of
               a
               Scale
               in
               this
               Book
               ,
               at
               the
               beginning
               .
            
          
           
             
               Another
               
                 Example
                 .
              
            
             
               So
               in
               the
               last
               Figure
               foregoing
               but
               one
               ,
               the
               side
               D
               E
               ,
               203
               inches
               ,
               which
               squared
               ,
               or
               multiplied
               in
               it self
               ,
               is
               41209.
               
            
             
               
                 
                   
                     203
                  
                
                 
                   
                     203
                  
                
                 
                   
                     609
                  
                
                 
                   
                     000
                  
                
                 
                   
                     406
                  
                
                 
                   
                     41209
                  
                
              
            
             
               Then
               the
               other
               side
               G
               E
               ,
               108
               ,
               multiplied
               in
               it selfe
               ,
               which
               is
               squaring
               of
               it
               ,
               is
               12664
               ,
               as
               you
               see
               .
            
             
               
                 
                   
                     108
                  
                
                 
                   
                     108
                  
                
                 
                   
                     864
                  
                
                 
                   
                     000
                  
                
                 
                   
                     168
                  
                
                 
                   
                     11664
                  
                
              
            
             
               Which
               substracted
               from
               the
               other
               multiplication
               ,
               as
               11664
               substracted
               from
               41209
               ,
               resteth
               29545
               ,
               the
               square
               Root
               extracted
               from
               it
               ,
               or
               the
               side
               of
               the
               greatest
               square
               that
               can
               be
               taken
               from
               the
               substraction
               being
               found
               ,
               is
               171
               ,
               and
               ¾
               ;
               which
               171
               ¾
               ,
               substracted
               from
               203
               ,
               the
               length
               of
               the
               Sweepe
               for
               one
               side
               ,
               is
               alwayes
               the
               length
               of
               the
               Sweepe
               ,
               resteth
               31
               inches
               ¼
               ,
               for
               the
               Rising
               of
               the
               line
               E
               F
               ,
               and
               the
               like
               for
               any
               other
               Rising
               .
            
             
               
                 
                   
                     41209
                  
                
                 
                   
                     11664
                  
                
                 
                   
                     29545
                  
                
              
            
             
               
                 
                   
                     (
                     3
                  
                
                 
                   
                     156
                     (
                     08
                  
                
                 
                   
                     29549
                     (
                     ●7
                  
                
                 
                   
                     .2
                     .
                  
                
                 
                   
                     34
                  
                
              
            
          
           
             
             
               Another
               
                 Example
                 .
              
            
             
               As
               at
               the
               place
               K
               I
               ,
               the
               Rising
               thereof
               is
               required
               ,
               the
               side
               D
               I
               is
               as
               D
               E
               ,
               203
               inches
               .
            
             
               
                 Note
                 ,
              
               The
               length
               of
               the
               Sweepe
               being
               found
               ,
               alwayes
               is
               one
               of
               the
               sides
               ,
               in
               the
               finding
               the
               Rising
               of
               any
               Timber
               ,
               and
               is
               alwayes
               one
               of
               the
               numbers
               ,
               which
               when
               you
               have
               squared
               ,
               note
               in
               a
               piece
               of
               Paper
               by
               it self
               ,
               where
               you
               may
               alwayes
               see
               what
               it
               is
               ,
               so
               that
               in
               the
               finding
               of
               Risings
               ,
               after
               the
               Sweepe
               is
               found
               ,
               all
               you
               have
               to
               do
               ,
               is
               to
               know
               how
               many
               feet
               ,
               or
               inches
               ,
               the
               Timber
               you
               seek
               for
               is
               removed
               from
               the
               beginning
               ,
               or
               foot
               of
               the
               Rising
               line
               ,
               which
               is
               the
               second
               side
               ,
               and
               in
               this
               third
               
                 Example
              
               it
               is
               11
               foot
               ,
               or
               132
               inches
               K
               I
               ,
               from
               the
               foot
               of
               the
               line
               A
               ,
               which
               squared
               ,
               is
               17424
               ,
               which
               must
               be
               substracted
               from
               the
               square
               made
               of
               Radius
               ,
               which
               in
               the
               other
               example
               is
               41209
               ,
               and
               so
               resteth
               23775
               ,
               from
               which
               extract
               the
               side
               of
               the
               Square
               therein
               contained
               ,
               and
               it
               is
               154
               inches
               and
               ¼
               ,
               which
               substracted
               from
               the
               length
               of
               the
               Sweep
               ,
               leaveth
               48
               inches
               for
               the
               Rising
               ,
               and
               ¾
               inches
               ,
               or
               4
               foot
               ,
               and
               ¾
               of
               an
               inch
               ,
               and
               so
               much
               is
               the
               Rising
               of
               the
               said
               Timber
               .
            
             
               
                 
                   
                     132
                  
                
                 
                   
                     132
                  
                
                 
                   
                     264
                  
                
                 
                   
                     396
                  
                
                 
                   
                     132
                  
                
                 
                   
                     17424
                  
                
              
            
             
               
                 
                   
                     41209
                  
                
                 
                   
                     17424
                  
                
                 
                   
                     23775
                  
                
              
            
             
               
                 
                   
                     10
                  
                
                 
                   
                     132
                     (
                     69
                  
                
                 
                   
                     23785
                     (
                     154
                  
                
                 
                   
                     .2.0
                     .
                  
                
                 
                   
                     3
                  
                
              
            
             
               One
               
                 Example
              
               in
               the
               
                 Draught
                 ,
              
               The
               length
               of
               that
               Sweepe
               we
               found
               heretofore
               to
               be
               713
               inches
               ,
               then
               we
               
               will
               seek
               to
               finde
               the
               Rising
               for
               Timber
               13
               ,
               standing
               aft
               from
               the
               point
               E
               ,
               or
               foot
               of
               the
               Rising
               line
               324
               inches
               ,
               these
               are
               the
               given
               Sides
               ;
               then
               proceed
               ;
               square
               the
               Semidiameter
               of
               the
               Sweepe
               713
               ,
               so
               it
               maketh
               squared
               508363
               ;
               then
               square
               the
               distance
               of
               the
               Timber
               13
               ,
               which
               is
               324
               ,
               and
               it
               maketh
               104976
               ;
               these
               substracted
               from
               the
               former
               figures
               ,
               resteth
               403387
               ,
               the
               square
               Root
               thereof
               is
               635
               ¼
               ,
               nearest
               ,
               which
               substracted
               from
               the
               Radius
               713
               ,
               resteth
               77
               inches
               and
               ¼
               ,
               that
               is
               6
               foot
               5
               inches
               ,
               which
               with
               4
               inches
               Dead
               Rising
               ,
               is
               6
               foot
               9
               inches
               ¼
               ;
               and
               so
               much
               is
               the
               Rising
               of
               Timber
               13
               from
               the
               Keele
               .
            
             
               I
               suppose
               these
               
                 Examples
              
               are
               sufficient
               to
               illustrate
               the
               truth
               and
               plainness
               of
               this
               
                 Arithmeticall
              
               Work
               ,
               for
               the
               truth
               of
               it
               ;
               it
               hath
               this
               to
               say
               for
               it self
               ,
               that
               it
               is
               the
               very
               exact
               truth
               it self
               :
               The
               great
               
                 Objection
              
               may
               be
               ,
               that
               many
               know
               not
               the
               way
               to
               Extract
               the
               Square
               Root
               ,
               and
               therefore
               cannot
               attaine
               to
               this
               Work
               ,
               by
               reason
               of
               that
               let
               ,
               or
               hinderance
               .
            
             
               To
               this
               I
               Answer
               ,
               There
               are
               many
               Books
               that
               will
               instruct
               thee
               in
               it
               ,
               that
               thou
               mayest
               buy
               ,
               or
               borrow
               ;
               but
               to
               answer
               thee
               better
               ,
               I
               will
               briefly
               shew
               thee
               the
               manner
               of
               Extracting
               the
               Square
               ,
               not
               doubting
               but
               thou
               canst
               performe
               Addition
               ,
               Substraction
               ,
               Multiplication
               ,
               and
               Division
               already
               .
            
          
        
         
           
           
             CHAP.
             VIII
             .
             
               How
               to
               Extract
               the
               Square
               Root
               .
            
          
           
             KNow
             then
             that
             a
             square
             number
             hath
             its
             sides
             equall
             every
             way
             ,
             as
             are
             the
             sides
             of
             4
             ,
             represented
             by
             ⸬
             pricks
             ;
             and
             you
             see
             that
             every
             way
             of
             all
             the
             4
             sides
             it
             containeth
             2
             ,
             and
             so
             2
             times
             2
             ,
             make
             4
             ,
             which
             is
             the
             squaring
             of
             a
             number
             ,
             so
             you
             see
             ⋮
             ⋮
             ⋮
             9
             pricks
             is
             a
             square
             ,
             or
             9
             is
             a
             square
             number
             ,
             whose
             side
             is
             3
             ,
             and
             3
             times
             3
             make
             9
             ,
             but
             2
             times
             3
             is
             not
             a
             square
             number
             ,
             as
             you
             see
             :
             :
             :
             ,
             being
             but
             2
             one
             way
             ,
             and
             the
             other
             way
             3
             ,
             that
             make
             but
             6
             ;
             so
             then
             all
             the
             numbers
             between
             4
             and
             9
             ,
             are
             not
             square
             numbers
             :
             by
             the
             like
             reason
             ,
             a
             square
             ,
             made
             of
             the
             Next
             square
             number
             4
             is
             16
             ,
             for
             4
             times
             4
             is
             16
             ,
             as
             by
             the
             Pricks
             you
             may
             see
             it
             represented
             here
             ,
             every
             of
             the
             4
             sides
             containing
             4
             ,
             make
             a
             squared
             number
             of
             16
             ,
             and
             all
             the
             numbers
             that
             are
             between
             9
             and
             16
             ,
             as
             2
             times
             4
             ,
             or
             3
             times
             4
             ,
             are
             not
             squares
             ,
             but
             have
             a
             fraction
             annexed
             to
             them
             ;
             so
             also
             any
             number
             betwen
             16
             and
             25
             ,
             are
             not
             squares
             ,
             as
             4
             times
             5
             ,
             or
             2
             times
             5
             ,
             or
             3
             times
             5
             ,
             these
             are
             not
             square
             numbers
             ,
             but
             5
             times
             5
             is
             a
             squared
             number
             ,
             and
             maketh
             25
             ,
             where
             note
             ,
             that
             to
             square
             a
             number
             ,
             and
             to
             extract
             the
             square
             root
             ,
             is
             two
             different
             things
             ;
             for
             when
             we
             say
             ,
             to
             square
             a
             number
             ,
             is
             to
             multiply
             it
             in
             it self
             ,
             or
             by
             it
             itselfe
             ;
             or
          
           
           
           
             Thus
             you
             may
             conceive
             of
             the
             Squares
             of
             6
             ,
             for
             6
             times
             6
             make
             36
             ;
             7
             times
             7
             make
             49
             ;
             8
             times
             8
             make
             64
             ;
             9
             times
             9
             make
             81
             ;
             10
             times
             10
             make
             100
             :
             there
             is
             all
             the
             squares
             made
             of
             the
             9
             Figures
             ,
             expressed
             by
             this
             little
             Table
             annexed
             ,
             as
             against
             each
             Figure
             is
             the
             square
             made
             of
             them
             ,
             as
             2
             times
             2
             is
             4
             ,
             so
             is
             4
             against
             2
             ,
             as
             you
             see
             .
          
           
             
               
                 
                   1
                
                 
                   1
                
              
               
                 
                   2
                
                 
                   4
                
              
               
                 
                   3
                
                 
                   9
                
              
               
                 
                   4
                
                 
                   16
                
              
               
                 
                   5
                
                 
                   25
                
              
               
                 
                   6
                
                 
                   36
                
              
               
                 
                   7
                
                 
                   49
                
              
               
                 
                   8
                
                 
                   64
                
              
               
                 
                   9
                
                 
                   81
                
              
               
                 
                   10
                
                 
                   100
                
              
            
          
           
             Now
             to
             extract
             the
             square
             Root
             from
             greater
             numbers
             ,
             as
             from
             144
             proceed
             thus
             ,
             write
             downe
             the
             summe
             given
             ,
             as
             followeth
             ,
             and
             make
             a
             quotient
             on
             the
             right
             hand
             ,
             as
             you
             see
             ,
             then
             set
             pricks
             under
             every
             other
             figure
             beginning
             at
             the
             right
             hand
             ,
             and
             set
             pricks
             towards
             the
             left
             hand
             ,
             under
             every
             other
             figure
             ,
             so
             in
             this
             number
             144
             ,
             consisting
             of
             3
             figures
             ,
             there
             is
             2
             pricks
             ,
             and
             so
             many
             figures
             must
             the
             quotient
             consist
             of
             ;
             then
             begin
             at
             the
             left
             hand
             of
             the
             summ
             ,
             and
             say
             ,
             or
             enquire
             for
             the
             greatest
             square
             in
             the
             figure
             ,
             or
             figures
             ,
             over
             the
             first
             prick
             ,
             at
             the
             left
             hand
             ,
             which
             here
             is
             but
             1
             ,
             therefore
             you
             can
             take
             but
             1
             ,
             for
             1
             is
             alwayes
             the
             Square
             ,
             or
             Cube
             of
             1
             ,
             therefore
             write
             1
             in
             the
             quotient
             ,
             and
             substract
             that
             1
             from
             the
             1
             over
             the
             left
             hand
             prick
             ,
          
           
             
               
                 
                   144
                   (
                
              
               
                 
                   ..
                
              
            
          
           
             
               
                 
                   0
                
              
               
                 
                   144
                   (
                   1
                
              
               
                 
                   ..
                
              
            
             
             and
             Cancell
             it
             ,
             nothing
             remainining
             ,
             write
             a
             Cipher
             over
             it
             ,
             as
             you
             see
             ,
             so
             have
             you
             one
             figure
             of
             the
             quotient
             ,
             then
             double
             your
             figure
             found
             in
             the
             quotient
             ,
             as
             2
             times
             1
             is
             2
             ;
             write
             that
             2
             under
             the
             figure
             between
             the
             next
             prickes
             ,
             which
             is
             the
             Divisor
             for
             the
             second
             figure
             ,
             then
             say
             ,
             how
             many
             times
             2
             can
             I
             have
             in
             4
             ,
             over
             the
             Divisor
             ,
             I
             say
             2
             ,
             therefore
             I
             write
             2
             in
             the
             quotient
             ,
             saying
             ,
             2
             times
             2
             is
             4
             ,
             which
             substract
             from
             the
             4
             over
             head
             ,
             Cancell
             the
             Divisor
             ,
             and
             the
             4
             over
             head
             ,
             and
             write
             a
             Cipher
             over
             it
             ,
             then
             square
             the
             last
             figure
             found
             in
             the
             quotient
             ,
             saying
             ,
             2
             times
             2
             is
             4
             ,
             which
             substract
             from
             the
             4
             over
             the
             prick
             ,
             and
             so
             resteth
             0
             ,
             therefore
             cancell
             the
             4
             ,
             and
             write
             Ciphers
             over
             head
             ,
             signifying
             ,
             that
             the
             number
             given
             to
             finde
             the
             roote
             of
             ,
             is
             a
             just
             square
             number
             ,
             the
             roote
             or
             side
             is
             12
             ,
             the
             proofe
             hereof
             is
             by
             Multiplication
             of
             the
             quotient
             in
             it self
             ,
             as
             12
             by
             12
             make
             144
             ,
             which
             ,
             if
             it
             be
             the
             same
             with
             the
             summ
             given
             to
             be
             Extracted
             ,
             it
             is
             rightly
             done
             ▪
             if
             it
             do
             not
             agree
             ,
             it
             is
             not
             true
             .
          
           
             
               
                 
                   000
                
              
               
                 
                   144
                   (
                   12
                
              
               
                 
                   .2
                   .
                
              
            
          
           
             
               
                 Example
              
               of
               another
               
                 Summ.
                 
              
            
             
               Let
               625
               be
               given
               to
               finde
               the
               Square
               Root
               of
               it
               ,
               write
               down
               the
               summ
               ,
               make
               a
               quotient
               ,
               and
               set
               pricks
               under
               every
               other
               figure
               ;
               then
               enquire
               for
               the
               greatest
               square
               in
               the
               figure
               ,
               over
               the
               pricke
               ,
               at
               the
               left
               hand
               ;
               I
               say
               ,
               2
               is
               the
               greatest
               square
               can
               be
               taken
               :
               for
               3
               times
               3
               is
               9
               ,
               and
               here
               the
               figure
               is
               but
               6
               ;
               so
               I
               write
               2
               in
               the
               quotient
               ,
               and
               square
               it
               ,
               saying
               ,
               2
               times
               2
               is
               4
               ,
               taken
               from
               6
               ,
               so
               resteth
               2
               ;
               I
               cancell
               the
               6
               ,
               and
               write
               2
            
             
               
                 
                   
                     2
                  
                
                 
                   
                     625
                     (
                     2
                  
                
                 
                   
                     ..
                  
                
              
               
               over
               it
               ,
               as
               you
               see
               ,
               then
               double
               the
               figure
               in
               the
               quotient
               ,
               saying
               ,
               2
               times
               2
               is
               4
               ;
               this
               4
               is
               the
               second
               Divisor
               ,
               I
               write
               it
               between
               the
               two
               next
               pricks
               ,
               and
               say
               ,
               how
               many
               times
               4
               ,
               can
               I
               have
               in
               22
               ,
               and
               I
               finde
               5
               times
               ;
               for
               5
               times
               4
               is
               20
               ,
               taken
               from
               22
               ,
               the
               figures
               over
               4
               ,
               so
               resteth
               2
               ;
               therefore
               I
               write
               5
               in
               the
               quotient
               ,
               and
               saying
               ,
               5
               times
               4
               make
               20
               ▪
               therefore
               I
               cancell
               the
               4
               Divisor
               ,
               and
               the
               22
               ,
               and
               write
               2
               overhead
               ,
               then
               square
               the
               last
               figure
               found
               ,
               5
               by
               5
               make
               25
               ,
               taken
               from
               25
               over
               head
               ▪
               resteth
               nothing
               ,
               so
               the
               number
               given
               is
               a
               square
               number
               .
            
             
               
                 
                   
                     2
                  
                
                 
                   
                     625
                     (
                     2
                  
                
                 
                   
                     .4
                     .
                  
                
              
            
             
               
                 
                   
                     22
                  
                
                 
                   
                     625
                     (
                     25
                  
                
                 
                   
                     .4
                     .
                  
                
              
            
             
               
                 
                   
                     22
                  
                
                 
                   
                     625
                     (
                     25
                  
                
                 
                   
                     .4
                     .
                  
                
              
            
             
               A
               Summ
               of
               5476
               ,
               given
               to
               finde
               the
               nearest
               Square
               Root
               in
               it
               ,
               write
               down
               the
               Summ
               ,
               and
               make
               a
               quotient
               and
               prick
               underneath
               ,
               as
               afore
               shewed
               ;
               say
               ,
               What
               is
               the
               greatest
               Square
               in
               the
               figures
               over
               the
               left
               hand
               prick
               ?
               and
               I
               finde
               it
               to
               be
               7
               ,
               for
               7
               times
               7
               make
               49
               ,
               but
               8
               times
               8
               make
               64
               ,
               10
               too
               much
               ,
               therefore
               I
               write
               7
               in
               the
               quotient
               ,
               and
               take
               7
               times
               7
               ,
               that
               is
               49
               from
               54
               ,
               so
               resteth
               5
               ,
               which
               I
               write
               over
               the
               prick
               ,
               and
               Cancell
               the
               5
               and
               the
               4
               ;
               then
               I
               double
               the
               figure
               in
               the
               quotient
               ,
               which
               maketh
               14
               ,
               for
               the
               Divisor
               ,
               I
               write
               the
               first
               figure
               of
               the
               Divisor
               ,
               if
               there
               be
               more
               then
               1
               under
               the
               figure
               ,
               between
               the
               two
               next
               pricks
               ,
               and
               all
               the
               other
               figures
               ,
               in
               their
               places
               ,
               toward
               the
               left
               hand
               ;
               then
               inquire
               how
               many
               times
               can
               1
               be
               taken
               from
               5
               ,
               overhead
               ,
               and
               I
               finde
               it
               may
               be
               taken
               4
               times
               ;
               I
               write
               therefore
               4
               ▪
            
             
               
                 
                   
                     5
                  
                
                 
                   
                     5476
                     (
                     7
                  
                
                 
                   
                     ..
                  
                
              
            
             
               
                 
                   
                     1
                  
                
                 
                   
                     51
                  
                
                 
                   
                     5476
                     (
                     74
                  
                
                 
                   
                     ..
                  
                
                 
                   
                     14
                  
                
              
               
               in
               the
               quotient
               ,
               and
               say
               ,
               4
               times
               1
               is
               4
               ,
               from
               5
               ;
               so
               resteth
               1
               :
               I
               Cancell
               the
               1
               and
               the
               5
               ,
               and
               write
               1
               over
               the
               5
               ,
               then
               I
               say
               ,
               4
               times
               4
               make
               16
               ,
               from
               17
               resteth
               1
               :
               I
               Cancell
               the
               4
               Divisor
               ,
               and
               write
               1
               over
               7
               ,
               and
               Cancell
               the
               other
               1
               and
               the
               7
               ;
               then
               I
               square
               the
               last
               figure
               found
               ,
               for
               so
               it
               must
               be
               at
               every
               prick
               ,
               4
               times
               4
               make
               16
               ,
               which
               I
               substract
               from
               the
               16
               over
               the
               last
               prick
               ,
               and
               so
               I
               see
               nothing
               remaineth
               ,
               that
               sheweth
               the
               sum
               given
               ,
               to
               be
               a
               just
               square
               summ
               .
            
             
               
                 
                   
                     10
                  
                
                 
                   
                     510
                  
                
                 
                   
                     5476
                     (
                     74
                  
                
                 
                   
                     ..
                  
                
                 
                   
                     14
                  
                
              
            
          
           
             
               
                 Example
              
               of
               another
               
                 Summ.
                 
              
            
             
               As
               if
               528563
               be
               given
               to
               finde
               the
               greatest
               side
               of
               the
               Square
               therein
               ,
               I
               write
               down
               the
               Summ
               ,
               as
               followeth
               ,
               and
               make
               the
               quotient
               ,
               and
               set
               the
               pricks
               under
               every
               other
               figure
               ,
               as
               you
               see
               ;
               and
               seeing
               there
               is
               3
               pricks
               ,
               it
               telleth
               ,
               that
               there
               must
               be
               3
               figures
               in
               the
               quotient
               ,
               then
               beginning
               at
               the
               figures
               over
               the
               left
               hand
               pricke
               ,
               I
               take
               the
               greatest
               square
               in
               52
               ,
               and
               I
               finde
               it
               7
               ,
               for
               7
               times
               7
               make
               49
               ;
               therefore
               I
               write
               down
               7
               in
               the
               quotient
               ,
               and
               Substract
               49
               from
               52
               ,
               so
               resteth
               3
               ,
               therefore
               Cancell
               the
               52
               ,
               and
               write
               3
               over
               the
               2
               ,
               as
               you
               see
               ;
               then
               double
               the
               quotient
               7
               ,
               it
               maketh
               14
               ,
               for
               a
               new
               Divisor
               ,
               which
               write
               down
               ,
               the
               first
               figure
               thereof
               ,
               under
               the
               figure
               between
               the
               two
               next
               pricks
               ,
               namely
               4
               under
               8
               ,
               and
               the
               other
               figure
               of
               the
               Divisor
               one
               place
               farther
               to
               the
               left
               hand
               ,
               under
               the
               3
               ,
               as
               you
               see
               ;
               then
               take
               the
               Divisor
               1
               as
               many
               times
               as
               you
               can
               ,
               from
               the
               figure
            
             
               
                 
                   
                     3
                  
                
                 
                   
                     528563
                     (
                     7
                  
                
                 
                   
                     ...
                  
