The description and vse of the sphaere· Deuided into three principall parts. Whereof the first intreateth especially of the circles of the vppermost moueable sphære, and of the manifold vses of euery one of them seuerally. The second sheweth the plentifull vse of the vppermost sphære, and of the circles thereof joyntly. The third contayneth the description of the orbes whereof the sphæres of the sunne and moone haue been supposed to bee made, with their motions and vses. By Edvvard Wright. The contents of each part are more particularly set downe in the table.
         Wright, Edward, 1558?-1615.
      
       
         
           1627
        
      
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         99855533
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             The description and vse of the sphaere· Deuided into three principall parts. Whereof the first intreateth especially of the circles of the vppermost moueable sphære, and of the manifold vses of euery one of them seuerally. The second sheweth the plentifull vse of the vppermost sphære, and of the circles thereof joyntly. The third contayneth the description of the orbes whereof the sphæres of the sunne and moone haue been supposed to bee made, with their motions and vses. By Edvvard Wright. The contents of each part are more particularly set downe in the table.
             Wright, Edward, 1558?-1615.
          
           [8], 95, [1] p. : ill. (woodcut)
           
             Printed by B[ernard] A[lsop] and T. Fawcet, for Iohn Tap, and are to bee sold at his shop at S. Magnus corner,
             London :
             1627.
          
           
             Printer's name from STC.
             Reproduction of the original in the Henry E. Huntington Library and Art Gallery.
             Lacks N4. Title page and pages 82-end from the British Library copy filmed at end.
          
        
      
    
     
       
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           Celestial globes -- Early works to 1800.
           Astronomy -- Early works to 1800.
        
      
    
     
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           THE
           DESCRIPTION
           AND
           VSE
           OF
           THE
           SPHAERE
           .
           
             Deuided
             into
             three
             principall
             Parts
          
           .
           WHEREOF
           The
           first
           intreateth
           especially
           of
           the
           Circles
           of
           the
           vppermost
           moueable
           SPHAERE
           ,
           and
           of
           the
           manifold
           vses
           of
           euery
           one
           of
           them
           seuerally
           .
           The
           second
           sheweth
           the
           plentifull
           vse
           of
           the
           vppermost
           Sphaere
           ,
           and
           of
           the
           Circles
           thereof
           joyntly
           .
           The
           third
           contayneth
           the
           Description
           of
           the
           Orbes
           whereof
           the
           Sphaeres
           of
           the
           Sunne
           and
           Moone
           haue
           beene
           supposed
           to
           bee
           made
           ,
           with
           their
           Motions
           and
           Vses
           .
        
         
           By
           EDVVARD
           WRIGHT
           .
        
         
           The
           Contents
           of
           each
           Part
           are
           more
           particularly
           set
           downe
           in
           the
           Table
           .
        
         
           LONDON
           ,
           Printed
           by
           
             B.
             A.
          
           and
           
             T.
             Fawcet
          
           ,
           for
           
             Iohn
             Tap
          
           ,
           and
           are
           to
           bee
           sold
           at
           his
           Shop
           at
           S.
           Magnus
           corner
           .
           1627.
           
        
      
       
         
         
         
           A
           TABLE
           OF
           THE
           CONTENTS
           OF
           this
           Booke
           .
        
         
           
             The
             first
             Part.
             Of
             the
             Circles
             of
             the
             vppermost
             SPHAERE
             ,
             and
             their
             seuerall
             vses
             .
          
           
             
               THe
               Definition
               and
               deuision
               of
               this
               Sphaere
               ,
               Chap.
               1.
               
            
             
               The
               description
               of
               the
               Horizon
               ,
               Chap.
               2.
               
            
             
               The
               vses
               of
               the
               Horizon
               ,
               Chap.
               3.
               
            
             
               The
               description
               of
               the
               Meridian
               ,
               Chap.
               4.
               
            
             
               The
               vses
               of
               the
               Meridian
               ,
               Chap.
               5.
               
            
             
               The
               description
               of
               the
               Houre-circle
               ,
               and
               Poles
               of
               this
               Sphaere
               ,
               Chap.
               6.
               
            
             
               Of
               the
               Equinoctiall
               circle
               ,
               and
               why
               it
               is
               so
               called
               and
               how
               diuided
               ,
               together
               with
               his
               manifold
               vses
               ,
               Chap.
               7.
               
            
             
               The
               description
               of
               the
               Zodiacke
               of
               this
               Sphaere
               ,
               Chap.
               8.
               
            
             
               The
               vses
               of
               the
               Zodiacke
               ,
               Chap.
               9.
               
            
             
               The
               description
               of
               the
               two
               Colures
               ,
               together
               with
               the
               vses
               common
               to
               them
               both
               ,
               Chap.
               10.
               
            
             
               The
               vses
               of
               the
               Equinoctiall
               colure
               ,
               Chap.
               11.
               
            
             
               The
               vses
               of
               the
               Solstitiall
               colure
               ,
               Chap.
               12.
               
            
             
               The
               description
               of
               the
               two
               Tropickes
               ,
               Chap.
               13.
               
            
             
               The
               vses
               of
               the
               Tropickes
               ,
               Chap.
               14.
               
            
             
               The
               Polar
               circles
               ,
               Chap.
               15.
               
            
             
               Vses
               of
               the
               Polar
               circles
               ,
               Chap.
               16.
               
            
             
               Of
               the
               Zones
               ,
               Chap.
               17.
               
            
             
               The
               difference
               of
               shadowes
               that
               the
               Sunne
               maketh
               in
               these
               Zones
               ,
               Chap.
               18.
               
            
          
        
         
           
           
             The
             second
             Part.
             Of
             the
             vses
             of
             the
             vppermost
             Sphaere
             ,
             and
             of
             the
             Circles
             thereof
             joyntly
             .
          
           
             
               TO
               rectifie
               the
               Sphaere
               ,
               that
               is
               to
               sett
               the
               Sphaere
               to
               the
               Latitude
               of
               that
               place
               for
               which
               you
               would
               vse
               it
               ,
               Prop.
               1.
               
            
             
               To
               know
               ▪
               the
               place
               of
               the
               Sunne
               by
               this
               Sphaere
               ,
               Prop.
               2.
               
            
             
               To
               know
               the
               declination
               of
               the
               Sunne
               ,
               or
               of
               any
               point
               of
               the
               Ecliptick
               ,
               Prop.
               3.
               
            
             
               To
               know
               the
               right
               Ascention
               of
               the
               Sunne
               ,
               or
               any
               point
               of
               the
               Zodiack
               ,
               Prop.
               4.
               
            
             
               To
               know
               the
               oblique
               ascension
               of
               the
               Sunne
               ,
               or
               of
               any
               Starre
               or
               point
               in
               the
               Zodiack
               ,
               Prop.
               5.
               
            
             
               To
               finde
               the
               difference
               of
               Ascension
               ,
               Prop.
               6.
               
            
             
               To
               finde
               at
               what
               time
               the
               Sunne
               riseth
               or
               setteth
               ,
               Prop.
               7.
               
            
             
               To
               finde
               the
               length
               of
               the
               Artificiall
               Day
               or
               Night
               ,
               Prop.
               8.
               
            
             
               To
               know
               the
               time
               of
               the
               Sunne
               rising
               ,
               or
               Sunne
               setting
               ,
               Prop.
               9.
               
            
             
               To
               find
               the
               length
               of
               the
               artificiall
               Day
               or
               Night
               ,
               otherwise
               by
               the
               Sphaere
               ,
               Prop.
               10.
               
            
             
               To
               know
               the
               Meridian
               altitude
               of
               the
               Sunne
               at
               any
               place
               ,
               whose
               latitude
               is
               knowne
               ,
               Prop.
               11.
               
            
             
               To
               know
               how
               high
               the
               Sunne
               is
               about
               the
               Horizon
               at
               any
               time
               of
               the
               day
               ,
               Prop.
               12.
               
            
             
               To
               find
               the
               houre
               of
               the
               day
               by
               the
               height
               of
               the
               Sunne
               ,
               the
               place
               of
               the
               Sunne
               ,
               and
               height
               of
               the
               Pole
               being
               giuen
               ,
               Prop.
               13.
               
            
             
               To
               find
               the
               bredth
               of
               the
               Sunnes
               rising
               or
               setting
               ,
               that
               is
               ,
               how
               farre
               he
               riseth
               or
               setteth
               from
               the
               point
               of
               true
               East
               or
               West
               at
               any
               time
               ,
               Prop.
               14.
               
            
             
               
               To
               finde
               the
               place
               of
               the
               Sunne
               ,
               his
               declination
               ,
               and
               the
               quarter
               of
               the
               yeare
               being
               knowne
               ,
               Prop.
               15.
               
            
             
               To
               finde
               what
               day
               of
               the
               moneth
               it
               is
               by
               knowledge
               of
               the
               Sunnes
               declination
               ,
               Prop.
               16.
               
            
             
               The
               day
               of
               the
               moneth
               being
               knowne
               to
               find
               at
               what
               time
               the
               day
               breaketh
               ,
               Prop.
               17.
               
            
             
               To
               finde
               how
               long
               the
               twylight
               continueth
               ,
               Prop.
               18.
               
            
             
               To
               finde
               how
               much
               the
               declination
               of
               the
               Sunne
               must
               alter
               at
               any
               time
               of
               the
               yeare
               ,
               to
               make
               the
               day
               one
               houre
               longer
               or
               shorter
               ,
               Prop.
               19.
               
            
             
               To
               finde
               how
               many
               dayes
               it
               is
               ere
               the
               day
               lengthen
               or
               shorten
               an
               houre
               ,
               Prop.
               20.
               
            
             
               To
               make
               an
               horizontal
               Diall
               by
               the
               Sphaere
               ,
               Prop.
               21.
               
            
             
               How
               to
               make
               a
               direct
               murall
               Diall
               by
               the
               Sphaere
               ,
               Prop.
               22.
               
            
             
               To
               make
               any
               direct
               inclining
               ,
               or
               direct
               reclining
               Dyall
               by
               the
               Sphaere
               ,
               Prop.
               23.
               
            
             
               To
               know
               at
               what
               time
               the
               Moone
               ,
               or
               any
               other
               of
               the
               Planets
               ,
               or
               fixed
               Starres
               that
               are
               within
               the
               bredth
               of
               the
               Zodiack
               rise
               or
               sett
               ,
               or
               come
               to
               the
               Meridian
               :
               as
               also
               with
               what
               degree
               of
               the
               ecliptick
               they
               rise
               set
               or
               midde
               Heauen
               ,
               together
               with
               their
               declinations
               ,
               and
               their
               right
               and
               oblique
               ascensions
               ,
               and
               descensions
               ,
               and
               their
               amplitudes
               or
               bredths
               of
               rising
               or
               setting
               ,
               Prop.
               24.
               
            
             
               To
               know
               how
               long
               the
               Moone
               ,
               or
               any
               of
               the
               Planets
               or
               fixed
               Starres
               doe
               shine
               ,
               or
               continue
               aboue
               the
               Horizon
               ,
               Prop.
               25.
               
            
             
               To
               find
               which
               of
               the
               Planets
               of
               fixed
               Starres
               (
               that
               are
               within
               the
               compasse
               of
               the
               Zodiack
               )
               are
               aboue
               or
               vnder
               the
               Horizon
               at
               any
               time
               of
               the
               day
               or
               night
               ,
               Prop.
               26.
               
            
             
               To
               find
               in
               what
               time
               any
               Signe
               ,
               or
               part
               of
               the
               Ecliptick
               ,
               riseth
               or
               setteth
               ,
               Prop.
               27.
               
            
             
               To
               finde
               the
               houre
               of
               the
               Night
               by
               any
               of
               the
               Planets
               ,
               or
               fixed
               Starres
               in
               the
               Zodiack
               ,
               that
               appeare
               aboue
               the
               Horizon
               ,
               Prop.
               28.
               
            
             
               To
               know
               at
               any
               time
               of
               the
               yeare
               ,
               what
               Starres
               in
               the
               Zodiack
               arise
               or
               set
               Cosmically
               ,
               Achronycally
               ,
               or
               Heliacally
               ,
               Prop.
               29.
               
            
          
        
      
       
         
         
           
             
               The
               Meridian
               Line
               .
            
          
        
      
    
     
       
         
         
           Of
           the
           vse
           of
           the
           SPHAERE
           and
           GLOBE
           .
           Pars
           ,
           1.
           
        
         
           
             The
             Description
             of
             the
             Sphaere
             and
             Globe
             ,
             diuided
             into
             three
             principall
             parts
             ..
          
           
             Whereof
             this
             first
             intreateth
             specially
             of
             the
             Circles
             of
             the
             vppermost
             moueable
             Sphaere
             and
             of
             their
             peculiar
             vses
             .
          
        
         
           
             CHAP.
             I.
             The
             definition
             and
             diuision
             of
             the
             Sphaere
             .
          
           
             THis
             Sphaere
             ,
             is
             nothing
             else
             but
             a
             representation
             of
             the
             Coelestiall
             orbes
             and
             circles
             ,
             that
             haue
             beene
             imagined
             for
             the
             easier
             vnderstanding
             ,
             expressing
             ,
             and
             counting
             of
             the
             motions
             and
             appa●ences
             ,
             eyther
             common
             to
             the
             whole
             Heauens
             ,
             or
             proper
             to
             the
             Sunne
             and
             Moone
             .
          
           
             The
             circles
             of
             this
             Sphaere
             are
             eyther
             inmoueable
             ,
             as
             the
             two
             greatest
             and
             vtmost
             circles
             ,
             the
             Horizon
             and
             Meridian
             ,
             (
             whereto
             is
             adioyned
             the
             little
             houre
             circle
             that
             is
             fixed
             to
             the
             Meridian
             )
             or
             else
             moueable
             ▪
             as
             all
             the
             rest
             contayned
             within
             these
             .
          
        
         
           
           
             CHAP.
             II.
             The
             Description
             of
             the
             Horizon
             .
          
           
             THe
             greatest
             and
             vtmost
             circle
             of
             the
             Sphaere
             that
             lyeth
             leuell
             on
             all
             sides
             from
             the
             ground
             ,
             is
             called
             the
             Horizon
             ,
             which
             is
             deuided
             into
             7.
             limbs
             ,
             or
             borders
             .
             The
             first
             and
             vtmost
             of
             them
             conteyneth
             the
             32.
             points
             of
             the
             Compasse
             ,
             or
             the
             windes
             (
             as
             they
             are
             at
             this
             day
             deuided
             and
             vsed
             by
             Sea-men
             )
             with
             their
             Latine
             names
             adjoyned
             vnto
             them
             .
             The
             second
             limbe
             conteyneth
             the
             names
             and
             diuisions
             of
             the
             12.
             
             Windes
             as
             they
             were
             wont
             to
             bee
             deuided
             in
             old
             time
             .
             The
             third
             is
             deuided
             into
             the
             moneths
             and
             dayes
             of
             the
             new
             Kalender
             ,
             first
             established
             by
             Pope
             GREGORIE
             the
             XIII
             .
             and
             now
             vsed
             in
             many
             places
             beyond
             the
             Seas
             .
             In
             the
             fourth
             limbe
             are
             set
             downe
             the
             moneths
             and
             dayes
             of
             the
             ordinarie
             Kalender
             vsed
             in
             England
             .
             Next
             within
             this
             ,
             are
             placed
             the
             12.
             
             Signes
             and
             degrees
             of
             the
             Zodiacke
             ,
             that
             so
             the
             place
             of
             the
             Sunne
             might
             bee
             presently
             knowne
             for
             any
             day
             of
             the
             yeare
             giuen
             ,
             or
             contrariwise
             ,
             that
             the
             day
             of
             the
             Moneth
             might
             be
             readily
             found
             by
             the
             place
             of
             the
             Sunne
             .
             After
             this
             ,
             followeth
             the
             sixt
             limbe
             conteyning
             the
             32.
             
             Windes
             or
             points
             of
             the
             Compasse
             ,
             with
             letters
             representing
             the
             names
             now
             in
             vse
             amongst
             English
             Marriners
             .
             The
             seuenth
             and
             last
             limbe
             next
             the
             innermost
             edge
             of
             the
             Horizon
             ,
             is
             deuided
             into
             360.
             degrees
             with
             figures
             set
             to
             euery
             tenth
             degree
             ,
             beginning
             from
             the
             points
             of
             East
             and
             West
             ,
             and
             ending
             at
             North
             and
             South
             ;
             that
             so
             the
             number
             of
             any
             degree
             of
             the
             Horizon
             might
             bee
             the
             easilier
             knowne
             :
             Which
             Circle
             appeareth
             
             most
             plainely
             to
             them
             that
             are
             in
             a
             plaine
             Champion
             Countrie
             ,
             or
             vpon
             the
             Sea
             close
             by
             the
             water
             in
             a
             cleare
             calme
             day
             .
          
        
         
           
             CHAP.
             III.
             The
             vses
             of
             the
             Horizon
             .
          
           
             1.
             
             IT
             deuideth
             the
             vpper
             and
             visible
             part
             of
             the
             Heauens
             from
             the
             nether
             halfe
             that
             is
             hidden
             out
             of
             our
             sight
             .
          
           
             2.
             
             It
             sheweth
             partly
             the
             difference
             of
             a
             right
             and
             oblique
             Sphaere
             ,
             for
             when
             this
             circle
             and
             the
             Equinoctiall
             ,
             crosse
             each
             other
             at
             the
             right
             Angles
             ,
             it
             is
             said
             to
             be
             a
             right
             Sphaere
             ,
             otherwise
             when
             they
             make
             oblique
             Angles
             one
             with
             another
             ,
             it
             is
             called
             an
             oblique
             Sphaere
             .
          
           
             3.
             
             In
             an
             oblique
             Sphaere
             this
             circle
             seuereth
             those
             Starres
             which
             neuer
             rise
             nor
             set
             ,
             but
             are
             alwayes
             eyther
             aboue
             or
             beneath
             the
             Horizon
             ,
             from
             such
             Starres
             as
             rise
             and
             set
             in
             euery
             24.
             houres
             .
             For
             all
             the
             Northerly
             starres
             that
             are
             no
             further
             distant
             from
             the
             North
             pole
             ,
             then
             the
             North
             pole
             is
             from
             the
             Horizon
             ,
             doe
             neuer
             set
             ,
             but
             are
             alwayes
             aboue
             the
             Horizon
             :
             And
             contrariwise
             ,
             those
             Starres
             that
             bee
             about
             the
             South
             pole
             ,
             no
             further
             distant
             from
             it
             then
             it
             is
             from
             the
             Horizon
             ,
             doe
             neuer
             rise
             ,
             but
             are
             alwayes
             hidden
             out
             of
             sight
             vnder
             the
             Horizon
             .
          
           
             4.
             
             In
             respect
             of
             this
             circle
             ,
             the
             Sunne
             ,
             Moone
             and
             Starres
             ,
             or
             any
             other
             part
             or
             point
             of
             the
             Heauens
             ,
             are
             sayd
             to
             rise
             or
             set
             :
             For
             when
             they
             come
             vp
             from
             vnder
             the
             Horizon
             ,
             they
             are
             sayd
             to
             rise
             ;
             otherwise
             when
             they
             goe
             from
             aboue
             the
             Horizon
             downe
             vnderneath
             the
             same
             ,
             they
             are
             sayd
             to
             set
             .
          
           
           
             5.
             
             And
             hereof
             it
             commeth
             that
             the
             ascendent
             ,
             and
             descendent
             are
             found
             by
             this
             Circle
             :
             for
             that
             part
             of
             the
             Ecliptick
             that
             is
             at
             the
             East
             part
             of
             the
             Horizon
             arising
             ,
             is
             the
             Ascendent
             ;
             and
             the
             point
             opposite
             to
             this
             at
             the
             West
             part
             of
             the
             Horizon
             ,
             may
             be
             called
             the
             Descendent
             .
          
           
             6.
             
             This
             Circle
             partly
             sheweth
             the
             difference
             of
             ascention
             of
             any
             part
             or
             point
             of
             the
             Heauens
             .
          
           
             7.
             
             In
             this
             Circle
             we
             reckon
             how
             farre
             the
             Sunne
             ,
             the
             Moone
             ,
             or
             any
             Starre
             ,
             or
             point
             of
             Heauen
             ,
             ariseth
             from
             the
             point
             of
             due
             East
             .
          
           
             8.
             
             The
             Horizon
             determineth
             the
             time
             of
             the
             artificiall
             day
             and
             night
             :
             for
             we
             call
             the
             time
             w●●rein
             the
             Sunne
             abideth
             aboue
             the
             Horizon
             ,
             an
             artificiall
             day
             :
             And
             the
             time
             that
             he
             continueth
             vnder
             the
             Horizon
             ,
             is
             the
             artificiall
             night
             .
          
           
             9.
             
             This
             Circle
             sheweth
             the
             reason
             of
             the
             equality
             of
             artificiall
             dayes
             and
             nights
             ,
             in
             a
             right
             Sphaere
             :
             and
             of
             the
             inequality
             of
             them
             in
             an
             oblique
             Sphaere
             .
             For
             in
             a
             right
             Sphaere
             ,
             the
             Horizon
             deuideth
             all
             the
             paralels
             of
             the
             Sunne
             or
             Circles
             of
             the
             naturall
             dayes
             ,
             into
             equall
             parts
             :
             But
             in
             an
             oblique
             Sphaere
             ,
             it
             deuideth
             them
             into
             vnequall
             parts
             .
          
           
             10.
             
             By
             meanes
             of
             this
             Circle
             ,
             wee
             know
             what
             Starres
             ,
             and
             what
             Eclipses
             ,
             Coniunctions
             ,
             or
             other
             aspects
             of
             the
             Planets
             may
             bee
             seene
             in
             our
             Hemisphere
             at
             any
             time
             .
          
           
             11.
             
             From
             the
             Horizon
             is
             measured
             the
             twilight
             :
             For
             in
             the
             morning
             the
             Sunne
             being
             vnder
             the
             Horizon
             about
             18.
             degrees
             of
             the
             verticall
             ,
             Circle
             ,
             the
             twilight
             beginneth
             :
             And
             when
             the
             Sunne
             is
             so
             much
             vnder
             the
             Horizon
             at
             Euening
             ,
             the
             twilight
             endeth
             .
          
           
           
             12.
             
             This
             Circle
             is
             of
             especiall
             vse
             in
             Geography
             ,
             for
             from
             it
             wee
             begin
             to
             account
             the
             eleuation
             of
             the
             Pole
             ,
             and
             of
             the
             Equinoctiall
             circle
             ,
             whereby
             the
             Latitude
             of
             any
             place
             is
             knowne
             .
          
           
             13.
             
             In
             Astrologie
             for
             erecting
             a
             figure
             ,
             this
             Circle
             sheweth
             the
             beginning
             of
             the
             first
             and
             seauenth
             Houses
             .
          
        
         
           
             CHAP.
             IIII.
             The
             description
             of
             the
             Meridian
             .
          
           
             NExt
             the
             Horizon
             ,
             succeeds
             the
             Meridian
             standing
             vpright
             on
             edge
             ,
             and
             crossing
             the
             Horizon
             at
             right
             angles
             in
             the
             points
             of
             North
             and
             South
             .
             This
             circle
             is
             diuided
             on
             both
             sides
             at
             the
             inner
             edge
             into
             360
             ▪
             Degrees
             ,
             with
             figures
             set
             to
             euery
             tenth
             degree
             ,
             beginning
             at
             the
             Equinoctiall
             ,
             and
             ending
             at
             the
             Poles
             with
             90.
             and
             beginning
             also
             at
             the
             Poles
             ,
             and
             ending
             at
             the
             Equinoctiall
             with
             90.
             
             The
             numbers
             beginning
             at
             the
             Pole
             ,
             serue
             to
             set
             the
             Sphaere
             readily
             to
             any
             eleuation
             desired
             .
             The
             other
             numbers
             beginning
             at
             the
             Equinoctiall
             ,
             shew
             presently
             the
             declination
             of
             any
             degree
             of
             the
             Zodiacke
             ,
             or
             of
             any
             point
             assigned
             in
             the
             Sphaere
             ,
             one
             quarter
             of
             the
             Meridian
             on
             eyther
             side
             thereof
             from
             the
             Equinoctiall
             to
             both
             Poles
             ,
             sheweth
             the
             Climates
             ,
             and
             the
             quantities
             of
             the
             longest
             dayes
             .
          
        
         
           
             CHAP.
             V.
             The
             vses
             of
             the
             Meridian
             .
          
           
             1.
             
             IT
             deuideth
             the
             World
             into
             two
             halfes
             or
             Hemisphaeres
             :
             that
             is
             ,
             the
             East
             and
             the
             West
             hemisphaeres
             .
             The
             Easterly
             hemisphaere
             is
             all
             that
             
             part
             of
             the
             world
             which
             is
             on
             the
             East-side
             of
             the
             Meridian
             ,
             and
             the
             other
             halfe
             may
             bee
             called
             the
             West
             hemisphaere
             .
          
           
             2.
             
             It
             sheweth
             the
             North
             and
             South
             parts
             of
             the
             world
             ,
             for
             the
             two
             intersections
             of
             the
             Meridian
             with
             the
             Horizon
             ,
             shew
             the
             very
             points
             of
             North
             and
             South
             .
             The
             South
             point
             is
             that
             which
             is
             directly
             vnder
             the
             Sunne
             at
             noone
             :
             And
             the
             point
             right
             ouer
             against
             this
             ,
             is
             called
             the
             North-point
             .
          
           
             3.
             
             It
             deuideth
             the
             arches
             of
             the
             Equinoctiall
             ,
             and
             of
             all
             his
             Paralels
             ,
             into
             two
             equall
             parts
             both
             aboue
             and
             beneath
             the
             Horizon
             .
          
           
             4.
             
             And
             therefore
             it
             deuideth
             the
             artificiall
             Day
             and
             Night
             into
             two
             equall
             parts
             .
          
           
             5.
             
             And
             consequently
             ,
             it
             sheweth
             midday
             and
             midnight
             .
          
           
             6.
             
             In
             an
             oblique
             Sphaere
             it
             serueth
             in
             stead
             of
             a
             right
             Horizon
             (
             that
             is
             )
             an
             Horizon
             that
             maketh
             right
             angles
             with
             the
             Equinoctiall
             .
          
           
             7.
             
             Therefore
             the
             Astronomers
             begin
             their
             account
             of
             times
             (
             which
             are
             measured
             by
             the
             equall
             motion
             of
             the
             Equinoctiall
             )
             from
             the
             Meridian
             :
             the
             principall
             of
             which
             times
             ,
             is
             the
             naturall
             day
             which
             is
             vsually
             begun
             from
             midday
             ,
             or
             midnight
             .
          
           
             8.
             
             This
             Circle
             sheweth
             the
             highest
             and
             lowest
             heights
             of
             the
             Sunne
             and
             Starres
             ,
             which
             is
             most
             manifest
             in
             those
             Starres
             that
             are
             alwayes
             aboue
             the
             Horizon
             .
             These
             heights
             are
             called
             the
             Meridian
             altitudes
             of
             the
             Sun
             or
             Starres
             ,
             which
             heights
             are
             chiefely
             obserued
             by
             Astronomers
             and
             Nauigators
             with
             great
             diligence
             .
          
           
           
             9.
             
             In
             this
             Circle
             ,
             wee
             obserue
             the
             distance
             of
             the
             Tropickes
             ,
             and
             the
             greatest
             obliquitie
             of
             the
             Zodiacke
             .
          
           
             10.
             
             In
             this
             Circle
             ,
             wee
             obserue
             and
             count
             the
             Latitudes
             of
             places
             ,
             the
             height
             of
             the
             Pole
             ,
             and
             of
             the
             Equinoctiall
             .
             For
             the
             height
             of
             the
             Pole
             or
             Equinoctiall
             ,
             is
             nothing
             else
             but
             the
             arch
             of
             the
             Meridian
             contained
             betweene
             the
             Pole
             or
             Equinoctiall
             and
             the
             Horizon
             .
             The
             height
             of
             the
             Pole
             is
             alwayes
             equall
             to
             the
             Latitude
             of
             the
             place
             .
             The
             height
             of
             the
             Equinoctiall
             is
             equall
             to
             the
             Complement
             of
             the
             Latitude
             and
             therefore
             it
             being
             substracted
             out
             of
             90.
             〈◊〉
             shall
             remaine
             the
             height
             of
             the
             Pole.
             
          
           
             11.
             
             The
             Meridian
             sheweth
             the
             longit●●●
             of
             places
             in
             Geographie
             .
          
           
             12.
             
             In
             the
             Meridian
             ,
             are
             measured
             the
             bredth
             of
             the
             Zones
             and
             Climates
             .
          
           
             13.
             
             This
             circle
             in
             Astrologie
             ,
             sheweth
             the
             highest
             and
             lowest
             parts
             of
             Heauen
             ,
             which
             are
             the
             beginnings
             of
             two
             principall
             Houses
             :
             that
             is
             ,
             the
             fourth
             and
             the
             tenth
             houses
             .
          
        
         
           
             CHAP.
             VI.
             The
             description
             of
             the
             Houre-circle
             ,
             and
             Poles
             .
          
           
             THe
             little
             Circle
             fastned
             to
             the
             Meridia●
             is
             called
             the
             Houre-circle
             ,
             which
             is
             deuided
             into
             24.
             equall
             parts
             ,
             signifying
             and
             representi●●
             vnto
             vs
             so
             many
             equall
             houres
             ,
             whereof
             both
             the
             〈◊〉
             houres
             are
             fixed
             iust
             vpon
             the
             Meridian
             ,
             becaus●●●hen
             the
             Sunne
             commeth
             to
             the
             Meridian
             ,
             it
             is
             iust
             twelue
             a
             clocke
             :
             the
             vpper
             XII
             .
             serueth
             for
             the
             Day
             ;
             and
             the
             other
             XII
             .
             beneath
             serueth
             for
             the
             Night
             .
          