                
              
            
             
               
                 
                   
                     3
                  
                
                 
                   
                     528563
                     (
                     7
                  
                
                 
                   
                     ...
                  
                
                 
                   
                     14
                  
                
              
               
               3
               over
               head
               ,
               so
               as
               that
               after
               the
               Division
               be
               made
               ,
               there
               may
               be
               the
               square
               of
               the
               last
               figure
               of
               the
               quotient
               ,
               taken
               from
               the
               figures
               over
               the
               next
               prick
               ,
               as
               I
               can
               take
               1
               but
               2
               times
               from
               2
               ,
               therefore
               I
               write
               2
               in
               the
               quotient
               ,
               and
               Cancell
               the
               Divisor
               1
               ,
               saying
               ,
               2
               times
               1
               is
               2
               ,
               from
               3
               ;
               so
               resteth
               1
               :
               I
               Cancell
               the
               figure
               3
               also
               ,
               and
               write
               1
               overhead
               ,
               as
               you
               see
               :
               then
               2
               times
               4
               is
               8
               ,
               from
               8
               over
               head
               resteth
               nothing
               ;
               therefore
               I
               Cancell
               the
               second
               figure
               of
               the
               Divisor
               ,
               4
               and
               8
               ,
               and
               write
               a
               Cipher
               over
               8
               ,
               as
               you
               see
               ;
               then
               the
               next
               place
               being
               a
               prick
               ,
               I
               must
               square
               the
               last
               figure
               found
               ,
               saying
               ,
               2
               times
               2
               make
               4
               ,
               from
               5
               ;
               the
               figure
               over
               the
               prick
               resteth
               1
               ,
               as
               you
               see
               ;
               therefore
               I
               Cancell
               the
               5
               ,
               and
               write
               1
               over
               it
               ,
               as
               you
               see
               ,
               and
               here
               is
               a
               fraction
               of
               101.
               
            
             
               
                 
                   
                     1
                  
                
                 
                   
                     30
                  
                
                 
                   
                     528563
                     (
                     72
                  
                
                 
                   
                     14
                  
                
              
            
             
               
                 
                   
                     1
                  
                
                 
                   
                     301
                  
                
                 
                   
                     528563
                     (
                     72
                  
                
                 
                   
                     14
                  
                
              
            
             
               Then
               for
               a
               new
               Divisor
               ,
               Double
               the
               quotient
               72
               ,
               and
               it
               makes
               144
               ,
               which
               is
               a
               new
               Divisor
               ,
               the
               first
               figure
               thereof
               write
               under
               the
               figure
               between
               the
               next
               pricks
               ,
               as
               the
               first
               4
               under
               6
               ,
               in
               the
               summ
               ;
               and
               the
               other
               figures
               towards
               the
               left
               hand
               ,
               in
               the
               order
               as
               you
               see
               :
               then
               ,
               how
               many
               times
               1
               in
               10
               over
               head
               ,
               and
               I
               see
               I
               cannot
               take
               8
               times
               ,
               for
               that
               there
               will
               not
               be
               left
               to
               take
               out
               the
               other
               figures
               from
               ,
               nor
               for
               the
               square
               of
               the
               last
               figure
               ,
               which
               if
               it
               were
               8
               ,
               would
               be
               64
               from
               the
               figure
               over
               the
               pricke
               ,
               therefore
               I
               take
               but
               7
               ,
               for
               by
               a
               light
               examination
               I
               see
               that
               will
               doe
               ,
               therefore
               I
               write
               down
               7
               in
               the
               quotient
               ,
               and
               proceed
               to
               the
            
             
               
                 
                   
                     1
                  
                
                 
                   
                     301
                  
                
                 
                   
                     528563
                     (
                     727
                  
                
                 
                   
                     14
                     4
                  
                
                 
                   
                     14
                  
                
              
               
               Division
               ,
               thus
               ,
               7
               times
               1
               is
               7
               ,
               from
               10
               over
               head
               remaineth
               3
               ,
               which
               I
               write
               down
               ,
               and
               Cancell
               the
               10
               ,
               as
               you
               see
               ;
               then
               7
               times
               4
               is
               28
               ,
               from
               31
               over
               head
               ,
               so
               remaineth
               3
               ,
               which
               I
               also
               write
               down
               ,
               and
               Cancell
               the
               31
               ;
               then
               again
               ,
               7
               times
               4
               ,
               the
               other
               figure
               of
               the
               Divisor
               ,
               is
               also
               28
               ,
               which
               taken
               from
               36
               over
               head
               ,
               resteth
               8
               ,
               which
               I
               write
               down
               over
               6
               ,
               and
               so
               Cancell
               the
               36
               ,
               and
               then
               the
               Summ
               standeth
               as
               you
               see
               .
            
             
               
                 
                   
                     13
                  
                
                 
                   
                     301
                  
                
                 
                   
                     528563
                     (
                     727
                  
                
                 
                   
                     14
                     4
                  
                
                 
                   
                     14
                  
                
              
            
             
               
                 
                   
                     133
                  
                
                 
                   
                     301
                  
                
                 
                   
                     528563
                     (
                     727
                  
                
                 
                   
                     14
                     4
                  
                
                 
                   
                     14
                  
                
              
            
             
               
                 
                   
                     133
                  
                
                 
                   
                     3018
                  
                
                 
                   
                     528563
                     (
                     727
                  
                
                 
                   
                     14
                     4
                  
                
                 
                   
                     14
                  
                
              
            
             
               
                 
                   
                     133
                     (
                     3
                  
                
                 
                   
                     530●8
                     (
                     4
                  
                
                 
                   
                     528563
                     (
                     727
                  
                
                 
                   
                     14
                     4
                  
                
                 
                   
                     14
                  
                
              
            
             
               Then
               lastly
               ,
               square
               the
               last
               figure
               of
               the
               quotient
               ,
               7
               times
               7
               make
               49
               ,
               taken
               from
               83
               ,
               the
               figures
               over
               the
               prick
               ,
               resteth
               34
               ,
               as
               a
               fraction
               ,
               and
               the
               Summ
               is
               finished
               :
               But
               in
               regard
               here
               is
               a
               fraction
               ,
               by
               that
               it
               tells
               you
               ,
               that
               the
               Summ
               given
               was
               no
               square
               number
               ;
               and
               the
               greatest
               square
               therein
               is
               727
               ,
               the
               proofe
               is
               by
               Multiplication
               adding
               in
               the
               fraction
               thus
               ,
               727
               Multiplied
               by
               727
               ,
               make
               528529
               ,
               then
               adding
               in
               the
               fraction
               of
               34
               ,
               maketh
               it
               528563
               ,
               the
               just
               Summ
               given
               .
            
             
               But
               some
               may
               Object
               ,
               and
               say
               ,
               That
               this
               is
               a
               very
               tedious
               way
               of
               Work
               ,
               and
               will
               take
               up
               a
               great
               deale
               of
               time
               ;
               It
               is
               true
               ,
               it
               is
               more
               labour
               then
               demonstration
               ,
               but
               the
               truth
               of
               it
               might
               very
               well
               plead
               for
               patience
               to
               Work
               it
               ,
               but
               it
               is
               not
               necessary
               you
               performe
               all
               the
               parts
               by
               it
               ,
               that
               is
               ,
               in
               every
               particular
               :
               as
               the
               exact
               hanging
               of
               the
               Waal
               at
               every
               Timber
               ,
               but
               it
               may
               suffice
               
               at
               every
               third
               or
               fourth
               Timber
               ,
               to
               finde
               the
               hanging
               of
               the
               Waals
               ,
               onely
               the
               Risings
               alow
               ,
               afoare
               and
               abaft
               ,
               I
               would
               work
               to
               every
               Timber
               there
               .
            
             
               But
               to
               make
               it
               more
               briefe
               ,
               here
               followeth
               a
               Table
               that
               the
               numbers
               are
               therein
               contrived
               to
               the
               same
               purpose
               ,
               to
               avoide
               the
               tedious
               Extraction
               of
               the
               Root
               ,
               and
               onely
               use
               Addition
               and
               Substraction
               ,
               onely
               being
               but
               a
               very
               little
               difference
               between
               the
               finding
               the
               Risings
               by
               this
               Table
               ,
               and
               by
               the
               
                 Draught
                 ,
              
               for
               in
               this
               kinde
               of
               
                 Arithmeticall
              
               Work
               ,
               it
               mattereth
               not
               ,
               whether
               or
               no
               there
               be
               any
               
                 Draught
              
               drawn
               at
               all
               ,
               or
               no
               ,
               if
               the
               builder
               onely
               note
               in
               his
               Book
               the
               length
               by
               the
               Keele
               ,
               and
               the
               breadth
               at
               the
               Beame
               ,
               the
               Racke
               of
               the
               Stem
               ,
               Racke
               of
               the
               Post
               ,
               depth
               of
               the
               Water
               ,
               to
               Sayle
               in
               depth
               of
               the
               Hould
               ,
               height
               of
               the
               Waals
               abaft
               ,
               afoare
               ,
               at
               the
               Midships
               ,
               and
               all
               the
               remarkable
               things
               to
               be
               noted
               ,
               he
               may
               be
               able
               to
               Build
               a
               Vessell
               ,
               and
               never
               draw
               a
               
                 Draught
              
               at
               all
               ,
               and
               yet
               affirm
               his
               Worke
               to
               be
               absolutely
               true
               ,
               according
               to
               Art
               ,
               and
               a
               great
               deale
               more
               exact
               then
               by
               
                 Draught
                 :
              
               I
               shall
               in
               few
               words
               shew
               you
               the
               use
               of
               the
               Table
               ,
               and
               so
               conclude
               .
            
          
        
         
           
           
             
               CHAP.
               IX
               .
            
             A
             Description
             of
             the
             Table
             of
             Squares
             .
          
           
             TO
             save
             the
             Practitioner
             a
             labour
             of
             Extracting
             of
             Roots
             ,
             for
             here
             they
             are
             ready
             done
             to
             thy
             hand
             of
             purpose
             ,
             and
             all
             the
             use
             of
             
               Arithmetick
            
             required
             is
             onely
             Substraction
             ,
             as
             
               Example
            
             in
             the
             Figure
             of
             the
             Sweep
             foregoing
             ,
             being
             found
             to
             be
             203
             inches
             ,
             as
             you
             saw
             it
             found
             before
             ,
             which
             is
             ,
             I
             say
             ,
             alwayes
             one
             side
             of
             the
             Triangle
             ,
             made
             of
             the
             side
             DI
             ,
             then
             knowing
             the
             length
             of
             ●I
             ,
             132
             inches
             ,
             which
             is
             the
             distance
             of
             the
             point
             ,
             of
             which
             the
             Rising
             is
             sought
             at
             ;
             seek
             in
             the
             Tables
             ,
             under
             the
             Title
             of
             inches
             ,
             at
             the
             head
             of
             the
             Tables
             ,
             for
             132
             ,
             you
             will
             finde
             it
             in
             the
             second
             Page
             ,
             and
             the
             twelfth
             line
             ;
             and
             right
             against
             it
             ,
             in
             the
             same
             line
             ,
             under
             the
             next
             Title
             of
             Squares
             ,
             you
             have
             17424
             ,
             the
             square
             made
             of
             132
             ,
             which
             Substract
             from
             the
             Square
             made
             of
             203
             ,
             which
             is
             41209
             ,
             which
             is
             found
             in
             the
             second
             Page
             of
             the
             Tables
             ,
             and
             the
             third
             line
             :
             Now
             the
             other
             number
             17424
             ,
             Substracted
             from
             41209
             ,
             so
             resteth
             23775
             ;
             seek
             the
             number
             nearest
             to
             it
             in
             the
             Table
             ,
             under
             the
             Title
             of
             Squares
             ,
             which
             you
             will
             finde
             in
             the
             second
             Page
             ,
             34
             line
             ,
             you
             finde
             not
             just
             the
             same
             number
             ,
             for
             in
             stead
             of
             23775
             ,
             you
             finde
             23716
             too
             little
             by
             59
             ,
             and
             the
             Root
             answering
             thereto
             ,
             is
             in
             the
             same
             line
             ,
             under
             the
             Title
             of
             inches
             ,
             towards
             the
             left
             
             hand
             ,
             which
             is
             154
             ;
             now
             if
             you
             take
             the
             next
             square
             lower
             to
             the
             left
             hand
             35
             line
             ,
             it
             is
             24025
             ,
             250
             too
             much
             ,
             so
             you
             may
             see
             it
             is
             nearer
             to
             the
             34th
             line
             ,
             because
             there
             it
             was
             too
             little
             but
             by
             59
             ,
             so
             that
             you
             may
             see
             it
             will
             be
             ¾
             of
             an
             inch
             less
             then
             the
             number
             of
             inches
             ,
             belonging
             to
             the
             35th
             line
             ,
             and
             about
             ¼
             of
             an
             inch
             more
             then
             the
             numbers
             in
             the
             34th
             line
             ;
             so
             that
             you
             see
             it
             is
             answered
             ,
             the
             third
             side
             D
             0
             is
             154
             ,
             and
             ¼
             of
             an
             inch
             ,
             which
             Substracted
             from
             the
             whole
             Sweep
             203
             ,
             leaveth
             48¾
             inches
             for
             the
             Rising
             ,
             so
             you
             have
             no
             need
             of
             extraction
             of
             the
             Rootes
             by
             these
             Tables
             ,
             it
             is
             already
             done
             to
             your
             hand
             ;
             the
             Columne
             that
             is
             between
             the
             inches
             and
             the
             squares
             ,
             and
             written
             feet
             inches
             in
             the
             head
             ,
             is
             to
             shew
             you
             ,
             how
             may
             feet
             ,
             and
             inches
             of
             the
             foot
             any
             number
             of
             inches
             is
             ;
             as
             here
             ,
             the
             number
             203
             inches
             sought
             ,
             and
             found
             in
             the
             Tables
             ,
             in
             the
             second
             page
             ,
             and
             third
             line
             ,
             just
             against
             it
             ,
             in
             the
             same
             line
             ,
             between
             that
             and
             the
             squares
             ,
             is
             16
             —
             11
             ,
             shewing
             that
             it
             is
             16
             feet
             and
             11
             inches
             ;
             or
             if
             the
             square
             were
             given
             ,
             as
             41209
             ,
             found
             at
             the
             second
             page
             ,
             and
             third
             line
             ,
             next
             toward
             the
             left
             hand
             ,
             you
             have
             16
             foot
             ,
             11
             inches
             ;
             and
             if
             you
             seek
             for
             it
             in
             inches
             ,
             in
             the
             third
             Columne
             toward
             the
             left
             hand
             ,
             and
             the
             same
             line
             ,
             you
             have
             203
             inches
             :
             Thus
             is
             it
             very
             ready
             to
             reduce
             inches
             into
             foot
             measure
             ,
             or
             feet
             into
             inches
             .
          
           
             
               Another
               
                 Example
                 .
              
            
             
               In
               the
               same
               figure
               ,
               to
               finde
               the
               Rising
               at
               the
               point
               
                 F
                 ,
              
               the
               sweep
               being
               203
               inches
               ,
               as
               before
               is
               said
               ,
               is
               alwayes
               one
               side
               ,
               throughout
               the
               whole
               Work
               of
               the
               same
               Rising
               line
               is
               41209
               ,
               as
               is
               found
               in
               the
               second
               page
               ,
               the
               
               third
               line
               ;
               the
               other
               fide
               from
               the
               point
               A
               to
               F
               ,
               is
               9
               foot
               ,
               or
               108
               inches
               ,
               whose
               square
               is
               11664
               ,
               found
               in
               the
               first
               page
               ,
               and
               the
               28th
               line
               ;
               now
               substract
               the
               square
               made
               of
               the
               side
               A
               F
               ,
               11664
               ,
               from
               the
               square
               of
               the
               side
               D
               E
               ,
               so
               remaineth
               29545
            
             
               
                 
                   
                     41209
                  
                
                 
                   
                     11664
                  
                
                 
                   
                     29545
                  
                
              
            
             
               Seek
               in
               the
               Table
               of
               squares
               for
               that
               number
               ,
               and
               I
               finde
               in
               the
               second
               page
               ,
               and
               12
               line
               ,
               and
               the
               sixth
               Columne
               ,
               29584
               ,
               the
               nearest
               number
               to
               it
               ,
               yet
               it
               is
               a
               little
               too
               much
               near
               the
               ¼
               of
               an
               inch
               ;
               and
               toward
               the
               left
               hand
               in
               the
               same
               line
               ,
               the
               next
               Column
               under
               the
               title
               
                 feet
                 inch
                 ,
              
               you
               finde
               14
               ;
               4
               signifying
               that
               to
               be
               14
               foot
               ,
               4
               inches
               :
               and
               in
               one
               Columne
               more
               to
               the
               left
               hand
               ,
               and
               the
               same
               line
               ,
               you
               see
               under
               the
               Title
               of
               
                 inches
              
               172
               over
               the
               head
               you
               tituled
               
                 inches
                 ,
              
               which
               must
               be
               subracted
               from
               203
               inch
               ,
               so
               remaineth
               3
               inches
               for
               the
               Rising
               of
               F
               E
               ,
               which
               is
               2
               foot
               ,
               7
               inches
               ,
               as
               in
               the
               first
               page
               of
               the
               Table
               ,
               and
               the
               31
               line
               .
            
             
               
                 
                   
                     203
                  
                
                 
                   
                     172
                  
                
                 
                   
                     031
                  
                
              
            
             
               These
               few
               
                 Examples
              
               I
               think
               may
               be
               sufficient
               to
               shew
               the
               use
               of
               the
               following
               Tables
               of
               squares
               ,
               the
               benefit
               where
               of
               may
               be
               very
               great
               ,
               for
               such
               as
               shall
               make
               use
               of
               the
               same
               :
               If
               any
               desire
               the
               finding
               of
               the
               Fractions
               of
               these
               squares
               ,
               when
               he
               findeth
               not
               his
               just
               figures
               in
               the
               squares
               ,
               let
               him
               do
               thus
               ,
               substract
               the
               Figures
               under
               his
               number
               ,
               from
               the
               Figures
               above
               his
               number
               ,
               which
               shall
               be
               the
               denominator
               ,
               then
               these
               Figures
               given
               ,
               substracted
               ,
               from
               which
               the
               next
               squares
               less
               ,
               shall
               be
               the
               denominator
               to
               that
               Fraction
               .
            
             
               As
               for
               
                 Example
                 ,
              
               In
               the
               foregoing
               figures
               ,
               after
               substraction
               ,
               should
               have
               been
               29553
               ;
               the
               nearest
               agreeing
               in
               the
               Tables
               ,
               is
               29584
               ,
               the
               next
               lesser
               square
               number
               in
               the
               Table
               is
               29241
               ,
               which
               is
               more
               a
               great
               deale
               too
               little
               ,
               
               then
               the
               other
               is
               too
               great
               ;
               then
               substract
               the
               lesser
               square
               number
               29241
               ,
               from
               29584
               ,
               and
               so
               resteth
               343
               ,
               which
               must
               be
               the
               denominator
               ,
               then
               again
               substract
               the
               true
               number
               given
               ,
               29553
               ,
               the
               next
               lesser
               square
               number
               in
               the
               Table
               is
               29241
               ,
               which
               must
               be
               substracted
               ,
               I
               say
               ,
               from
               the
               true
               number
               given
               ,
               29553
               ,
               and
               so
               resteth
               after
               substraction
               312
               ,
               which
               is
               the
               Numerator
               to
               the
               Fraction
               ,
               and
               must
               be
               thus
               written
               ,
               ●
               so
               then
               the
               number
               belonging
               to
               29584
               ,
               is
               171
               inches
               ,
               and
               312
               /
               343
               parts
               of
               an
               inch
               ,
               which
               being
               abreviated
               ,
               is
               something
               more
               then
               ¼
               of
               one
               inch
               ,
               and
               not
               full
               ⅞
               of
               one
               inch
               .
            
             
               
                 
                   
                     29584
                  
                
                 
                   
                     29241
                  
                
                 
                   
                     343
                  
                
              
            
             
               Thus
               he
               that
               pleaseth
               may
               finde
               the
               rising
               of
               any
               Timber
               ,
               or
               narrowing
               of
               any
               place
               by
               these
               Tables
               and
               the
               help
               of
               Substraction
               ,
               exactly
               to
               any
               Circle
               whatsoever
               ,
               but
               it
               may
               suffice
               ,
               that
               a
               Man
               ,
               going
               to
               his
               Tables
               ,
               may
               see
               which
               square
               his
               figures
               have
               greatest
               affinity
               with
               ,
               and
               may
               estimate
               the
               difference
               near
               enough
               ,
               without
               seeking
               for
               the
               fraction
               ,
               which
               will
               be
               easily
               known
               by
               much
               practise
               herein
               .
            
          
           
             
               HEre
               followeth
               a
               
                 Table
              
               of
               
                 Square
                 Roots
                 ,
              
               ready
               Extracted
               ,
               from
               one
               Inch
               to
               1300
               Inches
               ,
               which
               is
               to
               108
               foot
               ▪
               and
               4
               Inches
               ,
               and
               it
               is
               thus
               contraved
               ,
               That
               from
               one
               Inch
               ,
               to
               840
               Inches
               ,
               all
               the
               Inches
               are
               reduced
               into
               Feet
               and
               Inches
               ▪
               for
               the
               ease
               and
               help
               of
               Workmen
               ,
               who
               alway
               take
               their
               Measures
               by
               Feet
               and
               Inches
               ;
               but
               from
               thence
               to
               the
               end
               of
               the
               table
               you
               have
               the
               Inches
               onely
               ,
               and
               the
               Squares
               thereof
               against
               them
               as
               the
               Titles
               over
               every
               Page
               do
               make
               appear
               .
            
             
             
               
                 
                   A
                   Table
                   of
                   
                     Square
                     Roots
                     .
                  