           
           
             The
             Index
             ,
             or
             the
             Painter
             in
             forme
             of
             an
             Arrow
             ,
             fastned
             vpon
             the
             Pinne
             that
             commeth
             through
             the
             midst
             and
             Center
             of
             this
             circle
             ,
             is
             made
             to
             shew
             and
             point
             out
             the
             said
             houres
             as
             need
             shall
             requite
             ,
             in
             the
             vse
             of
             the
             Sphaere
             .
          
           
             The
             vse
             of
             this
             houre
             Circle
             shall
             be
             shewed
             hereafter
             ,
             when
             we
             shall
             speake
             of
             the
             common
             vse
             of
             many
             circles
             of
             the
             Sphaere
             together
             .
             And
             these
             two
             Circles
             (
             that
             is
             ,
             the
             Meridian
             and
             Horizon
             )
             are
             called
             immoueable
             ,
             because
             they
             keepe
             themselues
             alwayes
             ,
             and
             in
             all
             places
             ouer
             the
             same
             parts
             of
             the
             Earth
             ;
             where
             as
             all
             the
             rest
             (
             conteyned
             within
             these
             two
             )
             moue
             round
             about
             altogether
             with
             one
             motion
             in
             the
             space
             of
             foure
             and
             twenty
             houres
             .
          
           
             This
             motion
             (
             being
             common
             to
             the
             whole
             Heauens
             )
             is
             made
             about
             two
             Points
             or
             Poles
             ,
             represented
             in
             this
             Sphaere
             ,
             by
             the
             two
             Wyre
             pinnes
             about
             which
             the
             Sphaere
             is
             turned
             ;
             whereof
             the
             one
             that
             commeth
             through
             the
             middest
             of
             the
             little
             Circle
             fastned
             to
             the
             Meridian
             (
             which
             wee
             call
             the
             houre
             Circle
             )
             representeth
             vnto
             vs
             the
             Pole
             Articke
             or
             the
             North
             Pole
             :
             the
             other
             because
             it
             is
             opposite
             to
             this
             ,
             is
             called
             the
             Antartick
             pole
             ,
             that
             is
             the
             right
             opposit
             ,
             to
             ,
             or
             right
             ouer
             against
             the
             North
             pole
             ,
             which
             is
             also
             the
             South
             pole
             .
          
        
         
           
             CHAP.
             VII
             .
             Of
             the
             Equinoctiall
             Circle
             .
          
           
             THat
             Circle
             which
             compasseth
             about
             the
             midst
             of
             the
             Sphaere
             ,
             
             and
             is
             euery
             where
             of
             equall
             distance
             from
             both
             Poles
             ,
             is
             called
             the
             Equinoctiall
             circle
             ,
             or
             the
             Equator
             ;
             either
             because
             it
             is
             equally
             
             distant
             from
             both
             Poles
             of
             the
             world
             ;
             or
             ●●se
             because
             the
             Sunne
             comming
             vnder
             this
             Circle
             maketh
             equality
             of
             dayes
             and
             nights
             throughout
             the
             world
             .
          
           
             It
             is
             deuided
             at
             the
             vtmost
             edge
             ,
             or
             both
             sides
             thereof
             into
             360.
             
             Degrees
             ,
             with
             figures
             〈◊〉
             to
             euery
             tenth
             degree
             ,
             beginning
             at
             the
             beginning
             of
             Aries
             ,
             and
             proceeding
             Eastwards
             ,
             till
             you
             become
             about
             to
             the
             same
             point
             againe
             .
          
           
             
               This
               Circle
               hath
               many
               vses
            
             .
          
           
             1.
             
             It
             is
             the
             measure
             of
             the
             first
             〈◊〉
             .
             For
             this
             onely
             amongst
             all
             the
             Circle
             of
             the
             Sphaere
             is
             moued
             equally
             both
             in
             a
             right
             and
             〈…〉
             Sphaere
             ,
             because
             ●
             alone
             being
             perpendicular
             to
             the
             〈…〉
             world
             ,
             about
             which
             the
             Sphaere
             is
             equally
             turned
             ,
             is
             deuided
             into
             two
             haltes
             by
             euery
             Horizon
             in
             the
             same
             points
             .
          
           
             2.
             
             It
             is
             the
             measure
             of
             time
             ;
             because
             it
             measureth
             the
             quantitie
             of
             the
             artificiall
             and
             naturall
             dayes
             ,
             of
             which
             Moneths
             and
             Yeares
             are
             made
             :
             It
             measureth
             also
             the
             quantitie
             of
             Houres
             and
             of
             other
             times
             which
             the
             Sunne
             maketh
             going
             vnder
             the
             Zodiacke
             .
             And
             therefore
             the
             degrees
             of
             the
             Equinoctiall
             are
             called
             tempora
             (
             that
             is
             )
             times
             .
          
           
             3.
             
             It
             sheweth
             the
             two
             Equinoctiall
             points
             in
             the
             Eclipticke
             ,
             cutting
             the
             Ecliptick
             in
             two
             places
             ,
             which
             are
             the
             beginnings
             of
             Aries
             and
             Libra
             :
             and
             the
             Sun
             when
             hee
             commeth
             to
             those
             two
             points
             ,
             is
             equally
             distant
             from
             both
             Poles
             of
             the
             World
             ,
             and
             maketh
             equalitie
             of
             dayes
             and
             nights
             in
             all
             places
             ;
             which
             hapneth
             in
             our
             time
             about
             the
             10.
             or
             11.
             day
             of
             March
             ,
             and
             the
             13.
             or
             14.
             of
             September
             .
          
           
             4.
             
             The
             irregularitie
             of
             the
             Zodiacke
             ,
             and
             of
             all
             
             the
             Signes
             and
             degrees
             thereof
             ,
             is
             measured
             by
             this
             Circle
             .
             For
             seeing
             the
             most
             part
             of
             the
             apparences
             of
             the
             first
             motion
             are
             referred
             to
             the
             Zodiacke
             ,
             which
             is
             not
             turned
             about
             his
             owne
             Poles
             ,
             but
             about
             the
             Poles
             of
             the
             Sphaere
             ,
             and
             therefore
             must
             needs
             bee
             vnequally
             turned
             about
             ;
             it
             was
             needfull
             that
             this
             inequalitie
             should
             be
             ruled
             and
             measured
             by
             some
             other
             equall
             motion
             .
          
           
             5.
             
             It
             deuideth
             the
             Sphaere
             into
             two
             halfes
             (
             which
             they
             call
             Hemisphaeres
             )
             that
             is
             ,
             into
             the
             North
             halfe
             or
             hemisphaere
             ,
             wherein
             is
             the
             North
             pole
             ,
             and
             into
             the
             South
             hemisphaere
             ,
             wherein
             is
             the
             South
             pole
             .
          
           
             6.
             
             So
             it
             deuideth
             the
             Zodiacke
             into
             the
             North
             halfe
             ,
             and
             the
             South
             halfe
             ;
             or
             into
             the
             North
             signes
             ,
             and
             the
             South
             signes
             .
          
           
             7.
             
             From
             this
             Circle
             are
             numbred
             the
             declinations
             of
             the
             Starres
             ,
             and
             of
             the
             degrees
             and
             parts
             of
             the
             Eclipticke
             ,
             and
             of
             any
             other
             point
             of
             Heauen
             .
          
           
             8.
             
             And
             in
             this
             Circle
             are
             counted
             the
             right
             ascentions
             of
             the
             same
             Degrees
             and
             Starres
             ,
             &c.
             
             For
             the
             right
             ascention
             of
             any
             starre
             or
             point
             of
             the
             Heauens
             ,
             is
             nothing
             else
             but
             the
             Arch
             of
             the
             Equinoctiall
             circle
             contained
             betweene
             the
             beginning
             of
             Aries
             and
             the
             Meridian
             ,
             the
             same
             Starre
             or
             point
             being
             first
             brought
             vnder
             the
             Meridian
             .
          
           
             9.
             
             In
             the
             Equinoctiall
             is
             counted
             the
             ascentionall
             difference
             and
             the
             oblique
             Ascention
             and
             Descention
             of
             any
             point
             of
             Heauen
             .
             And
             from
             the
             same
             Circle
             is
             reckoned
             the
             distance
             of
             the
             Sunne
             rising
             from
             the
             true
             East
             point
             .
             For
             the
             oblique
             ascention
             or
             descention
             is
             nothing
             else
             but
             the
             arch
             of
             the
             Equinoctiall
             ,
             contained
             betweene
             the
             beginning
             of
             Aries
             ,
             and
             that
             
             point
             of
             the
             Equinoctiall
             Eastwards
             ,
             which
             ariseth
             or
             setteth
             together
             with
             the
             Starre
             or
             point
             that
             is
             giuen
             ,
             in
             an
             oblique
             Sphaere
             .
             And
             the
             difference
             ascentionall
             or
             descentionall
             is
             nought
             else
             but
             the
             arch
             of
             the
             Equator
             ,
             whereby
             the
             right
             and
             oblique
             ascention
             or
             descention
             of
             a
             Starre
             ,
             or
             any
             other
             point
             in
             Heauen
             doe
             differ
             each
             from
             other
             .
             The
             distance
             of
             the
             sunnes
             rising
             from
             the
             true
             East
             point
             (
             which
             in
             Latine
             is
             called
             
               Amplitudo
               ortiua
               ,
            
             )
             is
             the
             arch
             of
             the
             Horizon
             contayned
             betweene
             the
             Equinoctiall
             and
             the
             paralell
             of
             the
             Sunne
             ,
             or
             his
             Center
             when
             he
             riseth
             .
          
           
             10.
             
             In
             Geographie
             wee
             count
             the
             Longitudes
             of
             places
             in
             this
             Circle
             ;
             and
             from
             it
             we
             reckon
             the
             Latitudes
             ,
             in
             the
             Globe
             of
             the
             earth
             ,
             and
             in
             Maps
             ,
             and
             sea
             Charts
             .
             For
             the
             longitude
             of
             a
             place
             is
             nothing
             else
             but
             the
             arch
             of
             the
             Equinoctiall
             circle
             contayned
             betweene
             two
             Meridians
             ,
             whereof
             one
             goeth
             by
             the
             canary
             Ilands
             ,
             and
             the
             other
             by
             the
             place
             that
             is
             giuen
             ,
             And
             the
             latitude
             of
             a
             place
             is
             the
             arch
             of
             a
             Meridian
             contayned
             betweene
             the
             Equinoctiall
             ,
             and
             the
             Zenith
             of
             the
             place
             that
             was
             giuen
             .
          
           
             11.
             
             In
             Dialling
             this
             Circle
             is
             of
             especiall
             vse
             .
             For
             by
             meanes
             of
             it
             the
             spaces
             of
             the
             houres
             are
             deuided
             in
             all
             kindes
             of
             Dials
             ,
             horizontall
             ,
             erect
             ,
             direct
             ,
             declining
             ,
             inclining
             ,
             reclining
             ,
             &c.
             
          
           
             12.
             
             In
             Astrologie
             the
             twelue
             Houses
             are
             set
             out
             by
             the
             equall
             diuisions
             of
             this
             Circle
             into
             twelue
             parts
             ,
             according
             to
             the
             way
             deuised
             by
             Regiomontanus
             ,
             which
             way
             is
             commonly
             called
             rationall
             or
             reasonable
             .
             And
             this
             Circle
             gouerneth
             the
             directions
             ,
             whereby
             things
             to
             come
             are
             artificially
             fore-told
             .
          
        
         
           
           
             CHAP.
             VIII
             .
             The
             description
             of
             the
             Zodiacke
             .
          
           
             THe
             great
             broad
             Circle
             that
             compasseth
             about
             the
             Sphaere
             obliquely
             ,
             comming
             nearer
             the
             Pole
             of
             the
             Sphaere
             in
             one
             place
             then
             in
             another
             ,
             is
             called
             the
             Zodiacke
             .
          
           
             Round
             about
             through
             the
             middest
             of
             this
             Circle
             ,
             is
             drawne
             the
             Circumference
             commonly
             called
             the
             Eclipticke
             line
             ,
             deuiding
             the
             whole
             Sphaere
             ,
             and
             the
             whole
             bredth
             of
             the
             Zodiacke
             throughout
             ,
             into
             two
             equall
             parts
             .
          
           
             In
             this
             Sphaere
             there
             are
             represented
             vnto
             vs
             two
             Eclipticke
             lines
             .
             The
             one
             may
             be
             called
             the
             middle
             ,
             or
             fixed
             Eclipticke
             ,
             which
             keepeth
             alwayes
             the
             same
             distance
             or
             obliquitie
             from
             the
             Equinoctiall
             .
             The
             other
             may
             bee
             called
             the
             true
             or
             moueable
             Eclipticke
             ,
             because
             it
             maketh
             not
             alwayes
             the
             same
             angles
             of
             intersection
             with
             the
             Equator
             ,
             but
             sometimes
             greater
             ,
             sometimes
             lesse
             .
             For
             the
             greatest
             obliquitie
             of
             the
             Zodiacke
             ,
             which
             not
             long
             before
             Ptolomees
             time
             was
             obserued
             to
             bee
             23.
             
             Degrees
             and
             52.
             
             Minutes
             ;
             in
             Copernicus
             his
             time
             ,
             was
             hardly
             found
             to
             exceed
             23.
             degrees
             28.
             minutes
             ,
             according
             to
             his
             obseruation
             ,
             and
             therefore
             hee
             thought
             that
             the
             difference
             betweene
             the
             greatest
             and
             least
             obliquitie
             of
             the
             Zodiacke
             ,
             was
             24.
             
             Minutes
             :
             and
             the
             middle
             or
             meane
             obliquitie
             betweene
             both
             these
             ,
             to
             bee
             23.
             
             Degrees
             40.
             
             Minutes
             .
          
           
             The
             manner
             of
             the
             variation
             of
             this
             obliquitie
             may
             in
             some
             sort
             bee
             shewed
             by
             this
             Sphaere
             ,
             if
             we
             suppose
             the
             fixed
             Eclipticke
             drawne
             round
             about
             through
             
             the
             middest
             of
             the
             Zodiack
             to
             be
             23.
             degrees
             40.
             min.
             distant
             from
             the
             Equinoctial
             at
             the
             beginning
             of
             Cancer
             and
             Capricorne
             :
             and
             the
             moueable
             Eclipticke
             (
             fastned
             as
             it
             were
             vpon
             two
             Poles
             at
             the
             beginning
             of
             Aries
             and
             Libra
             ,
             and
             so
             hauing
             alwayes
             the
             same
             points
             of
             intersection
             with
             the
             middle
             Eclipticke
             and
             Equinoctiall
             )
             to
             bee
             moued
             vp
             and
             downe
             aboue
             and
             beneath
             the
             middle
             Eclipticke
             ,
             by
             the
             space
             of
             12.
             
             Minutes
             at
             the
             beginning
             of
             Cancer
             and
             Capricorne
             :
             and
             this
             motion
             to
             finish
             his
             reuolution
             once
             in
             3432.
             
             Iulian
             yeares
             .
          
           
             The
             bredth
             of
             the
             Zodiacke
             is
             bounded
             by
             the
             greatest
             latitudes
             of
             the
             Planets
             ,
             especially
             of
             Venus
             and
             Mars
             ,
             which
             sometimes
             hath
             almost
             7.
             degrees
             of
             latitude
             .
          
           
             The
             Zodiacke
             is
             diuided
             by
             the
             Equinoctiall
             into
             two
             semicircles
             .
          
           
             The
             one
             aboue
             the
             Equinoctiall
             is
             called
             the
             Northerly
             semicircle
             :
             the
             other
             halfe
             beneath
             the
             Equinoctiall
             ,
             is
             the
             Southerne
             semicircle
             of
             the
             Zodiacke
             .
          
           
             So
             long
             as
             the
             Sunne
             moueth
             vnder
             the
             first
             of
             these
             semicircles
             ,
             the
             dayes
             are
             longer
             then
             the
             nights
             ,
             otherwise
             they
             are
             shorter
             .
          
           
             Each
             of
             these
             semicircles
             is
             againe
             deuided
             into
             two
             parts
             ,
             and
             so
             the
             whole
             Zodiack
             into
             foure
             quarters
             :
             the
             first
             from
             Aries
             to
             Cancer
             ,
             may
             be
             called
             the
             vernall
             or
             Spring-quarter
             ,
             which
             in
             this
             Sphaere
             is
             also
             shewed
             by
             the
             word
             Ver
             (
             signifying
             the
             Spring
             :
             )
             The
             next
             from
             Cancer
             to
             Libra
             ,
             the
             Summer
             quarter
             ,
             wherein
             is
             written
             the
             word
             Ae●tas
             signifying
             the
             Summer
             .
             The
             3.
             from
             Libra
             to
             Capricorne
             ,
             is
             the
             Haruest
             quarter
             ,
             wherein
             you
             shall
             finde
             
             in
             this
             Sphaere
             the
             word
             Autumnus
             which
             signifieth
             Autumne
             or
             Haruest
             .
             The
             fourth
             and
             the
             last
             ,
             from
             the
             beginning
             of
             Capricorne
             to
             Aries
             ,
             is
             called
             the
             winter
             Quarter
             ,
             which
             in
             this
             Sphaere
             is
             shewed
             by
             this
             word
             Hiems
             ,
             which
             signifieth
             the
             Winter
             .
             And
             these
             foure
             quarters
             of
             the
             Zodiacke
             are
             thus
             called
             by
             the
             names
             of
             the
             Quarters
             of
             the
             yeare
             ,
             because
             the
             Sunne
             mouing
             vnder
             those
             quarters
             of
             the
             Zodiacke
             ,
             maketh
             those
             foure
             Quarters
             of
             the
             yeare
             .
             Euery
             one
             of
             these
             quarters
             of
             the
             Zodiacke
             is
             againe
             deuided
             into
             three
             parts
             ,
             and
             so
             the
             whole
             compasse
             of
             the
             Zodiacke
             into
             12.
             which
             are
             called
             the
             12.
             
             Signes
             ,
             whereof
             euery
             one
             contayneth
             30.
             
             Degrees
             in
             length
             from
             West
             to
             East
             ,
             and
             is
             in
             bredth
             equall
             to
             the
             bredth
             of
             the
             Zodiacke
             .
             These
             Signes
             ,
             and
             the
             Zodiacke
             it selfe
             haue
             their
             beginning
             from
             that
             common
             meeting
             ,
             or
             crossing
             of
             the
             Eclipticke
             ,
             and
             the
             Equinoctiall
             ,
             where
             the
             Eclipticke
             beginneth
             to
             arise
             aboue
             the
             Equinoctiall
             towards
             the
             North
             pole
             :
             and
             they
             are
             called
             by
             these
             names
             ;
             
               Aries
               ,
               Taurus
               ,
               Gemini
               ,
               Cancer
               ,
               Leo
               ,
               Virgo
               ,
               Libra
               ,
               Scorpio
               ,
               Sagitarie
               ,
               Capricorne
               ,
               Aquarie
               ,
               Pisces
               .
            
             That
             is
             to
             say
             ,
             The
             Ramme
             ,
             the
             Bull
             ,
             the
             Twinnes
             ,
             the
             Crab
             ,
             the
             Lyon
             ,
             the
             Virgin
             ,
             the
             Ballance
             ,
             the
             Scorpion
             ,
             the
             Shooter
             ,
             the
             Goat
             ,
             the
             Water-pourer
             ,
             the
             Fishes
             .
             And
             they
             are
             signified
             by
             these
             Characters
             ,
             ♈
             ♉
             ,
             ♊
             ,
             ♋
             ,
             ♌
             ,
             ♍
             ,
             ♎
             ,
             ♏
             ,
             ♐
             ,
             ♑
             ,
             ♒
             ,
             ♓
             .
             This
             deuision
             of
             the
             Zodiacke
             into
             12.
             
             Signes
             and
             of
             euery
             signe
             into
             30.
             
             Degrees
             ,
             nature
             it selfe
             seemeth
             to
             haue
             shewed
             by
             the
             motions
             of
             the
             Sun
             and
             Moone
             .
             For
             in
             what
             time
             the
             Sunne
             moueth
             once
             about
             the
             whole
             compasse
             of
             the
             Zodiacke
             ,
             the
             Moone
             maketh
             twelue
             reuolutions
             through
             the
             same
             .
             Therefore
             as
             
             the
             time
             of
             a
             yeare
             is
             deuided
             into
             12.
             
             Moones
             ,
             so
             the
             Zodiacke
             is
             deuided
             into
             12.
             
             Signes
             :
             And
             as
             euery
             Moneth
             contayneth
             30.
             dayes
             ,
             so
             euery
             signe
             is
             deuided
             into
             30.
             parts
             ,
             which
             they
             call
             Degrees
             ,
             which
             signifieth
             as
             much
             as
             steps
             ,
             because
             the
             Sunne
             steppeth
             ,
             or
             goeth
             forwards
             almost
             so
             much
             as
             a
             degree
             in
             euery
             day
             ,
             from
             the
             West
             Eastwards
             vnder
             the
             Zodiacke
             .
          
           
             The
             Zodiacke
             is
             otherwise
             also
             deuided
             into
             two
             semicircles
             ,
             the
             one
             (
             from
             Capricorne
             to
             Cancer
             )
             ascending
             ,
             because
             that
             so
             long
             as
             the
             Sunne
             or
             any
             of
             the
             Planets
             are
             in
             that
             semicircle
             ,
             they
             still
             ascend
             and
             rise
             higher
             and
             higher
             aboue
             the
             Horizon
             .
             The
             other
             semicircle
             of
             the
             Zodiacke
             ,
             from
             Cancer
             to
             Capricorne
             ,
             is
             called
             descending
             ,
             because
             the
             Sunne
             or
             Planets
             being
             in
             that
             semicircle
             ,
             come
             downe
             euery
             day
             lower
             then
             other
             .
          
           
             The
             12.
             
             Signes
             are
             by
             the
             Astrologians
             diuersly
             deuided
             ,
             first
             into
             chiefe
             ,
             meane
             ,
             and
             common
             signes
             .
             The
             chiefe
             signes
             (
             which
             are
             also
             called
             Cardinall
             ,
             that
             is
             the
             principall
             signes
             )
             are
             
               Aries
               ,
               Cancer
               ,
               Libra
            
             ,
             and
             Capricorne
             ,
             because
             they
             come
             next
             after
             the
             principall
             points
             of
             the
             Zodiacke
             ,
             that
             is
             ,
             the
             two
             Equinoctiall
             points
             at
             the
             beginnings
             of
             Aries
             ,
             and
             Libra
             ;
             and
             the
             two
             solstitiall
             points
             of
             Cancer
             and
             Capricorne
             .
             The
             meane
             signes
             (
             which
             are
             also
             called
             fixed
             )
             are
             
               Taurus
               ,
               Leo
               ,
               Scorpio
            
             ,
             and
             Aquarius
             .
             They
             are
             called
             meane
             ,
             because
             they
             are
             placed
             betweene
             the
             chiefe
             or
             principall
             ,
             and
             the
             common
             signes
             .
             They
             are
             called
             fixed
             signes
             ,
             because
             that
             when
             the
             Sunne
             is
             in
             those
             signes
             ,
             wee
             finde
             a
             more
             perfect
             temperature
             of
             the
             Ayre
             ,
             then
             when
             he
             is
             in
             the
             other
             signes
             .
          
           
           
             The
             common
             signes
             (
             which
             are
             also
             called
             double
             bodyed
             )
             are
             
               Gemini
               ,
               Virgo
               ,
               Sagitarie
            
             ,
             and
             Pisces
             .
             They
             are
             called
             common
             ,
             because
             they
             take
             part
             of
             the
             nature
             of
             the
             fixed
             signes
             going
             before
             them
             ,
             and
             of
             the
             Cardinall
             signes
             following
             after
             them
             .
             They
             are
             called
             double
             bodied
             ,
             by
             reason
             of
             their
             Images
             ,
             as
             they
             are
             imagined
             in
             the
             eight
             Sphaere
             ,
             which
             are
             compounded
             of
             two
             bodies
             :
             For
             there
             be
             two
             Twinnes
             ;
             and
             the
             Virgin
             holdeth
             an
             eare
             of
             corne
             in
             her
             hand
             ;
             Sagitarie
             is
             made
             of
             a
             Man
             and
             an
             Horse
             ;
             and
             there
             are
             two
             Fishes
             .
             The
             placing
             ,
             and
             nature
             of
             these
             signes
             brought
             in
             this
             diuision
             .
          
           
             The
             Astrologians
             also
             deuide
             the
             12.
             
             Signes
             into
             foure
             trigons
             of
             triplicities
             ,
             so
             called
             because
             they
             are
             distant
             the
             third
             part
             of
             a
             Circle
             ,
             one
             from
             another
             .
             The
             first
             triplicitie
             contayneth
             
               Aries
               ,
               Leo
            
             ,
             and
             Sagitarius
             ;
             and
             is
             called
             the
             fiery
             trigon
             ,
             or
             triplicitie
             :
             The
             second
             triplicitie
             contayneth
             
               Taurus
               ,
               Virgo
            
             ,
             and
             Capricorne
             ;
             and
             is
             called
             the
             earthly
             trigon
             .
             The
             third
             triplicitie
             contayneth
             
               Gemini
               ,
               Libra
            
             ,
             and
             Aquarius
             ;
             and
             is
             called
             the
             ayrie
             trigon
             .
             The
             fourth
             triplicitie
             contayning
             
               Cancer
               ,
               Scorpio
            
             ,
             and
             Pisces
             ;
             is
             called
             the
             watrie
             trigon
             .
             Nature
             it selfe
             is
             the
             cause
             of
             this
             diuision
             of
             the
             Signes
             also
             .
             For
             into
             these
             Trigons
             of
             the
             signes
             ,
             shee
             hath
             distributed
             the
             Coniunctions
             of
             the
             three
             superiour
             Planets
             :
             especially
             the
             coniunctions
             of
             Saturne
             and
             Iupiter
             ,
             which
             the
             Astrologians
             call
             great
             coniunctions
             .
             For
             examples
             sake
             ,
             if
             there
             bee
             a
             great
             coniunction
             in
             Aries
             ,
             the
             same
             shall
             be
             twenty
             yeares
             after
             in
             Sagitarie
             ,
             and
             other
             twenty
             yeares
             after
             in
             Leo
             ;
             and
             after
             as
             many
             more
             yeares
             ,
             it
             returneth
             againe
             into
             Aries
             .
             The
             reuolution
             of
             one
             Trigon
             contayneth
             
             almost
             200.
             yeares
             ,
             after
             which
             time
             the
             same
             great
             conjunctions
             remoue
             into
             the
             next
             trigon
             .
          
        
         
           
             CHAP.
             IX
             .
             The
             vse
             of
             the
             Zodiack
             .
          
           
             1.
             
             THe
             Zodiack
             is
             the
             measure
             of
             the
             second
             motions
             ,
             as
             the
             Equinoctiall
             is
             the
             measure
             of
             the
             first
             motion
             .
          
           
             2.
             
             For
             in
             this
             Circle
             wee
             reckon
             the
             longitudes
             ,
             and
             from
             it
             we
             count
             the
             latitudes
             of
             all
             the
             Starres
             .
             For
             the
             longitude
             of
             a
             Starre
             is
             nothing
             else
             but
             the
             arch
             of
             the
             Ecliptck
             conteyned
             betweene
             the
             beginning
             of
             Aries
             ,
             and
             the
             circle
             of
             the
             Starres
             latitude
             .
             And
             the
             latitude
             is
             the
             Arch
             of
             a
             great
             circle
             ,
             drawne
             by
             the
             poles
             of
             the
             Ecliptick
             ,
             conteyned
             betweene
             the
             Starre
             and
             the
             Ecliptick
             .
          
           
             3.
             
             According
             to
             this
             circle
             ,
             the
             whole
             Heauen
             ,
             yea
             ,
             the
             whole
             world
             is
             deuided
             into
             twelue
             Signes
             .
             Whereof
             it
             commeth
             that
             because
             of
             this
             Circle
             ,
             aswell
             the
             fixed
             ,
             as
             the
             wandring
             Starres
             which
             we
             call
             Planets
             ,
             yea
             ,
             and
             those
             Starres
             also
             that
             appeare
             of
             a
             sudden
             ,
             as
             blazing
             Starres
             or
             Comets
             ,
             and
             other
             Meteors
             ,
             are
             said
             to
             be
             in
             this
             or
             that
             signe
             ;
             and
             that
             three
             manner
             of
             wayes
             .
          
           
             First
             ,
             to
             be
             in
             a
             signe
             ,
             is
             to
             be
             vnder
             some
             one
             of
             the
             12.
             parts
             of
             the
             Ecliptick
             .
             Thus
             the
             Starres
             which
             are
             vnder
             the
             Ecliptick
             ,
             but
             especially
             the
             Sunne
             which
             runneth
             alwayes
             vnder
             it
             ,
             are
             said
             to
             be
             in
             the
             Signes
             .
          
           
             Secondly
             ,
             because
             the
             Zodiack
             hath
             latitude
             ,
             those
             Starres
             are
             said
             to
             be
             in
             a
             signe
             ,
             which
             although
             they
             be
             beside
             the
             Ecliptick
             ,
             yet
             are
             vnder
             the
             Zodiack
             ,
             and
             so
             any
             of
             the
             other
             Planets
             ,
             which
             for
             the
             most
             
             part
             wander
             beside
             the
             Ecliptick
             ,
             may
             be
             said
             to
             bee
             in
             some
             signe
             .
          