                
                 
                   
                     Inch
                  
                   
                     Feet
                     Inches
                  
                   
                     Squares
                  
                
                 
                   
                     1
                  
                   
                      
                  
                   
                     1
                  
                   
                     1
                  
                
                 
                   
                     2
                  
                   
                      
                  
                   
                     2
                  
                   
                     4
                  
                
                 
                   
                     3
                  
                   
                      
                  
                   
                     3
                  
                   
                     9
                  
                
                 
                   
                     4
                  
                   
                      
                  
                   
                     4
                  
                   
                     16
                  
                
                 
                   
                     5
                  
                   
                      
                  
                   
                     5
                  
                   
                     25
                  
                
                 
                   
                     6
                  
                   
                      
                  
                   
                     6
                  
                   
                     36
                  
                
                 
                   
                     7
                  
                   
                      
                  
                   
                     7
                  
                   
                     49
                  
                
                 
                   
                     8
                  
                   
                      
                  
                   
                     8
                  
                   
                     64
                  
                
                 
                   
                     9
                  
                   
                      
                  
                   
                     9
                  
                   
                     81
                  
                
                 
                   
                     10
                  
                   
                      
                  
                   
                     10
                  
                   
                     100
                  
                
                 
                   
                     11
                  
                   
                      
                  
                   
                     11
                  
                   
                     121
                  
                
                 
                   
                     12
                  
                   
                     1
                  
                   
                     00
                  
                   
                     144
                  
                
                 
                   
                     13
                  
                   
                     1
                  
                   
                     1
                  
                   
                     169
                  
                
                 
                   
                     14
                  
                   
                     1
                  
                   
                     2
                  
                   
                     196
                  
                
                 
                   
                     15
                  
                   
                     1
                  
                   
                     3
                  
                   
                     225
                  
                
                 
                   
                     16
                  
                   
                     1
                  
                   
                     4
                  
                   
                     256
                  
                
                 
                   
                     17
                  
                   
                     1
                  
                   
                     5
                  
                   
                     289
                  
                
                 
                   
                     18
                  
                   
                     1
                  
                   
                     6
                  
                   
                     324
                  
                
                 
                   
                     19
                  
                   
                     1
                  
                   
                     7
                  
                   
                     361
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     8
                  
                   
                     400
                  
                
                 
                   
                     21
                  
                   
                     1
                  
                   
                     9
                  
                   
                     441
                  
                
                 
                   
                     22
                  
                   
                     1
                  
                   
                     10
                  
                   
                     484
                  
                
                 
                   
                     23
                  
                   
                     1
                  
                   
                     11
                  
                   
                     529
                  
                
                 
                   
                     24
                  
                   
                     2
                  
                   
                     00
                  
                   
                     576
                  
                
                 
                   
                     25
                  
                   
                     2
                  
                   
                     01
                  
                   
                     625
                  
                
                 
                   
                     26
                  
                   
                     2
                  
                   
                     2
                  
                   
                     676
                  
                
                 
                   
                     27
                  
                   
                     2
                  
                   
                     3
                  
                   
                     729
                  
                
                 
                   
                     28
                  
                   
                     2
                  
                   
                     4
                  
                   
                     784
                  
                
                 
                   
                     29
                  
                   
                     2
                  
                   
                     5
                  
                   
                     841
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     6
                  
                   
                     900
                  
                
                 
                   
                     31
                  
                   
                     2
                  
                   
                     7
                  
                   
                     961
                  
                
                 
                   
                     32
                  
                   
                     2
                  
                   
                     8
                  
                   
                     1024
                  
                
                 
                   
                     33
                  
                   
                     2
                  
                   
                     9
                  
                   
                     1089
                  
                
                 
                   
                     34
                  
                   
                     2
                  
                   
                     10
                  
                   
                     1156
                  
                
                 
                   
                     35
                  
                   
                     2
                  
                   
                     11
                  
                   
                     1225
                  
                
                 
                   
                     36
                  
                   
                     3
                  
                   
                     00
                  
                   
                     1296
                  
                
                 
                   
                     37
                  
                   
                     3
                  
                   
                     1
                  
                   
                     1369
                  
                
                 
                   
                     38
                  
                   
                     3
                  
                   
                     2
                  
                   
                     1444
                  
                
                 
                   
                     39
                  
                   
                     3
                  
                   
                     3
                  
                   
                     1521
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     4
                  
                   
                     1600
                  
                
                 
                   
                     41
                  
                   
                     3
                  
                   
                     5
                  
                   
                     16●1
                  
                
                 
                   
                     42
                  
                   
                     3
                  
                   
                     6
                  
                   
                     1764
                  
                
                 
                   
                     43
                  
                   
                     3
                  
                   
                     7
                  
                   
                     1849
                  
                
                 
                   
                     44
                  
                   
                     3
                  
                   
                     8
                  
                   
                     1936
                  
                
                 
                   
                     45
                  
                   
                     3
                  
                   
                     9
                  
                   
                     2025
                  
                
                 
                   
                     46
                  
                   
                     3
                  
                   
                     10
                  
                   
                     2116
                  
                
                 
                   
                     47
                  
                   
                     3
                  
                   
                     11
                  
                   
                     2209
                  
                
                 
                   
                     48
                  
                   
                     4
                  
                   
                     00
                  
                   
                     2304
                  
                
                 
                   
                     49
                  
                   
                     4
                  
                   
                     1
                  
                   
                     2401
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     2
                  
                   
                     2500
                  
                
                 
                   
                     51
                  
                   
                     4
                  
                   
                     3
                  
                   
                     2601
                  
                
                 
                   
                     52
                  
                   
                     4
                  
                   
                     4
                  
                   
                     2704
                  
                
                 
                   
                     53
                  
                   
                     4
                  
                   
                     5
                  
                   
                     2809
                  
                
                 
                   
                     54
                  
                   
                     4
                  
                   
                     6
                  
                   
                     2916
                  
                
                 
                   
                     55
                  
                   
                     4
                  
                   
                     7
                  
                   
                     3025
                  
                
                 
                   
                     56
                  
                   
                     4
                  
                   
                     8
                  
                   
                     3136
                  
                
                 
                   
                     57
                  
                   
                     4
                  
                   
                     9
                  
                   
                     3249
                  
                
                 
                   
                     58
                  
                   
                     4
                  
                   
                     10
                  
                   
                     3364
                  
                
                 
                   
                     59
                  
                   
                     4
                  
                   
                     11
                  
                   
                     3481
                  
                
                 
                   
                     60
                  
                   
                     5
                  
                   
                     00
                  
                   
                     3600
                  
                
                 
                   
                     61
                  
                   
                     5
                  
                   
                     1
                  
                   
                     3721
                  
                
                 
                   
                     62
                  
                   
                     5
                  
                   
                     2
                  
                   
                     3844
                  
                
                 
                   
                     63
                  
                   
                     5
                  
                   
                     3
                  
                   
                     3964
                  
                
                 
                   
                     64
                  
                   
                     5
                  
                   
                     4
                  
                   
                     4096
                  
                
                 
                   
                     65
                  
                   
                     5
                  
                   
                     5
                  
                   
                     4225
                  
                
                 
                   
                     66
                  
                   
                     5
                  
                   
                     6
                  
                   
                     4356
                  
                
                 
                   
                     67
                  
                   
                     5
                  
                   
                     7
                  
                   
                     4489
                  
                
                 
                   
                     68
                  
                   
                     5
                  
                   
                     8
                  
                   
                     4624
                  
                
                 
                   
                     69
                  
                   
                     5
                  
                   
                     9
                  
                   
                     4761
                  
                
                 
                   
                     70
                  
                   
                     5
                  
                   
                     10
                  
                   
                     4900
                  
                
                 
                   
                     71
                  
                   
                     5
                  
                   
                     11
                  
                   
                     5041
                  
                
                 
                   
                     72
                  
                   
                     6
                  
                   
                     00
                  
                   
                     5184
                  
                
                 
                   
                     73
                  
                   
                     6
                  
                   
                     1
                  
                   
                     5329
                  
                
                 
                   
                     74
                  
                   
                     6
                  
                   
                     2
                  
                   
                     5476
                  
                
                 
                   
                     75
                  
                   
                     6
                  
                   
                     3
                  
                   
                     5625
                  
                
                 
                   
                     76
                  
                   
                     6
                  
                   
                     4
                  
                   
                     5776
                  
                
                 
                   
                     77
                  
                   
                     6
                  
                   
                     5
                  
                   
                     5929
                  
                
                 
                   
                     78
                  
                   
                     6
                  
                   
                     6
                  
                   
                     6084
                  
                
                 
                   
                     79
                  
                   
                     6
                  
                   
                     7
                  
                   
                     6241
                  
                
                 
                   
                     80
                  
                   
                     6
                  
                   
                     8
                  
                   
                     6400
                  
                
                 
                   
                     81
                  
                   
                     6
                  
                   
                     9
                  
                   
                     6561
                  
                
                 
                   
                     82
                  
                   
                     6
                  
                   
                     10
                  
                   
                     6724
                  
                
                 
                   
                     83
                  
                   
                     6
                  
                   
                     11
                  
                   
                     6889
                  
                
                 
                   
                     84
                  
                   
                     7
                  
                   
                     00
                  
                   
                     7056
                  
                
                 
                   
                     85
                  
                   
                     7
                  
                   
                     1
                  
                   
                     7225
                  
                
                 
                   
                     86
                  
                   
                     7
                  
                   
                     2
                  
                   
                     7396
                  
                
                 
                   
                     87
                  
                   
                     7
                  
                   
                     3
                  
                   
                     7569
                  
                
                 
                   
                     88
                  
                   
                     7
                  
                   
                     4
                  
                   
                     7744
                  
                
                 
                   
                     89
                  
                   
                     7
                  
                   
                     5
                  
                   
                     7921
                  
                
                 
                   
                     90
                  
                   
                     7
                  
                   
                     6
                  
                   
                     8●00
                  
                
                 
                   
                     91
                  
                   
                     7
                  
                   
                     7
                  
                   
                     8●81
                  
                
                 
                   
                     92
                  
                   
                     7
                  
                   
                     8
                  
                   
                     8464
                  
                
                 
                   
                     93
                  
                   
                     7
                  
                   
                     9
                  
                   
                     8649
                  
                
                 
                   
                     94
                  
                   
                     7
                  
                   
                     10
                  
                   
                     8836
                  
                
                 
                   
                     95
                  
                   
                     7
                  
                   
                     11
                  
                   
                     9025
                  
                
                 
                   
                     96
                  
                   
                     8
                  
                   
                     0
                  
                   
                     9226
                  
                
                 
                   
                     97
                  
                   
                     8
                  
                   
                     1
                  
                   
                     9409
                  
                
                 
                   
                     98
                  
                   
                     8
                  
                   
                     2
                  
                   
                     9604
                  
                
                 
                   
                     99
                  
                   
                     8
                  
                   
                     3
                  
                   
                     9801
                  
                
                 
                   
                     100
                  
                   
                     8
                  
                   
                     4
                  
                   
                     10000
                  
                
                 
                   
                     101
                  
                   
                     8
                  
                   
                     5
                  
                   
                     10201
                  
                
                 
                   
                     102
                  
                   
                     8
                  
                   
                     6
                  
                   
                     10404
                  
                
                 
                   
                     103
                  
                   
                     8
                  
                   
                     7
                  
                   
                     10609
                  
                
                 
                   
                     104
                  
                   
                     8
                  
                   
                     8
                  
                   
                     10816
                  
                
                 
                   
                     105
                  
                   
                     8
                  
                   
                     9
                  
                   
                     11025
                  
                
                 
                   
                     106
                  
                   
                     8
                  
                   
                     10
                  
                   
                     11236
                  
                
                 
                   
                     107
                  
                   
                     8
                  
                   
                     11
                  
                   
                     11449
                  
                
                 
                   
                     108
                  
                   
                     9
                  
                   
                     0
                  
                   
                     11664
                  
                
                 
                   
                     109
                  
                   
                     9
                  
                   
                     1
                  
                   
                     11881
                  
                
                 
                   
                     110
                  
                   
                     9
                  
                   
                     2
                  
                   
                     12100
                  
                
                 
                   
                     111
                  
                   
                     9
                  
                   
                     3
                  
                   
                     12321
                  
                
                 
                   
                     112
                  
                   
                     9
                  
                   
                     4
                  
                   
                     12544
                  
                
                 
                   
                     113
                  
                   
                     9
                  
                   
                     5
                  
                   
                     12769
                  
                
                 
                   
                     114
                  
                   
                     9
                  
                   
                     6
                  
                   
                     12996
                  
                
                 
                   
                     115
                  
                   
                     9
                  
                   
                     7
                  
                   
                     13225
                  
                
                 
                   
                     116
                  
                   
                     9
                  
                   
                     8
                  
                   
                     13456
                  
                
                 
                   
                     117
                  
                   
                     9
                  
                   
                     9
                  
                   
                     13689
                  
                
                 
                   
                     118
                  
                   
                     9
                  
                   
                     10
                  
                   
                     13924
                  
                
                 
                   
                     219
                  
                   
                     9
                  
                   
                     11
                  
                   
                     14162
                  
                
                 
                   
                     120
                  
                   
                     10
                  
                   
                     0
                  
                   
                     14400
                  
                
                 
                   
                     
                     121
                  
                   
                     10
                  
                   
                     1
                  
                   
                     14641
                  
                
                 
                   
                     122
                  
                   
                     10
                  
                   
                     2
                  
                   
                     14884
                  
                
                 
                   
                     123
                  
                   
                     10
                  
                   
                     3
                  
                   
                     15229
                  
                
                 
                   
                     124
                  
                   
                     10
                  
                   
                     4
                  
                   
                     15376
                  
                
                 
                   
                     125
                  
                   
                     10
                  
                   
                     5
                  
                   
                     15625
                  
                
                 
                   
                     126
                  
                   
                     10
                  
                   
                     6
                  
                   
                     15876
                  
                
                 
                   
                     127
                  
                   
                     10
                  
                   
                     7
                  
                   
                     16029
                  
                
                 
                   
                     128
                  
                   
                     10
                  
                   
                     8
                  
                   
                     16384
                  
                
                 
                   
                     129
                  
                   
                     10
                  
                   
                     9
                  
                   
                     16641
                  
                
                 
                   
                     130
                  
                   
                     10
                  
                   
                     10
                  
                   
                     16900
                  
                
                 
                   
                     131
                  
                   
                     10
                  
                   
                     11
                  
                   
                     17161
                  
                
                 
                   
                     132
                  
                   
                     11
                  
                   
                     00
                  
                   
                     17424
                  
                
                 
                   
                     133
                  
                   
                     11
                  
                   
                     1
                  
                   
                     17689
                  
                
                 
                   
                     134
                  
                   
                     11
                  
                   
                     2
                  
                   
                     17956
                  
                
                 
                   
                     135
                  
                   
                     11
                  
                   
                     3
                  
                   
                     18225
                  
                
                 
                   
                     136
                  
                   
                     11
                  
                   
                     4
                  
                   
                     18496
                  
                
                 
                   
                     137
                  
                   
                     11
                  
                   
                     5
                  
                   
                     18769
                  
                
                 
                   
                     138
                  
                   
                     11
                  
                   
                     6
                  
                   
                     19044
                  
                
                 
                   
                     139
                  
                   
                     11
                  
                   
                     7
                  
                   
                     19321
                  
                
                 
                   
                     140
                  
                   
                     11
                  
                   
                     8
                  
                   
                     19600
                  
                
                 
                   
                     141
                  
                   
                     11
                  
                   
                     9
                  
                   
                     19881
                  
                
                 
                   
                     142
                  
                   
                     11
                  
                   
                     10
                  
                   
                     20164
                  
                
                 
                   
                     143
                  
                   
                     11
                  
                   
                     11
                  
                   
                     20449
                  
                
                 
                   
                     144
                  
                   
                     12
                  
                   
                     00
                  
                   
                     20736
                  
                
                 
                   
                     145
                  
                   
                     12
                  
                   
                     01
                  
                   
                     21025
                  
                
                 
                   
                     146
                  
                   
                     12
                  
                   
                     2
                  
                   
                     22416
                  
                
                 
                   
                     147
                  
                   
                     12
                  
                   
                     3
                  
                   
                     21609
                  
                
                 
                   
                     148
                  
                   
                     12
                  
                   
                     4
                  
                   
                     21904
                  
                
                 
                   
                     149
                  
                   
                     12
                  
                   
                     5
                  
                   
                     22201
                  
                
                 
                   
                     150
                  
                   
                     12
                  
                   
                     6
                  
                   
                     22500
                  
                
                 
                   
                     151
                  
                   
                     12
                  
                   
                     7
                  
                   
                     22801
                  
                
                 
                   
                     152
                  
                   
                     12
                  
                   
                     8
                  
                   
                     23104
                  
                
                 
                   
                     153
                  
                   
                     12
                  
                   
                     9
                  
                   
                     23409
                  
                
                 
                   
                     154
                  
                   
                     12
                  
                   
                     10
                  
                   
                     23716
                  
                
                 
                   
                     155
                  
                   
                     12
                  
                   
                     11
                  
                   
                     24025
                  
                
                 
                   
                     156
                  
                   
                     13
                  
                   
                     00
                  
                   
                     24336
                  
                
                 
                   
                     157
                  
                   
                     13
                  
                   
                     1
                  
                   
                     24649
                  
                
                 
                   
                     158
                  
                   
                     13
                  
                   
                     2
                  
                   
                     24964
                  
                
                 
                   
                     159
                  
                   
                     13
                  
                   
                     3
                  
                   
                     25381
                  
                
                 
                   
                     160
                  
                   
                     13
                  
                   
                     4
                  
                   
                     25600
                  
                
                 
                   
                     161
                  
                   
                     13
                  
                   
                     5
                  
                   
                     25921
                  
                
                 
                   
                     162
                  
                   
                     13
                  
                   
                     6
                  
                   
                     26244
                  
                
                 
                   
                     163
                  
                   
                     13
                  
                   
                     7
                  
                   
                     26569
                  
                
                 
                   
                     164
                  
                   
                     13
                  
                   
                     8
                  
                   
                     26956
                  
                
                 
                   
                     165
                  
                   
                     13
                  
                   
                     9
                  
                   
                     27225
                  
                
                 
                   
                     166
                  
                   
                     13
                  
                   
                     10
                  
                   
                     27556
                  
                
                 
                   
                     167
                  
                   
                     13
                  
                   
                     11
                  
                   
                     27889
                  
                
                 
                   
                     168
                  
                   
                     14
                  
                   
                     00
                  
                   
                     28224
                  
                
                 
                   
                     169
                  
                   
                     14
                  
                   
                     1
                  
                   
                     28561
                  
                
                 
                   
                     170
                  
                   
                     14
                  
                   
                     2
                  
                   
                     28900
                  
                
                 
                   
                     171
                  
                   
                     14
                  
                   
                     3
                  
                   
                     29241
                  
                
                 
                   
                     172
                  
                   
                     14
                  
                   
                     4
                  
                   
                     29584
                  
                
                 
                   
                     173
                  
                   
                     14
                  
                   
                     5
                  
                   
                     29929
                  
                
                 
                   
                     174
                  
                   
                     14
                  
                   
                     6
                  
                   
                     30276
                  
                
                 
                   
                     175
                  
                   
                     14
                  
                   
                     7
                  
                   
                     30625
                  
                
                 
                   
                     176
                  
                   
                     14
                  
                   
                     8
                  
                   
                     31076
                  
                
                 
                   
                     177
                  
                   
                     14
                  
                   
                     9
                  
                   
                     31329
                  
                
                 
                   
                     178
                  
                   
                     14
                  
                   
                     10
                  
                   
                     31684
                  
                
                 
                   
                     179
                  
                   
                     14
                  
                   
                     11
                  
                   
                     32041
                  
                
                 
                   
                     180
                  
                   
                     15
                  
                   
                     00
                  
                   
                     32400
                  
                
                 
                   
                     181
                  
                   
                     15
                  
                   
                     1
                  
                   
                     32761
                  
                
                 
                   
                     182
                  
                   
                     15
                  
                   
                     2
                  
                   
                     33124
                  
                
                 
                   
                     183
                  
                   
                     15
                  
                   
                     3
                  
                   
                     33489
                  
                
                 
                   
                     184
                  
                   
                     15
                  
                   
                     4
                  
                   
                     33856
                  
                
                 
                   
                     185
                  
                   
                     15
                  
                   
                     5
                  
                   
                     34025
                  
                
                 
                   
                     186
                  
                   
                     15
                  
                   
                     6
                  
                   
                     34596
                  
                
                 
                   
                     187
                  
                   
                     15
                  
                   
                     7
                  
                   
                     34969
                  
                
                 
                   
                     188
                  
                   
                     15
                  
                   
                     8
                  
                   
                     35344
                  
                
                 
                   
                     189
                  
                   
                     15
                  
                   
                     9
                  
                   
                     35721
                  
                
                 
                   
                     190
                  
                   
                     15
                  
                   
                     10
                  
                   
                     36100
                  
                
                 
                   
                     191
                  
                   
                     15
                  
                   
                     11
                  
                   
                     36481
                  
                
                 
                   
                     192
                  
                   
                     16
                  
                   
                     00
                  
                   
                     36864
                  
                
                 
                   
                     193
                  
                   
                     16
                  
                   
                     1
                  
                   
                     37249
                  
                
                 
                   
                     194
                  
                   
                     16
                  
                   
                     2
                  
                   
                     37636
                  
                
                 
                   
                     195
                  
                   
                     16
                  
                   
                     3
                  
                   
                     38025
                  
                
                 
                   
                     196
                  
                   
                     16
                  
                   
                     4
                  
                   
                     38416
                  
                
                 
                   
                     197
                  
                   
                     16
                  
                   
                     5
                  
                   
                     38809
                  
                
                 
                   
                     198
                  
                   
                     16
                  
                   
                     6
                  
                   
                     39204
                  
                
                 
                   
                     199
                  
                   
                     16
                  
                   
                     7
                  
                   
                     39601
                  
                
                 
                   
                     200
                  
                   
                     16
                  
                   
                     8
                  
                   
                     40000
                  
                
                 
                   
                     201
                  
                   
                     16
                  
                   
                     9
                  
                   
                     40401
                  
                
                 
                   
                     202
                  
                   
                     16
                  
                   
                     10
                  
                   
                     40844
                  
                
                 
                   
                     203
                  
                   
                     16
                  
                   
                     11
                  
                   
                     41209
                  
                
                 
                   
                     204
                  
                   
                     17
                  
                   
                     00
                  
                   
                     41616
                  
                
                 
                   
                     205
                  
                   
                     17
                  
                   
                     1
                  
                   
                     42025
                  
                
                 
                   
                     206
                  
                   
                     17
                  
                   
                     2
                  
                   
                     42436
                  
                
                 
                   
                     207
                  
                   
                     17
                  
                   
                     3
                  
                   
                     42849
                  
                
                 
                   
                     208
                  
                   
                     17
                  
                   
                     4
                  
                   
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                     2
                  
                   
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                     3
                  
                   
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                     4
                  
                   
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                     5
                  
                   
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                     2
                  
                   
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                     3
                  
                   
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                     4
                  
                   
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                     5
                  
                   
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                     6
                  
                   
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                     2
                  
                   
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                     3
                  
                   
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                     4
                  
                   
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                     5
                  
                   
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                     7
                  
                   
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                     2
                  
                   
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                     3
                  
                   
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                     405
                  
                   
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                     4
                  
                   
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                     413
                  
                   
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                     414
                  
                   
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                     415
                  
                   
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                     419
                  
                   
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                     420
                  
                   
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                     0
                  
                   
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                     1
                  
                   
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                     3
                  
                   
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                     424
                  
                   
                     35
                  
                   
                     4
                  
                   
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                     425
                  
                   
                     35
                  
                   
                     5
                  
                   
                     180625
                  
                
                 
                   
                     426
                  
                   
                     35
                  
                   
                     6
                  
                   
                     181476
                  
                
                 
                   
                     427
                  
                   
                     35
                  
                   
                     7
                  
                   
                     182329
                  
                
                 
                   
                     428
                  
                   
                     35
                  
                   
                     8
                  
                   
                     183184
                  
                
                 
                   
                     429
                  
                   
                     35
                  
                   
                     9
                  
                   
                     184041
                  
                
                 
                   
                     430
                  
                   
                     35
                  
                   
                     10
                  
                   
                     184900
                  
                
                 
                   
                     431
                  
                   
                     35
                  
                   
                     11
                  
                   
                     185761
                  
                
                 