           
             Thirdly
             ,
             if
             we
             vnderstand
             six
             great
             Circles
             to
             bee
             drawne
             by
             the
             beginnings
             of
             the
             twelue
             signes
             ,
             and
             by
             the
             poles
             of
             the
             Eclipticke
             ;
             by
             these
             circles
             the
             whole
             heauen
             (
             or
             rather
             the
             whole
             world
             )
             is
             deuided
             into
             twelue
             parts
             ,
             which
             with
             a
             generall
             name
             are
             called
             signes
             :
             Thus
             all
             the
             Starres
             aswell
             fixed
             as
             Planets
             and
             Comets
             ,
             which
             are
             without
             the
             Zodiacke
             in
             any
             of
             these
             parts
             ,
             may
             be
             said
             to
             be
             in
             some
             signe
             .
          
           
             4.
             
             In
             this
             circle
             are
             noted
             the
             degrees
             of
             the
             signes
             ,
             with
             which
             the
             Starres
             doe
             rise
             and
             set
             ,
             as
             well
             in
             a
             right
             as
             in
             an
             oblique
             Sphaere
             .
             For
             because
             this
             circle
             is
             the
             chiefest
             ,
             all
             Caelestiall
             apparances
             (
             or
             at
             least
             the
             most
             part
             of
             them
             )
             are
             referred
             vnto
             it
             ,
             and
             not
             vnto
             the
             Equinoctiall
             .
             But
             the
             Equinoctiall
             measureth
             the
             times
             of
             their
             risings
             and
             settings
             .
          
           
             5.
             
             The
             obliquitie
             of
             the
             Ecliptick
             is
             the
             cause
             of
             the
             inequalitie
             ,
             aswell
             of
             naturall
             dayes
             in
             both
             Sphaeres
             ,
             as
             of
             artificiall
             dayes
             in
             an
             oblique
             Sphaere
             .
             For
             seeing
             it
             is
             moued
             vnequally
             ,
             because
             it
             is
             moued
             vpon
             other
             Poles
             then
             his
             owne
             ,
             the
             Sunne
             which
             is
             the
             author
             ,
             and
             maker
             of
             times
             mouing
             vnder
             it
             ,
             must
             needs
             make
             vnequall
             dayes
             .
          
           
             6.
             
             The
             chiefe
             times
             are
             defined
             by
             this
             circle
             ,
             as
             the
             time
             of
             a
             yeare
             ,
             by
             the
             motion
             of
             the
             Sunne
             ;
             the
             time
             of
             a
             moneth
             by
             the
             motion
             of
             the
             Moone
             ,
             through
             the
             whole
             compasse
             of
             this
             circle
             .
             Also
             the
             foure
             quarters
             of
             the
             yeare
             ,
             Spring
             ,
             Summer
             ,
             Autumne
             ,
             and
             Winter
             ,
             whereto
             may
             be
             added
             Plato
             his
             great
             yeare
             ,
             which
             is
             the
             time
             wherein
             the
             fixed
             Starres
             make
             one
             reuolution
             about
             the
             axtree
             and
             poles
             of
             the
             Zodiack
             ,
             
             if
             God
             would
             haue
             the
             world
             to
             last
             so
             long
             .
          
           
             7.
             
             The
             Eclipticke
             line
             sheweth
             the
             places
             ,
             and
             times
             of
             the
             Eclipses
             :
             For
             the
             Sunne
             and
             Moone
             ,
             are
             Eclipsed
             onely
             vnder
             it
             ,
             or
             neere
             vnto
             it
             .
          
           
             8.
             
             As
             the
             description
             of
             the
             Tropicks
             dependeth
             on
             the
             obliquitie
             of
             the
             Eclipticke
             ,
             so
             the
             polar
             Circles
             are
             described
             by
             the
             Poles
             thereof
             .
          
           
             9.
             
             Hereof
             it
             commeth
             ,
             that
             by
             reason
             of
             the
             same
             obliquitie
             ,
             the
             Zones
             and
             Climats
             are
             set
             forth
             and
             bounded
             .
          
           
             10.
             
             This
             Circle
             is
             of
             especiall
             vse
             in
             Astrologie
             ,
             for
             it
             distinguisheth
             the
             points
             of
             the
             12.
             
             Houses
             ,
             and
             in
             it
             the
             Aspects
             and
             configurations
             of
             the
             Planets
             are
             obserued
             .
             The
             chiefest
             judgement
             aswell
             in
             casting
             Figures
             as
             in
             reuolutions
             and
             directions
             is
             taken
             from
             this
             circle
             .
          
        
         
           
             CHAP.
             X.
             The
             description
             of
             the
             two
             Colures
             .
          
           
             THe
             two
             circles
             crossing
             each
             other
             at
             right
             Angles
             in
             the
             poles
             of
             the
             Sphaere
             ,
             are
             called
             the
             Colures
             :
             whereof
             the
             one
             that
             passeth
             by
             the
             common
             meeting
             of
             the
             Eclipticke
             and
             Equinoctiall
             ,
             is
             called
             
               Colurus
               aequinoctiorum
            
             ,
             that
             is
             the
             Equinoctiall
             Colure
             ,
             or
             the
             colure
             of
             equall
             dayes
             and
             nights
             .
             The
             other
             passing
             by
             the
             poles
             of
             the
             Eclipticke
             ,
             and
             the
             Solstitiall
             points
             ,
             is
             called
             
               Colurus
               solstitiorum
            
             ,
             the
             Solstitiall
             colure
             ,
             or
             colure
             of
             the
             Sunne-standings
             .
          
           
             
               Vses
               common
               to
               both
               Colures
               .
            
             
               1.
               
               By
               meanes
               of
               these
               two
               Colures
               ,
               all
               the
               mouable
               circles
               of
               the
               materiall
               Sphaere
               are
               framed
               together
               ,
               
               that
               so
               they
               might
               be
               turned
               about
               ,
               like
               as
               the
               whole
               Heauens
               are
               moued
               .
            
             
               2.
               
               The
               Poles
               are
               fastened
               in
               the
               common
               meeting
               of
               these
               two
               Circles
               :
               and
               the
               Poles
               are
               also
               shewed
               by
               the
               same
               common
               meetings
               .
            
             
               3.
               
               They
               shew
               the
               foure
               principall
               points
               of
               the
               Eclipticke
               ;
               that
               is
               ,
               the
               two
               Equinoctiall
               ,
               and
               the
               two
               Solstitiall
               points
               .
            
             
               4.
               
               These
               circles
               shew
               those
               points
               of
               the
               Eclipticke
               ,
               wherein
               the
               Sunne
               is
               either
               equally
               distant
               from
               both
               poles
               of
               the
               Sphaere
               ,
               or
               commeth
               neerest
               to
               either
               of
               them
               :
               In
               which
               points
               the
               Sunne
               maketh
               the
               dayes
               longest
               or
               shortest
               ,
               or
               of
               a
               meane
               length
               betweene
               both
               these
               in
               an
               oblique
               Sphaere
               .
            
             
               5.
               
               They
               deuide
               the
               Ecliptick
               into
               foure
               quarters
               ,
               in
               which
               the
               Sunne
               maketh
               foure
               quarters
               of
               the
               yeare
               ,
               the
               Spring
               ,
               the
               Summer
               ,
               Autumne
               ,
               and
               Winter
               .
            
             
               6.
               
               They
               deuide
               the
               Ecliptick
               and
               Equinoctiall
               into
               such
               foure
               quarters
               ,
               as
               in
               a
               right
               Sphaere
               doe
               rise
               together
               in
               equall
               time
               .
            
          
        
         
           
             CHAP.
             XI
             .
             Vses
             of
             the
             Equinoctiall
             Colure
             .
          
           
             1.
             
             THe
             section
             of
             this
             Circle
             with
             the
             Ecliptick
             ;
             sheweth
             the
             Equinoctiall
             points
             ,
             wherein
             the
             Equinoctiall
             and
             the
             Eclipticke
             doe
             deuide
             and
             crosse
             each
             other
             .
             In
             which
             points
             the
             Sunne
             maketh
             equality
             of
             dayes
             and
             nights
             throughout
             the
             whole
             world
             :
             whereof
             this
             circle
             is
             also
             called
             
               Colurus
               Aequinoctiorum
            
             ;
             that
             is
             ,
             the
             colure
             of
             equall
             dayes
             and
             nights
             ,
             or
             the
             Equinoctiall
             colure
             .
          
           
           
             2.
             
             It
             deuideth
             the
             Eclipticke
             into
             the
             North
             and
             South
             halfes
             .
          
           
             3.
             
             It
             deuideth
             the
             Signes
             wherein
             the
             Sunne
             maketh
             the
             dayes
             longer
             then
             the
             nights
             ,
             from
             those
             signes
             wherein
             the
             dayes
             are
             made
             shorter
             then
             the
             nights
             .
          
           
             4.
             
             It
             sheweth
             which
             halfes
             of
             the
             Eclipticke
             and
             Equator
             ,
             doe
             arise
             together
             in
             equall
             time
             in
             an
             oblique
             Sphaere
             .
          
           
             5.
             
             It
             sheweth
             the
             two
             high
             Sunne-standings
             in
             a
             right
             Sphaere
             ,
             in
             the
             time
             of
             which
             Sunne-standings
             ,
             the
             Sunne
             passeth
             by
             the
             Zenith
             .
          
        
         
           
             CHAP.
             XII
             .
             Vses
             of
             the
             Solstitiall
             Colure
             .
          
           
             1.
             
             THe
             common
             meetings
             of
             this
             circle
             with
             the
             Ecliptick
             ,
             shew
             the
             Solstitiall
             or
             Tropicall
             points
             ;
             in
             which
             points
             the
             Sunne
             seemeth
             to
             stand
             ,
             and
             then
             returneth
             backe
             againe
             :
             for
             which
             cause
             this
             circle
             is
             called
             the
             Colure
             of
             the
             Sun-standings
             .
             These
             points
             are
             called
             tropicall
             (
             which
             is
             as
             much
             to
             say
             as
             turne-points
             ,
             or
             points
             of
             returne
             )
             because
             that
             when
             the
             Sunne
             going
             alwayes
             vnder
             the
             Eclipticke
             commeth
             to
             these
             points
             ,
             which
             are
             furthest
             distant
             from
             the
             Equinoctiall
             circle
             ,
             it
             returneth
             againe
             towards
             the
             same
             circle
             .
             But
             they
             were
             called
             Solstitiall
             or
             Sun-ding
             points
             ,
             because
             that
             whilest
             the
             Sunne
             is
             about
             those
             points
             ,
             the
             difference
             of
             the
             Sunnes
             returning
             is
             (
             for
             certaine
             dayes
             )
             insensible
             .
             Hereof
             the
             Sunne
             is
             said
             to
             make
             his
             station
             ,
             or
             to
             stand
             ,
             when
             he
             commeth
             to
             either
             of
             those
             points
             .
             They
             that
             dwell
             without
             the
             Tropickes
             ,
             haue
             two
             
             sunne-standings
             ,
             that
             is
             the
             Summer
             sun-standing
             ,
             or
             high
             sun-standing
             (
             when
             the
             Sunne
             in
             Summer
             time
             is
             at
             the
             highest
             ,
             and
             next
             vnto
             our
             Zenith
             being
             in
             the
             beginning
             of
             Cancer
             )
             and
             the
             winterly
             ,
             or
             low
             sun-standing
             ,
             when
             the
             Sunne
             in
             Winter
             time
             is
             lowest
             in
             the
             Meridian
             ,
             and
             furthest
             from
             our
             Zenith
             .
             But
             they
             that
             dwell
             within
             the
             Tropicks
             (
             by
             a
             certaine
             similitude
             taken
             from
             our
             sun-standings
             ,
             wherein
             the
             Sunne
             is
             either
             highest
             or
             lowest
             )
             are
             said
             to
             haue
             foure
             sun-standings
             ;
             that
             is
             two
             high
             sun-standings
             ,
             when
             the
             Sunne
             passeth
             by
             their
             Zenith
             (
             the
             highest
             point
             in
             the
             Heauens
             )
             which
             hapneth
             twice
             euery
             yeare
             in
             two
             places
             ,
             equally
             distant
             from
             the
             beginnings
             of
             Cancer
             and
             Capricorne
             :
             and
             two
             low
             sun-standings
             ,
             when
             the
             Sunne
             is
             in
             the
             beginning
             of
             Cancer
             and
             Capricorne
             .
          
           
             2.
             
             In
             this
             Circle
             by
             the
             arch
             conteyned
             betweene
             the
             Equator
             and
             Eclipticke
             ,
             we
             measure
             the
             greatest
             declination
             of
             the
             Sunne
             ,
             or
             obliquity
             of
             the
             Eclipticke
             ,
             which
             in
             Ptolomees
             time
             was
             23.
             degrees
             51.
             minutes
             ,
             and
             one
             third
             part
             of
             a
             minute
             .
             But
             euer
             since
             that
             time
             it
             hath
             beene
             found
             by
             obseruation
             to
             decrease
             ;
             so
             as
             in
             this
             our
             age
             ,
             it
             is
             no
             more
             then
             23.
             degrees
             and
             one
             halfe
             ,
             or
             little
             more
             :
             Notwithstanding
             Copernicus
             thought
             that
             the
             greatest
             obliquity
             was
             23.
             degrees
             28.
             minutes
             .
          
           
             3.
             
             It
             sheweth
             the
             places
             of
             the
             Eclipticke
             ,
             in
             which
             the
             Sunne
             (
             comming
             neerest
             to
             our
             Zenith
             )
             maketh
             the
             artificiall
             day
             longest
             ;
             or
             going
             furthest
             from
             the
             same
             point
             ,
             maketh
             the
             same
             shortest
             .
          
           
             4.
             
             It
             deuideth
             the
             Zodiacke
             into
             two
             halfes
             ,
             the
             one
             ascending
             ,
             and
             the
             other
             descending
             .
          
           
           
             5.
             
             Hereby
             also
             the
             signes
             are
             distinguished
             ,
             which
             doe
             rise
             rightly
             ,
             and
             which
             rise
             obliquely
             in
             an
             oblique
             Sphaere
             .
             For
             the
             descending
             halfe
             riseth
             rightly
             ,
             and
             the
             ascending
             halfe
             riseth
             obliquely
             .
          
           
             6.
             
             So
             the
             points
             of
             the
             Eclipticke
             are
             shewed
             by
             this
             Circle
             ,
             wherein
             the
             greatest
             difference
             of
             right
             and
             oblique
             ascensions
             happeneth
             .
             It
             distinguisheth
             those
             signes
             in
             which
             when
             the
             Sunne
             moueth
             ,
             the
             artificiall
             dayes
             are
             increased
             ,
             and
             the
             nights
             decrease
             ;
             from
             those
             signes
             wherein
             the
             dayes
             are
             diminished
             ,
             and
             the
             nights
             increase
             .
          
           
             7.
             
             In
             this
             circle
             are
             the
             bredths
             of
             the
             Zones
             bounded
             ;
             for
             the
             obliquity
             of
             the
             Eclipticke
             doubled
             ,
             sheweth
             the
             bredth
             of
             the
             torrid
             or
             burnt
             Zone
             :
             the
             distance
             of
             the
             poles
             of
             the
             Ecliptick
             ,
             and
             of
             the
             Poles
             of
             the
             Equator
             ,
             shew
             the
             bredth
             of
             the
             cold
             or
             frozen
             Zones
             ;
             and
             the
             other
             two
             Arches
             remaining
             ,
             shew
             the
             bredths
             of
             the
             temperate
             Zones
             .
          
        
         
           
             CHAP.
             XIII
             The
             Description
             of
             the
             two
             Tropickes
             .
          
           
             THe
             two
             smaller
             Circles
             Equidistant
             in
             all
             places
             from
             the
             Equinoctiall
             ,
             and
             comming
             vnder
             these
             Solstitiall
             points
             of
             the
             Eclipticke
             on
             both
             sides
             ,
             are
             called
             the
             Tropicks
             ,
             that
             is
             circles
             of
             returne
             .
          
           
             And
             they
             are
             so
             called
             ,
             because
             that
             when
             the
             Sun
             commeth
             to
             them
             ,
             it
             beginneth
             to
             returne
             backe
             againe
             towards
             the
             Equinoctiall
             circle
             .
             Or
             else
             they
             may
             be
             so
             called
             ,
             because
             they
             are
             described
             by
             the
             turning
             about
             of
             the
             Tropicall
             points
             of
             Cancer
             and
             Capricorne
             .
             They
             are
             also
             called
             solstitiall
             Circles
             ;
             that
             is
             Circles
             of
             the
             sun-standings
             ;
             because
             that
             by
             
             reason
             of
             the
             insensible
             alteration
             of
             the
             declination
             of
             the
             Ecliptick
             ,
             for
             some
             space
             both
             before
             ,
             and
             after
             the
             Tropicall
             points
             ,
             the
             Sunne
             (
             in
             respect
             of
             his
             Meridian
             altitudes
             ,
             or
             in
             respect
             of
             the
             motion
             he
             hath
             towards
             the
             North
             or
             South
             ,
             by
             reason
             of
             the
             obliquity
             of
             the
             Eclipticke
             )
             seemeth
             to
             stand
             (
             as
             it
             were
             )
             for
             certaine
             dayes
             in
             those
             places
             .
          
           
             There
             be
             two
             Tropicks
             ,
             the
             Tropick
             of
             Cancer
             ,
             and
             the
             tropicke
             of
             Capricorne
             .
          
           
             The
             tropick
             of
             Cancer
             ,
             toucheth
             the
             Ecliptick
             in
             the
             beginning
             of
             Cancer
             ,
             which
             is
             the
             most
             northerly
             point
             of
             the
             Ecliptick
             :
             or
             it
             is
             the
             Tropick
             described
             in
             the
             first
             mouable
             Sphaere
             ,
             by
             the
             Summer
             solstitiall
             point
             .
          
           
             This
             circle
             is
             called
             the
             Tropick
             of
             Cancer
             ,
             because
             it
             toucheth
             the
             Ecliptick
             in
             the
             beginning
             of
             Cancer
             .
          
           
             It
             is
             also
             called
             the
             Summer
             Tropick
             ,
             and
             the
             Tropick
             of
             the
             Summer
             sun-standing
             ,
             because
             that
             when
             the
             Sunne
             commeth
             to
             it
             ,
             the
             Summer
             beginneth
             .
             It
             is
             called
             the
             North
             tropick
             ,
             because
             it
             is
             in
             the
             North
             part
             of
             the
             world
             :
             and
             the
             Circle
             of
             the
             high
             sunne-standing
             ,
             because
             the
             Sunne
             comming
             to
             it
             ,
             is
             highest
             in
             the
             Meridian
             ,
             and
             next
             vnto
             our
             Zenith
             which
             dwell
             in
             the
             North
             part
             of
             the
             world
             ,
             without
             the
             Tropicks
             .
             The
             Tropick
             of
             Capricorne
             is
             the
             Tropick
             which
             toucheth
             the
             Ecliptick
             in
             the
             first
             point
             of
             Capricorne
             .
             It
             is
             called
             the
             Tropick
             of
             Capricorne
             ,
             because
             it
             toucheth
             the
             Ecliptick
             in
             the
             beginning
             of
             Capricorne
             .
             It
             is
             called
             the
             winter
             Tropicke
             and
             Tropick
             of
             the
             Winter
             sun-standing
             ,
             because
             the
             Sunne
             commeth
             to
             it
             in
             Winter
             .
          
           
           
             It
             is
             also
             called
             the
             circle
             of
             the
             lowest
             Sunne-standing
             ,
             because
             that
             when
             the
             Sunne
             commeth
             to
             this
             Tropicke
             ,
             it
             is
             furthest
             distant
             from
             our
             Zenith
             ,
             and
             hath
             his
             lowest
             height
             in
             the
             Meridian
             .
          
        
         
           
             CHAP.
             XIIII
             .
             Vses
             of
             the
             Tropickes
             .
          
           
             1.
             
             THe
             Tropicks
             shew
             the
             Tropicall
             ,
             or
             Solstitiall
             points
             of
             the
             Eclipticke
             :
             that
             is
             ,
             the
             points
             wherein
             the
             Sunne
             seemeth
             to
             stand
             ,
             and
             beginneth
             to
             returne
             backe
             againe
             .
          
           
             2.
             
             They
             bound
             out
             the
             greatest
             declinations
             of
             the
             Sunne
             ,
             which
             in
             our
             times
             is
             about
             23.
             degrees
             and
             an
             halfe
             .
          
           
             3.
             
             Therefore
             they
             doe
             also
             bound
             out
             the
             obliquity
             of
             the
             Ecliptick
             ,
             for
             they
             are
             the
             bounds
             of
             the
             Sunnes
             way
             ,
             beyond
             which
             the
             Sunne
             goeth
             not
             at
             any
             time
             .
          
           
             4.
             
             The
             Sunne
             comming
             to
             either
             of
             these
             circles
             ,
             is
             either
             neerest
             ,
             or
             furthest
             distant
             from
             our
             verticall
             point
             .
          
           
             5.
             
             In
             an
             oblique
             Sphaere
             ,
             they
             measure
             out
             the
             shortest
             ,
             and
             longest
             artificiall
             day
             and
             night
             .
          
           
             6.
             
             The
             Tropicks
             (
             aswell
             in
             Heauen
             as
             in
             Earth
             ,
             conteyne
             betwixt
             them
             the
             Torrid
             Zone
             ,
             and
             separate
             it
             from
             the
             temperate
             .
          
        
         
           
             CHAP.
             XV.
             The
             Polar
             Circles
             .
          
           
             THe
             two
             smallest
             circles
             that
             are
             next
             about
             the
             poles
             of
             the
             Sphaere
             ,
             are
             called
             the
             polar
             circles
             .
             They
             are
             drawne
             by
             the
             poles
             of
             the
             Eclipticke
             ,
             
             and
             are
             euery
             where
             Equidistant
             from
             the
             Equinoctiall
             ,
             and
             from
             the
             poles
             of
             the
             Sphaere
             .
          
           
             They
             are
             called
             polar
             Circles
             ,
             either
             because
             they
             are
             neere
             the
             poles
             of
             the
             Sphaere
             ,
             or
             else
             because
             they
             are
             described
             by
             the
             motion
             of
             the
             poles
             of
             the
             Eclipticke
             .
          
           
             And
             therefore
             there
             be
             two
             polar
             Circles
             ,
             that
             is
             ,
             so
             many
             as
             there
             are
             poles
             of
             the
             Ecliptick
             :
             the
             Polar
             circle
             Artick
             ,
             and
             the
             Polar
             Antartick
             .
          
           
             The
             Articke
             polar
             circle
             ,
             is
             that
             which
             passeth
             by
             the
             North
             pole
             of
             the
             Ecliptick
             ,
             or
             which
             is
             described
             by
             the
             North
             pole
             of
             the
             Ecliptick
             being
             carried
             about
             with
             the
             motion
             of
             the
             first
             moueable
             Sphaere
             .
          
           
             The
             Antartick
             polar
             circle
             ,
             is
             that
             which
             goeth
             by
             the
             South
             pole
             of
             the
             Eclipticke
             ,
             being
             described
             with
             the
             first
             motion
             by
             the
             Antartick
             pole
             of
             the
             Ecliptick
             .
          
           
             The
             distance
             of
             these
             polar
             Circles
             from
             the
             poles
             of
             the
             Sphaere
             ,
             is
             equall
             to
             the
             distance
             of
             the
             tropicks
             from
             the
             Equinoctiall
             ,
             which
             in
             our
             time
             is
             about
             23.
             degr
             .
             and
             an
             halfe
             :
             for
             so
             much
             as
             is
             the
             obliquity
             of
             the
             Zodiack
             (
             whereto
             the
             distance
             of
             the
             Tropicks
             from
             the
             Equinoctiall
             is
             alwayes
             equall
             )
             so
             much
             are
             the
             poles
             of
             the
             Ecliptick
             distant
             from
             the
             Poles
             of
             the
             world
             .
          
        
         
           
             CHAP.
             XVI
             .
             Vses
             of
             the
             Polar
             Circles
             .
          
           
             1.
             
             THe
             Polar
             Circles
             shew
             the
             poles
             of
             the
             Zodiack
             ,
             and
             shew
             their
             distance
             from
             the
             poles
             of
             the
             Equinoctiall
             .
          
           
             2.
             
             The
             temperate
             Zones
             are
             bounded
             by
             these
             
             polar
             circles
             ;
             for
             the
             Articke
             circle
             boundeth
             the
             North
             side
             of
             the
             North
             temperate
             Zone
             ;
             and
             the
             Antartick
             circle
             boundeth
             out
             the
             South
             side
             of
             the
             South
             temperate
             Zone
             .
          
           
             3.
             
             The
             Polar
             circles
             separate
             the
             temperate
             Zones
             ,
             from
             the
             cold
             Zones
             which
             they
             compasse
             round
             about
             ,
             and
             inclose
             within
             them
             .
          
           
             Therefore
             the
             foure
             lesser
             circles
             ,
             that
             is
             the
             two
             Polar
             circles
             ,
             and
             the
             Tropicks
             ,
             deuide
             Heauen
             and
             Earth
             ,
             into
             fiue
             Zones
             .
          
        
         
           
             CHAP.
             XVII
             .
             Of
             the
             Zones
             .
          
           
             A
             Zone
             is
             a
             space
             of
             Heauen
             ,
             or
             Earth
             ,
             conteyned
             betweene
             two
             of
             the
             smaller
             Circles
             ;
             or
             inclosed
             within
             the
             compasse
             of
             either
             Polar
             circle
             .
          
           
             They
             are
             called
             Zones
             (
             that
             is
             as
             much
             to
             say
             as
             girdles
             )
             because
             they
             compasse
             about
             Heauen
             or
             Earth
             like
             a
             girdle
             .
          
           
             The
             Zones
             are
             deuided
             by
             auncient
             Writers
             into
             two
             kindes
             ;
             that
             is
             into
             temperate
             ,
             and
             vntemperate
             Zones
             .
          
           
             A
             temperate
             Zone
             is
             the
             space
             of
             Heauen
             or
             earth
             ,
             conteyned
             betweene
             either
             of
             the
             Tropicks
             ,
             and
             the
             next
             Polar
             circle
             .
          
           
             There
             be
             two
             temperate
             Zones
             ;
             the
             one
             North
             ,
             the
             other
             South
             .
          
           
             The
             North
             temperate
             Zone
             is
             conteyned
             betweene
             the
             Tropicke
             of
             Cancer
             ,
             and
             the
             Artick
             polar
             circle
             .
          
           
             The
             South
             temperate
             Zone
             is
             that
             which
             is
             conteyned
             
             betweene
             the
             Tropicke
             of
             Capricorne
             ,
             and
             the
             Antartick
             polar
             circle
             .
          
           
             They
             are
             called
             temperate
             Zones
             ,
             because
             they
             haue
             a
             better
             temperature
             of
             the
             ayre
             for
             the
             most
             part
             ,
             and
             more
             meer
             for
             habitation
             ,
             then
             the
             vntemperate
             Zones
             .
             The
             bredth
             of
             eyther
             temperate
             Zone
             is
             alwayes
             equall
             to
             the
             complement
             of
             the
             distance
             of
             the
             Tropicks
             ,
             and
             therefore
             in
             this
             age
             is
             about
             43.
             degrees
             ,
             that
             is
             2580.
             
             English
             miles
             .
          
           
             There
             be
             two
             kinde
             of
             vntemperate
             Zones
             ,
             the
             one
             exceeding
             in
             heat
             ,
             the
             other
             in
             cold
             ,
             for
             the
             most
             part
             .
          
           
             The
             hot
             vntemperate
             Zone
             ,
             (
             called
             also
             the
             Torrid
             ;
             that
             is
             ,
             the
             burnt
             or
             broyled
             zone
             )
             is
             that
             space
             of
             Heauen
             or
             Earth
             ,
             which
             is
             conteyned
             betweene
             the
             tropicks
             .
          
           
             It
             is
             called
             the
             burnt
             Zone
             ,
             because
             that
             by
             reason
             of
             the
             Sunnes
             continuall
             going
             ouer
             that
             zone
             ;
             and
             casting
             his
             beames
             directly
             downe
             thereupon
             ,
             it
             is
             scorched
             with
             ouer-much
             heat
             ,
             and
             is
             not
             so
             meet
             to
             be
             inhabited
             as
             the
             temperate
             zones
             .
          
           
             The
             bredth
             of
             this
             Zone
             is
             alwayes
             equall
             to
             the
             obliquitie
             of
             the
             Zodiack
             ,
             or
             greatest
             declination
             of
             the
             Sunne
             ,
             doubled
             ;
             which
             in
             our
             time
             is
             about
             47.
             degrees
             ,
             that
             is
             2820.
             
             English
             miles
             .
          
           
             The
             cold
             or
             frozen
             zones
             ,
             are
             the
             spaces
             of
             Heauen
             or
             earth
             ,
             conteyned
             within
             the
             Polar
             circles
             .
          
           
             There
             be
             two
             cold
             zones
             ,
             the
             one
             North
             ,
             conteyned
             within
             the
             compasse
             of
             the
             Articke
             circle
             :
             the
             other
             South
             ,
             conteyned
             within
             the
             compasse
             of
             the
             Antartick
             Polar
             circle
             .
          
           
             These
             zones
             exceed
             in
             cold
             ,
             because
             they
             want
             
             the
             sight
             of
             the
             sunne
             for
             a
             great
             part
             of
             the
             yeare
             ,
             and
             when
             the
             Sunne
             appeareth
             vnto
             them
             ,
             his
             beames
             fall
             so
             obliquely
             vpon
             them
             ,
             that
             they
             can
             (
             in
             all
             likelyhood
             )
             receiue
             but
             small
             heat
             thereby
             for
             the
             most
             part
             .
          
           
             The
             bredth
             of
             these
             Zones
             is
             measured
             from
             the
             Poles
             of
             the
             world
             to
             the
             Polar
             circles
             ,
             and
             therefore
             must
             alwayes
             bee
             so
             much
             as
             the
             Polar
             circles
             are
             distant
             from
             the
             Poles
             :
             that
             is
             ,
             in
             our
             age
             about
             23.
             
             Degrees
             and
             a
             halfe
             ,
             which
             make
             1410.
             