                   
                     432
                  
                   
                     36
                  
                   
                     0
                  
                   
                     186624
                  
                
                 
                   
                     433
                  
                   
                     36
                  
                   
                     1
                  
                   
                     187789
                  
                
                 
                   
                     434
                  
                   
                     36
                  
                   
                     2
                  
                   
                     188●56
                  
                
                 
                   
                     435
                  
                   
                     36
                  
                   
                     3
                  
                   
                     1898●5
                  
                
                 
                   
                     436
                  
                   
                     36
                  
                   
                     4
                  
                   
                     190096
                  
                
                 
                   
                     437
                  
                   
                     36
                  
                   
                     5
                  
                   
                     190960
                  
                
                 
                   
                     438
                  
                   
                     36
                  
                   
                     6
                  
                   
                     191044
                  
                
                 
                   
                     439
                  
                   
                     36
                  
                   
                     7
                  
                   
                     192721
                  
                
                 
                   
                     440
                  
                   
                     36
                  
                   
                     8
                  
                   
                     193600
                  
                
                 
                   
                     441
                  
                   
                     36
                  
                   
                     9
                  
                   
                     194481
                  
                
                 
                   
                     442
                  
                   
                     36
                  
                   
                     10
                  
                   
                     195364
                  
                
                 
                   
                     443
                  
                   
                     36
                  
                   
                     11
                  
                   
                     196249
                  
                
                 
                   
                     444
                  
                   
                     37
                  
                   
                     0
                  
                   
                     197136
                  
                
                 
                   
                     445
                  
                   
                     37
                  
                   
                     1
                  
                   
                     198025
                  
                
                 
                   
                     446
                  
                   
                     37
                  
                   
                     2
                  
                   
                     198916
                  
                
                 
                   
                     447
                  
                   
                     37
                  
                   
                     3
                  
                   
                     199809
                  
                
                 
                   
                     448
                  
                   
                     37
                  
                   
                     4
                  
                   
                     200704
                  
                
                 
                   
                     449
                  
                   
                     37
                  
                   
                     5
                  
                   
                     201601
                  
                
                 
                   
                     450
                  
                   
                     37
                  
                   
                     6
                  
                   
                     202509
                  
                
                 
                   
                     451
                  
                   
                     37
                  
                   
                     7
                  
                   
                     203401
                  
                
                 
                   
                     452
                  
                   
                     37
                  
                   
                     8
                  
                   
                     204304
                  
                
                 
                   
                     453
                  
                   
                     37
                  
                   
                     9
                  
                   
                     205●90
                  
                
                 
                   
                     454
                  
                   
                     37
                  
                   
                     10
                  
                   
                     206116
                  
                
                 
                   
                     455
                  
                   
                     37
                  
                   
                     11
                  
                   
                     2070●5
                  
                
                 
                   
                     456
                  
                   
                     38
                  
                   
                     0
                  
                   
                     207936
                  
                
                 
                   
                     457
                  
                   
                     38
                  
                   
                     1
                  
                   
                     208849
                  
                
                 
                   
                     458
                  
                   
                     38
                  
                   
                     2
                  
                   
                     209●64
                  
                
                 
                   
                     459
                  
                   
                     38
                  
                   
                     3
                  
                   
                     210681
                  
                
                 
                   
                     460
                  
                   
                     38
                  
                   
                     4
                  
                   
                     2116●0
                  
                
                 
                   
                     461
                  
                   
                     38
                  
                   
                     5
                  
                   
                     212521
                  
                
                 
                   
                     462
                  
                   
                     38
                  
                   
                     6
                  
                   
                     213444
                  
                
                 
                   
                     463
                  
                   
                     38
                  
                   
                     7
                  
                   
                     214369
                  
                
                 
                   
                     464
                  
                   
                     38
                  
                   
                     8
                  
                   
                     215296
                  
                
                 
                   
                     465
                  
                   
                     38
                  
                   
                     9
                  
                   
                     2162●5
                  
                
                 
                   
                     466
                  
                   
                     38
                  
                   
                     10
                  
                   
                     217156
                  
                
                 
                   
                     467
                  
                   
                     38
                  
                   
                     11
                  
                   
                     218089
                  
                
                 
                   
                     468
                  
                   
                     39
                  
                   
                     0
                  
                   
                     219024
                  
                
                 
                   
                     469
                  
                   
                     39
                  
                   
                     1
                  
                   
                     219961
                  
                
                 
                   
                     470
                  
                   
                     39
                  
                   
                     2
                  
                   
                     220●●0
                  
                
                 
                   
                     471
                  
                   
                     39
                  
                   
                     3
                  
                   
                     221841
                  
                
                 
                   
                     472
                  
                   
                     39
                  
                   
                     4
                  
                   
                     222784
                  
                
                 
                   
                     473
                  
                   
                     39
                  
                   
                     5
                  
                   
                     223729
                  
                
                 
                   
                     474
                  
                   
                     39
                  
                   
                     6
                  
                   
                     224676
                  
                
                 
                   
                     475
                  
                   
                     39
                  
                   
                     7
                  
                   
                     225625
                  
                
                 
                   
                     476
                  
                   
                     39
                  
                   
                     8
                  
                   
                     226576
                  
                
                 
                   
                     477
                  
                   
                     39
                  
                   
                     9
                  
                   
                     227429
                  
                
                 
                   
                     478
                  
                   
                     39
                  
                   
                     10
                  
                   
                     228484
                  
                
                 
                   
                     479
                  
                   
                     39
                  
                   
                     11
                  
                   
                     229141
                  
                
                 
                   
                     480
                  
                   
                     40
                  
                   
                     0
                  
                   
                     2304●●
                  
                
                 
                   
                     
                     481
                  
                   
                     40
                  
                   
                     1
                  
                   
                     231361
                  
                
                 
                   
                     482
                  
                   
                     40
                  
                   
                     2
                  
                   
                     232324
                  
                
                 
                   
                     483
                  
                   
                     40
                  
                   
                     3
                  
                   
                     233289
                  
                
                 
                   
                     484
                  
                   
                     40
                  
                   
                     4
                  
                   
                     234216
                  
                
                 
                   
                     485
                  
                   
                     40
                  
                   
                     5
                  
                   
                     235225
                  
                
                 
                   
                     486
                  
                   
                     40
                  
                   
                     6
                  
                   
                     236196
                  
                
                 
                   
                     487
                  
                   
                     40
                  
                   
                     7
                  
                   
                     237●69
                  
                
                 
                   
                     488
                  
                   
                     40
                  
                   
                     8
                  
                   
                     238144
                  
                
                 
                   
                     489
                  
                   
                     40
                  
                   
                     9
                  
                   
                     239121
                  
                
                 
                   
                     490
                  
                   
                     40
                  
                   
                     10
                  
                   
                     240100
                  
                
                 
                   
                     491
                  
                   
                     40
                  
                   
                     11
                  
                   
                     240981
                  
                
                 
                   
                     492
                  
                   
                     41
                  
                   
                     0
                  
                   
                     2420●4
                  
                
                 
                   
                     493
                  
                   
                     41
                  
                   
                     1
                  
                   
                     243049
                  
                
                 
                   
                     494
                  
                   
                     41
                  
                   
                     2
                  
                   
                     244036
                  
                
                 
                   
                     495
                  
                   
                     41
                  
                   
                     3
                  
                   
                     245025
                  
                
                 
                   
                     496
                  
                   
                     41
                  
                   
                     4
                  
                   
                     246016
                  
                
                 
                   
                     497
                  
                   
                     41
                  
                   
                     5
                  
                   
                     246509
                  
                
                 
                   
                     498
                  
                   
                     41
                  
                   
                     6
                  
                   
                     247004
                  
                
                 
                   
                     499
                  
                   
                     41
                  
                   
                     7
                  
                   
                     249001
                  
                
                 
                   
                     500
                  
                   
                     41
                  
                   
                     8
                  
                   
                     250000
                  
                
                 
                   
                     501
                  
                   
                     41
                  
                   
                     9
                  
                   
                     251001
                  
                
                 
                   
                     502
                  
                   
                     41
                  
                   
                     10
                  
                   
                     252004
                  
                
                 
                   
                     503
                  
                   
                     41
                  
                   
                     11
                  
                   
                     253009
                  
                
                 
                   
                     504
                  
                   
                     42
                  
                   
                     0
                  
                   
                     254016
                  
                
                 
                   
                     505
                  
                   
                     42
                  
                   
                     1
                  
                   
                     255025
                  
                
                 
                   
                     506
                  
                   
                     42
                  
                   
                     2
                  
                   
                     256036
                  
                
                 
                   
                     507
                  
                   
                     42
                  
                   
                     3
                  
                   
                     257049
                  
                
                 
                   
                     508
                  
                   
                     42
                  
                   
                     4
                  
                   
                     258064
                  
                
                 
                   
                     509
                  
                   
                     42
                  
                   
                     5
                  
                   
                     269081
                  
                
                 
                   
                     510
                  
                   
                     42
                  
                   
                     6
                  
                   
                     260100
                  
                
                 
                   
                     511
                  
                   
                     42
                  
                   
                     7
                  
                   
                     261121
                  
                
                 
                   
                     512
                  
                   
                     42
                  
                   
                     8
                  
                   
                     262144
                  
                
                 
                   
                     513
                  
                   
                     42
                  
                   
                     9
                  
                   
                     363169
                  
                
                 
                   
                     514
                  
                   
                     42
                  
                   
                     10
                  
                   
                     264196
                  
                
                 
                   
                     515
                  
                   
                     42
                  
                   
                     11
                  
                   
                     265225
                  
                
                 
                   
                     516
                  
                   
                     43
                  
                   
                     0
                  
                   
                     266256
                  
                
                 
                   
                     517
                  
                   
                     43
                  
                   
                     1
                  
                   
                     267289
                  
                
                 
                   
                     518
                  
                   
                     43
                  
                   
                     2
                  
                   
                     268324
                  
                
                 
                   
                     519
                  
                   
                     43
                  
                   
                     3
                  
                   
                     269361
                  
                
                 
                   
                     520
                  
                   
                     43
                  
                   
                     4
                  
                   
                     270400
                  
                
                 
                   
                     521
                  
                   
                     43
                  
                   
                     5
                  
                   
                     271441
                  
                
                 
                   
                     522
                  
                   
                     43
                  
                   
                     6
                  
                   
                     272448
                  
                
                 
                   
                     523
                  
                   
                     43
                  
                   
                     7
                  
                   
                     273529
                  
                
                 
                   
                     524
                  
                   
                     43
                  
                   
                     8
                  
                   
                     274576
                  
                
                 
                   
                     525
                  
                   
                     43
                  
                   
                     9
                  
                   
                     275625
                  
                
                 
                   
                     526
                  
                   
                     43
                  
                   
                     10
                  
                   
                     276676
                  
                
                 
                   
                     527
                  
                   
                     43
                  
                   
                     11
                  
                   
                     2777●9
                  
                
                 
                   
                     528
                  
                   
                     44
                  
                   
                     0
                  
                   
                     278784
                  
                
                 
                   
                     529
                  
                   
                     44
                  
                   
                     1
                  
                   
                     280●41
                  
                
                 
                   
                     530
                  
                   
                     44
                  
                   
                     2
                  
                   
                     280900
                  
                
                 
                   
                     531
                  
                   
                     44
                  
                   
                     3
                  
                   
                     281961
                  
                
                 
                   
                     532
                  
                   
                     44
                  
                   
                     4
                  
                   
                     284●24
                  
                
                 
                   
                     533
                  
                   
                     44
                  
                   
                     5
                  
                   
                     2870●9
                  
                
                 
                   
                     534
                  
                   
                     44
                  
                   
                     6
                  
                   
                     285156
                  
                
                 
                   
                     535
                  
                   
                     44
                  
                   
                     7
                  
                   
                     286225
                  
                
                 
                   
                     536
                  
                   
                     44
                  
                   
                     8
                  
                   
                     287296
                  
                
                 
                   
                     537
                  
                   
                     44
                  
                   
                     9
                  
                   
                     288369
                  
                
                 
                   
                     538
                  
                   
                     44
                  
                   
                     10
                  
                   
                     290444
                  
                
                 
                   
                     539
                  
                   
                     44
                  
                   
                     11
                  
                   
                     290521
                  
                
                 
                   
                     540
                  
                   
                     45
                  
                   
                     0
                  
                   
                     291600
                  
                
                 
                   
                     541
                  
                   
                     45
                  
                   
                     1
                  
                   
                     292681
                  
                
                 
                   
                     542
                  
                   
                     45
                  
                   
                     2
                  
                   
                     293764
                  
                
                 
                   
                     543
                  
                   
                     45
                  
                   
                     3
                  
                   
                     294849
                  
                
                 
                   
                     544
                  
                   
                     45
                  
                   
                     4
                  
                   
                     295936
                  
                
                 
                   
                     545
                  
                   
                     45
                  
                   
                     5
                  
                   
                     297025
                  
                
                 
                   
                     546
                  
                   
                     45
                  
                   
                     6
                  
                   
                     298016
                  
                
                 
                   
                     547
                  
                   
                     45
                  
                   
                     7
                  
                   
                     299209
                  
                
                 
                   
                     548
                  
                   
                     45
                  
                   
                     8
                  
                   
                     300304
                  
                
                 
                   
                     549
                  
                   
                     45
                  
                   
                     9
                  
                   
                     301401
                  
                
                 
                   
                     550
                  
                   
                     45
                  
                   
                     10
                  
                   
                     302500
                  
                
                 
                   
                     551
                  
                   
                     45
                  
                   
                     11
                  
                   
                     303601
                  
                
                 
                   
                     552
                  
                   
                     46
                  
                   
                     0
                  
                   
                     304704
                  
                
                 
                   
                     553
                  
                   
                     46
                  
                   
                     1
                  
                   
                     305809
                  
                
                 
                   
                     554
                  
                   
                     46
                  
                   
                     2
                  
                   
                     306916
                  
                
                 
                   
                     555
                  
                   
                     46
                  
                   
                     3
                  
                   
                     308025
                  
                
                 
                   
                     556
                  
                   
                     46
                  
                   
                     4
                  
                   
                     309136
                  
                
                 
                   
                     557
                  
                   
                     46
                  
                   
                     5
                  
                   
                     310●49
                  
                
                 
                   
                     558
                  
                   
                     46
                  
                   
                     6
                  
                   
                     311364
                  
                
                 
                   
                     559
                  
                   
                     46
                  
                   
                     7
                  
                   
                     312481
                  
                
                 
                   
                     560
                  
                   
                     46
                  
                   
                     8
                  
                   
                     313600
                  
                
                 
                   
                     561
                  
                   
                     46
                  
                   
                     9
                  
                   
                     314721
                  
                
                 
                   
                     562
                  
                   
                     46
                  
                   
                     10
                  
                   
                     315844
                  
                
                 
                   
                     563
                  
                   
                     46
                  
                   
                     11
                  
                   
                     316969
                  
                
                 
                   
                     564
                  
                   
                     47
                  
                   
                     0
                  
                   
                     318096
                  
                
                 
                   
                     565
                  
                   
                     47
                  
                   
                     1
                  
                   
                     319225
                  
                
                 
                   
                     566
                  
                   
                     47
                  
                   
                     2
                  
                   
                     320356
                  
                
                 
                   
                     567
                  
                   
                     47
                  
                   
                     3
                  
                   
                     321489
                  
                
                 
                   
                     568
                  
                   
                     47
                  
                   
                     4
                  
                   
                     322624
                  
                
                 
                   
                     569
                  
                   
                     47
                  
                   
                     5
                  
                   
                     323761
                  
                
                 
                   
                     570
                  
                   
                     47
                  
                   
                     6
                  
                   
                     324900
                  
                
                 
                   
                     571
                  
                   
                     47
                  
                   
                     7
                  
                   
                     326041
                  
                
                 
                   
                     572
                  
                   
                     47
                  
                   
                     8
                  
                   
                     327184
                  
                
                 
                   
                     573
                  
                   
                     47
                  
                   
                     9
                  
                   
                     328329
                  
                
                 
                   
                     574
                  
                   
                     47
                  
                   
                     10
                  
                   
                     330276
                  
                
                 
                   
                     575
                  
                   
                     47
                  
                   
                     11
                  
                   
                     330625
                  
                
                 
                   
                     576
                  
                   
                     48
                  
                   
                     0
                  
                   
                     331776
                  
                
                 
                   
                     577
                  
                   
                     48
                  
                   
                     1
                  
                   
                     332929
                  
                
                 
                   
                     578
                  
                   
                     48
                  
                   
                     2
                  
                   
                     384048
                  
                
                 
                   
                     579
                  
                   
                     48
                  
                   
                     3
                  
                   
                     335241
                  
                
                 
                   
                     580
                  
                   
                     48
                  
                   
                     4
                  
                   
                     336400
                  
                
                 
                   
                     581
                  
                   
                     48
                  
                   
                     5
                  
                   
                     337561
                  
                
                 
                   
                     582
                  
                   
                     48
                  
                   
                     6
                  
                   
                     338724
                  
                
                 
                   
                     583
                  
                   
                     48
                  
                   
                     7
                  
                   
                     340089
                  
                
                 
                   
                     584
                  
                   
                     48
                  
                   
                     8
                  
                   
                     341056
                  
                
                 
                   
                     585
                  
                   
                     48
                  
                   
                     9
                  
                   
                     3422●5
                  
                
                 
                   
                     586
                  
                   
                     48
                  
                   
                     10
                  
                   
                     343396
                  
                
                 
                   
                     587
                  
                   
                     48
                  
                   
                     11
                  
                   
                     344669
                  
                
                 
                   
                     588
                  
                   
                     49
                  
                   
                     0
                  
                   
                     345744
                  
                
                 
                   
                     589
                  
                   
                     49
                  
                   
                     1
                  
                   
                     346921
                  
                
                 
                   
                     590
                  
                   
                     49
                  
                   
                     2
                  
                   
                     348100
                  
                
                 
                   
                     591
                  
                   
                     49
                  
                   
                     3
                  
                   
                     349281
                  
                
                 
                   
                     592
                  
                   
                     49
                  
                   
                     4
                  
                   
                     350464
                  
                
                 
                   
                     593
                  
                   
                     49
                  
                   
                     5
                  
                   
                     351649
                  
                
                 
                   
                     594
                  
                   
                     49
                  
                   
                     6
                  
                   
                     352836
                  
                
                 
                   
                     595
                  
                   
                     49
                  
                   
                     7
                  
                   
                     353925
                  
                
                 
                   
                     596
                  
                   
                     49
                  
                   
                     8
                  
                   
                     354216
                  
                
                 
                   
                     597
                  
                   
                     49
                  
                   
                     9
                  
                   
                     355409
                  
                
                 
                   
                     598
                  
                   
                     49
                  
                   
                     10
                  
                   
                     356●04
                  
                
                 
                   
                     599
                  
                   
                     49
                  
                   
                     11
                  
                   
                     358801
                  
                
                 
                   
                     600
                  
                   
                     50
                  
                   
                     0
                  
                   
                     360000
                  
                
                 
                   
                     
                     601
                  
                   
                     50
                  
                   
                     1
                  
                   
                     361201
                  
                
                 
                   
                     602
                  
                   
                     50
                  
                   
                     2
                  
                   
                     362404
                  
                
                 
                   
                     603
                  
                   
                     50
                  
                   
                     3
                  
                   
                     363609
                  
                
                 
                   
                     604
                  
                   
                     50
                  
                   
                     4
                  
                   
                     364816
                  
                
                 
                   
                     605
                  
                   
                     50
                  
                   
                     5
                  
                   
                     366025
                  
                
                 
                   
                     606
                  
                   
                     50
                  
                   
                     6
                  
                   
                     367236
                  
                
                 
                   
                     607
                  
                   
                     50
                  
                   
                     7
                  
                   
                     368449
                  
                
                 
                   
                     608
                  
                   
                     50
                  
                   
                     8
                  
                   
                     369664
                  
                
                 
                   
                     609
                  
                   
                     50
                  
                   
                     9
                  
                   
                     370881
                  
                
                 
                   
                     610
                  
                   
                     50
                  
                   
                     10
                  
                   
                     372100
                  
                
                 
                   
                     611
                  
                   
                     50
                  
                   
                     11
                  
                   
                     373321
                  
                
                 
                   
                     612
                  
                   
                     51
                  
                   
                     0
                  
                   
                     374544
                  
                
                 
                   
                     613
                  
                   
                     51
                  
                   
                     1
                  
                   
                     375769
                  
                
                 
                   
                     614
                  
                   
                     51
                  
                   
                     2
                  
                   
                     376996
                  
                
                 
                   
                     615
                  
                   
                     51
                  
                   
                     3
                  
                   
                     378225
                  
                
                 
                   
                     616
                  
                   
                     51
                  
                   
                     4
                  
                   
                     379456
                  
                
                 
                   
                     617
                  
                   
                     51
                  
                   
                     5
                  
                   
                     380689
                  
                
                 
                   
                     618
                  
                   
                     51
                  
                   
                     6
                  
                   
                     381924
                  
                
                 
                   
                     619
                  
                   
                     51
                  
                   
                     7
                  
                   
                     383161
                  
                
                 
                   
                     620
                  
                   
                     51
                  
                   
                     8
                  
                   
                     384400
                  
                
                 
                   
                     621
                  
                   
                     51
                  
                   
                     9
                  
                   
                     385641
                  
                
                 
                   
                     622
                  
                   
                     51
                  
                   
                     10
                  
                   
                     386884
                  
                
                 
                   
                     623
                  
                   
                     51
                  
                   
                     11
                  
                   
                     388129
                  
                
                 
                   
                     624
                  
                   
                     52
                  
                   
                     0
                  
                   
                     389376
                  
                
                 
                   
                     625
                  
                   
                     52
                  
                   
                     1
                  
                   
                     390625
                  
                
                 
                   
                     626
                  
                   
                     52
                  
                   
                     2
                  
                   
                     391876
                  
                
                 
                   
                     627
                  
                   
                     52
                  
                   
                     3
                  
                   
                     393129
                  
                
                 
                   
                     628
                  
                   
                     52
                  
                   
                     4
                  
                   
                     394384
                  
                
                 
                   
                     629
                  
                   
                     52
                  
                   
                     5
                  
                   
                     395641
                  
                
                 
                   
                     630
                  
                   
                     52
                  
                   
                     6
                  
                   
                     396900
                  
                
                 
                   
                     631
                  
                   
                     52
                  
                   
                     7
                  
                   
                     398161
                  
                
                 
                   
                     632
                  
                   
                     52
                  
                   
                     8
                  
                   
                     399424
                  
                
                 
                   
                     633
                  
                   
                     52
                  
                   
                     9
                  
                   
                     400489
                  
                
                 
                   
                     634
                  
                   
                     52
                  
                   
                     10
                  
                   
                     401956
                  
                
                 
                   
                     635
                  
                   
                     52
                  
                   
                     11
                  
                   
                     403225
                  
                
                 
                   
                     636
                  
                   
                     53
                  
                   
                     0
                  
                   
                     404496
                  
                
                 
                   
                     637
                  
                   
                     53
                  
                   
                     1
                  
                   
                     405769
                  
                
                 
                   
                     638
                  
                   
                     53
                  
                   
                     2
                  
                   
                     407044
                  
                
                 
                   
                     639
                  
                   
                     53
                  
                   
                     3
                  
                   
                     408321
                  
                
                 
                   
                     640
                  
                   
                     53
                  
                   
                     4
                  
                   
                     409600
                  
                
                 