             English
             miles
             .
          
        
         
           
             CHAP.
             XVIII
             .
             The
             difference
             of
             Shadowes
             that
             the
             Sunne
             maketh
             in
             these
             Zones
             .
          
           
             THey
             that
             dwell
             in
             the
             torride
             Zone
             ,
             doe
             cast
             their
             shadowes
             which
             the
             Sunne
             maketh
             at
             noone
             (
             which
             we
             may
             therefore
             call
             their
             noone
             shadowes
             )
             both
             towards
             the
             North
             ,
             and
             towards
             the
             South
             :
             towards
             the
             North
             ,
             when
             the
             sunne
             is
             betwixt
             their
             zenith
             and
             the
             south
             point
             of
             the
             Horizon
             ;
             and
             towards
             the
             South
             ,
             where
             the
             sunne
             is
             betweene
             their
             Zenith
             and
             the
             North.
             
          
           
             For
             seeing
             the
             zenith
             of
             them
             that
             dwell
             in
             that
             Zone
             is
             betweene
             the
             Tropicks
             ,
             the
             sunne
             must
             needs
             bee
             sometimes
             Northwards
             from
             their
             zenith
             ,
             and
             so
             make
             a
             south
             shadow
             :
             and
             sometime
             Southwards
             ,
             and
             then
             make
             a
             north
             shadow
             .
             For
             which
             cause
             they
             that
             inhabite
             this
             Zone
             are
             called
             Amphiscij
             ;
             that
             is
             ,
             such
             as
             cast
             their
             noone
             shadowes
             on
             both
             sides
             .
          
           
             But
             they
             that
             dwell
             in
             the
             temperate
             Zones
             ,
             are
             
             called
             Heteroscij
             ;
             that
             is
             ,
             such
             as
             cast
             their
             shadowes
             at
             noone
             ,
             one
             way
             onely
             .
             For
             they
             that
             dwell
             in
             the
             North
             temperate
             Zone
             ,
             haue
             the
             Sunne
             alwayes
             at
             noone
             from
             their
             Zenith
             Southwards
             ,
             and
             therefore
             must
             needs
             alwayes
             cast
             their
             noone
             shadowes
             Northwards
             .
             Whereas
             contrariwise
             they
             that
             inhabit
             the
             South
             temperate
             Zone
             ,
             hauing
             the
             Sunne
             at
             noone
             alwayes
             Northwards
             from
             their
             Zenith
             ,
             must
             needs
             haue
             their
             shadowes
             at
             noone
             ,
             alwayes
             towards
             the
             South
             .
          
           
             And
             they
             that
             are
             in
             the
             cold
             Zones
             ,
             are
             called
             Periscij
             ;
             that
             is
             ,
             such
             as
             cast
             their
             shadowes
             round
             about
             them
             .
             For
             seeing
             the
             Sunne
             continueth
             euery
             yeare
             for
             certaine
             dayes
             together
             ,
             alwayes
             aboue
             their
             Horizon
             ,
             and
             therefore
             moueth
             round
             about
             them
             without
             setting
             :
             it
             must
             needs
             bee
             ,
             that
             their
             shadowes
             also
             are
             carried
             round
             about
             them
             ,
             falling
             towards
             all
             parts
             of
             the
             world
             in
             the
             space
             of
             24.
             houres
             .
             *
             ⁎
             *
          
        
      
       
         
         
           THE
           SECOND
           PART
           .
           Of
           the
           vses
           of
           the
           vppermost
           SPHAERE
           ,
           and
           of
           the
           Circles
           thereof
           joyntly
           .
        
         
           
             PROP.
             I.
             To
             rectifie
             the
             Sphaere
             to
             the
             Latitude
             .
             &c.
             
          
           
             FIrst
             finde
             by
             obseruation
             ,
             or
             otherwise
             the
             height
             of
             the
             Pole
             ,
             or
             Latitude
             of
             that
             place
             for
             which
             you
             would
             rectifie
             the
             Sphaere
             .
             Then
             (
             by
             turning
             about
             the
             Meridian
             of
             the
             Sphaere
             ;
             lift
             vp
             or
             put
             downe
             the
             North
             Pole
             of
             the
             Sphaere
             (
             about
             which
             the
             houre
             circle
             is
             fastened
             )
             till
             the
             arch
             of
             the
             Meridian
             from
             the
             North
             part
             of
             the
             Horizon
             vpwards
             vnto
             the
             Pole
             ,
             be
             iust
             so
             many
             degrees
             as
             the
             eleuation
             of
             the
             Pole
             or
             latitude
             of
             the
             place
             was
             found
             to
             be
             :
             for
             so
             haue
             you
             the
             Sphaere
             duly
             rectified
             .
          
           
             As
             for
             example
             ,
             the
             Latitude
             of
             the
             Citie
             of
             London
             is
             51.
             degrees
             and
             32.
             minutes
             ,
             therefore
             if
             you
             lift
             vp
             the
             North
             Pole
             of
             the
             Sphaere
             ,
             aboue
             the
             North
             part
             of
             the
             Horizon
             ,
             so
             many
             degrees
             and
             minutes
             you
             shall
             haue
             your
             Sphaere
             rectified
             for
             that
             place
             .
          
        
         
           
           
             PROP.
             II.
             To
             know
             the
             place
             of
             the
             Sunne
             ;
             &c.
             
          
           
             LOoke
             the
             day
             of
             the
             moneth
             (
             for
             which
             you
             desire
             to
             know
             the
             place
             of
             the
             Sunne
             )
             in
             the
             Horizon
             ,
             and
             see
             what
             signe
             and
             degree
             of
             the
             Zodiacke
             vpon
             the
             Horizon
             answereth
             thereto
             ;
             for
             there
             haue
             you
             the
             place
             of
             the
             Sunne
             .
          
           
             Take
             for
             example
             the
             25.
             of
             December
             :
             looke
             this
             day
             therefore
             in
             the
             Horizon
             ,
             and
             you
             shall
             finde
             answerable
             thereto
             13.
             degrees
             ,
             and
             about
             40.
             minutes
             of
             Capricorne
             ,
             which
             is
             the
             place
             of
             the
             Sunne
             at
             that
             time
             .
          
        
         
           
             PROP.
             III.
             To
             know
             the
             declination
             of
             the
             Sunne
             ,
             &c.
             
          
           
             BRing
             the
             point
             whose
             declination
             you
             desire
             to
             know
             ,
             vnto
             the
             Meridian
             of
             the
             Sphaere
             ,
             and
             look
             what
             number
             of
             degrees
             and
             minutes
             of
             the
             Meridian
             is
             conteyned
             betweene
             that
             point
             ,
             and
             the
             Equinoctiall
             ,
             for
             so
             much
             is
             the
             declination
             .
          
           
             As
             if
             you
             would
             know
             the
             declination
             of
             the
             10.
             degree
             of
             Taurus
             ,
             bring
             that
             degree
             to
             the
             Meridian
             ,
             and
             you
             shall
             finde
             the
             arch
             of
             the
             Meridian
             between
             that
             degree
             and
             the
             Equinoctiall
             ,
             to
             be
             14.
             degrees
             and
             about
             51.
             minutes
             .
          
        
         
           
             PROP.
             IIII.
             To
             know
             the
             right
             ascention
             of
             the
             Sunne
             ,
             &c.
             
          
           
             BRing
             that
             point
             (
             as
             before
             )
             to
             the
             Meridian
             ,
             and
             see
             then
             how
             many
             degrees
             and
             minutes
             of
             the
             Equinoctiall
             are
             conteyned
             betweene
             the
             beginning
             
             of
             Aries
             and
             the
             Meridian
             :
             for
             that
             is
             the
             right
             ascension
             of
             that
             point
             .
             So
             you
             shall
             finde
             the
             right
             ascension
             of
             the
             10.
             degr
             .
             of
             Taurus
             to
             be
             37.
             degr
             .
             35.
             min.
             for
             if
             you
             bring
             that
             degree
             of
             Taurus
             to
             the
             Meridian
             ,
             you
             shall
             finde
             so
             many
             degrees
             and
             min.
             between
             the
             beginning
             of
             Aries
             ,
             and
             the
             Meridian
             .
          
        
         
           
             PROP.
             V.
             To
             know
             the
             oblique
             ascension
             of
             the
             Sunne
             ,
             &c.
             
          
           
             SEt
             the
             Sphaere
             to
             the
             eleuation
             of
             the
             place
             for
             which
             you
             desire
             to
             know
             the
             oblique
             ascension
             ;
             then
             bring
             the
             Sunne
             ,
             Starre
             ,
             or
             point
             whose
             oblique
             ascention
             you
             would
             know
             ,
             vnto
             the
             East
             semicircle
             of
             the
             Horizon
             ,
             and
             looke
             how
             many
             degrees
             and
             minutes
             of
             the
             Equinoctiall
             circle
             ,
             are
             conteyned
             between
             the
             East
             point
             of
             the
             Horizon
             ,
             and
             the
             beginning
             of
             Aries
             ;
             for
             so
             much
             is
             the
             oblique
             ascension
             desired
             :
             As
             for
             example
             ,
             if
             you
             see
             the
             Sphaere
             to
             the
             Latitude
             of
             London
             51.
             degr
             .
             32.
             min.
             and
             then
             bring
             the
             10.
             degree
             of
             Taurus
             to
             the
             East
             part
             of
             the
             Horizon
             ,
             you
             shall
             finde
             about
             19.
             degrees
             and
             an
             halfe
             of
             the
             Equinoctiall
             ,
             at
             the
             same
             East
             part
             of
             the
             Horizon
             ;
             which
             is
             the
             oblique
             ascension
             of
             that
             degree
             of
             Taurus
             ,
             for
             the
             Latitude
             of
             the
             Citie
             of
             London
             .
          
        
         
           
             PROP.
             VI.
             To
             finde
             the
             difference
             of
             Ascension
             .
          
           
             COmpare
             the
             right
             and
             oblique
             ascensions
             of
             the
             Sunne
             ,
             (
             or
             of
             any
             point
             of
             the
             Zodiacke
             )
             together
             ,
             and
             subtract
             the
             lesse
             from
             the
             greater
             ,
             for
             the
             remainder
             shall
             bee
             the
             difference
             of
             ascension
             .
             As
             for
             example
             ,
             the
             right
             ascension
             of
             the
             10.
             degree
             
             of
             Taurus
             ,
             being
             found
             by
             the
             4.
             
             Propo.
             to
             be
             37.
             degrees
             ,
             35.
             min.
             and
             the
             oblique
             ascention
             of
             the
             same
             degree
             at
             London
             ,
             by
             the
             5.
             
             Prop.
             19.
             degree
             30.
             min.
             by
             subtraction
             of
             the
             lesse
             out
             of
             the
             greater
             ,
             the
             difference
             shall
             be
             found
             to
             be
             18.
             degr
             .
             and
             5.
             minutes
             ,
             which
             is
             the
             difference
             of
             ascension
             sought
             for
             .
          
        
         
           
             PROP.
             VII
             .
             To
             finde
             at
             what
             time
             the
             Sunne
             riseth
             or
             setteth
             .
          
           
             REduce
             the
             difference
             of
             Ascention
             into
             houres
             and
             minutes
             (
             taking
             for
             euery
             15
             degrees
             1.
             houre
             ,
             and
             for
             euery
             one
             degree
             that
             remayneth
             4.
             minutes
             ,
             and
             for
             euery
             minute
             of
             a
             degree
             4
             seconds
             )
             for
             these
             houres
             ,
             minutes
             and
             seconds
             ,
             being
             added
             to
             6.
             houres
             ,
             if
             the
             Sunne
             bee
             in
             any
             of
             the
             South
             signes
             ;
             or
             subtracted
             ,
             if
             hee
             be
             in
             the
             North
             signes
             ,
             sheweth
             the
             time
             of
             the
             Sun-rising
             .
             And
             contrariwise
             ,
             the
             same
             houres
             and
             minutes
             subtracted
             from
             sixe
             houres
             when
             the
             Sunne
             is
             in
             the
             South
             signes
             ,
             or
             added
             when
             he
             is
             in
             the
             North
             signes
             ,
             sheweth
             the
             the
             time
             of
             the
             Sunne-setting
             .
          
           
             As
             for
             example
             ,
             the
             Sunne
             being
             in
             the
             10.
             degree
             of
             Taurus
             which
             happeneth
             about
             the
             20.
             or
             21.
             day
             of
             Aprill
             )
             I
             would
             know
             at
             what
             houre
             and
             minute
             the
             Sunne
             riseth
             ,
             and
             setteth
             at
             London
             :
             Hauing
             therefore
             found
             by
             the
             former
             Proposition
             the
             difference
             of
             ascention
             to
             be
             18.
             degr
             .
             and
             5.
             minutes
             I
             take
             for
             15.
             degrees
             thereof
             one
             houre
             ,
             and
             for
             the
             three
             degr
             .
             remaining
             ,
             12.
             minutes
             of
             an
             houre
             ,
             and
             for
             the
             5.
             minutes
             ,
             20.
             seconds
             of
             an
             houre
             .
             Which
             houre
             ,
             minutes
             and
             seconds
             being
             subtracted
             out
             of
             6.
             houres
             ,
             because
             the
             Sunne
             is
             in
             a
             North
             signe
             ,
             
             there
             remaineth
             the
             time
             of
             the
             Sunnes
             rising
             at
             4.
             a
             clocke
             47.
             minutes
             ,
             40.
             seconds
             .
             And
             adding
             the
             same
             houre
             ,
             min.
             and
             seconds
             to
             6.
             houres
             ,
             you
             haue
             the
             time
             of
             the
             Sun-setting
             that
             day
             at
             7.
             a
             clocke
             ,
             12.
             min.
             and
             20.
             seconds
             .
          
        
         
           
             PROP.
             VIII
             .
             To
             finde
             the
             length
             of
             the
             artificiall
             day
             or
             night
             .
          
           
             THe
             artificiall
             day
             ,
             is
             the
             time
             conteyned
             between
             the
             Sun-rising
             and
             the
             Sun-setting
             :
             and
             the
             artificiall
             night
             is
             the
             time
             betweene
             Sunne-setting
             and
             Sun-rising
             .
             The
             length
             of
             both
             these
             is
             found
             after
             this
             manner
             :
             hauing
             found
             the
             difference
             of
             ascension
             ,
             and
             reduced
             it
             into
             houres
             and
             minutes
             (
             as
             in
             the
             former
             Proposition
             )
             double
             th●se
             houres
             and
             minutes
             ,
             and
             adde
             them
             to
             12.
             houres
             if
             the
             Sunne
             be
             in
             the
             North
             signes
             ,
             or
             subtract
             them
             from
             12.
             houres
             if
             the
             Sunne
             be
             in
             the
             South
             signes
             ,
             for
             so
             shall
             you
             haue
             the
             length
             of
             the
             day
             :
             But
             (
             contrariwise
             )
             subtract
             the
             same
             houres
             and
             minutes
             (
             being
             doubled
             )
             from
             12.
             houres
             ,
             the
             Sunne
             being
             in
             the
             North
             signes
             ;
             and
             adde
             them
             to
             12.
             houres
             when
             he
             is
             in
             the
             South-signes
             ;
             so
             haue
             you
             the
             length
             of
             the
             night
             .
          
           
             Or
             else
             ,
             double
             the
             time
             of
             the
             Sun-setting
             ,
             so
             haue
             you
             the
             length
             of
             the
             day
             .
             And
             double
             the
             time
             of
             the
             Sun-rising
             ,
             so
             haue
             you
             the
             length
             of
             the
             right
             .
          
           
             As
             the
             time
             of
             the
             Sun-rising
             being
             found
             by
             the
             former
             Proposition
             to
             be
             4
             houres
             48.
             minutes
             after
             mignight
             at
             London
             ,
             the
             Sunne
             being
             in
             the
             10.
             degr
             .
             of
             Taurus
             ,
             by
             doubling
             the
             time
             of
             the
             Sun-rising
             ,
             the
             length
             of
             the
             night
             shall
             be
             found
             to
             be
             9.
             houres
             and
             36.
             minutes
             .
             And
             doubling
             the
             time
             of
             the
             sun-setting
             
             that
             is
             7.
             houres
             ,
             and
             12.
             minutes
             ,
             you
             haue
             the
             length
             of
             the
             day
             ,
             14.
             houres
             ;
             and
             24.
             minutes
             .
          
        
         
           
             PROP.
             IX
             .
             To
             know
             the
             time
             of
             the
             Sun
             rising
             and
             Sun
             setting
             .
          
           
             THe
             place
             of
             the
             Sunne
             being
             found
             by
             the
             2.
             
             Proposition
             ,
             bring
             the
             same
             to
             the
             Meridian
             ,
             and
             withall
             set
             the
             point
             of
             the
             Index
             of
             the
             houre
             circle
             ,
             to
             the
             12.
             houre
             in
             the
             same
             circle
             :
             Then
             bring
             the
             place
             of
             the
             Sunne
             to
             the
             Horizon
             Eastwards
             ;
             and
             the
             point
             of
             the
             houre
             Index
             shall
             shew
             you
             in
             the
             houre
             circle
             ,
             the
             time
             of
             the
             Sun-rising
             .
             But
             if
             you
             bring
             the
             place
             of
             the
             Sunne
             to
             the
             Horizon
             Westwards
             ,
             the
             point
             of
             the
             Index
             will
             shew
             in
             the
             houre
             circle
             the
             time
             of
             the
             Sun-setting
             .
          
           
             As
             for
             example
             ,
             the
             Sunne
             being
             in
             the
             10.
             degree
             of
             Taurus
             ,
             bring
             the
             same
             degree
             to
             the
             Meridian
             ,
             and
             bring
             the
             point
             of
             the
             houre
             Index
             also
             to
             the
             Meridian
             :
             then
             (
             the
             Sphaere
             being
             set
             to
             the
             Latitude
             of
             London
             )
             bring
             the
             same
             10.
             degree
             of
             Taurus
             to
             the
             East
             part
             of
             the
             Horizon
             ,
             for
             then
             the
             houre
             Index
             will
             shew
             you
             in
             the
             houre
             circle
             ,
             that
             the
             Sunne
             riseth
             at
             4.
             of
             the
             clocke
             and
             48.
             minutes
             .
          
           
             And
             bringing
             the
             same
             degree
             to
             the
             West
             semicircle
             of
             the
             Horizon
             ,
             the
             same
             Index
             will
             shew
             the
             time
             of
             the
             Sun-setting
             to
             be
             7.
             houres
             and
             12.
             min.
             after
             noone
             .
          
        
         
           
             PROP.
             X.
             To
             finde
             the
             length
             of
             the
             artificiall
             day
             or
             night
             .
          
           
             BRing
             the
             place
             of
             the
             Sun
             (
             being
             found
             as
             before
             to
             the
             East
             semicircle
             of
             the
             Horizon
             :
             set
             the
             
             houre
             Index
             12.
             a
             clocke
             in
             the
             Houre
             circle
             :
             turne
             about
             the
             Sphaere
             from
             the
             East
             Westwards
             ,
             till
             the
             place
             of
             the
             sunne
             come
             to
             the
             Horizon
             ,
             and
             marke
             how
             many
             houres
             the
             Index
             hath
             runne
             ouer
             vpon
             the
             Houre
             circle
             in
             the
             meane
             time
             ,
             for
             so
             much
             is
             the
             length
             of
             the
             day
             .
          
           
             And
             to
             finde
             the
             length
             of
             the
             night
             :
             Bring
             the
             place
             of
             the
             sunne
             to
             the
             West
             semicircle
             of
             the
             Horizon
             ,
             and
             set
             the
             Index
             to
             12.
             a
             clocke
             as
             before
             ;
             Then
             turning
             forwards
             the
             Sphaere
             from
             East
             Westward
             till
             the
             place
             of
             the
             sunne
             come
             to
             the
             East
             semicircle
             of
             the
             Horizon
             ;
             see
             how
             many
             houres
             the
             Index
             passeth
             ouer
             in
             the
             Houre-circle
             ,
             for
             so
             many
             houres
             long
             is
             the
             night
             .
          
           
             As
             for
             example
             ;
             supposing
             the
             Sunne
             to
             be
             as
             before
             in
             the
             10.
             degree
             of
             Taurus
             ,
             bring
             the
             same
             degree
             to
             the
             East
             part
             of
             the
             Horizon
             ,
             and
             the
             point
             of
             the
             Index
             to
             the
             Meridian
             :
             then
             turning
             about
             the
             Sphaere
             ,
             till
             the
             same
             degree
             come
             to
             the
             West
             part
             of
             the
             Horizon
             ;
             you
             shall
             finde
             that
             in
             the
             meane
             time
             ,
             the
             point
             of
             the
             Index
             shal
             passe
             ouer
             14.
             houres
             and
             24.
             minutes
             ,
             which
             is
             the
             length
             of
             the
             day
             .
             Likewise
             ,
             if
             you
             bring
             the
             same
             10.
             degr
             .
             of
             Taurus
             to
             the
             West
             part
             of
             the
             Horizon
             ,
             and
             the
             Index
             to
             the
             Meridian
             ,
             and
             turne
             about
             the
             Sphaere
             ,
             till
             that
             degree
             come
             to
             the
             East
             semicircle
             of
             the
             Horizon
             ,
             the
             number
             of
             houres
             that
             the
             Index
             runneth
             ouer
             in
             the
             meane
             time
             vpon
             the
             Houre
             circle
             ,
             shall
             be
             found
             to
             bee
             9.
             
             Degrees
             ,
             and
             36.
             
             Minutes
             .
          
        
         
           
           
             PROP.
             XI
             .
             To
             know
             the
             Meridian
             altitude
             ,
             or
             the
             height
             of
             the
             Sunne
             at
             noone
             ,
             for
             any
             time
             and
             place
             .
          
           
             SEt
             the
             Sphaere
             to
             the
             latitude
             of
             the
             place
             where
             you
             d●sire
             to
             know
             the
             Sunnes
             height
             at
             noone
             :
             bring
             the
             place
             of
             the
             Sunne
             (
             being
             found
             as
             before
             by
             the
             2.
             
             Prop.
             )
             to
             the
             Meridian
             ,
             then
             see
             how
             many
             degrees
             of
             the
             Meridian
             ,
             are
             contayned
             betweene
             the
             Horizon
             ,
             and
             the
             place
             of
             the
             sunne
             ,
             for
             so
             much
             is
             the
             height
             of
             the
             Sunne
             at
             noone
             .
          
           
             In
             like
             sort
             it
             may
             be
             knowne
             how
             much
             the
             Sunne
             is
             vnder
             the
             Horizon
             at
             midnight
             ,
             after
             this
             manner
             :
             Bring
             the
             place
             of
             the
             sunne
             in
             the
             Zodiacke
             to
             the
             Meridian
             vnder
             the
             Horizon
             ,
             and
             see
             how
             many
             degrees
             of
             the
             Meridian
             ,
             are
             contayned
             betweene
             the
             vpper-side
             of
             the
             Horizon
             ,
             and
             the
             place
             of
             the
             Sunne
             downewards
             :
             and
             so
             shall
             you
             haue
             that
             you
             sought
             for
             .
          
           
             Or
             else
             if
             you
             cannot
             well
             come
             to
             the
             Meridian
             vnder
             the
             Horizon
             :
             bring
             that
             point
             of
             the
             Eclipticke
             which
             is
             opposite
             to
             the
             place
             of
             the
             sunne
             ,
             vnto
             the
             Meridian
             aboue
             the
             Horizon
             ;
             for
             the
             arch
             of
             the
             Meridian
             ,
             or
             the
             number
             of
             degrees
             and
             minutes
             of
             the
             Meridian
             ,
             betweene
             that
             point
             and
             the
             Horizon
             sheweth
             how
             much
             the
             sunne
             is
             vnder
             the
             Horizon
             at
             midnight
             .
          
           
             After
             this
             manner
             ▪
             the
             Sunne
             being
             in
             the
             10.
             degr
             .
             of
             Taurus
             ,
             you
             shall
             find
             that
             his
             Meridian
             altitude
             at
             London
             is
             53.
             degrees
             ,
             and
             about
             one
             halfe
             .
          
           
             As
             also
             that
             hee
             is
             vnder
             the
             Horizon
             at
             midnight
             about
             23.
             degrees
             and
             a
             halfe
             at
             London
             .
          
        
         
           
           
             PROP.
             XII
             .
             To
             know
             how
             high
             the
             Sunne
             is
             aboue
             the
             Horizon
             at
             any
             time
             of
             the
             day
             .
          
           
             BRing
             the
             place
             of
             the
             Sun
             (
             found
             by
             the
             2.
             
             Prop.
             )
             to
             the
             Meridian
             :
             set
             the
             houre
             Index
             to
             12.
             a
             clock
             vpon
             the
             houre
             circle
             :
             turne
             the
             Sphaere
             about
             till
             the
             Index
             come
             to
             the
             houre
             at
             which
             you
             desire
             to
             know
             the
             height
             of
             the
             Sunne
             aboue
             the
             Horizon
             ;
             take
             the
             distance
             of
             the
             place
             of
             the
             Sunne
             from
             the
             Horizon
             with
             a
             large
             payre
             of
             Compasses
             :
             then
             set
             both
             feet
             of
             the
             Compasses
             in
             the
             Ecliptick
             ,
             and
             looke
             how
             many
             degrees
             are
             conteyned
             betweene
             them
             ,
             for
             so
             much
             is
             the
             height
             of
             the
             Sunne
             .
          
           
             Thus
             may
             you
             finde
             by
             the
             Sphaere
             ,
             that
             when
             the
             Sunne
             is
             in
             the
             tenth
             degree
             of
             Taurus
             ,
             his
             height
             at
             10.
             of
             the
             clocke
             in
             the
             fore-noone
             (
             the
             Sphaere
             being
             duly
             rectified
             by
             the
             first
             Proposition
             )
             shall
             be
             about
             45.
             degrees
             and
             an
             halfe
             at
             London
             .
          
        
         
           
             PROP.
             XIII
             .
             To
             finde
             the
             houre
             of
             the
             day
             by
             the
             height
             of
             the
             Sunne
             ;
             &c.
             
          
           
             SEt
             the
             pole
             Artick
             of
             the
             Sphaere
             to
             his
             eleuation
             for
             that
             place
             where
             you
             desire
             to
             know
             the
             houre
             of
             the
             day
             :
             bring
             the
             place
             of
             the
             Sunne
             in
             the
             Zodiack
             to
             the
             Meridian
             ,
             and
             the
             houre
             Index
             to
             12.
             a
             clocke
             of
             the
             houre
             circle
             :
             take
             so
             many
             degrees
             of
             the
             Ecliptick
             betweene
             the
             feet
             of
             your
             Compasses
             ,
             as
             the
             height
             of
             the
             Sunne
             amounteth
             vnto
             .
          
           
             Then
             set
             one
             foot
             of
             your
             Compasses
             in
             the
             place
             of
             the
             Sunne
             ,
             and
             turne
             the
             Sphaere
             about
             ,
             Eastwards
             ,
             if
             it
             be
             in
             the
             fore-noone
             ,
             or
             West-wards
             ,
             if
             
             in
             the
             after-noone
             ,
             till
             you
             can
             but
             onely
             touch
             the
             Horizon
             with
             the
             other
             foot
             of
             your
             Compasses
             ;
             for
             then
             the
             Index
             pointeth
             out
             the
             houre
             of
             the
             day
             in
             the
             Houre
             circle
             .
          
           
             As
             suppose
             you
             obserue
             the
             height
             of
             the
             Sun
             being
             in
             the
             10.
             degr
             .
             of
             Taurus
             ,
             and
             find
             him
             to
             bee
             30.
             degrees
             high
             in
             the
             fore-noone
             :
             you
             shall
             find
             (
             following
             the
             directions
             prescribed
             in
             this
             Proposition
             )
             that
             it
             shall
             then
             be
             about
             8.
             of
             the
             clocke
             in
             the
             morning
             .
          
        
         
           
             PROP.
             XIIII
             .
             To
             finde
             the
             Amplitude
             or
             bredth
             of
             the
             Sunnes
             rising
             ,
             or
             setting
             ,
             &c.
             
          
           
             THe
             pole
             of
             the
             Sphaere
             being
             set
             to
             his
             eleuation
             ,
             and
             the
             place
             of
             the
             Sunne
             to
             the
             East
             semicircle
             of
             the
             Horizon
             :
             see
             how
             many
             degrees
             of
             the
             Horizon
             ,
             are
             contayned
             betweene
             the
             place
             of
             the
             Sunne
             ,
             and
             the
             true
             East
             point
             ,
             for
             so
             you
             shall
             haue
             the
             bredth
             of
             the
             sunnes
             rising
             .
          
           
             Thus
             the
             sunne
             being
             in
             the
             10.
             degree
             of
             Taurus
             ,
             you
             shall
             find
             by
             the
             Sphaere
             ,
             that
             (
             for
             the
             latitude
             of
             London
             )
             hee
             riseth
             about
             23.
             degr
             .
             and
             a
             halfe
             Northwards
             ,
             from
             the
             true
             East
             point
             ,
             and
             that
             hee
             setteth
             as
             many
             degrees
             towards
             the
             North
             ,
             from
             the
             true
             West
             point
             .
          
        
         
           
             PROP.
             XV.
             To
             finde
             the
             place
             of
             the
             Sunne
             ,
             &c.
             
          
           
             THe
             quarter
             of
             the
             yeare
             being
             knowne
             ,
             bring
             the
             quarter
             of
             the
             Eclipticke
             that
             is
             answerable
             thereto
             ,
             vnder
             the
             Meridian
             ;
             and
             turne
             the
             Sphaere
             to
             or
             fro
             ,
             till
             there
             bee
             so
             many
             degrees
             and
             minutes
             of
             the
             
             Meridian
             ,
             conteyned
             betweene
             the
             Ecliptick
             and
             the
             Equator
             ,
             as
             the
             declination
             commeth
             to
             :
             then
             looke
             what
             degree
             of
             the
             Ecliptick
             is
             vnder
             the
             Meridian
             ,
             for
             that
             is
             the
             place
             of
             the
             Sunne
             .
          