                   
                     641
                  
                   
                     53
                  
                   
                     5
                  
                   
                     410881
                  
                
                 
                   
                     642
                  
                   
                     53
                  
                   
                     6
                  
                   
                     412164
                  
                
                 
                   
                     643
                  
                   
                     53
                  
                   
                     7
                  
                   
                     413449
                  
                
                 
                   
                     644
                  
                   
                     53
                  
                   
                     8
                  
                   
                     414736
                  
                
                 
                   
                     645
                  
                   
                     53
                  
                   
                     9
                  
                   
                     416025
                  
                
                 
                   
                     646
                  
                   
                     53
                  
                   
                     10
                  
                   
                     417316
                  
                
                 
                   
                     647
                  
                   
                     53
                  
                   
                     11
                  
                   
                     418609
                  
                
                 
                   
                     648
                  
                   
                     54
                  
                   
                     0
                  
                   
                     429904
                  
                
                 
                   
                     649
                  
                   
                     54
                  
                   
                     1
                  
                   
                     421201
                  
                
                 
                   
                     650
                  
                   
                     54
                  
                   
                     2
                  
                   
                     422500
                  
                
                 
                   
                     651
                  
                   
                     54
                  
                   
                     3
                  
                   
                     423801
                  
                
                 
                   
                     652
                  
                   
                     54
                  
                   
                     4
                  
                   
                     425104
                  
                
                 
                   
                     653
                  
                   
                     54
                  
                   
                     5
                  
                   
                     426403
                  
                
                 
                   
                     654
                  
                   
                     54
                  
                   
                     6
                  
                   
                     427716
                  
                
                 
                   
                     655
                  
                   
                     54
                  
                   
                     7
                  
                   
                     429025
                  
                
                 
                   
                     656
                  
                   
                     54
                  
                   
                     8
                  
                   
                     430336
                  
                
                 
                   
                     657
                  
                   
                     54
                  
                   
                     9
                  
                   
                     431449
                  
                
                 
                   
                     658
                  
                   
                     54
                  
                   
                     10
                  
                   
                     432969
                  
                
                 
                   
                     659
                  
                   
                     54
                  
                   
                     11
                  
                   
                     434181
                  
                
                 
                   
                     660
                  
                   
                     55
                  
                   
                     0
                  
                   
                     435600
                  
                
                 
                   
                     661
                  
                   
                     55
                  
                   
                     1
                  
                   
                     436921
                  
                
                 
                   
                     662
                  
                   
                     55
                  
                   
                     2
                  
                   
                     438244
                  
                
                 
                   
                     663
                  
                   
                     55
                  
                   
                     3
                  
                   
                     439569
                  
                
                 
                   
                     664
                  
                   
                     55
                  
                   
                     4
                  
                   
                     440896
                  
                
                 
                   
                     665
                  
                   
                     55
                  
                   
                     5
                  
                   
                     442225
                  
                
                 
                   
                     666
                  
                   
                     55
                  
                   
                     6
                  
                   
                     443556
                  
                
                 
                   
                     667
                  
                   
                     55
                  
                   
                     7
                  
                   
                     444889
                  
                
                 
                   
                     668
                  
                   
                     55
                  
                   
                     8
                  
                   
                     446224
                  
                
                 
                   
                     669
                  
                   
                     55
                  
                   
                     9
                  
                   
                     447561
                  
                
                 
                   
                     670
                  
                   
                     55
                  
                   
                     10
                  
                   
                     448900
                  
                
                 
                   
                     671
                  
                   
                     55
                  
                   
                     11
                  
                   
                     450241
                  
                
                 
                   
                     672
                  
                   
                     56
                  
                   
                     0
                  
                   
                     451544
                  
                
                 
                   
                     673
                  
                   
                     56
                  
                   
                     1
                  
                   
                     452829
                  
                
                 
                   
                     674
                  
                   
                     56
                  
                   
                     2
                  
                   
                     454276
                  
                
                 
                   
                     675
                  
                   
                     56
                  
                   
                     3
                  
                   
                     455625
                  
                
                 
                   
                     676
                  
                   
                     56
                  
                   
                     4
                  
                   
                     456976
                  
                
                 
                   
                     677
                  
                   
                     56
                  
                   
                     5
                  
                   
                     458329
                  
                
                 
                   
                     678
                  
                   
                     56
                  
                   
                     6
                  
                   
                     459684
                  
                
                 
                   
                     679
                  
                   
                     56
                  
                   
                     7
                  
                   
                     461041
                  
                
                 
                   
                     680
                  
                   
                     56
                  
                   
                     8
                  
                   
                     462400
                  
                
                 
                   
                     681
                  
                   
                     56
                  
                   
                     9
                  
                   
                     463761
                  
                
                 
                   
                     682
                  
                   
                     56
                  
                   
                     10
                  
                   
                     465124
                  
                
                 
                   
                     683
                  
                   
                     56
                  
                   
                     11
                  
                   
                     466489
                  
                
                 
                   
                     684
                  
                   
                     57
                  
                   
                     0
                  
                   
                     467856
                  
                
                 
                   
                     685
                  
                   
                     57
                  
                   
                     1
                  
                   
                     469225
                  
                
                 
                   
                     686
                  
                   
                     57
                  
                   
                     2
                  
                   
                     470596
                  
                
                 
                   
                     687
                  
                   
                     57
                  
                   
                     3
                  
                   
                     471939
                  
                
                 
                   
                     688
                  
                   
                     57
                  
                   
                     4
                  
                   
                     473344
                  
                
                 
                   
                     689
                  
                   
                     57
                  
                   
                     5
                  
                   
                     475721
                  
                
                 
                   
                     690
                  
                   
                     57
                  
                   
                     6
                  
                   
                     476700
                  
                
                 
                   
                     691
                  
                   
                     57
                  
                   
                     7
                  
                   
                     477841
                  
                
                 
                   
                     692
                  
                   
                     57
                  
                   
                     8
                  
                   
                     478864
                  
                
                 
                   
                     693
                  
                   
                     57
                  
                   
                     9
                  
                   
                     480269
                  
                
                 
                   
                     694
                  
                   
                     57
                  
                   
                     10
                  
                   
                     481636
                  
                
                 
                   
                     695
                  
                   
                     57
                  
                   
                     11
                  
                   
                     482825
                  
                
                 
                   
                     696
                  
                   
                     58
                  
                   
                     0
                  
                   
                     484416
                  
                
                 
                   
                     697
                  
                   
                     58
                  
                   
                     1
                  
                   
                     485809
                  
                
                 
                   
                     698
                  
                   
                     58
                  
                   
                     2
                  
                   
                     487204
                  
                
                 
                   
                     699
                  
                   
                     58
                  
                   
                     3
                  
                   
                     488601
                  
                
                 
                   
                     700
                  
                   
                     58
                  
                   
                     4
                  
                   
                     490000
                  
                
                 
                   
                     701
                  
                   
                     58
                  
                   
                     5
                  
                   
                     491401
                  
                
                 
                   
                     702
                  
                   
                     58
                  
                   
                     6
                  
                   
                     492804
                  
                
                 
                   
                     703
                  
                   
                     58
                  
                   
                     7
                  
                   
                     494209
                  
                
                 
                   
                     704
                  
                   
                     58
                  
                   
                     8
                  
                   
                     495616
                  
                
                 
                   
                     705
                  
                   
                     58
                  
                   
                     9
                  
                   
                     497025
                  
                
                 
                   
                     706
                  
                   
                     58
                  
                   
                     10
                  
                   
                     498436
                  
                
                 
                   
                     707
                  
                   
                     58
                  
                   
                     11
                  
                   
                     498849
                  
                
                 
                   
                     708
                  
                   
                     59
                  
                   
                     0
                  
                   
                     501264
                  
                
                 
                   
                     709
                  
                   
                     59
                  
                   
                     1
                  
                   
                     502681
                  
                
                 
                   
                     710
                  
                   
                     59
                  
                   
                     2
                  
                   
                     504100
                  
                
                 
                   
                     711
                  
                   
                     59
                  
                   
                     3
                  
                   
                     505521
                  
                
                 
                   
                     712
                  
                   
                     59
                  
                   
                     4
                  
                   
                     506944
                  
                
                 
                   
                     713
                  
                   
                     59
                  
                   
                     5
                  
                   
                     508669
                  
                
                 
                   
                     714
                  
                   
                     59
                  
                   
                     6
                  
                   
                     509796
                  
                
                 
                   
                     715
                  
                   
                     59
                  
                   
                     7
                  
                   
                     511225
                  
                
                 
                   
                     716
                  
                   
                     59
                  
                   
                     8
                  
                   
                     512656
                  
                
                 
                   
                     717
                  
                   
                     59
                  
                   
                     9
                  
                   
                     514089
                  
                
                 
                   
                     718
                  
                   
                     59
                  
                   
                     10
                  
                   
                     515824
                  
                
                 
                   
                     719
                  
                   
                     59
                  
                   
                     11
                  
                   
                     516961
                  
                
                 
                   
                     720
                  
                   
                     60
                  
                   
                     0
                  
                   
                     518400
                  
                
                 
                   
                     
                     721
                  
                   
                     60
                  
                   
                     1
                  
                   
                     519841
                  
                
                 
                   
                     722
                  
                   
                     60
                  
                   
                     2
                  
                   
                     521284
                  
                
                 
                   
                     723
                  
                   
                     60
                  
                   
                     3
                  
                   
                     522729
                  
                
                 
                   
                     724
                  
                   
                     60
                  
                   
                     4
                  
                   
                     524176
                  
                
                 
                   
                     725
                  
                   
                     60
                  
                   
                     5
                  
                   
                     525625
                  
                
                 
                   
                     726
                  
                   
                     60
                  
                   
                     6
                  
                   
                     526976
                  
                
                 
                   
                     727
                  
                   
                     60
                  
                   
                     7
                  
                   
                     528529
                  
                
                 
                   
                     728
                  
                   
                     60
                  
                   
                     8
                  
                   
                     529984
                  
                
                 
                   
                     729
                  
                   
                     60
                  
                   
                     9
                  
                   
                     521421
                  
                
                 
                   
                     730
                  
                   
                     60
                  
                   
                     10
                  
                   
                     522900
                  
                
                 
                   
                     731
                  
                   
                     60
                  
                   
                     11
                  
                   
                     524361
                  
                
                 
                   
                     732
                  
                   
                     61
                  
                   
                     0
                  
                   
                     535844
                  
                
                 
                   
                     733
                  
                   
                     61
                  
                   
                     1
                  
                   
                     537289
                  
                
                 
                   
                     734
                  
                   
                     61
                  
                   
                     2
                  
                   
                     538656
                  
                
                 
                   
                     735
                  
                   
                     61
                  
                   
                     3
                  
                   
                     540225
                  
                
                 
                   
                     736
                  
                   
                     61
                  
                   
                     4
                  
                   
                     541696
                  
                
                 
                   
                     737
                  
                   
                     61
                  
                   
                     5
                  
                   
                     543169
                  
                
                 
                   
                     738
                  
                   
                     61
                  
                   
                     6
                  
                   
                     544644
                  
                
                 
                   
                     739
                  
                   
                     61
                  
                   
                     7
                  
                   
                     546031
                  
                
                 
                   
                     740
                  
                   
                     61
                  
                   
                     8
                  
                   
                     547600
                  
                
                 
                   
                     741
                  
                   
                     61
                  
                   
                     9
                  
                   
                     549081
                  
                
                 
                   
                     742
                  
                   
                     61
                  
                   
                     10
                  
                   
                     550564
                  
                
                 
                   
                     743
                  
                   
                     61
                  
                   
                     11
                  
                   
                     552049
                  
                
                 
                   
                     744
                  
                   
                     62
                  
                   
                     0
                  
                   
                     553436
                  
                
                 
                   
                     745
                  
                   
                     62
                  
                   
                     1
                  
                   
                     555025
                  
                
                 
                   
                     746
                  
                   
                     62
                  
                   
                     2
                  
                   
                     556516
                  
                
                 
                   
                     747
                  
                   
                     62
                  
                   
                     3
                  
                   
                     558009
                  
                
                 
                   
                     748
                  
                   
                     62
                  
                   
                     4
                  
                   
                     559504
                  
                
                 
                   
                     749
                  
                   
                     62
                  
                   
                     5
                  
                   
                     561001
                  
                
                 
                   
                     750
                  
                   
                     62
                  
                   
                     6
                  
                   
                     562500
                  
                
                 
                   
                     751
                  
                   
                     62
                  
                   
                     7
                  
                   
                     564001
                  
                
                 
                   
                     752
                  
                   
                     62
                  
                   
                     8
                  
                   
                     565504
                  
                
                 
                   
                     753
                  
                   
                     62
                  
                   
                     9
                  
                   
                     567009
                  
                
                 
                   
                     754
                  
                   
                     62
                  
                   
                     10
                  
                   
                     568516
                  
                
                 
                   
                     755
                  
                   
                     62
                  
                   
                     11
                  
                   
                     570025
                  
                
                 
                   
                     756
                  
                   
                     63
                  
                   
                     0
                  
                   
                     571536
                  
                
                 
                   
                     757
                  
                   
                     63
                  
                   
                     1
                  
                   
                     573049
                  
                
                 
                   
                     758
                  
                   
                     63
                  
                   
                     2
                  
                   
                     574564
                  
                
                 
                   
                     759
                  
                   
                     63
                  
                   
                     3
                  
                   
                     576081
                  
                
                 
                   
                     760
                  
                   
                     63
                  
                   
                     4
                  
                   
                     577600
                  
                
                 
                   
                     761
                  
                   
                     63
                  
                   
                     5
                  
                   
                     579121
                  
                
                 
                   
                     762
                  
                   
                     63
                  
                   
                     6
                  
                   
                     580644
                  
                
                 
                   
                     763
                  
                   
                     63
                  
                   
                     7
                  
                   
                     582169
                  
                
                 
                   
                     764
                  
                   
                     63
                  
                   
                     8
                  
                   
                     583696
                  
                
                 
                   
                     765
                  
                   
                     63
                  
                   
                     9
                  
                   
                     585225
                  
                
                 
                   
                     766
                  
                   
                     63
                  
                   
                     10
                  
                   
                     586756
                  
                
                 
                   
                     767
                  
                   
                     63
                  
                   
                     11
                  
                   
                     588289
                  
                
                 
                   
                     768
                  
                   
                     64
                  
                   
                     0
                  
                   
                     589824
                  
                
                 
                   
                     769
                  
                   
                     64
                  
                   
                     1
                  
                   
                     591361
                  
                
                 
                   
                     770
                  
                   
                     64
                  
                   
                     2
                  
                   
                     592900
                  
                
                 
                   
                     771
                  
                   
                     64
                  
                   
                     3
                  
                   
                     594441
                  
                
                 
                   
                     772
                  
                   
                     64
                  
                   
                     4
                  
                   
                     595984
                  
                
                 
                   
                     773
                  
                   
                     64
                  
                   
                     5
                  
                   
                     597529
                  
                
                 
                   
                     774
                  
                   
                     64
                  
                   
                     6
                  
                   
                     599076
                  
                
                 
                   
                     775
                  
                   
                     64
                  
                   
                     7
                  
                   
                     600625
                  
                
                 
                   
                     776
                  
                   
                     64
                  
                   
                     8
                  
                   
                     602176
                  
                
                 
                   
                     777
                  
                   
                     64
                  
                   
                     9
                  
                   
                     604729
                  
                
                 
                   
                     778
                  
                   
                     64
                  
                   
                     10
                  
                   
                     606284
                  
                
                 
                   
                     779
                  
                   
                     64
                  
                   
                     11
                  
                   
                     607841
                  
                
                 
                   
                     780
                  
                   
                     65
                  
                   
                     0
                  
                   
                     608400
                  
                
                 
                   
                     781
                  
                   
                     65
                  
                   
                     1
                  
                   
                     609961
                  
                
                 
                   
                     782
                  
                   
                     65
                  
                   
                     2
                  
                   
                     611524
                  
                
                 
                   
                     783
                  
                   
                     95
                  
                   
                     3
                  
                   
                     613099
                  
                
                 
                   
                     784
                  
                   
                     65
                  
                   
                     4
                  
                   
                     614656
                  
                
                 
                   
                     785
                  
                   
                     65
                  
                   
                     5
                  
                   
                     616225
                  
                
                 
                   
                     786
                  
                   
                     65
                  
                   
                     6
                  
                   
                     617796
                  
                
                 
                   
                     787
                  
                   
                     65
                  
                   
                     7
                  
                   
                     619369
                  
                
                 
                   
                     788
                  
                   
                     65
                  
                   
                     8
                  
                   
                     620944
                  
                
                 
                   
                     789
                  
                   
                     65
                  
                   
                     9
                  
                   
                     622521
                  
                
                 
                   
                     790
                  
                   
                     65
                  
                   
                     10
                  
                   
                     624100
                  
                
                 
                   
                     791
                  
                   
                     65
                  
                   
                     11
                  
                   
                     625681
                  
                
                 
                   
                     792
                  
                   
                     66
                  
                   
                     0
                  
                   
                     627964
                  
                
                 
                   
                     793
                  
                   
                     66
                  
                   
                     1
                  
                   
                     628849
                  
                
                 
                   
                     794
                  
                   
                     66
                  
                   
                     2
                  
                   
                     630466
                  
                
                 
                   
                     795
                  
                   
                     66
                  
                   
                     3
                  
                   
                     632125
                  
                
                 
                   
                     796
                  
                   
                     66
                  
                   
                     4
                  
                   
                     633616
                  
                
                 
                   
                     797
                  
                   
                     66
                  
                   
                     5
                  
                   
                     635209
                  
                
                 
                   
                     798
                  
                   
                     66
                  
                   
                     6
                  
                   
                     637404
                  
                
                 
                   
                     799
                  
                   
                     66
                  
                   
                     7
                  
                   
                     638401
                  
                
                 
                   
                     800
                  
                   
                     66
                  
                   
                     8
                  
                   
                     〈◊〉
                  
                
                 
                   
                     801
                  
                   
                     66
                  
                   
                     9
                  
                   
                     641601
                  
                
                 
                   
                     802
                  
                   
                     66
                  
                   
                     10
                  
                   
                     642204
                  
                
                 
                   
                     803
                  
                   
                     66
                  
                   
                     11
                  
                   
                     644809
                  
                
                 
                   
                     804
                  
                   
                     67
                  
                   
                     0
                  
                   
                     646416
                  
                
                 
                   
                     805
                  
                   
                     67
                  
                   
                     1
                  
                   
                     648025
                  
                
                 
                   
                     806
                  
                   
                     67
                  
                   
                     2
                  
                   
                     649836
                  
                
                 
                   
                     807
                  
                   
                     67
                  
                   
                     3
                  
                   
                     651249
                  
                
                 
                   
                     808
                  
                   
                     67
                  
                   
                     4
                  
                   
                     652864
                  
                
                 
                   
                     809
                  
                   
                     67
                  
                   
                     5
                  
                   
                     654481
                  
                
                 
                   
                     810
                  
                   
                     67
                  
                   
                     6
                  
                   
                     656100
                  
                
                 
                   
                     811
                  
                   
                     67
                  
                   
                     7
                  
                   
                     657721
                  
                
                 
                   
                     812
                  
                   
                     67
                  
                   
                     8
                  
                   
                     659344
                  
                
                 
                   
                     813
                  
                   
                     67
                  
                   
                     9
                  
                   
                     660969
                  
                
                 
                   
                     814
                  
                   
                     67
                  
                   
                     10
                  
                   
                     662596
                  
                
                 
                   
                     815
                  
                   
                     67
                  
                   
                     11
                  
                   
                     664225
                  
                
                 
                   
                     816
                  
                   
                     68
                  
                   
                     0
                  
                   
                     665856
                  
                
                 
                   
                     817
                  
                   
                     68
                  
                   
                     1
                  
                   
                     667429
                  
                
                 
                   
                     818
                  
                   
                     68
                  
                   
                     2
                  
                   
                     669124
                  
                
                 
                   
                     819
                  
                   
                     68
                  
                   
                     3
                  
                   
                     671771
                  
                
                 
                   
                     820
                  
                   
                     68
                  
                   
                     4
                  
                   
                     672400
                  
                
                 
                   
                     821
                  
                   
                     68
                  
                   
                     5
                  
                   
                     674041
                  
                
                 
                   
                     822
                  
                   
                     68
                  
                   
                     6
                  
                   
                     675684
                  
                
                 
                   
                     823
                  
                   
                     68
                  
                   
                     7
                  
                   
                     677329
                  
                
                 
                   
                     824
                  
                   
                     68
                  
                   
                     8
                  
                   
                     678976
                  
                
                 
                   
                     825
                  
                   
                     68
                  
                   
                     9
                  
                   
                     680625
                  
                
                 
                   
                     826
                  
                   
                     68
                  
                   
                     10
                  
                   
                     682276
                  
                
                 
                   
                     827
                  
                   
                     68
                  
                   
                     11
                  
                   
                     684129
                  
                
                 
                   
                     828
                  
                   
                     69
                  
                   
                     0
                  
                   
                     685584
                  
                
                 
                   
                     829
                  
                   
                     69
                  
                   
                     1
                  
                   
                     688241
                  
                
                 
                   
                     830
                  
                   
                     69
                  
                   
                     2
                  
                   
                     688900
                  
                
                 
                   
                     831
                  
                   
                     69
                  
                   
                     3
                  
                   
                     689661
                  
                
                 
                   
                     832
                  
                   
                     69
                  
                   
                     4
                  
                   
                     692224
                  
                
                 
                   
                     833
                  
                   
                     69
                  
                   
                     5
                  
                   
                     693889
                  
                
                 
                   
                     834
                  
                   
                     69
                  
                   
                     6
                  
                   
                     695556
                  
                
                 
                   
                     835
                  
                   
                     69
                  
                   
                     7
                  
                   
                     697225
                  
                
                 
                   
                     836
                  
                   
                     69
                  
                   
                     1
                  
                   
                     698896
                  
                
                 
                   
                     837
                  
                   
                     69
                  
                   
                     9
                  
                   
                     700569
                  
                
                 
                   
                     838
                  
                   
                     69
                  
                   
                     10
                  
                   
                     702244
                  
                
                 
                   
                     839
                  
                   
                     69
                  
                   
                     11
                  
                   
                     703921
                  
                
                 
                   
                     〈◊〉
                  
                   
                     〈◊〉
                  
                   
                     〈◊〉
                  
                   
                     〈◊〉
                  
                
              
            
             
             
               
                 
                   
                     Inch
                  
                   
                     Squares
                  
                
                 
                   
                     841
                  
                   
                     707281
                  
                
                 
                   
                     842
                  
                   
                     708964
                  
                
                 
                   
                     843
                  
                   
                     710649
                  
                
                 
                   
                     844
                  
                   
                     711336
                  
                
                 
                   
                     845
                  
                   
                     714025
                  
                
                 
                   
                     846
                  
                   
                     715716
                  
                
                 
                   
                     847
                  
                   
                     717309
                  
                
                 
                   
                     848
                  
                   
                     719004
                  
                
                 
                   
                     849
                  
                   
                     720801
                  
                
                 
                   
                     850
                  
                   
                     722500
                  
                
                 
                   
                     851
                  
                   
                     724●01
                  
                
                 
                   
                     852
                  
                   
                     725904
                  
                
                 
                   
                     853
                  
                   
                     727609
                  
                
                 
                   
                     854
                  
                   
                     729216
                  
                
                 
                   
                     855
                  
                   
                     721025
                  
                
                 
                   
                     856
                  
                   
                     732736
                  
                
                 
                   
                     857
                  
                   
                     734449
                  
                
                 
                   
                     858
                  
                   
                     736164
                  
                
                 
                   
                     859
                  
                   
                     737681
                  
                
                 
                   
                     860
                  
                   
                     739600
                  
                
                 
                   
                     861
                  
                   
                     741321
                  
                
                 
                   
                     862
                  
                   
                     743044
                  
                
                 
                   
                     863
                  
                   
                     744769
                  
                
                 
                   
                     864
                  
                   
                     746396
                  
                
                 
                   
                     865
                  
                   
                     748225
                  
                
                 
                   
                     866
                  
                   
                     749956
                  
                
                 
                   
                     867
                  
                   
                     753689
                  
                
                 
                   
                     868
                  
                   
                     753824
                  
                
                 
                   
                     869
                  
                   
                     755161
                  
                
                 
                   
                     870
                  
                   
                     756900
                  
                
                 
                   
                     871
                  
                   
                     758641
                  
                
                 
                   
                     872
                  
                   
                     760384
                  
                
                 
                   
                     873
                  
                   
                     762129
                  
                
                 
                   
                     874
                  
                   
                     763776
                  
                
                 
                   
                     875
                  
                   
                     765625
                  
                
                 
                   
                     876
                  
                   
                     767376
                  
                
                 
                   
                     877
                  
                   
                     769129
                  
                
                 
                   
                     878
                  
                   
                     770884
                  
                
                 
                   
                     879
                  
                   
                     772641
                  
                
                 
                   
                     880
                  
                   
                     774400
                  
                
                 
                   
                     881
                  
                   
                     777161
                  
                
                 
                   
                     882
                  
                   
                     777924
                  
                
                 
                   
                     883
                  
                   
                     779589
                  
                
                 
                   
                     884
                  
                   
                     781456
                  
                
                 
                   
                     885
                  
                   
                     783225
                  
                
                 
                   
                     886
                  
                   
                     784996
                  
                
                 
                   
                     887
                  
                   
                     786769
                  
                
                 
                   
                     888
                  
                   
                     788544
                  
                
                 
                   
                     889
                  
                   
                     790321
                  
                
                 
                   
                     890
                  
                   
                     792100
                  
                
                 
                   
                     891
                  
                   
                     793081
                  
                
                 
                   
                     892
                  
                   
                     795664
                  
                
                 
                   
                     893
                  
                   
                     797449
                  
                
                 
                   
                     894
                  
                   
                     799236
                  
                
                 
                   
                     895
                  
                   
                     801025
                  
                
                 
                   
                     896
                  
                   
                     802816
                  
                
                 
                   
                     897
                  
                   
                     804609
                  
                
                 
                   
                     898
                  
                   
                     805904
                  
                
                 
                   
                     899
                  
                   
                     808201
                  
                
                 
                   
                     900
                  
                   
                     810000
                  
                
                 
                   
                     901
                  
                   
                     811801
                  
                
                 
                   
                     902
                  
                   
                     813604
                  
                
                 
                   
                     903
                  
                   
                     815400
                  
                
                 
                   
                     904
                  
                   
                     817216
                  
                
                 
                   
                     905
                  
                   
                     819025
                  
                
                 
                   
                     906
                  
                   
                     820836
                  
                
                 
                   
                     907
                  
                   
                     822649
                  
                
                 
                   
                     908
                  
                   
                     824464
                  
                
                 
                   
                     909
                  
                   
                     826281
                  
                
                 
                   
                     910
                  
                   
                     828100
                  
                
                 
                   
                     911
                  
                   
                     829921
                  
                
                 
                   
                     912
                  
                   
                     831741
                  
                
                 
                   
                     913
                  
                   
                     833569
                  
                
                 
                   
                     914
                  
                   
                     835369
                  
                
                 
                   
                     915
                  
                   
                     837225
                  
                
                 
                   
                     916
                  
                   
                     839056
                  
                
                 
                   
                     917
                  
                   
                     840789
                  
                
                 
                   
                     918
                  
                   
                     842724
                  
                
                 
                   
                     919
                  
                   
                     844561
                  
                
                 
                   
                     920
                  
                   
                     846400
                  
                
                 
                   
                     921
                  
                   
                     847241
                  
                
                 
                   
                     922
                  
                   
                     850084
                  
                
                 
                   
                     923
                  
                   
                     851929
                  
                
                 
                   
                     924
                  
                   
                     853746
                  
                
                 
                   
                     925
                  
                   
                     855625
                  
                
                 
                   
                     926
                  
                   
                     857476
                  
                
                 
                   
                     927
                  
                   
                     859329
                  
                
                 
                   
                     928
                  
                   
                     861●84
                  
                
                 
                   
                     929
                  
                   
                     863041
                  
                
                 
                   
                     930
                  
                   
                     864900
                  
                
                 
                   
                     931
                  
                   
                     866761
                  
                
                 
                   
                     932
                  
                   
                     868624
                  
                
                 
                   
                     933
                  
                   
                     870489
                  
                
                 
                   
                     934
                  
                   
                     872356
                  
                
                 
                   
                     935
                  
                   
                     874225
                  
                
                 
                   
                     936
                  
                   
                     876096
                  
                
                 
                   
                     937
                  
                   
                     877869
                  
                
                 
                   
                     938
                  
                   
                     879844
                  
                
                 
                   
                     939
                  
                   
                     881721
                  
                
                 
                   
                     940
                  
                   
                     883600
                  
                
                 
                   
                     941
                  
                   
                     885481
                  
                
                 
                   
                     942
                  
                   
                     886364
                  
                
                 
                   
                     943
                  
                   
                     889249
                  
                
                 
                   
                     944
                  
                   
                     881136
                  
                
                 
                   
                     945
                  
                   
                     893025
                  
                
                 
                   
                     946
                  
                   
                     894916
                  
                
                 
                   
                     947
                  
                   
                     896809
                  
                
                 
                   
                     948
                  
                   
                     898704
                  
                
                 
                   
                     949
                  
                   
                     900601
                  
                
                 
                   
                     950
                  
                   
                     902500
                  
                
                 
                   
                     951
                  
                   
                     904401
                  
                
                 
                   
                     952
                  
                   
                     906304
                  
                
                 
                   
                     953
                  
                   
                     908209
                  
                
                 
                   
                     954
                  
                   
                     910016
                  
                
                 
                   
                     955
                  
                   
                     912025
                  
                
                 
                   
                     956
                  
                   
                     913936
                  
                
                 
                   
                     957
                  
                   
                     915849
                  
                
                 
                   
                     958
                  
                   
                     917764
                  
                
                 
                   
                     959
                  
                   
                     919681
                  
                
                 
                   
                     960
                  
                   
                     921600
                  
                
                 
                   
                     961
                  
                   
                     923521
                  
                
                 
                   
                     962
                  
                   
                     926444
                  
                
                 
                   
                     963
                  
                   
                     928369
                  
                
                 
                   
                     964
                  
                   
                     929296
                  
                
                 
                   
                     965
                  
                   
                     931225
                  
                
                 
                   
                     966
                  
                   
                     933256
                  
                
                 
                   
                     967
                  
                   
                     935089
                  
                
                 
                   
                     968
                  
                   
                     937024
                  
                
                 
                   
                     969
                  
                   
                     939961
                  
                
                 
                   
                     970
                  
                   
                     940900
                  
                
                 
                   
                     971
                  
                   
                     942741
                  
                
                 
                   
                     972
                  
                   
                     944784
                  
                
                 
                   
                     973
                  
                   
                     946729
                  
                
                 
                   
                     974
                  
                   
                     948676
                  
                
                 
                   
                     975
                  
                   
                     950625
                  
                
                 
                   
                     976
                  
                   
                     952576
                  
                
                 
                   
                     977
                  
                   
                     954529
                  
                
                 
                   
                     978
                  
                   
                     956484
                  
                
                 
                   
                     979
                  
                   
                     958441
                  
                
                 
                   
                     980
                  
                   
                     960400
                  
                
                 
                   
                     981
                  
                   
                     962361
                  
                
                 
                   
                     982
                  
                   
                     964324
                  
                
                 
                   
                     983
                  
                   
                     966●89
                  
                
                 
                   
                     984
                  
                   
                     968256
                  
                
                 
                   
                     985
                  
                   
                     970225
                  
                
                 
                   
                     986
                  
                   
                     972196
                  
                
                 
                   
                     987
                  
                   
                     974169
                  
                
                 
                   
                     988
                  
                   
                     976144
                  
                
                 
                   
                     989
                  
                   
                     978121
                  
                
                 
                   
                     990
                  
                   
                     980100
                  
                
                 
                   
                     991
                  
                   
                     982081
                  
                
                 
                   
                     992
                  
                   
                     984064
                  
                
                 
                   
                     993
                  
                   
                     986049
                  
                
                 
                   
                     994
                  
                   
                     988036
                  
                
                 
                   
                     995
                  
                   
                     990025
                  
                
                 
                   
                     996
                  
                   
                     992016
                  
                
                 
                   
                     997
                  
                   
                     994009
                  
                
                 
                   
                     998
                  
                   
                     996004
                  
                
                 
                   
                     999
                  
                   
                     998001
                  
                
                 
                   
                     1000
                  
                   
                     1000000
                  
                
                 
                   
                     
                     1001
                  
                   
                     1002001
                  
                
                 
                   
                     1002
                  
                   
                     1004004
                  
                
                 
                   
                     1003
                  
                   
                     1006009
                  
                
                 
                   
                     1004
                  
                   
                     1008016
                  
                
                 
                   
                     1005
                  
                   
                     1010025
                  
                
                 
                   
                     1006
                  
                   
                     1012036
                  
                
                 
                   
                     1007
                  
                   
                     1014049
                  
                
                 
                   
                     1008
                  
                   
                     1016064
                  
                
                 
                   
                     1009
                  
                   
                     1018081
                  
                
                 
                   
                     1010
                  
                   
                     1020100
                  
                
                 
                   
                     1011
                  
                   
                     1022121
                  
                
                 
                   
                     1012
                  
                   
                     1024104
                  
                
                 
                   
                     1013
                  
                   
                     1026196
                  
                
                 
                   
                     1014
                  
                   
                     1028196
                  
                
                 
                   
                     1015
                  
                   
                     1030225
                  
                
                 
                   
                     1016
                  
                   
                     1032256
                  
                
                 
                   
                     1017
                  
                   
                     1034289
                  
                
                 
                   
                     1018
                  
                   
                     1036324
                  
                
                 
                   
                     1019
                  
                   
                     1038361
                  
                
                 
                   
                     1020
                  
                   
                     1040400
                  
                
                 
                   
                     1021
                  
                   
                     1042441
                  
                
                 
                   
                     1022
                  
                   
                     1044484
                  
                
                 
                   
                     1023
                  
                   
                     1046529
                  
                
                 
                   
                     1024
                  
                   
                     1048576
                  
                
                 
                   
                     1025
                  
                   
                     1050625
                  
                
                 
                   
                     1026
                  
                   
                     1052676
                  
                
                 
                   
                     1027
                  
                   
                     1054729
                  
                
                 
                   
                     1028
                  
                   
                     1056784
                  
                
                 
                   
                     1029
                  
                   
                     1058841
                  
                
                 
                   
                     1030
                  
                   
                     1060900
                  
                
                 
                   
                     1031
                  
                   
                     1060961
                  
                
                 
                   
                     1032
                  
                   
                     1065024
                  
                
                 
                   
                     1033
                  
                   
                     1067089
                  
                
                 
                   
                     1034
                  
                   
                     1069156
                  
                
                 
                   
                     1035
                  
                   
                     1071225
                  
                
                 
                   
                     1036
                  
                   
                     1073296
                  
                
                 
                   
                     1037
                  
                   
                     1075369
                  
                
                 
                   
                     1038
                  
                   
                     1077444
                  
                
                 
                   
                     1039
                  
                   
                     1079521
                  
                
                 
                   
                     1040
                  
                   
                     1081600
                  
                
                 
                   
                     1041
                  
                   
                     1082681
                  
                
                 
                   
                     1042
                  
                   
                     1085764
                  
                
                 
                   
                     1043
                  
                   
                     1087●49
                  
                
                 
                   
                     1044
                  
                   
                     1089936
                  
                
                 
                   
                     1045
                  
                   
                     1092025
                  
                
                 
                   
                     1046
                  
                   
                     1094116
                  
                
                 
                   
                     1047
                  
                   
                     1096209
                  
                
                 
                   
                     1048
                  
                   
                     1098304
                  
                
                 
                   
                     1049
                  
                   
                     1100401
                  
                
                 
                   
                     1050
                  
                   
                     1102550
                  
                
                 
                   
                     1051
                  
                   
                     1104601
                  
                
                 
                   
                     1052
                  
                   
                     1106704
                  
                
                 
                   
                     1053
                  
                   
                     1108809
                  
                
                 
                   
                     1054
                  
                   
                     1110916
                  
                
                 
                   
                     1055
                  
                   
                     1113025
                  
                
                 
                   
                     1056
                  
                   
                     1115136
                  
                
                 
                   
                     1057
                  
                   
                     1117249
                  
                
                 
                   
                     1058
                  
                   
                     1119364
                  
                
                 
                   
                     1059
                  
                   
                     1120489
                  
                
                 
                   
                     1060
                  
                   
                     1123600
                  
                
                 
                   
                     1061
                  
                   
                     1125721
                  
                
                 
                   
                     1062
                  
                   
                     1127844
                  
                
                 
                   
                     1063
                  
                   
                     1129969
                  
                
                 
                   
                     1064
                  
                   
                     1132096
                  
                
                 
                   
                     1065
                  
                   
                     1134225
                  
                
                 
                   
                     1066
                  
                   
                     1136358
                  
                
                 
                   
                     1067
                  
                   
                     1138489
                  
                
                 
                   
                     1068
                  
                   
                     1140624
                  
                
                 
                   
                     1069
                  
                   
                     1142761
                  
                
                 
                   
                     1070
                  
                   
                     1144900
                  
                
                 
                   
                     1071
                  
                   
                     1147041
                  
                
                 
                   
                     1072
                  
                   
                     1149184
                  
                
                 
                   
                     1073
                  
                   
                     1151329
                  
                
                 
                   
                     1074
                  
                   
                     1153476
                  
                
                 
                   
                     1075
                  
                   
                     1155625
                  
                
                 
                   
                     1076
                  
                   
                     1157976
                  
                
                 
                   
                     1077
                  
                   
                     1159929
                  
                
                 
                   
                     1078
                  
                   
                     1162074
                  
                
                 
                   
                     1079
                  
                   
                     1164241
                  
                
                 
                   
                     1080
                  
                   
                     1166400
                  
                
                 
                   
                     1081
                  
                   
                     1168561
                  
                
                 
                   
                     1082
                  
                   
                     1170724
                  
                
                 
                   
                     1083
                  
                   
                     1172889
                  
                
                 
                   
                     1084
                  
                   
                     1175056
                  
                
                 
                   
                     1085
                  
                   
                     1177225
                  
                
                 
                   
                     1086
                  
                   
                     1179396
                  
                
                 
                   
                     1087
                  
                   
                     1181569
                  
                
                 
                   
                     1088
                  
                   
                     1183744
                  
                
                 
                   
                     1089
                  
                   
                     1185921
                  
                
                 
                   
                     1090
                  
                   
                     1188100
                  
                
                 
                   
                     1091
                  
                   
                     1190281
                  
                
                 
                   
                     1092
                  
                   
                     1192464
                  
                
                 
                   
                     1093
                  
                   
                     1194649
                  
                
                 
                   
                     1094
                  
                   
                     1196836
                  
                
                 
                   
                     1095
                  
                   
                     1199025
                  
                
                 
                   
                     1096
                  
                   
                     1201216
                  
                
                 
                   
                     1097
                  
                   
                     1203409
                  
                
                 
                   
                     1098
                  
                   
                     1205604
                  
                
                 
                   
                     1099
                  
                   
                     1207801
                  
                
                 
                   
                     1100
                  
                   
                     1210000
                  
                
                 
                   
                     1101
                  
                   
                     1212201
                  
                
                 
                   
                     1102
                  
                   
                     1214404
                  
                
                 
                   
                     1103
                  
                   
                     1216609
                  
                
                 
                   
                     1104
                  
                   
                     1218816
                  
                
                 
                   
                     1105
                  
                   
                     1221025
                  
                
                 
                   
                     1106
                  
                   
                     1223396
                  
                
                 
                   
                     1107
                  
                   
                     1225449
                  
                
                 
                   
                     1108
                  
                   
                     1227664
                  
                
                 
                   
                     1109
                  
                   
                     1229881
                  
                
                 
                   
                     1110
                  
                   
                     1232100
                  
                
                 
                   
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                     1234321
                  
                
                 
                   
                     1112
                  
                   
                     1236544
                  
                
                 
                   
                     1113
                  
                   
                     1238769
                  
                
                 
                   
                     1114
                  
                   
                     1240969
                  
                
                 
                   
                     1115
                  
                   
                     1242625
                  
                
                 
                   
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                     1245459
                  
                
                 
                   
                     1117
                  
                   
                     1247689
                  
                
                 
                   
                     1118
                  
                   
                     1249924
                  
                
                 
                   
                     1119
                  
                   
                     1252161
                  
                
                 
                   
                     1120
                  
                   
                     1254400
                  
                
                 
                   
                     1121
                  
                   
                     1256●41
                  
                
                 
                   
                     1122
                  
                   
                     1258884
                  
                
                 
                   
                     1123
                  
                   
                     1261029
                  
                
                 
                   
                     1124
                  
                   
                     1263376
                  
                
                 
                   
                     1125
                  
                   
                     1265625
                  
                
                 
                   
                     1126
                  
                   
                     1267876
                  
                
                 
                   
                     1127
                  
                   
                     1270029
                  
                
                 
                   
                     1128
                  
                   
                     1272384
                  
                
                 
                   
                     1129
                  
                   
                     1274641
                  
                
                 
                   
                     1130
                  
                   
                     1276900
                  
                
                 
                   
                     1131
                  
                   
                     1279161
                  
                
                 
                   
                     1132
                  
                   
                     1281426
                  
                
                 
                   
                     1133
                  
                   
                     1283689
                  
                
                 
                   
                     1134
                  
                   
                     1285956
                  
                
                 
                   
                     1135
                  
                   
                     1288225
                  
                
                 
                   
                     1136
                  
                   
                     1287496
                  
                
                 
                   
                     1137
                  
                   
                     1292769
                  
                
                 
                   
                     1138
                  
                   
                     1294094
                  
                
                 
                   
                     1139
                  
                   
                     1297321
                  
                
                 
                   
                     1140
                  
                   
                     1299640
                  
                
                 
                   
                     1141
                  
                   
                     1301881
                  
                
                 
                   
                     1142
                  
                   
                     1304164
                  
                
                 
                   
                     1143
                  
                   
                     1306449
                  
                
                 
                   
                     1144
                  
                   
                     1308736
                  
                
                 
                   
                     1145
                  
                   
                     1311025
                  
                
                 
                   
                     1146
                  
                   
                     1313316
                  
                
                 
                   
                     1147
                  
                   
                     1315509
                  
                
                 
                   
                     1148
                  
                   
                     1317904
                  
                
                 
                   
                     1149
                  
                   
                     1320201
                  
                
                 
                   
                     1150
                  
                   
                     1322500
                  
                
                 
                   
                     1151
                  
                   
                     1324801
                  
                
                 
                   
                     1152
                  
                   
                     1327104
                  
                
                 
                   
                     1153
                  
                   
                     1329409
                  
                
                 
                   
                     1154
                  
                   
                     1331716
                  
                
                 
                   
                     1155
                  
                   
                     1334025
                  
                
                 
                   
                     1156
                  
                   
                     1336336
                  
                
                 
                   
                     1157
                  
                   
                     1338649
                  
                
                 
                   
                     1158
                  
                   
                     1340964
                  
                
                 
                   
                     1159
                  
                   
                     1343381
                  
                
                 
                   
                     1160
                  
                   
                     1345600
                  
                
                 
                   
                     
                     1161
                  
                   
                     1347921
                  
                
                 
                   
                     1162
                  
                   
                     1350244
                  
                
                 
                   
                     1163
                  
                   
                     1352569
                  
                
                 
                   
                     1164
                  
                   
                     1354396
                  
                
                 
                   
                     1165
                  
                   
                     1357225
                  
                
                 
                   
                     1166
                  
                   
                     1358556
                  
                
                 
                   
                     1167
                  
                   
                     1361689
                  
                
                 
                   
                     1168
                  
                   
                     1364124
                  
                
                 
                   
                     1169
                  
                   
                     1366921
                  
                
                 
                   
                     1170
                  
                   
                     1368900
                  
                
                 
                   
                     1171
                  
                   
                     1371240
                  
                
                 
                   
                     1172
                  
                   
                     1373584
                  
                
                 
                   
                     1173
                  
                   
                     1375929
                  
                
                 
                   
                     1174
                  
                   
                     1378276
                  
                
                 
                   
                     1175
                  
                   
                     1380625
                  
                
                 
                   
                     1176
                  
                   
                     1382979
                  
                
                 
                   
                     1177
                  
                   
                     1383329
                  
                
                 
                   
                     1178
                  
                   
                     1387284
                  
                
                 
                   
                     1179
                  
                   
                     1390041
                  
                
                 
                   
                     1180
                  
                   
                     1392400
                  
                
                 
                   
                     1181
                  
                   
                     1394761
                  
                
                 
                   
                     1182
                  
                   
                     1397124
                  
                
                 
                   
                     1183
                  
                   
                     1399489
                  
                
                 
                   
                     1184
                  
                   
                     1401856
                  
                
                 
                   
                     1185
                  
                   
                     1404225
                  
                
                 
                   
                     1186
                  
                   
                     1406606
                  
                
                 
                   
                     1187
                  
                   
                     1408904
                  
                
                 
                   
                     1188
                  
                   
                     1411124
                  
                
                 
                   
                     1189
                  
                   
                     1413711
                  
                
                 
                   
                     1190
                  
                   
                     1416100
                  
                
                 
                   
                     1191
                  
                   
                     1418481
                  
                
                 
                   
                     1192
                  
                   
                     1420864
                  
                
                 
                   
                     1193
                  
                   
                     1423249
                  
                
                 
                   
                     1194
                  
                   
                     1425639
                  
                
                 
                   
                     1195
                  
                   
                     1428025
                  
                
                 
                   
                     1196
                  
                   
                     1430416
                  
                
                 
                   
                     1197
                  
                   
                     1432809
                  
                
                 
                   
                     1198
                  
                   
                     1435204
                  
                
                 
                   
                     1199
                  
                   
                     1437601
                  
                
                 
                   
                     1200
                  
                   
                     1440000
                  
                
                 
                   
                     1201
                  
                   
                     1442401
                  
                
                 
                   
                     1202
                  
                   
                     1444804
                  
                
                 
                   
                     1203
                  
                   
                     1447209
                  
                
                 
                   
                     1204
                  
                   
                     1449616
                  
                
                 
                   
                     1205
                  
                   
                     1452025
                  
                
                 
                   
                     1206
                  
                   
                     1454436
                  
                
                 
                   
                     1207
                  
                   
                     1456849
                  
                
                 
                   
                     1208
                  
                   
                     1459264
                  
                
                 
                   
                     1209
                  
                   
                     1461681
                  
                
                 
                   
                     1210
                  
                   
                     1464100
                  
                
                 