           
             As
             suppose
             the
             declination
             of
             the
             Sun
             in
             some
             day
             of
             the
             Spring-time
             of
             the
             yeare
             be
             found
             to
             bee
             14.
             degr
             .
             51.
             min.
             (
             turning
             therefore
             the
             Sphaere
             to
             and
             fro
             ,
             till
             some
             part
             of
             the
             spring
             quarter
             of
             the
             Ecliptick
             ,
             come
             right
             vnder
             that
             degree
             and
             minute
             of
             declination
             in
             the
             Meridian
             )
             you
             may
             finde
             that
             the
             Sunne
             is
             then
             in
             the
             tenth
             degree
             of
             Taurus
             .
          
        
         
           
             PROP.
             XVI
             .
             To
             finde
             what
             day
             of
             the
             moneth
             it
             is
             ,
             &c.
             
          
           
             THe
             place
             of
             the
             Sunne
             being
             found
             by
             his
             declination
             (
             as
             is
             already
             shewed
             )
             seeke
             the
             place
             of
             the
             Sunne
             in
             the
             Horizon
             of
             the
             Sphaere
             ,
             and
             looke
             what
             day
             is
             answerable
             thereto
             ,
             for
             that
             is
             the
             day
             of
             the
             moneth
             which
             was
             sought
             for
             .
          
           
             As
             the
             place
             of
             the
             Sunne
             being
             found
             by
             his
             declination
             (
             as
             is
             shewed
             in
             the
             former
             Proposition
             )
             to
             be
             in
             the
             10.
             degree
             of
             Taurus
             ,
             the
             day
             of
             the
             moneth
             shall
             thus
             be
             found
             to
             be
             the
             21.
             of
             Aprill
             .
          
        
         
           
             PROP.
             XVII
             .
             The
             day
             of
             the
             moneth
             being
             knowne
             ,
             to
             finde
             at
             what
             time
             the
             day
             breaketh
             .
          
           
             FInde
             the
             place
             of
             the
             Sunne
             (
             by
             the
             2.
             
             Prop.
             )
             and
             bring
             it
             to
             the
             Meridian
             ,
             then
             bring
             the
             houre
             Index
             ,
             to
             12.
             a
             clocke
             vpon
             the
             houre
             circle
             .
          
           
             Finde
             out
             also
             the
             point
             of
             the
             Eclipticke
             that
             is
             right
             ouer
             against
             the
             place
             of
             the
             Sunne
             :
             then
             take
             
             betweene
             the
             feet
             of
             your
             Compasses
             17.
             degrees
             of
             the
             Eclipticke
             ,
             and
             setting
             one
             foot
             of
             the
             Compasses
             in
             the
             point
             opposite
             to
             the
             place
             of
             the
             Sunne
             ,
             turne
             the
             Sphaere
             Westwards
             ,
             till
             you
             can
             but
             onely
             touch
             the
             Horizon
             with
             the
             other
             foot
             ,
             for
             then
             the
             Index
             sheweth
             in
             the
             houre
             circle
             at
             what
             time
             the
             day
             breaketh
             .
          
           
             So
             the
             21.
             of
             Aprill
             ,
             the
             Sun
             being
             in
             the
             10
             degr
             .
             of
             Taurus
             ,
             you
             shall
             finde
             that
             the
             day
             breaketh
             about
             halfe
             an
             houre
             past
             2.
             of
             the
             clocke
             in
             the
             morning
             .
          
        
         
           
             PROP.
             XVIII
             .
             To
             finde
             how
             long
             the
             twylight
             continueth
             .
          
           
             FInde
             out
             by
             the
             former
             Prop.
             at
             what
             time
             the
             day
             breaketh
             ,
             and
             learne
             also
             at
             what
             time
             the
             Sunne
             riseth
             by
             the
             7.
             or
             9.
             
             Prop.
             
          
           
             Then
             subtract
             the
             lesser
             from
             the
             greater
             ,
             and
             there
             shall
             remayne
             the
             length
             of
             the
             twylight
             .
          
           
             Or
             else
             thus
             :
             hauing
             brought
             the
             point
             that
             is
             opposite
             to
             the
             place
             of
             the
             Sunne
             to
             be
             17.
             degrees
             aboue
             the
             Horizon
             West-wards
             ,
             in
             such
             sort
             as
             is
             shewed
             in
             the
             former
             Proposition
             ;
             and
             keeping
             the
             Sphaere
             in
             that
             position
             ,
             bring
             about
             the
             point
             of
             the
             houre
             Index
             vnto
             12.
             a
             clocke
             vpon
             the
             houre
             circle
             ;
             then
             tune
             the
             Sphaere
             Westwards
             vntill
             the
             degree
             or
             point
             of
             the
             Eclipticke
             that
             is
             opposite
             to
             the
             place
             of
             the
             sunne
             come
             to
             the
             Horizon
             :
             and
             see
             how
             many
             houres
             the
             point
             of
             the
             Index
             hath
             runne
             ouer
             in
             the
             meane
             time
             vpon
             the
             houre
             circle
             :
             for
             so
             many
             houres
             continueth
             the
             twylight
             .
          
           
             By
             eyther
             of
             these
             wayes
             ,
             the
             Sunne
             being
             in
             the
             10.
             degr
             .
             of
             Taurus
             ,
             you
             shall
             finde
             that
             the
             twylight
             
             (
             that
             is
             the
             time
             from
             the
             breake
             of
             the
             day
             till
             Sun-rise
             )
             is
             about
             2.
             houres
             and
             20.
             minutes
             .
          
        
         
           
             PROP.
             XIX
             .
             To
             finde
             how
             much
             the
             declination
             of
             the
             Sunne
             must
             alter
             at
             any
             time
             of
             the
             yeare
             ,
             to
             make
             the
             day
             an
             houre
             longer
             or
             shorter
             .
          
           
             BRing
             the
             place
             of
             the
             Sunne
             (
             found
             by
             the
             second
             Prop.
             )
             to
             the
             East
             semicircle
             of
             the
             Horizon
             ,
             and
             marke
             what
             degree
             or
             point
             of
             the
             Horizon
             it
             falleth
             vpon
             ;
             bring
             one
             of
             the
             Colures
             to
             the
             same
             degree
             or
             point
             ,
             and
             there
             make
             a
             pricke
             in
             that
             colure
             ;
             and
             holding
             the
             Sphaere
             immoueable
             ,
             )
             marke
             withall
             what
             degree
             of
             the
             Equinoctiall
             ,
             or
             of
             eyther
             of
             the
             Tropickes
             is
             then
             at
             the
             Horizon
             :
             Then
             turne
             the
             Sphaere
             7.
             degrees
             and
             an
             halfe
             forwards
             ,
             towards
             the
             West
             ,
             if
             the
             dayes
             shorten
             :
             but
             contrariwise
             if
             the
             dayes
             lengthen
             ;
             and
             holding
             the
             sphaere
             there
             immoueable
             ,
             make
             another
             prick
             in
             the
             colure
             at
             the
             Horizon
             :
             for
             the
             distance
             of
             these
             two
             prickes
             in
             the
             colure
             taken
             with
             the
             Compasses
             and
             brought
             to
             the
             Ecliptick
             ,
             or
             Equinoctiall
             ,
             sheweth
             how
             much
             the
             Sunnes
             declination
             must
             alter
             to
             make
             the
             day
             an
             houre
             longer
             ,
             if
             the
             dayes
             increase
             ;
             or
             shorter
             ,
             if
             they
             decrease
             .
          
           
             After
             this
             manner
             you
             shall
             finde
             that
             the
             sunne
             being
             in
             the
             10.
             degree
             of
             Taurus
             ,
             his
             declination
             must
             increase
             about
             5.
             degrees
             ,
             (
             or
             little
             more
             )
             to
             make
             the
             day
             an
             houre
             longer
             ;
             but
             when
             the
             sunne
             is
             in
             the
             20.
             degree
             of
             Pisces
             ,
             his
             declination
             ,
             or
             rather
             his
             Meridian
             altitude
             ,
             must
             increase
             about
             6.
             degrees
             to
             make
             the
             day
             an
             houre
             longer
             :
             and
             when
             hee
             is
             in
             the
             
             beginning
             of
             Capricorne
             ,
             his
             declination
             decreaseth
             scarce
             5.
             degrees
             to
             make
             the
             day
             an
             houre
             longer
             .
          
        
         
           
             PROP.
             XX.
             To
             find
             how
             many
             dayes
             it
             is
             ere
             the
             day
             lengthen
             or
             shorten
             an
             houre
             .
          
           
             BRing
             the
             foresaid
             prickes
             (
             made
             in
             the
             Colure
             by
             the
             former
             Proposition
             )
             vnto
             the
             Meridian
             ,
             and
             there
             make
             two
             markes
             iustly
             answerable
             vnto
             those
             prickes
             in
             the
             Colure
             :
             turne
             about
             the
             Sphaere
             till
             the
             Eclipticke
             line
             come
             iust
             vnder
             one
             of
             those
             markes
             ,
             and
             there
             make
             a
             pricke
             in
             the
             Eclipticke
             :
             then
             againe
             turne
             the
             Sphaere
             till
             the
             Ecliptick
             come
             iust
             vnder
             the
             other
             marke
             made
             in
             the
             Meridian
             ,
             and
             there
             make
             another
             pricke
             in
             the
             Eclipticke
             :
             (
             But
             here
             it
             is
             to
             bee
             noted
             ,
             that
             whereas
             the
             Eclipticke
             may
             be
             brought
             vnder
             that
             marke
             whether
             way
             soeuer
             you
             turne
             the
             Sphaere
             ,
             it
             must
             (
             I
             say
             be
             noted
             that
             the
             Sphaere
             must
             be
             turned
             that
             way
             which
             may
             soonest
             bring
             the
             Eclipticke
             vnder
             that
             marke
             .
             (
             Lastly
             ,
             finde
             out
             amongst
             the
             signes
             and
             degrees
             described
             vpon
             the
             Horizon
             ,
             the
             like
             arch
             to
             this
             ,
             that
             is
             contayned
             betweene
             these
             prickes
             in
             the
             Eclipticke
             :
             For
             the
             number
             of
             dayes
             answerable
             to
             this
             arch
             in
             the
             Horizon
             ,
             is
             the
             time
             wherein
             the
             day
             groweth
             an
             houre
             longer
             or
             shorter
             .
          
           
             Thus
             shall
             you
             finde
             ,
             that
             when
             the
             Sunne
             is
             in
             the
             beginning
             of
             Aries
             ,
             it
             will
             bee
             about
             18.
             dayes
             after
             ,
             ere
             the
             day
             be
             one
             houre
             longer
             .
             But
             when
             the
             Sun
             is
             in
             the
             beginning
             of
             Capricorne
             ,
             you
             shall
             finde
             that
             it
             will
             be
             almost
             twice
             so
             much
             ,
             that
             is
             neare
             34.
             dayes
             before
             the
             day
             will
             be
             an
             houre
             longer
             .
          
           
           
             Hereby
             therefore
             the
             error
             of
             them
             manifestly
             appeareth
             ,
             which
             thinke
             that
             in
             euery
             15.
             dayes
             ,
             the
             day
             is
             lengthened
             or
             shortened
             an
             houre
             ,
             whereas
             indeed
             the
             lengthning
             or
             shortning
             of
             the
             dayes
             ,
             keepeth
             no
             such
             rule
             .
             For
             when
             the
             Sunne
             is
             about
             the
             Equinoctiall
             points
             ,
             the
             dayes
             lenghthen
             or
             shorten
             very
             fast
             :
             but
             when
             he
             is
             neere
             the
             Tropicall
             points
             ,
             they
             grow
             longer
             or
             shorter
             very
             slowly
             .
          
        
         
           
             PROP.
             XXI
             .
             To
             make
             an
             Horizontall
             Diall
             .
          
           
             SEt
             the
             Sphaere
             to
             the
             eleuation
             of
             the
             place
             for
             which
             you
             would
             make
             the
             Diall
             turne
             about
             the
             Sphaere
             ,
             till
             the
             solstitiall
             Colure
             be
             15.
             degrees
             (
             measured
             in
             the
             Equinoctiall
             )
             from
             the
             Meridian
             ;
             and
             where
             the
             Colure
             crosseth
             the
             Horizon
             ,
             there
             make
             a
             prick
             ;
             then
             turne
             the
             Colure
             yet
             15.
             degr
             .
             further
             ,
             that
             is
             30.
             degrees
             from
             the
             Meridian
             ;
             and
             where
             the
             Colure
             crosseth
             the
             Horizon
             ,
             there
             make
             an
             other
             prick
             :
             againe
             turne
             the
             Colure
             forwards
             yet
             15.
             deg
             .
             more
             ,
             (
             that
             is
             45.
             degrees
             from
             the
             Meridian
             )
             and
             at
             the
             common
             meeting
             of
             the
             Colure
             and
             Horizon
             ,
             make
             the
             third
             prick
             in
             the
             Horizon
             ;
             and
             so
             proceed
             with
             the
             rest
             ,
             till
             you
             haue
             made
             so
             many
             pricks
             on
             that
             side
             of
             the
             Horizon
             as
             there
             are
             houres
             in
             halse
             the
             longest
             day
             .
             Then
             looke
             how
             many
             degrees
             the
             first
             ,
             second
             ,
             third
             ,
             fourth
             pricks
             ,
             &c.
             are
             from
             the
             Meridian
             ,
             for
             so
             many
             degrees
             must
             the
             houre
             lines
             of
             11.
             a
             clocke
             ,
             and
             one
             a
             clocke
             ;
             of
             10.
             and
             2
             ,
             of
             9.
             and
             3.
             of
             8.
             and
             4.
             &c.
             be
             from
             the
             12.
             a
             clock
             line
             in
             the
             Horizontall
             Dyall
             .
          
           
             After
             this
             manner
             in
             an
             Horizontall
             Diall
             made
             
             for
             the
             Latitude
             of
             London
             ,
             (
             which
             is
             51.
             degr
             .
             and
             32.
             minutes
             (
             you
             shall
             finde
             the
             distances
             of
             all
             the
             rest
             of
             the
             Houre-lines
             from
             the
             12.
             a
             clocke
             line
             as
             followeth
             :
             Betwixt
             twelue
             and
             11.
             and
             twelue
             and
             1.
             are
             conceyned
             12.
             degrees
             almost
             :
             Betweene
             12.
             and
             10.
             and
             12.
             and
             2.
             there
             are
             conteyned
             14.
             degr
             .
             and
             an
             halfe
             :
             Betweene
             12.
             and
             9.
             and
             12.
             and
             3.
             38.
             degr
             .
             Betweene
             12.
             and
             8.
             and
             12.
             and
             4.
             53.
             degr
             .
             Betweene
             12.
             and
             7.
             and
             12.
             and
             5.
             70.
             degrees
             and
             an
             halfe
             .
          
           
             Betweene
             12.
             and
             6.
             both
             before
             and
             after
             noone
             ,
             90.
             degr
             .
             The
             other
             houre
             spaces
             before
             6.
             in
             the
             morning
             ;
             and
             after
             6.
             in
             the
             euening
             ,
             are
             equall
             to
             the
             Houre
             spaces
             after
             sixe
             in
             the
             morning
             ,
             and
             before
             6.
             in
             the
             afternoone
             .
          
        
         
           
             PROP.
             XXII
             .
             How
             to
             make
             a
             direct
             mural
             Diall
             .
          
           
             SEt
             the
             Pole
             artick
             of
             the
             Sphaere
             so
             much
             vnder
             the
             Horizon
             as
             is
             the
             complement
             of
             the
             Poles
             eleuation
             :
             the
             Horizon
             therefore
             being
             thus
             set
             as
             it
             were
             to
             the
             Zenith
             of
             the
             Sphaere
             ,
             and
             so
             representing
             the
             verticall
             Circle
             of
             East
             and
             West
             (
             that
             is
             the
             plaine
             super
             fices
             of
             a
             direct
             mural
             Diall
             )
             you
             shall
             finde
             the
             distances
             of
             all
             the
             houre-lines
             ,
             (
             both
             before
             and
             after
             noone
             )
             from
             the
             12.
             a
             clock
             line
             ,
             in
             such
             sort
             as
             you
             did
             before
             for
             the
             Horizontall
             Dial.
             
          
           
             So
             you
             shall
             finde
             the
             distances
             of
             the
             houre-lines
             in
             an
             erect
             direct
             murall
             Dial
             made
             for
             the
             Latitude
             of
             London
             to
             bee
             as
             followeth
             :
             Betweene
             the
             twelue
             a
             clock
             line
             and
             the
             lines
             of
             11.
             and
             1.
             9
             ,
             degr
             .
             and
             about
             one
             third
             part
             of
             a
             degree
             :
             Betweene
             12.
             and
             10.
             and
             12.
             and
             2.
             19.
             degrees
             and
             one
             quarter
             ;
             
             Betweene
             12.
             and
             9.
             and
             12.
             and
             3.
             32.
             degr
             .
             or
             little
             more
             :
             betweene
             12.
             and
             8.
             and
             12.
             and
             4.
             48.
             degrees
             :
             betweene
             12.
             and
             7.
             and
             12.
             and
             5.
             67.
             degr
             .
             or
             little
             more
             :
             betweene
             12.
             and
             6.
             both
             before
             and
             afternoone
             90.
             degrees
             .
          
        
         
           
             PROP.
             XXIII
             .
             How
             to
             make
             any
             direct
             inclining
             ,
             or
             direct
             reclining
             Dial.
             
          
           
             REckon
             from
             the
             Equinoctiall
             vpwards
             in
             the
             Meridian
             ,
             so
             many
             degrees
             as
             the
             height
             of
             the
             Pole
             commeth
             to
             at
             that
             place
             where
             you
             would
             make
             your
             Diall
             ;
             for
             there
             is
             the
             verticall
             point
             or
             Zenith
             of
             that
             place
             :
             from
             this
             Zenith
             reckon
             Southwards
             in
             the
             Meridian
             ,
             the
             inclination
             of
             south
             Dials
             ,
             and
             the
             reclination
             of
             North
             Dialls
             ;
             but
             contrarywise
             ,
             reckon
             from
             the
             Zenith
             Northwards
             the
             inclination
             of
             North
             Dialls
             ,
             and
             the
             reclination
             of
             South
             Dialls
             .
             Then
             bring
             that
             degree
             of
             the
             Meridian
             ,
             where
             this
             reckoning
             endeth
             to
             the
             Horizon
             ,
             for
             so
             the
             Horizon
             representeth
             vnto
             you
             the
             plaine
             or
             the
             flat
             superficies
             of
             the
             Diall
             which
             you
             would
             make
             .
             Therefore
             you
             shall
             finde
             how
             〈…〉
             euery
             one
             of
             the
             houre
             lines
             should
             be
             dist●●●
             from
             the
             12.
             a
             clock
             line
             ,
             in
             such
             sort
             as
             you
             did
             before
             in
             making
             the
             Horizontall
             Diall
             .
          
           
             Thus
             in
             a
             South
             direct
             Diall
             inclining
             30.
             degr
             .
             or
             in
             a
             North
             direct
             reclining
             30.
             degrees
             made
             for
             the
             Latitude
             or
             eleuation
             of
             the
             Pole
             at
             London
             ,
             you
             may
             finde
             the
             distances
             of
             the
             eleuen
             a
             clock
             line
             ,
             and
             of
             the
             one
             a
             clock
             line
             ,
             from
             the
             12.
             a
             clock
             line
             ,
             to
             be
             about
             14.
             degrees
             .
          
           
             But
             the
             houre
             lines
             of
             10.
             in
             the
             forenoone
             ,
             and
             of
             
             2.
             in
             the
             afternoon
             ,
             are
             distant
             from
             the
             12.
             a
             clock
             line
             28.
             degr
             .
             &
             one
             halfe
             ;
             From
             12.
             to
             9.
             and
             to
             3.
             you
             shall
             find
             43.
             deg
             .
             From
             12.
             to
             8.
             in
             the
             forenoone
             ,
             and
             4.
             in
             the
             afternoone
             ,
             you
             shall
             haue
             58.
             deg
             .
             &
             an
             halfe
             :
             also
             from
             12.
             to
             7.
             &
             to
             5.
             shall
             be
             about
             74.
             deg
             .
             And
             from
             12.
             to
             6.
             in
             the
             morning
             ,
             &
             6.
             afternoone
             90.
             degrees
             .
          
           
             Likewise
             in
             a
             South
             direct
             reclining
             ,
             or
             North
             direct
             inclining
             20.
             deg
             .
             for
             the
             eleuation
             of
             London
             ;
             the
             spaces
             between
             12.
             
             &
             11.
             
             &
             12.
             
             &
             1.
             shall
             be
             about
             5.
             deg
             .
             or
             little
             lesse
             :
             Between
             12
             ,
             &
             10.
             
             &
             12
             ,
             &
             ●
             .
             about
             10.
             deg
             .
             &
             ●
             .
             third
             parts
             .
             From
             12
             ,
             to
             9.
             in
             the
             forenoone
             ,
             &
             3.
             in
             the
             afternoon
             ,
             18.
             almost
             ▪
             From
             12.
             to
             8.
             
             &
             4.
             ●g
             .
             deg
             .
             or
             little
             more
             .
             From
             the
             1●
             .
             a
             clock
             line
             ;
             to
             the
             line
             of
             7.
             a
             clock
             in
             the
             forenoone
             ,
             &
             5.
             in
             the
             afternoone
             ,
             50.
             deg
             .
             or
             thereabouts
             .
             From
             12.
             to
             6.
             both
             before
             and
             afternooe
             ▪
             90.
             deg
             .
             as
             in
             the
             former
             kindes
             of
             D●
             .
             In
             all
             which
             it
             is
             to
             be
             noted
             ,
             that
             there
             is
             alwaies
             〈◊〉
             distance
             betweene
             the
             houre
             lines
             of
             5
             ,
             &
             ●
             .
             &
             4
             ,
             &
             6.
             that
             there
             is
             betweene
             7
             ,
             &
             6.
             and
             8
             ,
             &
             6.
             in
             the
             forenoone
             ,
             and
             betweene
             5
             ,
             &
             ●
             .
             &
             4
             ,
             &
             ●
             .
             and
             7
             ,
             &
             6.
             
             &
             8
             ,
             &
             6.
             in
             the
             afternoone
             .
             So
             as
             the
             distances
             of
             all
             the
             houre
             lines
             from
             the
             12.
             a
             clock
             line
             being
             found
             from
             6.
             in
             the
             morning
             ,
             till
             6.
             at
             night
             ,
             the
             distances
             of
             the
             other
             Houre-lines
             before
             6.
             in
             the
             morning
             ,
             and
             after
             6.
             at
             night
             shall
             easily
             be
             had
             .
          
        
         
           
             PROP.
             XXIIII
             .
             To
             know
             at
             what
             time
             the
             Moone
             ,
             or
             any
             other
             of
             the
             Planets
             or
             fixed
             Stars
             ,
             that
             are
             within
             the
             bredth
             of
             the
             Zodiack
             ;
             rise
             or
             set
             ,
             or
             come
             to
             the
             Meridian
             ,
             &c.
             
          
           
             FInde
             the
             place
             of
             the
             Moone
             ,
             or
             any
             other
             of
             the
             Planets
             ,
             both
             in
             longitude
             and
             Latitude
             ,
             by
             the
             
             Epheme●ides
             :
             and
             finde
             the
             place
             (
             that
             is
             ,
             the
             Longitude
             and
             Latitude
             )
             of
             any
             of
             the
             fixed
             Star●es
             in
             the
             Zodiack
             by
             some
             table
             of
             the
             fixed
             Starres
             ,
             or
             otherwise
             ;
             and
             marke
             the
             same
             place
             of
             the
             Moone
             ;
             Planet
             or
             Starre
             ,
             in
             the
             Zodiack
             of
             the
             Sphaere
             :
             and
             hauing
             set
             the
             Sphaere
             to
             the
             Latitude
             of
             the
             place
             ,
             bring
             the
             place
             of
             the
             Sunne
             (
             found
             by
             the
             2.
             
             Proposition
             )
             to
             the
             Meridian
             ,
             and
             the
             Houre-index
             to
             12.
             a
             clock
             vpon
             the
             houre-circle●
             ,
             then
             turne
             the
             Sphaere
             till
             the
             place
             of
             the
             Moone
             ,
             Planet
             or
             Starre
             marked
             in
             the
             Zodiack
             ,
             come
             to
             the
             East
             semi-circle
             of
             the
             Horizon
             ;
             for
             then
             the
             Index
             sheweth
             the
             time
             when
             the
             Moone
             ,
             or
             that
             Planet
             or
             fixed
             Starre
             riseth
             .
          
           
             Al●●
             the
             number
             of
             degree
             in
             the
             Horizon
             ,
             contayned
             betweene
             the
             point
             of
             the
             Moones
             ,
             Planets
             ,
             or
             Starres
             rising
             ,
             and
             the
             point
             of
             true
             East
             ,
             sheweth
             the
             bredth
             ,
             ●●denesse
             ,
             or
             amplitude
             of
             rising
             ;
             And
             you
             may
             at
             the
             same
             instant
             ,
             〈◊〉
             ,
             what
             degree
             of
             the
             Ecliptick
             riseth
             with
             any
             of
             them
             ,
             and
             what
             the
             oblique
             ascension
             of
             any
             of
             them
             is
             :
             For
             if
             you
             tell
             hour
             many
             degrees
             of
             the
             Equinoctiall
             are
             〈…〉
             betweene
             the
             beginning
             of
             Aries
             in
             the
             Horizon
             ,
             proceeding
             Eastwards
             ,
             or
             according
             to
             the
             order
             of
             the
             signes
             :
             you
             shall
             haue
             the
             oblique
             ascension
             of
             the
             Moone
             ,
             Planet
             or
             Starre
             ,
             that
             〈…〉
             for
             .
          
           
             But
             bring
             the
             same
             place
             of
             the
             Moone
             ,
             Planet
             ,
             or
             Starre
             to
             the
             Meridian
             ,
             and
             the
             Index
             sheweth
             in
             the
             houre
             circle
             at
             what
             time
             they
             come
             to
             the
             Meridian
             :
             where
             you
             may
             also
             see
             ,
             first
             what
             degree
             of
             the
             Zodiath
             middeth
             Heauen
             (
             that
             is
             ,
             〈◊〉
             to
             the
             Meridian
             )
             with
             any
             of
             them
             ;
             secondly
             ,
             you
             may
             see
             how
             much
             the
             declination
             of
             any
             of
             them
             is
             ;
             for
             
             count
             how
             many
             degrees
             of
             the
             Meridian
             are
             contayned
             betweene
             the
             Equinoctiall
             and
             the
             place
             of
             the
             Moone
             ,
             Planet
             ,
             or
             fixed
             Starre
             ,
             and
             so
             much
             is
             the
             declination
             .
             Thirdly
             ,
             you
             may
             there
             see
             what
             the
             right
             ascension
             of
             any
             of
             them
             is
             :
             for
             the
             place
             of
             any
             of
             them
             being
             brought
             to
             the
             Meridian
             and
             there
             〈◊〉
             ,
             r●ckon
             Eastwards
             how
             many
             degrees
             of
             the
             Equinoctiall
             are
             contayned
             betweene
             the
             beginning
             of
             Aries
             and
             the
             Meridian
             ,
             so
             haue
             you
             the
             right
             ascension
             .
             Lastly
             ,
             bring
             the
             place
             of
             the
             Moone
             ,
             Planet
             or
             Star
             ,
             to
             the
             West
             semi-circle
             of
             the
             Horizon
             ;
             for
             then
             the
             Index
             sheweth
             the
             time
             of
             their
             setting
             ;
             and
             the
             number
             of
             the
             degrees
             of
             the
             Horizon
             betweene
             the
             point
             where
             any
             of
             them
             setteth
             ,
             and
             the
             Equinoctiall
             ,
             or
             true
             West
             point
             (
             where
             the
             Equinoctiall
             ,
             and
             Horizon
             crosse
             each
             other
             )
             is
             the
             amplitude
             or
             bredth
             of
             the
             setting
             of
             any
             of
             them
             ,
             shewing
             how
             much
             they
             set
             from
             the
             true
             West
             point
             .
          
           
             You
             may
             there
             also
             see
             what
             degree
             ;
             either
             of
             the
             Ecliptick
             ,
             or
             of
             the
             Equinoctiall
             ,
             setteth
             with
             any
             of
             the●
             and
             consequently
             you
             may
             know
             the
             oblique
             descension
             of
             any
             of
             them
             ,
             by
             reckoning
             how
             many
             degr
             .
             of
             the
             Equinoctiall
             there
             are
             from
             the
             beginning
             of
             Aries
             Eastwards
             ,
             till
             you
             come
             about
             to
             the
             West
             part
             of
             the
             Horizon
             .
          
           
             Take
             for
             example
             the
             great
             Starre
             called
             the
             Bulls
             eye
             ,
             whose
             place
             in
             longitude
             is
             about
             the
             4.
             degr
             .
             of
             Taurus
             ,
             and
             his
             latitude
             about
             5.
             degrees
             and
             an
             halfe
             Southwards
             .
          