                   
                     1211
                  
                   
                     1466521
                  
                
                 
                   
                     1212
                  
                   
                     1468944
                  
                
                 
                   
                     1213
                  
                   
                     1471369
                  
                
                 
                   
                     1214
                  
                   
                     1473796
                  
                
                 
                   
                     1215
                  
                   
                     1476225
                  
                
                 
                   
                     1216
                  
                   
                     1478656
                  
                
                 
                   
                     1217
                  
                   
                     1480989
                  
                
                 
                   
                     1218
                  
                   
                     1483924
                  
                
                 
                   
                     1219
                  
                   
                     1485961
                  
                
                 
                   
                     1220
                  
                   
                     1488400
                  
                
                 
                   
                     1221
                  
                   
                     1490841
                  
                
                 
                   
                     1222
                  
                   
                     1493244
                  
                
                 
                   
                     1223
                  
                   
                     1495729
                  
                
                 
                   
                     1224
                  
                   
                     1498246
                  
                
                 
                   
                     1225
                  
                   
                     1500125
                  
                
                 
                   
                     1226
                  
                   
                     1503076
                  
                
                 
                   
                     1227
                  
                   
                     1505529
                  
                
                 
                   
                     1228
                  
                   
                     1507984
                  
                
                 
                   
                     1229
                  
                   
                     1510441
                  
                
                 
                   
                     1230
                  
                   
                     1512900
                  
                
                 
                   
                     1231
                  
                   
                     1515361
                  
                
                 
                   
                     1232
                  
                   
                     1517824
                  
                
                 
                   
                     1233
                  
                   
                     1520289
                  
                
                 
                   
                     1234
                  
                   
                     1522656
                  
                
                 
                   
                     1235
                  
                   
                     1525225
                  
                
                 
                   
                     1236
                  
                   
                     1527696
                  
                
                 
                   
                     1237
                  
                   
                     1530169
                  
                
                 
                   
                     1238
                  
                   
                     1334244
                  
                
                 
                   
                     1239
                  
                   
                     1535121
                  
                
                 
                   
                     1240
                  
                   
                     1537600
                  
                
                 
                   
                     1241
                  
                   
                     15400●1
                  
                
                 
                   
                     1242
                  
                   
                     1542564
                  
                
                 
                   
                     1243
                  
                   
                     1545049
                  
                
                 
                   
                     1244
                  
                   
                     1547536
                  
                
                 
                   
                     1245
                  
                   
                     1550025
                  
                
                 
                   
                     1246
                  
                   
                     1552516
                  
                
                 
                   
                     1247
                  
                   
                     1555009
                  
                
                 
                   
                     1248
                  
                   
                     1557504
                  
                
                 
                   
                     1249
                  
                   
                     1560001
                  
                
                 
                   
                     1250
                  
                   
                     1562500
                  
                
                 
                   
                     1251
                  
                   
                     1565001
                  
                
                 
                   
                     1252
                  
                   
                     1567504
                  
                
                 
                   
                     1253
                  
                   
                     1570009
                  
                
                 
                   
                     1254
                  
                   
                     1572416
                  
                
                 
                   
                     1255
                  
                   
                     1575025
                  
                
                 
                   
                     1256
                  
                   
                     1577536
                  
                
                 
                   
                     1257
                  
                   
                     1580049
                  
                
                 
                   
                     1258
                  
                   
                     1582564
                  
                
                 
                   
                     1259
                  
                   
                     1585081
                  
                
                 
                   
                     1260
                  
                   
                     1587600
                  
                
                 
                   
                     1261
                  
                   
                     1590121
                  
                
                 
                   
                     1262
                  
                   
                     1592644
                  
                
                 
                   
                     1263
                  
                   
                     1595169
                  
                
                 
                   
                     1264
                  
                   
                     1597706
                  
                
                 
                   
                     1265
                  
                   
                     1600225
                  
                
                 
                   
                     1266
                  
                   
                     1602756
                  
                
                 
                   
                     1267
                  
                   
                     1605289
                  
                
                 
                   
                     1268
                  
                   
                     1607824
                  
                
                 
                   
                     1269
                  
                   
                     1609361
                  
                
                 
                   
                     1270
                  
                   
                     1612900
                  
                
                 
                   
                     1271
                  
                   
                     1615441
                  
                
                 
                   
                     1272
                  
                   
                     1617984
                  
                
                 
                   
                     1273
                  
                   
                     1620529
                  
                
                 
                   
                     1274
                  
                   
                     1622076
                  
                
                 
                   
                     1275
                  
                   
                     1625625
                  
                
                 
                   
                     1276
                  
                   
                     1628176
                  
                
                 
                   
                     1277
                  
                   
                     1530729
                  
                
                 
                   
                     1278
                  
                   
                     1633464
                  
                
                 
                   
                     1279
                  
                   
                     1635841
                  
                
                 
                   
                     1280
                  
                   
                     1638400
                  
                
                 
                   
                     1281
                  
                   
                     1640961
                  
                
                 
                   
                     1282
                  
                   
                     1643524
                  
                
                 
                   
                     1283
                  
                   
                     1645989
                  
                
                 
                   
                     1284
                  
                   
                     1645656
                  
                
                 
                   
                     1285
                  
                   
                     1651225
                  
                
                 
                   
                     1286
                  
                   
                     1653796
                  
                
                 
                   
                     1287
                  
                   
                     1656369
                  
                
                 
                   
                     1288
                  
                   
                     1658944
                  
                
                 
                   
                     1289
                  
                   
                     1661521
                  
                
                 
                   
                     1290
                  
                   
                     1664100
                  
                
                 
                   
                     1291
                  
                   
                     1666681
                  
                
                 
                   
                     1292
                  
                   
                     1669264
                  
                
                 
                   
                     1293
                  
                   
                     1671849
                  
                
                 
                   
                     1294
                  
                   
                     1674336
                  
                
                 
                   
                     1295
                  
                   
                     1677025
                  
                
                 
                   
                     1296
                  
                   
                     1679616
                  
                
                 
                   
                     1297
                  
                   
                     1682209
                  
                
                 
                   
                     1298
                  
                   
                     1683804
                  
                
                 
                   
                     1299
                  
                   
                     1687401
                  
                
                 
                   
                     1300
                  
                   
                     1690000
                  
                
              
            
          
        
         
           
           
             
               CHAP.
               XI
               .
            
             Shewing
             ,
             how
             to
             Hang
             a
             Rising
             line
             by
             severall
             Sweeps
             ,
             to
             make
             it
             rounder
             aftward
             ,
             then
             at
             the
             beginning
             of
             the
             same
             .
          
           
             IF
             any
             be
             desirous
             to
             have
             a
             Rising
             line
             rounder
             aftward
             then
             it
             is
             at
             the
             foar
             part
             of
             it
             ,
             they
             must
             proceed
             thus
             ;
             first
             Work
             by
             the
             Sweep
             that
             they
             would
             have
             first
             ,
             and
             then
             begin
             again
             ,
             and
             finde
             the
             other
             Sweep
             ,
             that
             they
             would
             have
             the
             roundest
             ;
             An
             
               Example
            
             of
             this
             will
             make
             it
             more
             plain
             ,
             as
             in
             the
             following
             Figure
             will
             appear
             .
          
           
             Let
             D
             E
             represent
             the
             length
             of
             a
             Rising
             line
             E
             I
             ,
             the
             height
             thereof
             8
             foot
             ,
             on
             the
             after
             end
             thereof
             ;
             first
             I
             finde
             the
             Sweep
             that
             Sweepeth
             it
             ,
             by
             Multiplying
             of
             20
             foot
             the
             length
             ,
             which
             is
             240
             inches
             :
             for
             if
             you
             look
             in
             the
             Tables
             ,
             under
             the
             Title
             of
             Feet-Inches
             ,
             for
             20
             feet
             ,
             you
             will
             see
             in
             the
             next
             Columne
             ,
             toward
             the
             left
             hand
             ,
             240
             ,
             over
             head
             is
             written
             Inches
             ,
             signifying
             ,
             that
             in
             20
             feet
             is
             240
             inches
             ;
             and
             just
             against
             it
             ,
             and
             in
             the
             same
             line
             ,
             toward
             the
             right
             hand
             ,
             under
             the
             Title
             of
             Squares
             ,
             you
             will
             see
             written
             57600
             ,
             signifying
             ,
             that
             the
             square
             of
             240
             is
             57600
             ,
             these
             numbers
             you
             will
             finde
             in
             the
             second
             Page
             of
             the
             Tables
             ,
             and
             the
             last
             line
             ,
             the
             seventh
             ,
             eighth
             ,
             and
             ninth
             Columns
             .
          
           
           
             This
             squared
             number
             57600
             ,
             made
             by
             the
             Multiplication
             of
             D
             E
             ,
             240
             inches
             ,
             must
             be
             divided
             by
             the
             height
             of
             the
             Rising
             line
             assigned
             E
             I
             ,
             8
             foot
             ,
             or
             96
             inches
             ,
             so
             remaineth
             in
             the
             quotient
             600
             ,
             to
             which
             must
             be
             added
             the
             height
             of
             the
             Rising
             ,
             as
             is
             afore
             taught
             ,
             and
             they
             make
             696
             ,
             which
             is
             the
             Diameter
             of
             the
             whole
             Circle
             :
             the
             half
             thereof
             is
             348
             inches
             ,
             which
             is
             29
             foot
             ,
             as
             you
             may
             see
             by
             dividing
             it
             by
             12
             ;
             or
             else
             ,
             if
             you
             turne
             to
             the
             Tables
             ,
             and
             seek
             under
             the
             Title
             of
             
               Inches
            
             for
             348
             ,
             you
             will
             see
             in
             the
             same
             line
             ,
             toward
             the
             left
             hand
             ,
             29
             feet
             ,
             which
             you
             will
             finde
             in
             the
             third
             Page
             ,
             and
             the
             28th
             line
             ,
             the
             seventh
             and
             eighth
             Column
             ;
             then
             I
             Work
             by
             that
             Sweep
             to
             3
             /
             5
             of
             the
             length
             of
             the
             Rising
             line
             ,
             or
             12
             foot
             of
             the
             same
             ,
             at
             the
             point
             C
             it
             is
             represented
             ,
             at
             which
             point
             I
             seek
             the
             Rising
             C
             B
             ,
             I
             seek
             in
             the
             Table
             for
             the
             
               Square
            
             made
             of
             144
             ,
             and
             I
             finde
             it
             in
             the
             second
             Page
             ,
             24
             line
             ,
             at
             the
             first
             Columne
             ;
             and
             toward
             the
             right
             hand
             ,
             under
             the
             Title
             of
             
               Squares
               ,
            
             I
             finde
             20736
             ,
             which
             is
             the
             Square
             made
             of
             144
             :
             then
             I
             seek
             for
             the
             Square
             made
             of
             the
             Sweep
             ,
             or
             side
             A
             B
             ,
             348
             inches
             ,
             and
             I
             finde
             it
             in
             the
             Tables
             to
             be
             121104
             ,
             from
             this
             121104
             I
             Substract
             the
             other
             Square
             ,
             made
             of
             the
             side
             D
             C
             ,
             144
             being
             20736
             ,
             and
             there
             remaineth
             100368
             ,
             whose
             Root
             I
             finde
             in
             the
             Tables
             ,
             in
             the
             third
             Page
             ,
             and
             the
             37th
             line
             ,
             and
             the
             sixth
             Columne
             ,
             100489
             ,
             which
             is
             too
             much
             by
             neare
             121
             ;
             but
             the
             other
             number
             afore
             it
             being
             much
             more
             too
             little
             ,
             the
             number
             answering
             hereunto
             is
             316
             inches
             ,
             and
             near
             ¼
             ,
             Substracted
             from
             348
             ,
             the
             whole
             side
             leaveth
             31
             inches
             ¼
             ,
             or
             two
             foot
             7
             inches
             ¼
             for
             the
             Rising
             ,
          
           
             
               
                 
                   0
                
              
               
                 
                   30
                
              
               
                 
                   57600
                   (
                   600
                
              
               
                 
                   9666
                
              
               
                 
                   89
                
              
            
          
           
             
               
                 
                   121104
                
              
               
                 
                   20736
                
              
               
                 
                   100368
                
              
            
             
             at
             the
             point
             C
             :
             Now
             to
             make
             a
             rounder
             Sweep
             aftward
             on
             ,
             or
             at
             the
             other
             end
             of
             the
             line
             ,
             as
             from
             B
             to
             F
             ,
             which
             runeth
             higher
             up
             ,
             or
             Roundeth
             more
             ,
             as
             from
             I
             to
             F
             :
             Here
             will
             be
             something
             more
             of
             trouble
             to
             finde
             the
             Sweep
             that
             shall
             exactly
             touch
             the
             two
             points
             assigned
             ,
             as
             from
             B
             to
             F
             ▪
             then
             to
             finde
             the
             former
             Sweep
             .
             Now
             the
             Demonstration
             wil
             shew
             it
             to
             be
             thus
             .
          
           
           
           
             Let
             B
             and
             F
             be
             the
             two
             points
             to
             which
             the
             Sweep
             is
             confined
             to
             touch
             ;
             draw
             a
             streight
             line
             from
             B
             to
             F
             ,
             as
             you
             see
             ,
             and
             so
             you
             have
             a
             Right
             lined
             Triangle
             ,
             made
             of
             the
             sides
             B
             H
             ,
             the
             length
             of
             the
             line
             to
             be
             swept
             by
             the
             second
             Sweep
             ,
             and
             the
             side
             H
             F
             ,
             the
             height
             of
             the
             same
             ,
             together
             with
             the
             Subtending
             side
             B
             F
             ;
             then
             a
             streight
             line
             drawn
             from
             the
             middle
             of
             the
             side
             B
             F
             ,
             and
             perpendicular
             ,
             or
             square
             ,
             to
             the
             same
             line
             B
             F
             ,
             and
             extended
             ,
             till
             it
             touch
             the
             side
             D
             A
             ,
             the
             place
             where
             it
             toucheth
             shall
             be
             the
             Centre
             of
             the
             same
             Sweep
             ,
             as
             is
             the
             line
             G
             H
             ,
             passing
             through
             the
             middle
             of
             the
             side
             B
             F
             ,
             at
             the
             point
             O
             ,
             which
             to
             finde
             Arithmetically
             ,
             proceed
             thus
             ;
             finde
             first
             the
             length
             of
             the
             side
             B
             F
             ,
             as
             before
             is
             taught
             ,
             of
             two
             sides
             of
             a
             Right
             Angled
             Triangle
             given
             ,
             to
             finde
             the
             third
             side
             ,
             which
             will
             be
             found
             to
             be
             134
             ½
             inches
             ,
             the
             halfe
             whereof
             is
             67
             inches
             ,
             ¼
             from
             B
             to
             O
             ,
             then
             if
             a
             perpendicular
             be
             let
             fall
             from
             O
             to
             the
             line
             B
             H
             ,
             it
             will
             cut
             that
             Base
             line
             also
             in
             halves
             ,
             as
             at
             the
             point
             P
             ,
             being
             48
             inches
             :
             then
             again
             ,
             finde
             the
             side
             O
             H
             ,
             and
             that
             will
             be
             ,
             in
             this
             Example
             ,
             equall
             to
             the
             side
             B
             O
             ,
             but
             in
             other
             cases
             it
             may
             not
             so
             fall
             out
             :
             So
             then
             ,
             those
             two
             sides
             being
             known
             ,
             as
             the
             side
             O
             H
             ,
             67
             ,
             ½
             inches
             ,
             and
             the
             side
             P
             H
             ,
             48
             inches
             ,
             and
             the
             whole
             length
             of
             the
             side
             K
             H
             ,
             240
             inches
             ,
             you
             may
             then
             Work
             by
             the
             Rule
             of
             Three
             ,
             saying
             ,
             if
             48
             ,
             the
             side
             P
             H
             ,
             give
             67
             ½
             inch
             ,
             for
             the
             side
             O
             H
             ,
             what
             will
             240
             give
             ,
             for
             the
             side
             K
             H
             ,
             as
             thus
             ;
          
           
             If
             48
             give
             67
             ½
             ,
             what
             will
             240
          
           
             
               
                 
                   240
                
                 
                   2
                
              
               
                 
                   67
                
                 
                   144
                
              
               
                 
                   1680
                
                 
                   4640
                
              
               
                 
                   1440
                
                 
                   16080
                   (
                   335
                
              
               
                 
                    
                
                 
                   48888
                
              
               
                 
                   16880
                
                 
                   44
                
              
            
          
           
           
             If
             you
             Multiply
             the
             two
             first
             numbers
             together
             ,
             and
             divide
             by
             the
             first
             number
             ,
             you
             will
             beget
             in
             the
             quotient
             335
             ,
             for
             the
             length
             of
             the
             whole
             side
             G
             H.
             
          
           
             I
             here
             neglected
             the
             ½
             inch
             in
             this
             Multiplication
             ,
             for
             the
             ½
             inch
             should
             have
             been
             Multiplied
             into
             the
             240
             ,
             by
             adding
             to
             the
             Summ
             16080
             ,
             120
             ,
             the
             halfe
             of
             240
             ,
             and
             it
             maketh
             16200
             ,
             which
             divided
             by
             48
             ,
             maketh
             337
             ⅓
             inches
             for
             the
             whole
             side
             G
             H
             ;
             So
             then
             ,
             these
             two
             sides
             being
             found
             ,
             find
             the
             side
             G
             K
             ,
             thus
             ,
             as
             before
             is
             taught
             ,
             look
             in
             the
             Table
             of
             
               Squares
            
             for
             the
             
               Square
            
             made
             of
             the
             side
             337
             ,
             and
             it
             will
             be
             113569
             ,
             from
             which
             Substract
             the
             
               Square
            
             made
             of
             240
             ,
             the
             other
             side
             ,
             being
             57600
             ,
             there
             resteth
             55969
             ,
             as
             you
             may
             see
             ,
             for
             that
             number
             sought
             for
             in
             the
             
               Tables
               ,
            
             and
             you
             find
             the
             nearest
             number
             to
             it
             ,
             to
             be
             56069
             ,
             and
             the
             roote
             of
             it
             to
             be
             237
             ,
             for
             the
             side
             G
             K
             ,
             to
             which
             must
             be
             added
             the
             Rising
             of
             the
             point
             C
             B
             ,
             or
             K
             D
             ,
             which
             is
             all
             one
             ,
             and
             is
             as
             we
             found
             it
             before
             to
             be
             ,
             31
             ¼
             inches
             ,
             added
             to
             237
             ,
             maketh
             268
             ¼
             inches
             ,
             or
             22
             foot
             4
             inches
             ;
             shewing
             ,
             that
             at
             22
             foot
             4
             inches
             ,
             from
             the
             point
             D
             ,
             towords
             G
             ,
             will
             be
             the
             point
             where
             the
             Centre
             of
             the
             Rounder
             Circle
             ought
             to
             stand
             :
             Then
             again
             ,
             you
             have
             the
             side
             G
             K
             ,
             found
             as
             before
             ,
             to
             be
             237
             ,
             and
             the
             side
             K
             B
             144
             ,
             and
             if
             you
             work
             as
             is
             taught
             before
             ,
             but
             remember
             ,
             that
             if
             the
             longest
             side
             be
             sought
             for
             ,
             as
             is
             now
             in
             the
             last
             side
             sought
             for
             ,
             G
             B
             being
             the
             longest
             side
             ,
             you
             must
             add
             the
             squares
             made
             of
             the
             other
             two
             sides
             together
             ,
             and
             the
             square
             of
             those
             two
             Summs
             shall
             be
             the
             longest
             side
             G
             B
             ,
             277
             inches
             ,
             that
             is
             23
             feet
             ,
             1
             inch
             ,
             which
             is
             the
             length
             of
             the
             second
             Sweep
             :
             and
             so
             have
             you
             the
             length
             of
             the
             Sweep
             .
             The
             same
             order
             you
             may
             observe
             to
             round
             your
             Sweep
             as
             often
             as
             you
             please
             .
          
           
             
               
                 
                   113569
                
              
               
                 
                   57600
                
              
               
                 
                   55969
                
              
            
          
           
             
               
                 
                   237
                
              
               
                 
                   31
                   ¼
                
              
               
                 
                   268
                   ¼
                
              
            
          
           
             If
             any
             have
             knowledge
             of
             the
             Doctrine
             of
             
               Triangles
               ,
            
             it
             may
             be
             found
             more
             readier
             ,
             that
             I
             leave
             to
             those
             that
             know
             the
             use
             thereof
             .
          
           
           
             Note
             also
             ,
             that
             when
             you
             seek
             for
             any
             number
             in
             the
             
               Tables
               ,
            
             take
             heed
             that
             you
             minde
             the
             number
             of
             Figures
             you
             seek
             for
             ,
             to
             agree
             in
             number
             with
             those
             that
             directeth
             you
             to
             seek
             for
             them
             .
          
           
             As
             for
             
               Example
               ,
            
             In
             the
             other
             figures
             abovementioned
             ,
             55969
             ,
             they
             are
             in
             number
             5
             ,
             by
             their
             places
             ,
             as
             you
             see
             ;
             then
             repairing
             to
             the
             Table
             ,
             I
             finde
             559504
             ,
             but
             telling
             the
             Figures
             ,
             I
             see
             that
             they
             are
             in
             number
             6
             ,
             but
             should
             be
             but
             5
             :
             therefore
             this
             number
             ,
             represented
             in
             the
             seventh
             Page
             ;
             and
             the
             28th
             line
             ,
             and
             third
             Columne
             ,
             is
             not
             the
             place
             I
             seek
             for
             ,
             then
             I
             turne
             toward
             the
             beginning
             of
             the
             Table
             ,
             till
             I
             see
             that
             the
             Columnes
             of
             
               Squares
            
             contain
             but
             5
             figures
             ,
             and
             there
             seek
             the
             nearest
             number
             agreeing
             to
             55969
             ,
             and
             in
             the
             second
             Page
             ,
             37th
             line
             ,
             last
             Column
             ,
             I
             finde
             56069
             ,
             the
             nearest
             agreeing
             to
             it
             ,
             which
             is
             the
             place
             answering
             to
             the
             other
             directory
             figures
             .
          
           
             Note
             also
             ,
             That
             the
             
               Example
            
             of
             finding
             the
             Sweep
             aforegoing
             ,
             is
             laid
             down
             by
             the
             small
             Scale
             of
             the
             
               Draught
               ,
            
             by
             which
             you
             may
             trie
             it
             for
             your
             better
             directions
             .
          
           
             And
             in
             that
             Table
             you
             may
             see
             that
             any
             farther
             then
             70
             foot
             ,
             being
             the
             end
             of
             the
             seventh
             Page
             ,
             I
             have
             not
             mentioned
             the
             
               Feet
            
             and
             
               Inches
            
             belonging
             to
             the
             number
             of
             
               Inches
               ,
            
             but
             have
             left
             it
             out
             because
             they
             are
             of
             little
             use
             any
             further
             ,
             because
             that
             will
             reach
             farr
             enough
             for
             the
             length
             of
             any
             Rising
             line
             of
             any
             Ship
             whatever
             :
             If
             any
             be
             desirous
             to
             convert
             any
             of
             the
             following
             numbers
             into
             inches
             ,
             he
             may
             do
             it
             by
             Dividing
             by
             12.
             
          
           
             Thus
             I
             think
             I
             have
             spoken
             enough
             to
             the
             Ingenuous
             ,
             concerning
             the
             singular
             use
             of
             the
             
               Tables
               ,
            
             or
             of
             this
             way
             of
             Working
             by
             Segments
             o
             Circles
             .
          