           
             Following
             therefore
             the
             directions
             prescribed
             in
             this
             Proposition
             ,
             you
             shall
             finde
             that
             vpon
             the
             first
             day
             of
             Aprill
             this
             present
             yeare
             ,
             1600.
             the
             same
             Starre
             
             riseth
             here
             at
             London
             about
             halfe
             an
             houre
             past
             7.
             of
             the
             clock
             in
             the
             morning
             ,
             and
             setteth
             about
             a
             quarter
             of
             an
             houre
             past
             10.
             at
             night
             ,
             and
             commeth
             to
             the
             Meridian
             about
             3.
             a
             clock
             afternoone
             :
             Also
             you
             shall
             finde
             that
             it
             riseth
             with
             the
             15.
             degree
             of
             Gemini
             ,
             and
             setteth
             with
             the
             last
             degr
             .
             of
             Taurus
             ,
             and
             commeth
             to
             the
             Meridian
             ,
             or
             middeth
             Heauen
             ,
             with
             the
             5.
             deg
             .
             of
             Gemini
             :
             Thirdly
             you
             shall
             finde
             his
             declination
             to
             be
             about
             15.
             deg
             .
             and
             2.
             third
             parts
             ,
             his
             right
             ascension
             63.
             degr
             .
             and
             a
             quarter
             ,
             his
             oblique
             asce●sion
             43.
             degr
             .
             and
             his
             oblique
             descension
             about
             84.
             deg
             .
             and
             an
             halfe
             :
             and
             lastly
             his
             amplitude
             of
             bredth
             of
             rising
             or
             letting
             about
             25.
             degr
             .
             and
             an
             halfe
             from
             the
             true
             East
             and
             West
             points
             towards
             the
             North.
             
          
        
         
           
             PROP.
             XXV
             .
             To
             know
             how
             long
             the
             Moone
             ,
             or
             any
             of
             the
             Planets
             of
             fixed
             Stars
             doe
             shine
             or
             continue
             aboue
             the
             Horizon
             .
          
           
             THe
             Sphaere
             bring
             set
             up
             the
             latitude
             of
             the
             place
             ,
             and
             the
             place
             of
             the
             Moone
             ,
             Planet
             ,
             or
             fixed
             Starre
             ,
             being
             found
             and
             marked
             in
             the
             Zodiack
             ,
             hoth
             in
             Longitude
             and
             Latitude
             ,
             (
             as
             in
             the
             〈◊〉
             Prop.
             )
             bring
             the
             place
             of
             the
             Moone
             ,
             Planet
             ,
             or
             Star
             ,
             〈◊〉
             East
             semi-circle
             of
             the
             Horizon
             ,
             and
             the
             Index
             of
             houres
             to
             12.
             a
             clock
             :
             Then
             〈◊〉
             about
             the
             Sphaere
             West-wards
             ,
             till
             the
             same
             place
             of
             the
             Moone
             ,
             or
             〈◊〉
             the
             same
             Planet
             ,
             or
             Starre
             ,
             come
             to
             the
             West
             semi-circle
             of
             the
             Horizon
             ,
             and
             marke
             〈◊〉
             how
             many
             houres
             the
             Index
             runneth
             ouer
             in
             the
             meane
             time
             vpon
             the
             houre
             circle
             ,
             for
             so
             many
             houres
             continueth
             the
             Moone
             ,
             Planet
             ,
             or
             Starre
             aboue
             the
             Horizon
             .
          
           
             Thus
             shall
             you
             finde
             that
             the
             foresaid
             〈…〉
             
             The
             Bulls
             eye
             〈…〉
             the
             Horizon
             at
             London
             ,
             about
             14.
             〈…〉
             and
             3.
             quarters
             .
          
        
         
           
             PROP.
             XXVI
             .
             To
             finde
             which
             of
             the
             Planets
             or
             fixed
             Starres
             are
             aboue
             or
             vnder
             the
             Horizon
             at
             any
             time
             ,
             &c.
             
          
           
             THe
             place
             of
             the
             Plantes
             or
             fixed
             Starres
             being
             marked
             in
             the
             Zodiack
             of
             the
             Sphaere
             ,
             as
             in
             the
             former
             propositions
             ,
             and
             the
             place
             of
             the
             Sunne
             brought
             to
             the
             Meridian
             ,
             and
             then
             the
             Index
             to
             12.
             
             〈…〉
             Sphaere
             〈◊〉
             the
             Index
             〈◊〉
             to
             that
             houre
             vpon
             the
             houre
             〈◊〉
             at
             which
             you
             desire
             to
             know
             what
             Planets
             are
             aboue
             or
             vnder
             the
             Horizon
             ;
             and
             then
             hold
             still
             the
             Sphaere
             ,
             and
             marke
             what
             Planets
             or
             Starres
             are
             aboue
             or
             vnder
             the
             Horizon
             in
             the
             Sphaere
             for
             the
             same
             Planets
             or
             Starres
             are
             aboue
             or
             vnder
             the
             Horizon
             in
             the
             Heauens
             .
          
           
             As
             for
             example
             :
             the
             1.
             of
             Aprill
             1600
             at
             9.
             of
             the
             clocke
             at
             night
             ,
             you
             may
             by
             the
             Proposition
             finde
             ;
             that
             the
             most
             part
             of
             the
             fixed
             Starres
             ,
             that
             are
             in
             the
             constestation
             of
             
               Taurus
               ,
               Gemini
               ,
               Cancer
               ,
               Leo
               ,
               Virgo
               ,
            
             and
             Libra
             ,
             together
             with
             the
             three
             superiour
             Planets
             ,
             〈◊〉
             ,
             ●upiter
             ,
             &
             Mars
             ,
             are
             at
             〈…〉
             to
             be
             seene
             aboue
             the
             Horizon
             ,
             and
             that
             the
             rest
             of
             the
             Planets
             and
             fixed
             Stars
             ,
             that
             are
             within
             the
             compasse
             of
             the
             Zodiack
             ,
             are
             vnder
             the
             Horizon
             ,
             and
             cannot
             then
             be
             seene
             .
          
        
         
           
             PROP.
             XXVII
             .
             To
             finde
             in
             what
             time
             any
             Signe
             or
             part
             of
             the
             Ecliptick
             riseth
             or
             setteth
             .
          
           
             BRing
             the
             beginning
             of
             the
             Signe
             ,
             or
             part
             of
             the
             Ecliptick
             to
             the
             East
             semi-circle
             of
             the
             Horizon
             ,
             
             if
             you
             would
             know
             in
             how
             long
             time
             it
             riseth
             ,
             or
             to
             the
             West
             part
             of
             the
             Horizon
             ,
             if
             you
             would
             know
             in
             what
             time
             it
             setteth
             ;
             then
             set
             the
             Index
             to
             12.
             a
             clock
             ,
             and
             turne
             forwards
             the
             Sphaere
             ,
             till
             the
             whole
             signe
             or
             part
             of
             the
             zodiack
             be
             risen
             ,
             or
             set
             :
             For
             then
             the
             Index
             sheweth
             vpon
             the
             houre
             circle
             in
             how
             long
             time
             ,
             that
             signe
             or
             part
             of
             the
             Zodiack
             riseth
             or
             setteth
             .
          
           
             Thus
             you
             may
             finde
             (
             for
             example
             )
             that
             the
             whole
             signe
             of
             Aries
             here
             at
             London
             riseth
             in
             one
             houre
             or
             somewhat
             lesse
             ,
             and
             setteth
             in
             two
             houres
             and
             three
             quarters
             ,
             or
             something
             more
             :
             And
             that
             the
             whole
             quarter
             of
             the
             Zodiack
             ,
             from
             the
             beginning
             of
             Aries
             to
             the
             beginning
             of
             Cancer
             ,
             riseth
             in
             lesse
             then
             foure
             houres
             ,
             but
             setteth
             in
             more
             then
             8.
             houres
             .
          
        
         
           
             PROP.
             XXVIII
             .
             To
             finde
             the
             houre
             of
             the
             night
             by
             any
             of
             the
             Planets
             or
             fixed
             Starres
             in
             the
             Zodiack
             ,
             &c.
             
          
           
             THe
             place
             (
             that
             is
             to
             say
             ,
             the
             longitude
             &
             latitude
             )
             of
             any
             Planet
             ,
             or
             fixed
             Starre
             in
             the
             Zodiacke
             ,
             that
             is
             aboue
             the
             Horizon
             ,
             being
             first
             found
             ,
             and
             marked
             in
             the
             Zodiack
             of
             the
             Sphaere
             ;
             bring
             the
             place
             of
             the
             Sunne
             (
             found
             by
             the
             2.
             
             Proposition
             )
             to
             the
             Meridian
             ,
             and
             the
             Index
             to
             12.
             a
             clocke
             vpon
             the
             houre
             circle
             :
             Then
             hauing
             found
             the
             height
             of
             the
             Starre
             ,
             or
             Planet
             by
             obseruation
             ,
             and
             the
             Sphaere
             also
             being
             set
             to
             the
             Latitude
             of
             the
             place
             of
             obseruation
             ,
             take
             betweene
             the
             feet
             of
             your
             Compasses
             ,
             so
             many
             degrees
             of
             the
             Ecliptick
             ,
             or
             Equinoctiall
             ,
             as
             the
             height
             of
             the
             Planet
             ,
             or
             Starre
             obserued
             ,
             commeth
             to
             ;
             and
             setting
             one
             foote
             of
             your
             Compasses
             in
             the
             place
             of
             the
             Planet
             ,
             or
             fixed
             Starre
             that
             you
             obserued
             in
             th
             Zodiack
             ,
             
             turne
             the
             Sphaere
             forwards
             or
             backwards
             ,
             till
             you
             can
             but
             onely
             touch
             the
             Horizon
             with
             the
             other
             foot
             :
             for
             then
             the
             Index
             in
             the
             houre
             circle
             ,
             shall
             shew
             you
             the
             houre
             of
             the
             night
             .
          
           
             Suppose
             (
             for
             example
             )
             I
             should
             obserue
             the
             height
             of
             the
             foresaid
             Bulles
             eye
             ,
             and
             should
             finde
             the
             same
             to
             be
             29.
             degrees
             the
             first
             day
             of
             March
             at
             euening
             :
             finding
             therefore
             the
             place
             of
             that
             Starre
             in
             the
             Zodiack
             of
             the
             Sphaere
             ,
             and
             bringing
             it
             (
             with
             helpe
             of
             the
             Compasses
             )
             to
             the
             height
             obserued
             (
             hauing
             first
             set
             the
             place
             the
             Sunne
             and
             houre-Index
             both
             together
             to
             the
             Meridian
             )
             the
             Index
             of
             the
             houres
             will
             shew
             ,
             that
             when
             that
             Starre
             hath
             that
             height
             of
             29.
             degrees
             ,
             it
             is
             about
             9.
             of
             the
             clock
             at
             night
             .
          
        
         
           
             PROP.
             XXIX
             .
             To
             know
             at
             any
             time
             of
             the
             yeare
             ,
             what
             Stars
             in
             the
             Zodiack
             ,
             arise
             or
             set
             ,
             Cosmically
             ,
             Achronically
             ,
             or
             Heliacally
             .
          
           
             SVch
             Stars
             as
             rise
             together
             with
             the
             Sunne
             ,
             are
             said
             to
             rise
             cosmically
             :
             and
             such
             Stars
             as
             set
             when
             the
             Sunne
             riseth
             ,
             are
             said
             to
             set
             cosmically
             ;
             But
             those
             Stars
             which
             set
             together
             with
             the
             Sun
             ,
             set
             achronycally
             ;
             and
             those
             Stars
             that
             rise
             when
             the
             Sunne
             setteth
             ,
             are
             said
             to
             rise
             achronically
             .
             Lastly
             ,
             those
             Starres
             that
             rise
             a
             little
             before
             the
             Sunne
             ,
             rise
             heliacally
             ;
             and
             those
             that
             set
             a
             little
             after
             the
             Sunne
             ,
             set
             heliacally
             .
          
           
             All
             which
             may
             thus
             bee
             found
             :
             Bring
             the
             place
             of
             the
             sunne
             to
             the
             East
             semicircle
             of
             the
             Horizon
             :
             for
             the
             Stars
             that
             are
             then
             a
             little
             aboue
             the
             Horizon
             rise
             heliacally
             ;
             but
             those
             that
             are
             in
             the
             Horizon
             in
             the
             East
             ,
             rise
             cosmically
             ;
             and
             they
             that
             are
             in
             the
             
             West
             semicircle
             of
             the
             Horizon
             set
             cosmically
             :
             But
             bring
             the
             place
             of
             the
             Sunne
             to
             the
             West
             semicircle
             of
             the
             Horizon
             ,
             for
             those
             Starres
             as
             are
             at
             the
             West
             part
             of
             the
             Horizon
             at
             the
             same
             time
             ,
             set
             achronycally
             ;
             but
             those
             that
             are
             then
             in
             the
             East
             semicircle
             of
             the
             Horizon
             ,
             rise
             achronycally
             :
             and
             they
             which
             are
             a
             little
             aboue
             the
             West
             semicircle
             of
             the
             Horizon
             set
             heliacally
             .
          
           
             Thus
             you
             may
             know
             that
             vpon
             the
             26.
             or
             27.
             day
             of
             May
             (
             it
             our
             latitude
             of
             London
             )
             the
             Bulles
             eye
             riseth
             cosmically
             ,
             and
             the
             Starres
             in
             Serpentarius
             his
             right
             foot
             ,
             set
             cosmically
             ,
             you
             may
             see
             also
             that
             the
             same
             day
             the
             Starre
             in
             the
             Bulls
             South
             horne
             setteth
             achronycally
             :
             and
             the
             Northermost
             starre
             in
             Serpentarius
             his
             right
             foot
             ,
             riseth
             achronycally
             :
             and
             lastly
             ,
             you
             may
             finde
             that
             about
             the
             same
             time
             the
             Ple●ades
             and
             the
             Starre
             in
             the
             Bulls
             North
             home
             ,
             rise
             heliacally
             ,
             and
             that
             the
             same
             Starre
             also
             ,
             and
             the
             former
             Twinnes
             feet
             set
             heliacally
             .
          
        
         
           
             PROP.
             XXX
             .
             To
             finde
             the
             foure
             principall
             or
             Cardinall
             points
             of
             Heauen
             (
             as
             the
             Astrologians
             call
             them
             )
             at
             any
             time
             .
          
           
             THese
             foure
             Cardinall
             points
             are
             nothing
             else
             but
             foure
             points
             of
             the
             Ecliptick
             ,
             whereof
             one
             is
             at
             the
             East
             part
             of
             the
             Horizon
             ,
             ascending
             ,
             and
             is
             therefore
             called
             the
             Ascendent
             :
             another
             is
             at
             the
             vpper
             part
             of
             the
             Meridian
             aboue
             the
             Horizon
             ,
             and
             is
             called
             the
             midst
             of
             Heauen
             ,
             and
             the
             hart
             of
             Heauen
             :
             the
             third
             is
             at
             the
             West
             part
             of
             the
             Horizon
             descending
             ,
             and
             may
             be
             therfore
             called
             the
             descendent
             :
             the
             fourth
             point
             is
             that
             which
             is
             at
             the
             nether
             part
             of
             the
             Meridian
             
             vnder
             the
             Horizon
             .
             Which
             foure
             points
             are
             the
             beginnings
             of
             the
             first
             ,
             tenth
             ,
             seuenth
             ,
             and
             fourth
             Houses
             .
             Therefore
             to
             finde
             these
             points
             at
             any
             time
             by
             the
             Sphaere
             ,
             bring
             the
             place
             of
             the
             Sunne
             (
             being
             found
             for
             that
             time
             by
             the
             2.
             
             Proposition
             )
             to
             the
             Meridian
             ,
             and
             the
             Index
             to
             12.
             a
             clocke
             :
             then
             turne
             the
             Sphaere
             till
             the
             Index
             come
             to
             that
             houre
             at
             which
             you
             desire
             to
             know
             those
             foure
             points
             ,
             and
             there
             hold
             the
             Sphaere
             that
             it
             moue
             not
             :
             and
             looke
             withall
             ,
             what
             points
             of
             the
             Ecliptick
             are
             at
             the
             East
             and
             West
             semicircle
             of
             the
             Horizon
             ;
             and
             at
             the
             vpper
             and
             nether
             parts
             of
             the
             Meridian
             :
             for
             those
             bee
             the
             foure
             principall
             or
             Cardinall
             points
             you
             sought
             for
             .
          
           
             Take
             for
             example
             the
             time
             of
             the
             Sunnes
             entrance
             into
             Aries
             this
             present
             yeare
             1600.
             which
             was
             vpon
             the
             tenth
             day
             of
             March
             about
             eight
             of
             the
             clocke
             in
             the
             morning
             ,
             or
             little
             after
             with
             vs
             here
             at
             London
             ,
             Hauing
             therefore
             brought
             the
             beginning
             of
             Aries
             together
             with
             the
             houre
             Index
             to
             the
             Meridian
             ,
             and
             then
             turned
             back
             the
             whole
             Sphaere
             till
             the
             Index
             come
             to
             8.
             of
             the
             clocke
             vpon
             the
             houre
             circle
             :
             you
             shall
             finde
             the
             ascendent
             at
             that
             time
             ,
             to
             be
             the
             27.
             degree
             of
             Taurus
             ;
             the
             middest
             or
             hart
             of
             Heauen
             ,
             the
             27.
             of
             
               Capricorne
               ▪
            
             the
             descendent
             ,
             the
             27.
             deg
             .
             of
             Scorpio
             ;
             and
             the
             lowest
             part
             of
             Heauen
             the
             27.
             degree
             of
             Cancer
             .
          
        
         
           
             PROP.
             XXXI
             .
             To
             finde
             out
             the
             bredth
             of
             any
             climate
             ,
             &c.
             
          
           
             LIft
             vp
             ,
             or
             put
             downe
             the
             pole
             of
             the
             Sphaere
             ,
             till
             you
             finde
             that
             there
             are
             7.
             deg
             .
             and
             an
             halfe
             of
             the
             Tropick
             of
             Cancer
             ,
             more
             or
             lesse
             aboue
             the
             Horizon
             ,
             
             then
             there
             were
             before
             ;
             and
             marke
             with
             all
             how
             much
             the
             pole
             of
             the
             Sphaere
             is
             raised
             ,
             or
             let
             fall
             in
             the
             meane
             time
             ,
             more
             then
             it
             was
             before
             ;
             for
             so
             much
             is
             the
             bredth
             of
             that
             climate
             .
          
           
             As
             far
             example
             :
             hauing
             set
             the
             Sphaere
             to
             our
             Latitude
             of
             London
             of
             51.
             deg
             .
             and
             an
             halfe
             ,
             with
             the
             point
             of
             your
             Compasses
             ,
             holding
             and
             guiding
             some
             point
             of
             the
             Tropick
             of
             Cancer
             right
             vnder
             the
             Horizon
             ;
             then
             lifting
             vp
             the
             Pole
             till
             you
             finde
             7.
             degrees
             and
             an
             halfe
             more
             aboue
             the
             Horizon
             then
             were
             before
             ,
             you
             shall
             finde
             the
             Pole
             eleuated
             about
             2.
             degr
             .
             and
             an
             halfe
             more
             then
             it
             was
             before
             .
          
           
             Likewise
             ,
             if
             you
             put
             downe
             the
             Pole
             till
             there
             be
             7.
             degrees
             and
             an
             halfe
             of
             the
             Tropicke
             of
             Cancer
             ,
             fewer
             aboue
             the
             Horizon
             then
             was
             before
             ;
             you
             shall
             finde
             the
             eleuation
             of
             the
             Pole
             to
             be
             about
             3.
             degrees
             lesse
             then
             before
             .
          
        
         
           
             PROP.
             XXXII
             .
             The
             reason
             of
             the
             inequalitie
             of
             naturall
             dayes
             ,
             &c.
             
          
           
             THe
             reason
             hereof
             is
             shewed
             partly
             by
             the
             inequality
             of
             the
             differences
             of
             right
             ascentions
             answerable
             to
             equall
             arcks
             of
             the
             Zodiack
             ;
             and
             partly
             by
             the
             vnequall
             apparent
             motion
             of
             the
             Sunne
             .
             For
             the
             first
             :
             the
             differences
             of
             right
             ascentions
             answerable
             to
             the
             parts
             of
             the
             Ecliptick
             ,
             about
             the
             Tropicall
             points
             of
             Cancer
             and
             Capricorne
             ,
             are
             much
             greater
             then
             about
             the
             Equinoctiall
             points
             of
             Aries
             and
             Libra
             .
          
           
             In
             so
             much
             that
             whereas
             the
             difference
             of
             right
             ascension
             answerable
             to
             one
             signe
             ,
             or
             30.
             degrees
             taken
             about
             those
             Tropicall
             points
             ,
             is
             more
             then
             32.
             degrees
             and
             an
             halfe
             :
             about
             the
             Equinoctiall
             points
             
             it
             is
             little
             more
             then
             27.
             degrees
             and
             an
             halfe
             ;
             as
             it
             may
             appeare
             by
             the
             Sphaere
             .
             So
             as
             you
             may
             hereby
             gather
             ,
             that
             the
             difference
             of
             ascention
             answerable
             to
             one
             degree
             ,
             which
             about
             the
             beginning
             of
             Capricorne
             is
             one
             degree
             ,
             and
             about
             6.
             minutes
             ;
             about
             the
             beginning
             of
             Aries
             ,
             or
             Libra
             ,
             is
             onely
             55
             minutes
             .
             Secondly
             ,
             the
             apparent
             motion
             of
             the
             Sun
             is
             much
             swifter
             about
             his
             Parig●●●
             ,
             in
             the
             signe
             of
             Capricorne
             ,
             then
             about
             his
             Apogaeum
             in
             Cancer
             ,
             or
             in
             other
             parts
             of
             the
             Zodiacke
             :
             so
             that
             whereas
             the
             Sunne
             being
             in
             Capricorne
             moueth
             61.
             minutes
             and
             something
             more
             in
             a
             day
             :
             in
             Aries
             or
             Libra
             he
             moueth
             but
             59.
             min.
             or
             very
             little
             more
             in
             the
             same
             time
             .
             Therefore
             seeing
             the
             naturall
             day
             is
             nothing
             else
             ,
             but
             the
             time
             wherein
             the
             Sunne
             moueth
             from
             the
             Meridian
             about
             ,
             till
             it
             returne
             again
             to
             the
             same
             part
             of
             the
             Meridian
             ;
             it
             must
             needs
             bee
             that
             alwayes
             in
             one
             naturall
             day
             ,
             there
             is
             made
             one
             whole
             reuolution
             of
             the
             Equinoctiall
             circle
             ,
             and
             so
             much
             more
             as
             is
             the
             difference
             of
             right
             ascention
             answerable
             to
             the
             apparent
             motion
             of
             the
             Sun
             in
             the
             meane
             time
             :
             which
             differences
             of
             ascention
             because
             they
             be
             vnequall
             ,
             for
             the
             two
             causes
             before
             alledged
             ;
             the
             naturall
             dayes
             must
             needs
             also
             bee
             vnequall
             ,
             the
             motion
             of
             the
             Equinoctiall
             circle
             about
             his
             owne
             center
             being
             (
             as
             it
             hath
             beene
             alwayes
             supposed
             to
             be
             )
             equall
             ,
             that
             is
             mouing
             alwayes
             an
             equall
             space
             in
             equall
             time
             .
          
           
             Which
             by
             this
             example
             may
             most
             plainly
             appeare
             :
             The
             Sunne
             being
             in
             Capricorne
             moueth
             61.
             minutes
             in
             a
             naturall
             day
             :
             difference
             of
             ascention
             agreeable
             thereto
             is
             67.
             minutes
             ,
             or
             something
             more
             .
             Therefore
             at
             that
             time
             ,
             in
             the
             space
             of
             one
             naturall
             day
             ,
             the
             
             Equinoctial
             circle
             must
             make
             one
             full
             reuolution
             ,
             and
             67.
             minutes
             more
             .
             But
             when
             the
             Sun
             is
             in
             Aries
             ,
             mouing
             onely
             59.
             minutes
             in
             a
             day
             ,
             and
             the
             difference
             of
             right
             ascention
             answerable
             thereto
             ,
             scarce
             54.
             minutes
             more
             then
             one
             reuolution
             of
             the
             Equinoctiall
             circle
             ;
             there
             shall
             passe
             onely
             54.
             minutes
             more
             in
             a
             naturall
             day
             ;
             so
             as
             here
             the
             Equinoctiall
             circle
             moueth
             not
             about
             so
             much
             in
             one
             day
             as
             before
             by
             13.
             minutes
             .
             Seeing
             then
             that
             15.
             degr
             .
             or
             little
             more
             of
             the
             Equinoctiall
             circle
             doe
             passe
             the
             Meridian
             in
             euery
             houre
             ,
             and
             consequently
             one
             degree
             of
             the
             Equinoctiall
             passeth
             the
             Meridian
             in
             4.
             minutes
             of
             an
             houre
             ,
             and
             one
             minute
             of
             a
             degree
             in
             4.
             seconds
             of
             an
             houre
             ;
             therefore
             13.
             minutes
             of
             the
             Equinoctiall
             shall
             passe
             the
             Meridian
             in
             52.
             seconds
             :
             that
             is
             ,
             almost
             in
             one
             minute
             of
             an
             houre
             :
             Whereby
             it
             manifestly
             appeareth
             that
             the
             naturall
             day
             ,
             that
             is
             to
             say
             ,
             the
             space
             of
             24.
             houres
             ,
             which
             is
             the
             time
             wherein
             the
             Sunne
             moueth
             from
             the
             Noone-stead
             to
             the
             same
             noone-stead
             againe
             ,
             is
             in
             our
             age
             greater
             almost
             by
             one
             minute
             of
             an
             houre
             ,
             when
             the
             sunne
             is
             in
             Capricorne
             ,
             then
             when
             hee
             is
             in
             Aries
             or
             
               Libra
               ▪
            
          
        
         
           
             PROP.
             XXXIII
             .
             To
             finde
             by
             the
             Sphaere
             how
             much
             the
             naturall
             dayes
             are
             longer
             at
             one
             time
             of
             the
             yeare
             then
             at
             another
             .
          
           
             FOr
             this
             purpose
             it
             will
             be
             best
             to
             take
             a
             good
             number
             of
             dayes
             together
             ;
             as
             for
             example
             ,
             take
             the
             whole
             moneth
             of
             December
             ,
             and
             the
             whole
             moneth
             of
             March
             :
             both
             which
             moneths
             consist
             of
             the
             same
             number
             of
             31.
             naturall
             dayes
             :
             find
             the
             place
             
             of
             the
             Sunne
             for
             the
             beginning
             and
             ending
             of
             both
             moneths
             ,
             which
             you
             may
             finde
             by
             the
             second
             Proposition
             to
             be
             for
             the
             beginning
             of
             March
             this
             present
             yeare
             1600.
             about
             20.
             degrees
             and
             13.
             minutes
             of
             Pisces
             ;
             and
             for
             the
             ending
             about
             20.
             degr
             .
             48.
             minutes
             of
             Aries
             :
             Also
             for
             the
             beginning
             of
             December
             the
             same
             yeare
             18.
             degr
             .
             46.
             minutes
             of
             S●gitarie
             ;
             and
             for
             the
             ending
             ,
             20.
             degrees
             24.
             minutes
             of
             Capricorne
             :
             Then
             seeke
             out
             the
             right
             ascensions
             of
             the
             same
             places
             of
             the
             Sunne
             for
             the
             beginnings
             and
             endings
             of
             both
             those
             moneths
             by
             the
             fourth
             Proposition
             ,
             and
             the
             differences
             of
             ascension
             answerable
             to
             the
             motion
             of
             the
             Sunne
             in
             each
             moneth
             ,
             by
             the
             sixt
             Proposition
             ;
             which
             you
             may
             finde
             by
             the
             Sphaere
             to
             be
             about
             33.
             degrees
             ,
             24
             ▪
             minutes
             for
             December
             ,
             and
             28.
             degrees
             ,
             39.
             minutes
             for
             March.
             Lastly
             ,
             finde
             out
             the
             difference
             of
             these
             differences
             of
             ascension
             by
             substracting
             the
             lesser
             out
             of
             the
             greater
             ;
             which
             in
             this
             example
             is
             4.
             degrees
             45.
             minutes
             ;
             which
             resolued
             into
             minutes
             of
             an
             houre
             ,
             by
             taking
             for
             euery
             degree
             4.
             minutes
             of
             an
             houre
             ,
             and
             for
             euery
             15.
             minutes
             of
             a
             degree
             ,
             one
             minute
             of
             an
             houre
             shall
             amount
             to
             19.
             minutes
             of
             an
             houre
             ,
             that
             is
             a
             quarter
             of
             an
             houre
             and
             4.
             minutes
             .
             And
             so
             much
             is
             the
             moneth
             of
             December
             longer
             then
             the
             moneth
             of
             March
             ;
             Notwithstanding
             both
             of
             them
             consist
             of
             the
             same
             number
             of
             31.
             naturall
             dayes
             .
          
        
      
       
         
         
           The
           third
           Part.
           
        
         
           Of
           the
           Orbes
           whereof
           the
           SPHAERES
           of
           the
           Sunne
           and
           Moone
           haue
           beene
           imagined
           to
           bee
           made
           ,
           and
           of
           their
           Motions
           and
           Vses
           .
        
         
           
             CHAP.
             I.
             Of
             the
             Orbes
             whereof
             the
             Sphare
             of
             the
             Sunne
             is
             made
             .
          
           
             WIthin
             the
             Sphaere
             or
             Orbe
             contayning
             all
             the
             Circles
             that
             wee
             haue
             hitherto
             spoken
             of
             ,
             and
             representing
             vnto
             vs
             the
             
               Primum
               mobile
            
             ;
             that
             is
             ,
             the
             first
             and
             highest
             moueable
             Heauen
             ,
             that
             hath
             been
             imagined
             by
             the
             Astronomers
             ,
             to
             shew
             the
             reason
             of
             that
             daily
             motion
             ,
             which
             appeareth
             to
             bee
             in
             all
             the
             Heauens
             ,
             and
             of
             all
             the
             apparences
             that
             follow
             thereupon
             ,
             are
             included
             the
             Sphaeres
             and
             Orbes
             of
             the
             Sunne
             and
             Moone
             .
          
           
             The
             sphaere
             of
             the
             Sunne
             contayneth
             three
             Orbes
             :
             The
             vppermost
             of
             them
             (
             which
             in
             this
             Sphaere
             is
             signified
             by
             the
             yellow
             Circle
             that
             commeth
             next
             within
             the
             compasse
             of
             the
             Zodiacke
             )
             is
             called
             
               Deferens
               apogaeum
               Solis
            
             ;
             that
             is
             ,
             the
             Orbe
             which
             carrieth
             about
             that
             point
             ,
             wherein
             the
             sunne
             is
             furthest
             distant
             from
             the
             earth
             .
          
           
           
             Next
             within
             this
             Orbe
             is
             placed
             the
             Eccentrick
             carying
             about
             the
             body
             of
             the
             Sunne
             ;
             which
             in
             this
             Sphaere
             is
             represented
             by
             the
             greene
             coloured
             circle
             that
             commeth
             next
             vnder
             the
             
               Deferens
               apogaeum
            
             .
          
           
             Againe
             ,
             within
             this
             Eccentrick
             is
             included
             the
             third
             Orbe
             of
             the
             Sphaere
             of
             the
             Sunne
             called
             
               Deferens
               Perigaeum
               solis
            
             ;
             that
             is
             ,
             the
             Orbe
             carying
             about
             that
             point
             wherein
             the
             Sun
             is
             nearest
             to
             the
             Earth
             .
             This
             is
             the
             nethermost
             of
             the
             three
             Orbes
             of
             the
             sunne
             ,
             and
             in
             this
             Sphaere
             is
             represented
             vnto
             you
             by
             the
             yellow
             coloured
             circle
             next
             vnder
             the
             sunnes
             Eccentricke
             .
          
        
         
           
             CHAP.
             II.
             Of
             the
             vppermost
             and
             nethermost
             Orbes
             of
             the
             Sphaere
             of
             the
             Sunne
             ,
             more
             particularly
             .
          
           
             IN
             the
             vppermost
             and
             nethermost
             of
             these
             three
             Orbes
             ,
             there
             be
             4.
             points
             especially
             to
             bee
             considered
             :
             That
             is
             ,
             the
             points
             where
             they
             bee
             narrowest
             and
             where
             they
             be
             broadest
             ,
             and
             where
             they
             are
             of
             a
             meane
             bredth
             betwixt
             the
             narrowest
             and
             broadest
             .
             For
             at
             the
             narrowest
             part
             of
             the
             vppermost
             Orbe
             ,
             where
             you
             may
             see
             written
             
               Aux
               solis
            
             ,
             and
             the
             broadest
             part
             of
             the
             nethermost
             Orbe
             ,
             is
             the
             place
             of
             the
             sunnes
             Apogaeum
             ;
             so
             that
             whensoeuer
             the
             Sun
             commeth
             there
             ,
             he
             is
             furthest
             distant
             from
             the
             earth
             .
             As
             you
             may
             easily
             try
             ,
             if
             (
             with
             a
             payre
             of
             Compasses
             ,
             or
             otherwise
             )
             you
             take
             the
             distance
             betwixt
             the
             Earth
             and
             the
             Sunne
             ,
             being
             brought
             about
             to
             that
             place
             ,
             and
             compare
             the
             same
             with
             the
             distances
             that
             the
             Sun
             hath
             from
             the
             Earth
             in
             other
             places
             .
             This
             point
             is
             called
             
               Aux
               Solis
            
             ,
             and
             
               Longitude
               longior
            
             ,
             that
             is
             ,
             the
             point
             of
             the
             sunnes
             furthest
             distance
             from
             the
             earth
             .
             But
             vnder
             the
             broadest
             
             part
             of
             the
             vppermost
             and
             vttermost
             Orbe
             ,
             where
             you
             see
             printed
             PERIGAEVM
             ,
             and
             right
             aboue
             the
             narrowest
             part
             of
             the
             nethermost
             Orbe
             ,
             is
             the
             place
             where
             the
             Sun
             commeth
             nearest
             to
             the
             Earth
             ,
             as
             you
             may
             easily
             find
             (
             with
             your
             Compasses
             ,
             or
             otherwise
             )
             in
             like
             sort
             as
             before
             was
             shewed
             .
             The
             point
             where
             the
             Sun
             commeth
             nearest
             to
             the
             earth
             ,
             is
             called
             
               oppositum
               A●gis
            
             ,
             and
             
               longitudo
               propior
            
             ,
             that
             is
             ,
             the
             point
             opposite
             to
             the
             Apogaeum
             ,
             and
             the
             nearest
             distance
             .
             And
             at
             those
             parts
             of
             this
             Orbe
             ,
             which
             are
             in
             the
             midst
             betweene
             the
             former
             ;
             the
             Sunne
             hath
             a
             meane
             distance
             from
             the
             earth
             :
             a
             meane
             (
             I
             say
             )
             betweene
             the
             least
             ,
             and
             greatest
             distance
             .
             The
             very
             point
             wherein
             this
             meane
             or
             middle
             distance
             hapneth
             ,
             is
             shewed
             by
             the
             points
             that
             are
             iust
             in
             the
             middest
             betweene
             the
             short
             lines
             AB
             ,
             and
             IK
             ,
             which
             are
             drawne
             ouerthwart
             on
             eyther
             side
             of
             this
             Orbe
             .
             These
             points
             are
             called
             
               longitudines
               media
            
             ;
             that
             is
             ,
             the
             meane
             distances
             of
             the
             Sunne
             ,
             because
             the
             sunne
             comming
             to
             these
             points
             ,
             hath
             a
             meane
             distance
             betweene
             the
             least
             and
             the
             greatest
             .
             About
             these
             points
             also
             ,
             the
             true
             motion
             of
             the
             sun
             ,
             is
             as
             it
             were
             in
             a
             meane
             between
             the
             slowest
             ,
             which
             hapneth
             the
             sunne
             being
             about
             the
             Apogaeum
             ,
             and
             the
             swiftest
             ,
             which
             hapneth
             about
             his
             Perigaeum
             .
          
           
             Moreouer
             the
             lines
             A
             ,
             and
             K
             ,
             shew
             the
             places
             wherin
             there
             is
             the
             greatest
             Prosthaphaerisis
             ,
             or
             Equation
             of
             the
             sunne
             :
             that
             is
             ,
             the
             greatest
             difference
             betweene
             the
             true
             ,
             and
             middle
             ,
             or
             meane
             place
             of
             the
             sunne
             .
          
           
             Lastly
             ,
             the
             distance
             betweene
             the
             lines
             I
             ,
             and
             K
             ,
             or
             A
             ,
             and
             B
             ,
             shew
             how
             much
             the
             eccentricitie
             of
             the
             sunnes
             eccentricke
             is
             ,
             that
             is
             ,
             how
             farre
             the
             Center
             of
             the
             eccentricke
             is
             distant
             from
             the
             Center
             of
             Earth
             .
          
        
         
           
           
             CHAP.
             III.
             To
             finde
             how
             much
             the
             Sunne
             is
             nearer
             or
             further
             from
             the
             earth
             ,
             at
             one
             time
             then
             at
             another
             .
          
           
             BY
             meanes
             of
             this
             Circle
             ,
             you
             may
             easily
             find
             with
             your
             Compasses
             ,
             how
             much
             the
             Sunne
             is
             nearer
             to
             ,
             or
             further
             from
             the
             earth
             at
             one
             time
             ,
             then
             at
             another
             :
             for
             hauing
             set
             one
             foot
             of
             the
             Compasses
             vpon
             the
             vtmost
             edge
             of
             the
             
               Deferens
               Apogaeum
            
             ,
             vnder
             the
             place
             of
             the
             Sunne
             in
             the
             Zodiacke
             ,
             found
             by
             the
             second
             Prop.
             stretch
             out
             the
             other
             foot
             ,
             to
             the
             innermost
             edge
             of
             the
             same
             Orbe
             ;
             for
             then
             ,
             if
             you
             set
             one
             foot
             of
             your
             Compasses
             ,
             vpon
             the
             vtmost
             edge
             of
             this
             Orbe
             ,
             at
             the
             Apogaeum
             ,
             the
             other
             foot
             turned
             inwards
             towards
             the
             center
             of
             the
             Sphaere
             ,
             will
             shew
             you
             how
             much
             the
             Sunne
             is
             nearer
             to
             the
             Earth
             at
             that
             time
             ,
             then
             when
             he
             is
             in
             his
             Apogaeum
             :
             for
             so
             much
             as
             that
             foot
             reacheth
             within
             the
             inner
             edge
             of
             the
             Orbe
             ,
             so
             much
             is
             the
             sunne
             nearer
             .
             Likewise
             if
             you
             set
             one
             foot
             of
             your
             Compasses
             ,
             vpon
             the
             vttermost
             edge
             of
             this
             Orbe
             ,
             at
             the
             Perigaeum
             ,
             and
             turne
             the
             other
             foot
             towards
             the
             center
             of
             the
             Sphaere
             ,
             so
             much
             as
             this
             foot
             of
             the
             Compasse
             ,
             is
             from
             the
             inner
             edge
             of
             the
             
               Deferens
               Paerigaeum
            
             ,
             so
             much
             is
             the
             Sun
             further
             distant
             from
             the
             earth
             at
             that
             time
             ,
             then
             when
             he
             is
             in
             his
             Paerigaeum
             .
          
        
         
           
             CHAP.
             IIII.
             Of
             the
             situation
             and
             motion
             of
             the
             uppermost
             ,
             and
             nethermost
             Orbes
             of
             the
             Sunne
             .
          
           
             THe
             vppermost
             ,
             and
             nethermost
             of
             these
             three
             Orbes
             ,
             called
             
               Deferens
               Apogaeum
            
             ,
             &
             
               Perigaeum
               solis
            
             ,
             doe
             alwayes
             answer
             each
             to
             other
             ,
             in
             such
             sort
             that
             the
             broadest
             part
             of
             the
             one
             ,
             is
             alwayes
             against
             the
             narrowest
             
             part
             of
             the
             other
             :
             And
             therefore
             both
             of
             them
             are
             moued
             thgether
             ,
             with
             one
             motion
             about
             the
             Axtree
             and
             poles
             of
             the
             Ecliptick
             ,
             making
             one
             reuolution
             vnder
             the
             Zodiack
             ,
             in
             the
             space
             of
             17000.
             yeares
             almost
             .
             For
             in
             Ptolemee
             his
             time
             (
             that
             is
             about
             the
             yeare
             of
             our
             Lord
             134.
             )
             the
             place
             of
             the
             Sunnes
             Apogaeum
             ,
             was
             about
             the
             middest
             of
             the
             6.
             deg
             .
             of
             Gemini
             ;
             as
             it
             may
             appeare
             by
             the
             4.
             
             Chapter
             of
             the
             3.
             booke
             of
             his
             Almagest
             .
             But
             in
             our
             time
             we
             finde
             that
             it
             cannot
             exceed
             the
             7.
             degr
             .
             of
             Cancer
             ,
             although
             after
             the
             account
             of
             Copernicus
             ,
             and
             of
             the
             Prutenicke
             tables
             ,
             it
             should
             be
             in
             the
             9.
             degr
             .
             of
             Cancer
             .
             So
             as
             ,
             if
             the
             rest
             of
             the
             motion
             of
             the
             Sunnes
             Apogaeum
             ,
             that
             is
             to
             come
             hereafter
             ,
             be
             proportionable
             to
             that
             is
             past
             ,
             the
             whole
             reuolution
             thereof
             shal
             be
             finished
             in
             1699.
             yeares
             vnder
             the
             Zodiack
             .
             For
             in
             1463.
             yeares
             betwixt
             Ptolemee
             his
             time
             and
             ours
             ,
             it
             hath
             moued
             about
             31.
             degn
             therefore
             it
             shall
             moue
             300.
             degrees
             ,
             (
             that
             is
             ,
             the
             compasse
             of
             the
             whole
             circle
             )
             in
             16990.
             yeares
             .
          
           
             Which
             number
             of
             yeares
             being
             deuided
             by
             360.
             it
             shall
             appeare
             that
             the
             Apogaeum
             of
             the
             Sunne
             moueth
             one
             degr
             .
             in
             little
             more
             then
             47.
             yeares
             whereby
             the
             yearely
             motion
             thereof
             may
             be
             sound
             to
             be
             little
             more
             then
             one
             minute
             and
             a
             quarter
             .
          
        
         
           
             CHAP.
             V.
             How
             to
             find
             the
             place
             of
             the
             Suns
             Aux
             or
             Apogaeum
             ,
             &c.
             
          
           
             THerefore
             the
             place
             of
             the
             Sunnes
             Apogaeum
             ,
             being
             found
             for
             the
             yeare
             1600.
             to
             be
             about
             7.
             degr
             .
             in
             Cancer
             ,
             the
             place
             thereof
             for
             any
             other
             yeare
             before
             or
             after
             ,
             may
             easely
             be
             found
             in
             our
             age
             ,
             onely
             
             by
             subtracting
             ,
             or
             adding
             for
             euery
             4
             ,
             yeares
             5
             ,
             min.
             and
             for
             euery
             single
             yeare
             1.
             minute
             and
             a
             quarter
             ,
             Although
             indeed
             we
             need
             not
             stand
             so
             precisely
             neyther
             vpon
             quarters
             of
             minutes
             ,
             neither
             yet
             vpon
             whole
             minutes
             ,
             in
             the
             place
             of
             the
             sunnes
             Apogaeum
             ,
             which
             cannot
             be
             by
             any
             Art
             so
             exactly
             found
             ,
             but
             that
             the
             diligentest
             man
             that
             is
             ,
             may
             erre
             many
             minutes
             therein
             .
          
           
             Take
             for
             example
             the
             yeare
             of
             our
             Lord
             1558.
             (
             in
             which
             our
             gracious
             Q.
             Elizabeth
             began
             her
             happie
             reigne
             ,
             which
             is
             now
             42.
             yeares
             since
             )
             taking
             therefore
             for
             euery
             4.
             yeares
             5.
             minutes
             ,
             that
             is
             ,
             for
             40.
             yeares
             50.
             minutes
             ,
             and
             for
             the
             two
             yeares
             remaining
             2.
             minutes
             and
             one
             halfe
             ;
             that
             is
             in
             all
             52.
             minutes
             and
             an
             halfe
             ,
             and
             subtracting
             the
             same
             out
             of
             7
             ,
             deg
             of
             Cancer
             ,
             there
             shall
             remaine
             the
             place
             of
             the
             sunnes
             Apogaeum
             at
             the
             beginning
             of
             her
             Maiesties
             reigne
             ,
             in
             6.
             degr
             .
             and
             about
             8.
             min.
             of
             Cancer
             .
          
           
             
               The
               vses
               of
               these
               two
               Orbes
               are
               these
               .
            
          
           
             1.
             
             First
             to
             make
             the
             sphaere
             of
             the
             Sunne
             concentricall
             ;
             for
             these
             Orbes
             be
             framed
             together
             ,
             that
             the
             narrowest
             part
             of
             the
             one
             ,
             answereth
             alwayes
             to
             the
             broadest
             part
             of
             the
             other
             :
             it
             commeth
             to
             passe
             by
             this
             meanes
             ,
             that
             both
             the
             out-side
             ,
             and
             the
             in-side
             of
             the
             Sphaere
             of
             the
             sunne
             ,
             haue
             alwayes
             the
             same
             center
             ,
             that
             the
             world
             it selfe
             hath
             .
          
           
             2.
             
             The
             second
             vse
             is
             to
             shew
             the
             reason
             ,
             and
             manner
             of
             the
             motion
             of
             the
             Sunnes
             Apogaeum
             and
             Perigaeum
             .
          
        
         
           
             CHAP.
             VI.
             Of
             the
             eccentrick
             of
             the
             Sunne
             ,
             &c.
             
          
           
             THe
             Orbe
             conteined
             betweene
             the
             two
             former
             ,
             and
             carying
             about
             the
             body
             of
             the
             Sunne
             it selfe
             ,
             
             is
             called
             the
             eccentricke
             of
             the
             Sunne
             ;
             because
             it
             hath
             another
             center
             ,
             then
             the
             center
             of
             the
             world
             .
             The
             especiall
             reason
             ,
             that
             moued
             the
             skilfull
             in
             this
             coelestiall
             science
             ,
             to
             make
             this
             Orbe
             (
             wherein
             the
             body
             of
             the
             sunne
             is
             carryed
             )
             eccentricall
             ,
             was
             because
             they
             found
             the
             apparent
             motion
             of
             the
             sunne
             vnder
             the
             ecliptick
             line
             to
             be
             vnequall
             ,
             that
             is
             ,
             swifter
             in
             the
             Southerly
             Signes
             :
             and
             slower
             in
             the
             Northerly
             .
          
           
             For
             Hipparehus
             ,
             and
             Ptolemee
             found
             in
             their
             times
             ,
             that
             the
             sunne
             continued
             in
             the
             Northerne
             semicircle
             of
             the
             ecliptick
             ,
             from
             Aries
             to
             Libra
             ,
             187.
             dayes
             :
             and
             in
             the
             other
             halfe
             of
             the
             Zodiack
             ,
             that
             is
             Southward
             from
             Libra
             to
             Aries
             ,
             178.
             dayes
             and
             a
             quarter
             onely
             .
             But
             in
             our
             time
             by
             diligent
             obseruation
             it
             is
             sound
             ,
             that
             the
             time
             of
             the
             sunnes
             continuance
             in
             the
             first
             of
             those
             semicircles
             from
             Aries
             to
             Libra
             ,
             is
             186.
             dayes
             14.
             houres
             and
             an
             halfe
             :
             and
             consequently
             in
             the
             other
             semicircle
             ,
             from
             Libra
             to
             Aries
             ,
             178.
             dayes
             15.
             houres
             and
             an
             halfe
             .
             Taking
             it
             therefore
             for
             a
             ground
             ,
             according
             to
             the
             doctrine
             of
             Aristotle
             ,
             that
             the
             motion
             of
             the
             coelestiall
             bodies
             is
             circular
             and
             equal
             ;
             it
             must
             needs
             follow
             ,
             that
             a
             greater
             part
             of
             the
             circle
             described
             by
             the
             proper
             motion
             of
             the
             sunne
             must
             be
             conteined
             vnder
             the
             Northerly
             semicircle
             of
             the
             ecliptick
             ,
             then
             vnder
             the
             Southerly
             :
             and
             consequently
             that
             the
             circle
             or
             Orbe
             that
             caryeth
             about
             the
             body
             of
             the
             Sunne
             vnder
             the
             ecliptick
             ,
             hath
             another
             center
             then
             the
             center
             of
             the
             Ecliptick
             .
          
           
             2.
             
             Another
             reason
             to
             proue
             ,
             that
             the
             Sunne
             is
             caryed
             in
             an
             eccentricall
             Circle
             ,
             is
             the
             vnequall
             apparent
             ,
             bignes
             of
             the
             Sunnes
             diameter
             ,
             the
             Sunne
             being
             of
             the
             same
             height
             aboue
             the
             Horizon
             and
             the
             
             ayre
             alike
             affected
             ,
             and
             alike
             cleare
             ;
             so
             as
             if
             there
             were
             any
             refraction
             by
             reason
             of
             the
             thicknes
             of
             the
             ayre
             ,
             it
             must
             needs
             be
             the
             same
             in
             both
             places
             .
             For
             in
             Sommer
             ,
             when
             the
             Sun
             is
             at
             ,
             or
             neare
             his
             Apogaeum
             ,
             his
             apparent
             diameter
             hath
             beene
             found
             by
             exquisit
             obseruation
             to
             be
             13.
             minutes
             48
             seconds
             .
             But
             in
             winter
             being
             about
             his
             Perigaeum
             33.
             min.
             
             54.
             seconds
             ,
             as
             it
             may
             appeare
             in
             Copernicus
             his
             reuolutions
             4.
             booke
             21.
             
             Chapter
             .
          
           
             Therefore
             seeing
             euery
             visible
             obiect
             appeareth
             greater
             when
             it
             is
             neare
             ,
             and
             lesse
             when
             it
             is
             further
             remoued
             from
             vs
             ,
             it
             is
             manifest
             that
             the
             Sun
             appearing
             greater
             in
             winter
             ,
             then
             in
             sommer
             ,
             must
             needes
             be
             nearer
             to
             the
             earth
             in
             winter
             ,
             then
             in
             sommer
             .
          
           
             The
             reason
             of
             which
             apparance
             is
             most
             easely
             shewed
             ,
             by
             supposing
             the
             Sunne
             to
             be
             moued
             ,
             in
             an
             eccentricall
             Orbe
             .
          
           
             3.
             
             A
             third
             reason
             may
             bee
             the
             vnequall
             greatnesse
             and
             continuance
             of
             the
             eclipses
             of
             the
             Moone
             ,
             euen
             at
             those
             times
             when
             she
             hath
             had
             the
             same
             latitude
             ,
             or
             distance
             from
             the
             Ecliptick
             ,
             and
             the
             same
             distance
             from
             the
             Center
             of
             the
             earth
             :
             which
             argueth
             that
             the
             conicall
             sharp
             pointed
             shadow
             of
             the
             earth
             ,
             in
             the
             place
             where
             the
             Moone
             in
             time
             of
             the
             Eclipse
             passeth
             through
             that
             shadow
             ,
             at
             the
             same
             distance
             from
             the
             earth
             ,
             is
             sometimes
             greater
             ,
             and
             sometimes
             lesser
             :
             wherof
             there
             can
             no
             cause
             be
             shewed
             more
             reasonable
             then
             this
             ,
             that
             the
             Sun
             is
             sometimes
             further
             distant
             from
             the
             earth
             ,
             and
             the
             maketh
             the
             shadow
             greater
             and
             sometimes
             nearer
             ,
             and
             so
             maketh
             it
             lesser
             .
             Whereby
             it
             is
             also
             manifestly
             proued
             ,
             that
             the
             Sun
             is
             moued
             about
             another
             center
             then
             the
             center
             of
             the
             
             earth
             ,
             and
             therefore
             that
             the
             circle
             or
             Orbe
             ,
             wherein
             the
             Sunne
             is
             moued
             ,
             is
             an
             Eccentricke
             .
          
        
         
           
             CHAP.
             VII
             .
             Of
             the
             vses
             of
             the
             Sunnes
             eccentricall
             Orbe
             .
          
           
             THerefore
             the
             vses
             of
             the
             Sunnes
             eccentricke
             may
             bee
             these
             :
          
           
             1.
             
             First
             to
             shew
             the
             reason
             of
             the
             apparent
             inequalitie
             ,
             which
             seemeth
             to
             bee
             in
             the
             motion
             of
             the
             Sunne
             :
             for
             although
             the
             Sunne
             mo●e
             equally
             in
             his
             owne
             O●be
             ,
             and
             about
             his
             owne
             center
             ;
             yet
             to
             them
             that
             are
             at
             the
             center
             of
             the
             world
             ,
             or
             vpon
             the
             earth
             ,
             he
             shall
             seeme
             to
             moue
             vnequally
             ;
             that
             is
             ,
             swiftly
             when
             he
             is
             in
             that
             part
             of
             his
             eccentricke
             which
             is
             nearest
             vnto
             the
             earth
             ;
             and
             slowly
             when
             he
             is
             farthest
             from
             the
             earth
             .
             And
             therefore
             in
             sommer
             ,
             when
             the
             Sunne
             is
             about
             his
             Apogaeum
             ,
             and
             in
             his
             greatest
             distance
             from
             the
             earth
             ,
             he
             seemeth
             to
             moue
             little
             aboue
             57.
             min.
             in
             one
             day
             .
             But
             in
             winter
             ,
             being
             about
             his
             Perigaeum
             and
             nearest
             vnto
             the
             earth
             ,
             he
             seemeth
             to
             moue
             more
             then
             16.
             minutes
             :
             whereas
             notwithstanding
             he
             moueth
             equally
             in
             his
             Eccentricke
             ,
             euery
             day
             about
             nine
             and
             fifty
             minutes
             and
             8.
             seconds
             ;
             and
             so
             finisheth
             his
             reuolution
             in
             365.
             dayes
             ,
             and
             six
             houres
             almost
             .
          
           
             2.
             
             The
             second
             vse
             of
             the
             Sunnes
             Eccentricke
             ,
             may
             be
             to
             shew
             the
             reason
             why
             the
             Sun
             appeareth
             greater
             at
             one
             time
             then
             at
             another
             ;
             for
             the
             Sun
             being
             in
             those
             parts
             of
             the
             eccentrick
             that
             are
             nearest
             vnto
             vs
             ,
             seemeth
             greatest
             ,
             and
             when
             he
             is
             in
             those
             parts
             of
             his
             eccentrick
             that
             are
             furthest
             from
             vs
             ,
             he
             appeareth
             to
             be
             least
             .
          
           
             3.
             
             And
             lastly
             the
             inequality
             of
             the
             Sunnes
             distance
             
             from
             the
             earth
             ,
             caused
             by
             his
             eccentrick
             ,
             is
             one
             especiall
             cause
             of
             the
             inequalitie
             of
             the
             Eclipses
             ,
             both
             of
             the
             Sunne
             and
             Moone
             .
          
        
         
           
             CHAP.
             VIII
             .
             The
             definitions
             of
             certaine
             Astronomicall
             wordes
             of
             art
             ,
             for
             the
             better
             vnderstanding
             of
             the
             Theorick
             of
             the
             Sunne
             .
          
           
             1.
             
             WHat
             the
             Aux
             or
             Apogaeum
             of
             the
             Sunne
             is
             it
             hath
             beene
             partly
             shewed
             already
             :
             that
             ●●mely
             it
             is
             that
             part
             ,
             or
             rather
             point
             of
             the
             Orbe
             carying
             the
             Sunnes
             Apogaeum
             ,
             wherein
             the
             said
             Orbe
             is
             thinnest
             ,
             or
             narrowest
             :
             Or
             it
             is
             that
             point
             of
             the
             eccentrick
             which
             is
             furthest
             distant
             from
             the
             earth
             ,
             and
             is
             alwayes
             shewed
             by
             a
             right
             line
             vnderstood
             to
             be
             drawn
             from
             the
             center
             of
             the
             world
             ,
             by
             the
             center
             of
             the
             eccentrick
             ,
             vnto
             the
             Orbe
             carying
             the
             Sunnes
             Apogaeum
             .
             Which
             line
             is
             therefore
             called
             the
             line
             of
             the
             Sun
             his
             Aux
             or
             the
             line
             of
             the
             Sunnes
             Apogaeum
             .
          
           
             2.
             
             The
             motion
             of
             the
             Aux
             ,
             or
             of
             the
             Apogaeum
             of
             the
             Sunne
             (
             which
             is
             also
             called
             the
             Sunnes
             Aux
             in
             the
             second
             signification
             )
             is
             nothing
             els
             but
             the
             arch
             of
             the
             Ecliptick
             ,
             conteyned
             betweene
             the
             beginning
             of
             Aries
             ,
             and
             the
             line
             of
             the
             Sunnes
             Apogaeum
             ,
             drawne
             forth
             to
             the
             Zodiack
             ;
             where
             this
             line
             also
             sheweth
             the
             place
             of
             the
             Sunnes
             Apogaeum
             .
          
           
             3.
             
             The
             middle
             or
             meane
             place
             of
             the
             Sunne
             in
             the
             Zodiack
             ,
             is
             shewed
             by
             a
             line
             drawne
             from
             the
             center
             of
             the
             world
             vnto
             the
             Zodiack
             ,
             equidistant
             from
             the
             center
             of
             the
             Eccentricke
             ,
             and
             of
             the
             Sunne
             .
          
           
             4.
             
             This
             line
             is
             therefore
             called
             the
             line
             of
             the
             meane
             or
             middle
             place
             of
             the
             Sun.
             
          
           
           
             5.
             
             The
             middle
             or
             meane
             motion
             of
             the
             Sunne
             is
             the
             arch
             of
             the
             ecliptick
             betweene
             the
             beginning
             of
             Aries
             ,
             and
             the
             middle
             place
             of
             the
             Sun.
             
          
           
             6.
             
             The
             true
             place
             of
             the
             Sunne
             is
             shewed
             by
             a
             streight
             line
             drawne
             from
             the
             center
             of
             the
             earth
             by
             the
             center
             of
             the
             Sun
             vnto
             the
             Zodiack
             ,
             which
             line
             is
             therefore
             called
             the
             line
             of
             the
             true
             place
             of
             the
             Sun.
             
          
           
             7.
             
             The
             true
             motion
             of
             the
             Sun
             is
             the
             arch
             of
             the
             eclipticke
             from
             the
             beginning
             of
             Aries
             ,
             vnto
             the
             true
             place
             of
             the
             Sun.
             
          
           
             8.
             
             The
             argument
             of
             the
             Sun
             (
             at
             the
             〈◊〉
             ●erme
             it
             )
             or
             the
             motion
             of
             the
             Sunnes
             Anomalie
             (
             as
             Copernicus
             calleth
             it
             )
             is
             the
             arch
             of
             the
             ecliptick
             conteyned
             betweene
             the
             place
             of
             the
             Sunnes
             Apogaeum
             and
             the
             middle
             place
             of
             the
             Sunne
             according
             to
             the
             order
             and
             succession
             of
             the
             Signes
             .
             This
             arch
             is
             called
             the
             argument
             ,
             or
             motion
             of
             the
             sunnes
             Anomalie
             or
             irregularitie
             ,
             because
             that
             by
             it
             is
             alwayes
             found
             how
             much
             the
             suns
             true
             motion
             which
             (
             is
             vnequall
             and
             irregular
             )
             differeth
             from
             his
             middle
             motion
             ;
             which
             difference
             they
             call
             the
             Suns
             equation
             ,
             or
             prosthapheresis
             .
          
           
             9.
             
             The
             equation
             ,
             or
             prosthapheresis
             of
             the
             Sun
             is
             nothing
             els
             but
             the
             arch
             of
             the
             ecliptick
             conteyned
             betweene
             the
             true
             ,
             and
             middle
             places
             of
             the
             sunne
             .
          