        
         
           
           
             
               CHAP.
               XII
               .
            
             Concerning
             Measuring
             of
             Ships
             .
          
           
             
               
                 
                   60
                
              
               
                 
                   20
                
              
               
                 
                   1200
                
              
               
                 
                   10
                
              
               
                 
                   120100
                
              
            
          
           
             I
             Shall
             say
             something
             concerning
             it
             ;
             the
             Shipwrights
             have
             to
             themselves
             a
             custome
             of
             measuring
             at
             
               London
               ,
            
             or
             on
             the
             River
             of
             
               Thames
            
             thus
             ,
             they
             multiply
             the
             length
             of
             the
             Keel
             into
             the
             bredth
             of
             the
             Ship
             ,
             at
             the
             broadest
             place
             ,
             taken
             from
             outside
             to
             outside
             ,
             and
             the
             product
             of
             that
             by
             the
             half
             bredth
             ,
             this
             second
             product
             of
             the
             multiplication
             they
             divide
             by
             94
             or
             sometimes
             100
             ,
             and
             according
             to
             that
             division
             ,
             the
             quotient
             thereof
             ;
             they
             are
             paid
             for
             so
             many
             Tuns
             ;
             as
             suppose
             in
             the
             former
             draught
             being
             in
             length
             60
             foot
             and
             20
             foot
             broad
             ,
             60
             ,
             being
             multiplyed
             by
             20
             ,
             the
             bredth
             ,
             produce
             1200
             ,
             that
             1200
             being
             again
             multiplied
             by
             10
             ,
             the
             half
             bredth
             produce
             12000
             ,
             if
             you
             divide
             by
             100
             ,
             you
             need
             do
             no
             more
             than
             cut
             off
             the
             two
             last
             figures
             toward
             the
             right
             hand
             ,
             which
             shall
             be
             the
             answer
             and
             rendreth
             the
             Ship
             to
             be
             120
             Tuns
             ,
             but
             if
             you
             divide
             the
             sum
             12000
             by
             94
             ,
             you
             wil
             have
             127
             2
             /
             3
             of
             a
             Tun
             very
             neer
             ,
             but
             this
             cannot
             be
             the
             true
             ability
             of
             the
             ship
             to
             carry
             or
             lift
             ,
             because
             two
             ships
             by
             this
             rule
             of
             equall
             breadth
             and
             length
             shall
             be
             of
             equall
             burthen
             ,
             notwithstanding
             the
             fulness
             or
             sharpness
             of
             those
             Vessels
             ,
             which
             may
             differ
             them
             very
             much
             ,
             or
             the
             one
             ship
             may
             have
             more
             timber
             than
             the
             other
             in
             her
             building
             ,
             &
             so
             shall
             carry
             less
             than
             the
             other
             :
             But
             the
             true
             way
             of
             measure
             must
             be
             by
             measure
             of
             the
             body
             and
             bulk
             of
             the
             ship
             underwater
             ,
             for
             if
             one
             ship
             be
             longer
             in
             the
             floor
             than
             another
             of
             the
             same
             bredth
             and
             length
             ,
             she
             shall
             be
             more
             in
             burthen
             than
             the
             
             other
             ;
             as
             a
             Flemish
             ship
             shall
             carry
             more
             than
             a
             French
             or
             Italian
             Vessell
             of
             the
             same
             length
             and
             bredth
             ;
             Therefore
             I
             say
             the
             measure
             of
             the
             ship
             being
             known
             by
             measuring
             her
             ,
             as
             a
             piece
             of
             timber
             may
             be
             measured
             of
             the
             same
             form
             ,
             to
             the
             draught
             of
             water
             assigned
             her
             ,
             the
             weight
             of
             the
             same
             body
             of
             the
             same
             water
             that
             the
             ship
             swimmeth
             in
             shall
             be
             the
             exact
             weight
             of
             the
             ship
             ;
             and
             all
             things
             therein
             ;
             loading
             ,
             rigging
             ,
             victuals
             included
             therein
             :
             then
             if
             the
             ship
             be
             measured
             to
             her
             light
             mark
             as
             she
             will
             swim
             at
             being
             lanched
             ,
             the
             weight
             of
             so
             much
             water
             being
             taken
             or
             substracted
             from
             the
             weight
             of
             the
             water
             when
             she
             is
             laden
             ,
             the
             residue
             shall
             be
             the
             weight
             that
             must
             load
             her
             ,
             or
             her
             ability
             of
             carrying
             ,
             called
             her
             burden
             ,
             by
             this
             means
             you
             may
             know
             the
             weight
             of
             the
             ship
             light
             ,
             and
             what
             she
             will
             carry
             to
             every
             foot
             of
             water
             assigned
             to
             her
             ,
             which
             cannot
             be
             done
             by
             no
             general
             rules
             in
             Arithmetick
             because
             of
             their
             great
             irregularity
             ,
             according
             to
             the
             differing
             minds
             of
             Shipwrights
             ;
             you
             may
             if
             you
             please
             first
             measure
             the
             content
             of
             the
             Keel
             and
             Post
             and
             Stem-rudder
             ,
             all
             of
             it
             that
             is
             without
             the
             Plank
             ,
             and
             under
             the
             water
             line
             ,
             and
             note
             it
             by
             it self
             ,
             then
             measure
             the
             body
             of
             the
             ship
             in
             the
             Midships
             ,
             made
             by
             the
             square
             made
             of
             the
             multiplying
             of
             the
             depth
             of
             the
             water
             line
             ,
             and
             the
             bredth
             ,
             then
             you
             may
             find
             ;
             the
             content
             of
             the
             want
             by
             the
             circular
             part
             of
             the
             ship
             under
             water
             ,
             being
             narrower
             downward
             ,
             and
             substract
             this
             from
             the
             whole
             content
             of
             the
             squared
             body
             of
             the
             depth
             of
             the
             Water-line
             and
             bredth
             of
             the
             ship
             ,
             and
             this
             shall
             be
             the
             solid
             content
             of
             that
             part
             of
             the
             ship
             ,
             I
             mean
             in
             solid
             foot
             measure
             of
             1728
             inches
             to
             the
             foot
             ,
             then
             proceed
             to
             the
             fore
             part
             or
             the
             after
             part
             of
             the
             ship
             ,
             and
             to
             3
             or
             4
             Timbers
             more
             ,
             find
             the
             mean
             bredth
             at
             the
             narrowing
             aloft
             at
             the
             water-line
             ,
             and
             alow
             at
             the
             floor
             and
             the
             mean
             depth
             ,
             and
             measure
             that
             piece
             of
             
             the
             ship
             ,
             as
             I
             told
             you
             of
             the
             middle
             part
             of
             the
             Ship
             ,
             and
             so
             measure
             the
             whole
             Ship
             by
             pieces
             and
             add
             them
             together
             ,
             and
             so
             many
             feet
             as
             it
             maketh
             ,
             so
             many
             feet
             of
             water
             shall
             be
             the
             weight
             of
             the
             said
             ship
             ;
             and
             the
             reason
             may
             be
             considered
             thus
             ;
             there
             is
             a
             ponderosity
             in
             warer
             ,
             but
             there
             is
             a
             greater
             in
             the
             ayre
             ,
             onely
             to
             the
             heaviest
             of
             things
             ;
             and
             there
             is
             a
             ponderosity
             in
             water
             it self
             ,
             but
             not
             so
             much
             as
             in
             other
             things
             more
             solid
             as
             in
             Iron
             :
             Suppose
             a
             Gun
             or
             an
             Anchor
             of
             Iron
             ,
             it
             sinketh
             in
             the
             water
             ,
             but
             yet
             it
             is
             not
             so
             heavy
             in
             the
             water
             as
             in
             the
             ayre
             ,
             by
             the
             weight
             of
             so
             much
             water
             as
             shall
             make
             a
             body
             of
             the
             same
             water
             equal
             to
             the
             body
             of
             the
             Gun
             or
             Anchor
             in
             magnitude
             ;
             which
             weight
             substracted
             from
             the
             weight
             of
             the
             Iron
             body
             weighed
             in
             the
             ayre
             ,
             and
             so
             much
             must
             be
             the
             weight
             of
             it
             in
             the
             water
             .
          
           
             Again
             ,
             if
             a
             body
             be
             lighter
             in
             weight
             ,
             than
             water
             of
             the
             same
             bigness
             ,
             it
             hath
             an
             ability
             of
             lifting
             in
             the
             water
             ,
             and
             can
             lift
             or
             carry
             so
             much
             as
             is
             that
             difference
             ,
             as
             a
             piece
             of
             cork
             or
             wood
             of
             firr-trees
             ,
             being
             lighter
             than
             water
             ,
             it
             swimmeth
             on
             the
             face
             of
             the
             water
             ,
             and
             refuseth
             to
             be
             depressed
             without
             more
             weight
             added
             to
             it
             .
          
           
             Thus
             a
             ship
             being
             a
             concave
             body
             ,
             is
             made
             capable
             of
             lifting
             according
             to
             the
             greatness
             or
             littleness
             of
             this
             concavity
             ,
             respect
             being
             had
             to
             the
             greatness
             of
             the
             Timber
             put
             into
             it
             ,
             or
             the
             nature
             of
             it
             ,
             all
             which
             maketh
             a
             ship
             swim
             deeper
             or
             lighter
             in
             the
             water
             .
          
           
             I
             have
             proved
             by
             the
             
               Thames
            
             water
             ,
             that
             fresh
             Water
             is
             lighter
             then
             salt
             water
             ,
             so
             then
             salt
             water
             being
             heavier
             than
             fresh
             ,
             causeth
             that
             a
             ship
             swimmeth
             deeper
             in
             the
             fresh
             water
             than
             in
             salt
             .
          
           
             I
             shall
             not
             need
             to
             say
             any
             thing
             more
             concerning
             the
             mesauring
             ,
             for
             it
             will
             be
             understood
             by
             those
             that
             have
             any
             
             Judgment
             in
             the
             mesuring
             of
             triangles
             ,
             the
             matter
             it self
             being
             but
             a
             nicity
             rather
             than
             usefll
             :
             I
             only
             touched
             it
             to
             shew
             those
             that
             are
             so
             curious
             minded
             ,
             which
             way
             they
             may
             accomplish
             their
             desires
             ;
             I
             shall
             forbear
             to
             give
             examples
             ,
             because
             it
             will
             much
             increase
             my
             Treatise
             ,
             and
             augment
             the
             Price
             ,
             which
             might
             prove
             more
             prejudicial
             to
             youngmen
             than
             advantagious
             .
          
        
         
           
             
               CHAP.
               XIII
               .
            
             Concerning
             the
             Masts
             of
             Ships
             .
          
           
             FRom
             the
             length
             and
             bredth
             is
             gained
             the
             Mainmasts
             length
             ,
             and
             all
             the
             other
             Masts
             as
             wel
             as
             yards
             ,
             is
             derived
             from
             thence
             ,
             and
             there
             is
             different
             proceedings
             in
             this
             case
             ,
             according
             to
             the
             largeness
             of
             the
             Ships
             ,
             thus
             ,
             the
             main
             Masts
             of
             small
             Ships
             to
             be
             three
             times
             as
             long
             as
             the
             Ship
             is
             in
             bredth
             ;
             as
             a
             ship
             of
             20
             foot
             broad
             ,
             by
             the
             same
             rule
             must
             have
             a
             Mast
             of
             60
             foot
             long
             .
          
           
             Others
             for
             greater
             Ships
             ,
             add
             the
             bredth
             to
             the
             length
             ,
             and
             to
             that
             the
             half
             bredth
             ,
             which
             some
             they
             divide
             by
             5
             ,
             and
             the
             quotient
             is
             the
             number
             of
             yards
             ,
             as
             a
             ship
             114
             foot
             long
             and
             34
             foot
             in
             bredth
             ,
             as
             the
             bredth
             added
             to
             the
             length
             ,
             and
             the
             half
             bredth
             added
             together
             ,
             make
             165
             ,
             that
             divided
             by
             5
             ,
             yields
             33
             ,
             and
             so
             many
             yards
             is
             the
             length
             to
             be
             of
             that
             Mast
             ,
             the
             fore-mast
             must
             be
             a
             yard
             shorter
             at
             the
             head
             ,
             that
             is
             to
             say
             besides
             the
             height
             of
             the
             step
             ,
             which
             commonly
             in
             most
             ships
             the
             step
             of
             the
             fore-mast
             standeth
             higher
             from
             the
             bottom
             of
             the
             ship
             than
             the
             step
             of
             the
             Main-mast
             ;
             the
             foremast
             must
             be
             shorter
             by
             that
             difference
             ,
             and
             one
             yard
             more
             ,
             or
             the
             bigness
             of
             the
             ship
             considered
             ,
             4
             foot
             shorter
             at
             the
             head
             ,
             or
             besides
             the
             difference
             below
             ,
          
           
             
               
                 
                   114
                
              
               
                 
                   34
                
              
               
                 
                   17
                
              
               
                 
                   165
                
              
               
                 
                   10
                
              
               
                 
                   165
                   (
                   33
                
              
               
                 
                   55
                
              
            
          
           
             The
             Top-masts
             two
             thirds
             of
             the
             length
             of
             the
             lower
             Masts
             .
          
           
           
             The
             Main-yard
             to
             be
             2
             /
             ●
             and
             ●
             /
             22
             of
             the
             Main-mast
             ,
             as
             in
             the
             Mast
             aforementioned
             of
             60
             foot
             long
             ,
             two
             thirds
             of
             60
             is
             40
             ,
             and
             the
             2
             /
             12
             of
             60
             is
             5
             ,
             added
             to
             40
             make
             45
             ,
             for
             the
             length
             of
             the
             main
             yard
             .
          
           
             The
             foreyard
             to
             be
             6
             /
             7
             of
             the
             Main-Yard
             ,
             as
             the
             Main-yard
             being
             45
             foot
             ,
             divide
             45
             by
             7
             ,
             so
             cometh
             6
             in
             the
             quotient
             ,
             and
             a
             fraction
             remaining
             of
             3
             ,
             signifying
             3
             /
             7
             ,
             so
             that
             the
             1
             /
             7
             of
             45
             will
             be
             6
             and
             3
             /
             7
             ,
             you
             must
             take
             6
             times
             so
             much
             ,
             a●
             6
             times
             6
             makes
             36
             ,
             and
             if
             you
             take
             6
             times
             3
             /
             7
             make
             18
             /
             7
             ,
             that
             is
             ,
             two
             whole
             numbers
             ,
             and
             4
             /
             7
             remaining
             ,
             which
             added
             to
             36
             ,
             make
             38
             ,
             and
             4
             /
             7
             of
             a
             foot
             for
             the
             length
             of
             the
             fore-yard
             .
          
           
             The
             Top-sail
             Yards
             must
             be
             half
             the
             length
             of
             the
             lower
             Yards
             ,
             the
             Mizne
             Yard
             usualy
             is
             made
             of
             equal
             length
             with
             the
             fore-yard
             ,
             the
             Crosjack
             yard
             ,
             of
             equal
             length
             with
             the
             Main
             top-sail
             yard
             ,
             and
             the
             mizen
             Top-sail
             yard
             to
             be
             half
             the
             length
             of
             the
             Crosjack
             yard
             .
          
           
             The
             mizen
             Mast
             to
             be
             of
             the
             length
             of
             the
             Main-top
             mast
             from
             the
             upper
             Decks
             ,
             and
             so
             much
             longer
             as
             is
             the
             height
             of
             the
             ship
             between
             Deck
             ,
             the
             Boltspreete
             to
             be
             of
             length
             equal
             to
             the
             fore-mast
             from
             the
             upper
             Deck
             of
             the
             Fore-castle
             upwards
             .
          
           
             For
             the
             bigness
             of
             these
             Masts
             ,
             to
             a
             yard
             in
             length
             ,
             ¾
             of
             an
             inch
             ,
             or
             else
             ¼
             of
             an
             inch
             to
             the
             foot
             ,
             and
             so
             of
             yards
             likewise
             ,
             only
             the
             Boltspreet
             somthing
             bigger
             ,
             would
             be
             the
             better
             if
             he
             be
             made
             as
             big
             as
             the
             fore-mast
             .
          
           
        
         
           
             
               CHAP.
               XIV
               .
            
             Concerning
             Rowing
             of
             Ships
             ,
             when
             they
             are
             becalm'd
             .
          
           
             I
             Have
             here
             invented
             a
             meanes
             of
             Rowing
             of
             a
             Ship
             ,
             by
             the
             heaving
             at
             the
             Capstane
             ,
             where
             will
             be
             many
             benefits
             ;
             First
             ,
             of
             a
             greater
             purchase
             of
             strength
             ,
             for
             it
             is
             evident
             ,
             that
             10
             Men
             at
             a
             Capstane
             shall
             heave
             a
             Ship
             a
             Head
             ,
             when
             30
             Men
             shall
             not
             Haall
             her
             a
             Head
             by
             hand
             ,
             nay
             50
             ;
             neither
             shall
             they
             be
             so
             soon
             tired
             ,
             for
             that
             Owers
             are
             a
             great
             weariness
             to
             the
             Armes
             ,
             beside
             a
             double
             motion
             of
             the
             body
             ,
             as
             when
             the
             stroak
             is
             fetched
             ,
             to
             way
             down
             the
             Ower
             ,
             that
             the
             blade
             may
             be
             elivated
             out
             of
             the
             Water
             ,
             where
             it
             must
             be
             kept
             so
             ,
             untill
             another
          
           
           
             Let
             the
             two
             lines
             ,
             C
             D
             ,
             and
             C
             D
             ,
             represent
             the
             sides
             of
             the
             Ship
             ,
             16
             foot
             broad
             ,
             as
             is
             the
             line
             C
             C
             ,
             16
             foot
             long
             ,
             by
             the
             Scale
             of
             the
             
               Draught
               ;
            
             and
             let
             the
             two
             long
             squares
             ,
             
               d
               d
               ,
            
             and
             
               d
               d
               ,
            
             represent
             the
             two
             Bitt-pins
             ,
             with
             the
             Cross-piece
             
               of
               ,
            
             let
             the
             Black
             ,
             between
             the
             two
             Bit-pins
             ,
             represent
             a
             Roule
             ,
             or
             Windless
             ,
             with
             a
             Surdge
             in
             the
             middle
             ,
             as
             is
             the
             Surdge
             of
             a
             Crab
             ,
             or
             Capstane
             ;
             in
             the
             two
             ends
             of
             this
             Roule
             let
             there
             be
             placed
             two
             Winches
             ,
             as
             you
             may
             see
             represented
             by
             Cranks
             ,
             
               a
            
             and
             
               a
               ;
            
             let
             there
             be
             made
             a
             hollow
             place
             in
             the
             Head
             of
             the
             Bit-pins
             for
             these
             two
             Winches
             to
             rest
             in
             ,
             that
             they
             may
             turne
             round
             in
             them
             ,
             and
             bide
             in
             them
             :
             then
             let
             there
             be
             two
             pieces
             of
             Timber
             ,
             equall
             in
             length
             ,
             to
             the
             space
             of
             the
             Ship
             you
             would
             have
             filled
             with
             Oares
             ,
             represented
             by
             the
             two
             black
             lists
             ,
             marked
             
               b
               b
               ,
            
             and
             
               b
               b
               ;
            
             then
             let
             there
             be
             fitted
             two
             small
             pieces
             ,
             made
             of
             good
             Ashe
             ,
             or
             some
             good
             strong
             Wood
             ,
             of
             equall
             length
             as
             is
             the
             two
             black
             Lists
             ,
             
               n
            
             L
             ,
             
               m
            
             L
             ,
             fastned
             into
             the
             pieces
             of
             the
             frame
             ,
             as
             at
             the
             points
             L
             and
             L
             ,
             by
             a
             Boult
             ,
             but
             so
             ,
             that
             they
             may
             play
             on
             that
             Boult
             ,
             and
             the
             other
             ends
             must
             be
             with
             a
             Hoale
             made
             in
             the
             ends
             ,
             put
             over
             the
             handles
             of
             the
             Cranks
             ,
             at
             
               n
            
             and
             
               m
               ,
            
             then
             in
             the
             two
             long
             pieces
             for
             the
             frame
             let
             the
             Oares
             be
             fixed
             ,
             as
             at
             the
             points
             1
             ,
             2
             ,
             3
             ,
             4
             ,
             5
             ,
             6
             ,
             7
             ,
             of
             each
             side
             of
             the
             Ship
             representing
             7
             Oares
             of
             a
             side
             ,
             they
             may
             be
             fastned
             in
             the
             Frame
             ,
             by
             a
             Mortis
             made
             therein
             ,
             and
             a
             Tenent
             on
             the
             Oar
             ,
             made
             to
             go
             slack
             ,
             in
             that
             the
             Oar
             may
             play
             ,
             and
             have
             liberty
             
             to
             fetch
             a
             Stroak
             ,
             in
             the
             middle
             whereof
             must
             be
             placed
             a
             Iron
             bolt
             ,
             to
             fasten
             him
             ,
             and
             keep
             the
             Oar
             from
             launching
             in
             and
             out
             ,
             and
             on
             the
             Roughtre
             ,
             or
             side
             of
             the
             Ship
             ▪
             as
             in
             C
             D
             and
             C
             D
             ,
             must
             be
             placed
             Thoule
             pins
             to
             each
             Oare
             ,
             as
             in
             Boats
             that
             Row
             ;
             then
             must
             you
             have
             a
             Halser
             splised
             together
             ,
             in
             manner
             of
             a
             Viall
             ,
             that
             must
             take
             two
             or
             three
             turnes
             about
             the
             Roule
             ,
             in
             the
             Surdge
             ,
             as
             you
             may
             imagine
             ,
             at
             the
             middle
             of
             the
             Black
             Roule
             ,
             or
             notch
             therein
             ,
             and
             pass
             from
             thence
             to
             the
             Capstane
             ,
             with
             two
             or
             three
             turnes
             there
             also
             ;
             then
             this
             Viall
             also
             ,
             reeved
             thorough
             some
             other
             Blocks
             ,
             as
             in
             manner
             of
             Snach
             block
             ,
             and
             these
             blocks
             placed
             between
             the
             Capstane
             and
             the
             Roule
             ,
             you
             may
             thereby
             increase
             that
             purchase
             so
             ,
             as
             that
             it
             may
             heave
             very
             easie
             ,
             and
             with
             great
             strength
             ,
             so
             as
             to
             be
             able
             to
             Row
             a
             Ship
             a
             Head
             in
             a
             calme
             ,
             or
             in
             little
             winde
             ,
             two
             ,
             threee
             or
             four
             leagues
             ,
             a
             watch
             or
             more
             ,
             according
             as
             the
             Ingine
             shall
             be
             better
             or
             worse
             fitted
             ;
             for
             if
             you
             marke
             in
             the
             Figure
             of
             the
             Work
             ,
             and
             suppose
             the
             Viall
             Reeved
             ,
             and
             by
             heaving
             of
             the
             Capstane
             ,
             shall
             turne
             the
             Roule
             ,
             as
             the
             Crankes
             goeth
             round
             ,
             it
             shall
             carrie
             with
             it
             about
             ,
             and
             then
             the
             small
             pieces
             shall
             cause
             the
             frame
             to
             pass
             forward
             to
             and
             again
             ,
             to
             fetch
             a
             stroake
             with
             the
             Oares
             .
          
        
         
           FINIS
           .