           
             This
             arch
             is
             called
             the
             sunnes
             equation
             ,
             because
             it
             maketh
             the
             suns
             middle
             motion
             equal
             to
             his
             true
             motion
             ,
             being
             added
             to
             it
             or
             subtracted
             from
             it
             ,
             as
             occasion
             requireth
             :
             for
             which
             cause
             it
             is
             more
             significantly
             and
             fitly
             called
             Prosthaphaeresis
             ,
             that
             is
             as
             much
             to
             say
             ,
             as
             that
             which
             is
             to
             be
             added
             to
             or
             subtracted
             from
             the
             middle
             motion
             ,
             that
             so
             we
             might
             
             haue
             the
             true
             motion
             .
             For
             so
             long
             as
             the
             Sunne
             is
             in
             the
             semicircle
             of
             his
             eccentrick
             ,
             discending
             from
             his
             Apogaeum
             to
             his
             ●●●gaeum
             ,
             so
             long
             this
             Prosthapheresis
             is
             to
             be
             subtracted
             from
             the
             middle
             motion
             :
             but
             the
             Sunne
             being
             in
             the
             other
             halfe
             of
             his
             eccentrick
             ascending
             ,
             the
             Prosthapheresis
             or
             equation
             of
             the
             Sun
             must
             be
             added
             to
             the
             middle
             motion
             ,
             that
             〈…〉
             motion
             and
             place
             of
             the
             Sunne
             may
             be
             found
             ,
             Because
             that
             in
             the
             first
             semicircle
             of
             the
             eccentricke
             descending
             ,
             the
             middle
             place
             of
             the
             Sunne
             goeth
             before
             the
             〈◊〉
             ,
             and
             the
             middle
             motion
             is
             〈…〉
             greater
             〈…〉
             the
             Sun
             ,
             and
             therefore
             the
             difference
             of
             these
             〈◊〉
             motions
             ,
             (
             that
             is
             to
             say
             ,
             the
             〈◊〉
             or
             Prosthaphaeresis
             )
             must
             be
             subtracted
             ,
             to
             findeth
             〈…〉
             for
             the
             true
             place
             of
             the
             Sunne
             goeth
             alwaies
             〈…〉
             motion
             and
             place
             of
             the
             same
             ,
          
        
         
           
             CHAP.
             IX
             .
             Of
             the
             vppermost
             Orbe
             of
             the
             Sphaere
             of
             the
             Moone
             carying
             the
             Dragons
             head
             and
             tayle
             .
          
           
             NExt
             within
             the
             Orbes
             of
             the
             Sun
             in
             this
             Sphaere
             are
             conteyned
             the
             Orbes
             of
             the
             Sphaere
             of
             the
             Moone
             :
             which
             〈…〉
             in
             number
             .
          
           
             The
             vppermost
             of
             them
             (
             which
             in
             this
             Sphaere
             is
             next
             vnder
             the
             Orbe
             that
             caryeth
             the
             Suns
             Perigaeum
             and
             is
             coloured
             with
             red
             )
             is
             called
             the
             Caryer
             of
             the
             Dragons
             head
             and
             tayle
             ,
             or
             〈…〉
             which
             is
             
             as
             much
             to
             say
             as
             the
             Caryer
             of
             the
             knots
             ,
             that
             is
             of
             the
             two
             intersections
             ,
             or
             pointes
             wherein
             the
             rest
             of
             the
             Orbes
             of
             the
             Moone
             ,
             doe
             crosse
             ouer-thwart
             this
             Orbe
             .
             This
             Orbe
             is
             deuided
             into
             foure
             nineties
             of
             degree
             ,
             for
             the
             easier
             reckoning
             of
             the
             motion
             and
             place
             of
             the
             Dragons
             head
             or
             tayle
             in
             this
             Sphaere
             .
             And
             it
             is
             moued
             about
             in
             18.
             
             Iulian
             yeares
             224.
             dayes
             3.
             houres
             and
             5.
             minutes
             almost
             ,
             from
             the
             East
             Westwards
             ,
             vnder
             the
             ecliptick
             .
             By
             reason
             of
             this
             motion
             it
             commeth
             to
             passe
             ,
             that
             the
             Eclipses
             ,
             or
             rather
             the
             places
             wherein
             the
             eclipses
             of
             the
             Sunne
             or
             Moone
             doe
             happen
             in
             the
             Heauens
             ,
             are
             remoued
             continually
             more
             backwards
             in
             the
             Zodiack
             ,
             contrary
             to
             the
             order
             and
             succession
             of
             the
             Signes
             .
          
           
             As
             for
             example
             ;
             the
             eclipse
             of
             the
             Moone
             hapning
             this
             present
             yeare
             1600.
             the
             20.
             of
             Ianuarie
             neare
             vnto
             the
             Dragons
             tayle
             about
             the
             9.
             degree
             and
             40.
             min.
             of
             Leo
             ;
             the
             next
             eclipse
             that
             shall
             happen
             neare
             the
             same
             intersection
             of
             the
             Dragons
             taile
             ,
             in
             the
             yeare
             1601.
             the
             29.
             of
             Nouember
             ,
             shall
             be
             in
             17.
             degrees
             and
             an
             halfe
             of
             Gemini
             ;
             And
             that
             eclipse
             which
             shall
             be
             the
             next
             yeare
             after
             neare
             the
             same
             intersection
             the
             19.
             of
             Nouember
             in
             the
             morning
             ,
             shall
             be
             about
             the
             6.
             degree
             and
             40.
             minutes
             of
             Gemini
             ,
             &c.
             
          
           
             All
             this
             remouing
             of
             the
             Eclipses
             backwards
             commeth
             to
             passe
             ,
             by
             reason
             of
             the
             motion
             of
             this
             Orbe
             carying
             the
             Dragons
             head
             and
             tayle
             ,
             contrary
             to
             the
             course
             and
             order
             of
             the
             Signes
             .
          
           
             This
             Orbe
             continueth
             alwaies
             right
             vnder
             ,
             
             and
             euen
             with
             the
             Orbes
             of
             the
             Sphaere
             of
             the
             Sunne
             which
             abide
             alwaies
             in
             all
             parts
             iust
             vnder
             the
             ecliptick
             line
             ,
             and
             hath
             his
             center
             agreeing
             ,
             and
             all
             one
             
             with
             the
             center
             of
             the
             world
             ,
             and
             of
             the
             ecliptick
             :
             And
             therefore
             the
             poles
             and
             axtree
             ,
             about
             which
             this
             Orbe
             is
             turned
             ,
             agree
             iustly
             with
             the
             axtree
             of
             the
             Ecliptick
             .
          
           
             The
             rest
             of
             the
             Orbes
             of
             the
             Moone
             ,
             
             that
             are
             conteyned
             within
             this
             ,
             haue
             all
             theire
             playnes
             agreeing
             in
             one
             ,
             and
             lying
             euen
             one
             with
             another
             .
             But
             the
             one
             halfe
             of
             all
             their
             playnes
             ,
             ariseth
             aboue
             the
             playne
             of
             the
             former
             Orbe
             ,
             and
             of
             the
             Ecliptick
             ,
             towards
             the
             North
             pole
             of
             the
             Zodiack
             :
             and
             the
             other
             halfe
             descendeth
             beneath
             the
             playne
             of
             the
             ecliptick
             ,
             toward
             the
             South
             pole
             :
             euen
             as
             the
             one
             halfe
             of
             the
             Zodiack
             ariseth
             aboue
             the
             Equinoctiall
             circle
             towards
             the
             North
             :
             and
             the
             other
             halfe
             descendeth
             towards
             the
             South
             .
             And
             as
             the
             angle
             of
             intersection
             ,
             or
             obliquitie
             of
             the
             ecliptick
             with
             the
             Equinoctiall
             circle
             ,
             is
             23.
             degr
             .
             and
             an
             halfe
             or
             little
             more
             :
             so
             the
             angle
             of
             intersection
             ,
             or
             obliquity
             of
             the
             playnes
             of
             these
             Orbes
             of
             the
             Moone
             ,
             from
             the
             plaine
             of
             the
             Ecliptick
             ,
             and
             of
             the
             former
             Orbe
             carying
             the
             Dragons
             head
             and
             taile
             ,
             is
             5.
             degrees
             ,
             or
             (
             according
             to
             
               Tig●●
               Brahe
            
             his
             obseruation
             )
             5.
             degr
             .
             and
             a
             quarter
             almost
             sometimes
             ,
             and
             sometimes
             lesse
             then
             5.
             degr
             .
          
           
             That
             point
             or
             intersection
             of
             these
             Orbes
             with
             the
             former
             ,
             from
             which
             they
             begin
             to
             arise
             about
             the
             playne
             of
             the
             ecliptick
             towards
             the
             North
             ,
             proceeding
             East-wards
             ,
             is
             called
             the
             Dragons
             head
             ;
             and
             is
             signified
             by
             this
             character
             ☊
             :
             and
             the
             other
             point
             or
             intersection
             diametrally
             opposite
             vnto
             this
             ,
             is
             called
             the
             Dragons
             tayle
             ,
             which
             is
             also
             signified
             by
             the
             former
             character
             turned
             vp
             side
             downe
             after
             this
             manner
             ,
             ☋
             .
          
           
           
             The
             two
             points
             of
             these
             Orbes
             that
             are
             furthest
             distant
             from
             the
             plaine
             of
             the
             〈◊〉
             ,
             are
             called
             the
             bounds
             or
             limites
             of
             the
             Moones
             latitude
             ,
             and
             they
             are
             90.
             deg
             .
             from
             the
             Dragons
             head
             and
             tayle
             ,
             and
             5.
             deg
             .
             and
             a
             quarter
             almost
             from
             the
             playne
             of
             the
             Ecliptick
             ,
             according
             to
             the
             obliquity
             ,
             or
             greatest
             declination
             of
             the
             playnes
             of
             these
             Orbes
             ,
             from
             the
             playne
             of
             the
             ecliptick
             :
             Of
             these
             two
             points
             ,
             that
             which
             is
             in
             the
             north
             side
             of
             the
             ecliptick
             ,
             is
             called
             the
             North
             limit
             ,
             or
             bound
             of
             the
             Moones
             latitude
             ;
             and
             contrariwise
             ,
             the
             other
             point
             opposit
             to
             this
             on
             the
             south
             side
             of
             the
             Ecliptick
             ,
             is
             called
             the
             South
             limite
             of
             the
             Moones
             latitude
             .
             And
             when
             the
             Moone
             commeth
             to
             eyther
             of
             these
             two
             points
             ,
             she
             hath
             her
             greatest
             latitude
             .
          
        
         
           
             CHAP.
             X.
             Of
             the
             Orbes
             carying
             the
             Moones
             Apogaeum
             and
             Perigaeum
             .
          
           
             NExt
             within
             the
             Orbe
             carying
             the
             Dragons
             head
             and
             tayle
             ,
             is
             contayned
             the
             Orbe
             called
             
               Deferens
               Apogaeum
               lunae
            
             which
             is
             the
             point
             wherein
             the
             Moone
             is
             furthest
             distant
             from
             the
             earth
             .
          
           
             And
             vnder
             this
             Orbe
             is
             placed
             the
             Moones
             Eccentrick
             ,
             which
             is
             also
             called
             
               Deferens
               Epiculum
               Lunae
            
             ;
             that
             is
             the
             Orbe
             carying
             the
             Moones
             Epicycle
             .
          
           
             Againe
             within
             this
             eccentrick
             of
             the
             Moone
             ,
             is
             conteyned
             the
             least
             and
             lowest
             Orbe
             ,
             of
             all
             that
             are
             in
             this
             Sphaere
             ,
             Which
             they
             call
             
               Diferens
               Perigaeum
               Lunae
            
             ;
             that
             is
             ,
             the
             Orbe
             carying
             the
             Moones
             Perigaeum
             ,
             which
             is
             the
             point
             wherein
             the
             Moone
             commeth
             nearest
             to
             the
             earth
             .
          
           
             The
             vppermost
             and
             nethermost
             of
             these
             three
             
             Orbes
             ,
             that
             is
             to
             say
             ,
             the
             Orbes
             carying
             the
             Moones
             Apogaeum
             and
             Perigaeum
             (
             both
             which
             Orbes
             in
             this
             Sphaere
             are
             coloured
             with
             blew
             )
             are
             alwaies
             placed
             in
             such
             sort
             ,
             that
             the
             nar●●west
             part
             of
             the
             one
             ,
             is
             continually
             answerable
             to
             the
             broadest
             part
             of
             the
             other
             ;
             whereby
             it
             commeth
             to
             passe
             ,
             that
             the
             Sphaere
             of
             the
             Moone
             is
             made
             concentricall
             ,
             that
             is
             to
             say
             ,
             to
             haue
             the
             same
             center
             with
             the
             world
             :
             which
             also
             is
             one
             especiall
             vse
             ,
             why
             these
             Orbes
             were
             deuided
             .
          
           
             Another
             vse
             of
             these
             Orbes
             ,
             is
             to
             shew
             the
             reason
             of
             the
             motion
             of
             the
             Moones
             Apogaeum
             and
             Perigaeum
             :
             Therefore
             both
             these
             Orbes
             are
             moued
             togither
             with
             one
             motion
             equally
             ,
             about
             the
             center
             of
             the
             world
             ,
             in
             the
             same
             time
             from
             the
             East
             Westwards
             ,
             in
             the
             space
             of
             32.
             dayes
             3.
             houres
             and
             5.
             minutes
             almost
             :
             So
             mouing
             in
             one
             day
             11.
             deg
             .
             12.
             min.
             and
             1.
             third
             part
             almost
             .
             The
             axtree
             ,
             about
             which
             these
             Orbes
             are
             moued
             equally
             ,
             passeth
             through
             the
             center
             of
             the
             world
             and
             of
             the
             ecliptick
             :
             but
             the
             poles
             of
             these
             Orbes
             differ
             from
             the
             poles
             of
             the
             Ecliptick
             and
             of
             the
             Orbe
             carying
             the
             Dragons
             head
             and
             tayle
             ,
             by
             the
             space
             of
             5.
             degr
             .
             and
             a
             quarter
             ,
             or
             thereabouts
             ,
             which
             poles
             are
             caryed
             about
             the
             poles
             of
             the
             Orbe
             carying
             the
             Dragons
             head
             and
             tayle
             ,
             with
             the
             motion
             of
             the
             same
             Orbe
             ,
             in
             the
             space
             of
             19.
             yeares
             almost
             .
             Whereby
             it
             commeth
             to
             passe
             ,
             that
             the
             poles
             of
             the
             Orbe
             carying
             the
             Apogaeum
             and
             Perigaeum
             of
             the
             Moone
             ,
             describe
             certaine
             litle
             circles
             about
             the
             poles
             of
             the
             Orbe
             that
             carieth
             the
             Dragons
             head
             and
             taile
             ,
             euen
             as
             the
             Arctick
             ,
             and
             Antarctick
             circle
             in
             the
             ordinary
             Sphaere
             ,
             are
             described
             by
             the
             motion
             of
             the
             poles
             of
             the
             Ecliptick
             ,
             caryed
             about
             dayly
             with
             the
             
             motion
             of
             the
             first
             and
             highest
             moueable
             Sphaere
             ,
             in
             the
             space
             of
             24.
             houres
             almost
             .
          
        
         
           
             CHAP.
             XI
             .
             Of
             the
             eccentricke
             of
             the
             Moone
             .
          
           
             THe
             Eccentrick
             of
             the
             Moone
             contained
             betweene
             the
             two
             former
             Orbes
             and
             coloured
             with
             a
             sad
             yealow
             colour
             in
             this
             Sphaere
             ,
             is
             moued
             equally
             about
             the
             center
             of
             the
             same
             Orbes
             ,
             from
             the
             West
             towards
             the
             East
             ,
             finishing
             his
             motion
             vnder
             the
             Zodiack
             ,
             in
             the
             space
             of
             27.
             dayes
             ,
             and
             8.
             houres
             almost
             :
             and
             with
             this
             motion
             ,
             it
             caryeth
             about
             the
             Moones
             Epicycle
             equally
             ,
             vnder
             the
             Zodiack
             .
          
           
             Therefore
             the
             motion
             of
             this
             Orbe
             ,
             about
             his
             owne
             center
             ,
             must
             needs
             be
             vnequall
             ,
             that
             is
             to
             say
             ,
             swifter
             in
             those
             parts
             that
             are
             about
             the
             Apogaeum
             ,
             and
             slower
             in
             the
             lower
             parts
             about
             the
             Perigaeum
             :
             Because
             that
             greater
             arches
             of
             the
             Eccentrick
             ,
             doe
             answer
             to
             equall
             arches
             of
             the
             Zodiack
             about
             the
             Apogaeum
             ,
             then
             about
             the
             Perigaeum
             of
             the
             Eccentrick
             .
          
           
             The
             axtree
             about
             which
             this
             Orbe
             is
             moued
             ,
             is
             alwaies
             in
             all
             places
             equidistant
             from
             the
             axtree
             of
             the
             Orbe
             carying
             the
             Apogaeum
             of
             the
             Moone
             :
             and
             the
             poles
             of
             the
             axtree
             of
             the
             Moones
             eccentrick
             ,
             are
             fastned
             in
             the
             Orbe
             carying
             the
             Moones
             Apogaeum
             ,
             equidistantly
             from
             the
             poles
             of
             the
             same
             Orbe
             :
             therefore
             these
             poles
             together
             with
             the
             whole
             axtree
             of
             the
             eccentrick
             ,
             are
             caryed
             and
             equally
             moued
             about
             the
             poles
             and
             axtree
             of
             the
             Orbe
             carying
             the
             Apogaeum
             from
             the
             East
             ,
             towards
             the
             West
             .
             With
             this
             motion
             therefore
             ,
             the
             poles
             and
             center
             of
             the
             eccentrick
             ,
             describe
             certaine
             litle
             circles
             of
             equall
             bignes
             ,
             about
             the
             
             poles
             ,
             and
             center
             of
             the
             Orbe
             carying
             the
             Apogaeum
             ,
             from
             the
             East
             West-wards
             .
             And
             therefore
             also
             the
             Apogaeum
             of
             the
             eccentrick
             ,
             is
             moued
             about
             equally
             ,
             vnder
             the
             ecliptick
             ,
             contrary
             to
             the
             order
             of
             Signes
             from
             the
             East
             West-wards
             .
             Whereby
             it
             commeth
             to
             passe
             ,
             that
             both
             the
             Apogaeum
             and
             center
             of
             the
             eccentricke
             ,
             are
             somtimes
             vnder
             the
             Ecliptick
             ,
             that
             is
             ,
             when
             they
             are
             vnder
             the
             Dragons
             head
             or
             taile
             :
             but
             for
             the
             most
             part
             they
             are
             beside
             the
             plaine
             of
             the
             ecliptick
             ,
             either
             towards
             the
             North
             ,
             or
             else
             towards
             the
             South
             .
          
           
             Hereby
             also
             it
             appeareth
             ,
             that
             the
             plaine
             of
             the
             Ecliptick
             doth
             not
             alwayes
             deuide
             the
             plaine
             of
             the
             eccentricke
             into
             epqall
             parts
             or
             halfes
             ;
             but
             then
             onely
             ,
             when
             the
             Center
             and
             Apogaeum
             of
             the
             Eccentrick
             ,
             is
             right
             vnder
             the
             Dragons
             head
             or
             tayle
             ;
             for
             then
             onely
             the
             plaine
             of
             the
             Ecliptick
             deuideth
             the
             plaine
             of
             the
             Eccentrick
             ,
             by
             the
             center
             therof
             ;
             and
             consequently
             deuideth
             it
             precisely
             into
             two
             halfes
             .
             Otherwise
             ,
             if
             the
             Apogaeum
             of
             the
             eccentrick
             ,
             be
             not
             vnder
             the
             Dragons
             head
             or
             tayle
             ,
             looke
             on
             which
             side
             of
             the
             plaine
             of
             the
             ecliptick
             the
             Apogaeum
             is
             ,
             for
             on
             the
             same
             side
             of
             the
             ecliptick
             is
             the
             greater
             part
             of
             the
             eccentrick
             .
          
        
         
           
             CHAP.
             XII
             .
             In
             what
             proportion
             the
             Moones
             eccentrick
             ,
             and
             Orbe
             ,
             carying
             her
             Apogaeum
             are
             moued
             .
          
           
             NOw
             the
             Eccentrick
             of
             the
             Moone
             ,
             and
             the
             Orbe
             carying
             her
             Apogaeum
             ,
             are
             moued
             in
             such
             sort
             ,
             that
             the
             middle
             place
             of
             the
             Sunne
             ,
             is
             alwayes
             right
             in
             the
             midst
             betweene
             the
             center
             of
             the
             Epicycle
             caried
             in
             the
             eccentrick
             ,
             and
             the
             Apogaeum
             of
             the
             Eccentrick
             ;
             except
             it
             be
             when
             the
             center
             of
             the
             epicycle
             is
             
             in
             coniunction
             ,
             or
             opposition
             to
             the
             middle
             place
             of
             of
             the
             Sunne
             .
             For
             in
             euery
             middle
             coniunction
             and
             opposition
             of
             the
             Sunne
             and
             Moone
             ,
             the
             center
             of
             the
             Epicycle
             ,
             and
             the
             Apogaeum
             of
             the
             eccentrick
             are
             vnited
             together
             ;
             But
             in
             the
             coniunction
             they
             are
             both
             conioyned
             with
             the
             middle
             place
             of
             the
             Sun
             ;
             and
             in
             the
             opposition
             they
             are
             both
             together
             opposite
             to
             the
             same
             .
             Whereof
             it
             followeth
             ,
             that
             in
             the
             first
             and
             last
             quarters
             of
             the
             Moone
             ,
             the
             center
             of
             her
             epicycle
             is
             diametrally
             opposite
             to
             the
             Apogaeum
             of
             her
             eccentrick
             .
          
           
             Hereof
             it
             commeth
             to
             passe
             ,
             that
             although
             the
             Moone
             haue
             the
             same
             position
             in
             her
             epicycle
             at
             the
             time
             of
             the
             new
             and
             full
             Moone
             ,
             and
             of
             the
             first
             and
             last
             quarters
             ;
             yet
             the
             equation
             ,
             or
             prosthaphaeresis
             of
             the
             Moones
             Argument
             (
             as
             they
             call
             it
             )
             that
             is
             the
             difference
             betweene
             the
             true
             ,
             and
             middle
             places
             of
             the
             Moone
             ,
             is
             alwayes
             greater
             in
             the
             first
             and
             last
             quarter
             ,
             then
             in
             the
             full
             and
             new
             Moone
             .
             Hereby
             likewise
             it
             appeareth
             that
             in
             the
             time
             contayned
             betweene
             new
             Moone
             and
             new
             Moone
             (
             which
             they
             call
             
               Mensem
               synodicum
            
             ,
             that
             is
             the
             moneth
             coniunctional
             ,
             or
             the
             time
             from
             coniunction
             to
             coniunction
             )
             the
             center
             of
             the
             epicycle
             maketh
             two
             complete
             reuolutions
             ,
             vnder
             the
             Orbe
             carying
             the
             Apogaeum
             of
             the
             Moones
             eccentrick
             .
          
           
             And
             therefore
             in
             euery
             moneth
             ,
             the
             center
             of
             the
             epicycle
             commeth
             twise
             to
             the
             Apogaeum
             and
             twise
             to
             the
             Perigaeum
             of
             the
             eccentrick
             ;
             and
             so
             the
             monthly
             motion
             of
             the
             center
             of
             the
             epicycle
             ,
             describeth
             an
             oual
             figure
             :
             the
             ends
             whereof
             are
             alwayes
             towards
             the
             place
             of
             the
             full
             and
             new
             Moone
             ,
             and
             the
             ●ides
             towards
             
             the
             places
             of
             the
             first
             and
             last
             quarter
             .
          
           
             By
             this
             that
             hath
             beene
             spoken
             ,
             it
             is
             also
             manifest
             ,
             that
             if
             the
             middle
             motion
             of
             the
             Sunne
             ,
             be
             subtracted
             out
             of
             the
             middle
             motion
             of
             the
             Moone
             ,
             there
             remaineth
             the
             middle
             motion
             of
             the
             Moones
             longitude
             from
             the
             sunne
             ,
             and
             that
             if
             this
             longitude
             againe
             be
             doubled
             ,
             you
             shall
             haue
             the
             motion
             of
             the
             center
             of
             the
             Moones
             Epicycle
             from
             the
             Apogaeum
             of
             her
             eccentrick
             ,
             which
             motion
             they
             call
             the
             center
             of
             the
             Moone
             ,
          
        
         
           
             CHAP.
             XIII
             .
             Of
             the
             Epicycle
             of
             the
             Moone
             ,
             and
             how
             it
             is
             moued
             .
          
           
             THe
             little
             Orbe
             placed
             in
             the
             Eccentrick
             ,
             is
             called
             the
             Epicycle
             of
             the
             Moone
             ;
             in
             the
             circumference
             whereof
             is
             also
             placed
             the
             body
             of
             the
             Moone
             ,
             represented
             by
             the
             round
             Beade
             ,
             set
             into
             the
             Moones
             Epicycle
             in
             this
             Sphaere
             .
          
           
             The
             plaine
             superficies
             of
             this
             epicycle
             agreeth
             euen
             with
             the
             plaine
             of
             the
             eccentrick
             :
             and
             the
             axtree
             about
             which
             it
             is
             moued
             ,
             is
             perpendicular
             to
             the
             plaine
             of
             the
             eccentrick
             .
             This
             Epicycle
             is
             moued
             equally
             from
             his
             middle
             Apogaeum
             ,
             about
             his
             owne
             center
             and
             axtree
             from
             the
             East
             Westwards
             ,
             contrary
             to
             the
             motion
             of
             the
             eccentrick
             ,
             carying
             forwards
             the
             body
             of
             the
             Moone
             with
             this
             motion
             13.
             degrees
             and
             almost
             4.
             min.
             euery
             day
             ,
             and
             finishing
             his
             reuolution
             in
             27.
             dayes
             13.
             houres
             and
             19.
             minutes
             almost
             .
          
           
             The
             middle
             Apogaeum
             of
             the
             Epicycle
             is
             shewed
             by
             a
             right
             line
             ,
             imagined
             to
             be
             drawne
             ,
             from
             that
             point
             of
             the
             little
             circle
             (
             described
             by
             the
             motion
             of
             the
             center
             of
             the
             Moones
             eccentrick
             )
             which
             is
             opposite
             
             to
             the
             center
             of
             the
             Eccentrick
             ,
             by
             the
             center
             of
             the
             Epicycle
             vnto
             the
             vpper
             part
             of
             the
             Epicycle
             .
          
           
             But
             the
             true
             Apogaeum
             of
             the
             Epicycle
             ,
             is
             shewed
             by
             a
             right
             line
             ,
             vnderstood
             to
             be
             drawne
             from
             the
             Center
             of
             the
             earth
             by
             the
             center
             of
             the
             Epicycle
             ,
             vnto
             the
             vpper
             part
             of
             the
             circumference
             thereof
             .
          
           
             By
             the
             motion
             of
             this
             Epicycle
             it
             may
             easily
             be
             conceiued
             why
             the
             Moone
             seemeth
             to
             moue
             sometimes
             swifter
             and
             somteimes
             slower
             :
             
             For
             seeing
             that
             the
             vpper
             part
             of
             the
             Epicycle
             ,
             moueth
             contrary
             to
             the
             motion
             of
             the
             Eccentrick
             from
             the
             East
             Westwards
             ,
             when
             the
             Moone
             commeth
             in
             that
             part
             ,
             shee
             must
             needs
             seeme
             to
             moue
             more
             slowly
             ,
             to
             them
             that
             are
             at
             the
             center
             of
             the
             world
             .
          
           
             But
             when
             the
             Moone
             commeth
             in
             the
             nether
             part
             of
             the
             Epicycle
             ,
             the
             Eccentrick
             caryeth
             the
             Epicycle
             and
             the
             Epicycle
             caryeth
             the
             body
             of
             the
             Moone
             both
             one
             way
             :
             that
             is
             ,
             from
             the
             West
             East-wards
             ,
             and
             therefore
             at
             that
             time
             the
             Moone
             seemeth
             to
             moue
             more
             swiftly
             .
             According
             as
             you
             may
             see
             in
             Ephemerides
             ,
             the
             d●●●ne
             motion
             of
             the
             Moone
             to
             be
             sometimes
             little
             more
             then
             11.
             degrees
             and
             sometimes
             againe
             little
             lesse
             then
             15.
             degrees
             .
             The
             true
             motion
             of
             the
             Moone
             seemeth
             then
             to
             be
             swifter
             ,
             when
             the
             Moone
             is
             in
             the
             Perigaeum
             of
             her
             Epicycle
             ,
             and
             the
             Epicycle
             in
             the
             Perigaeum
             of
             the
             Eccentrick
             ;
             because
             then
             she
             is
             not
             onely
             caryed
             forwards
             the
             same
             way
             both
             by
             her
             Epicycle
             and
             Eccentrick
             ,
             but
             she
             is
             also
             at
             that
             time
             nearest
             vnto
             vs
             for
             which
             cause
             her
             motion
             shall
             seeme
             swifter
             ,
             then
             when
             the
             Epicycle
             is
             in
             other
             parts
             of
             the
             Eccentrick
             .
             〈…〉
          
        
         
           
           
             CHAP.
             XIIII
             .
             The
             definitions
             of
             certayne
             Astronomicall
             wordes
             of
             Art
             ,
             for
             the
             better
             vnderstanding
             of
             the
             Theoricke
             of
             the
             Moone
             .
          
           
             1.
             
             THe
             line
             of
             the
             Moones
             middle
             motion
             ,
             is
             a
             line
             vnderstood
             to
             be
             drawne
             from
             the
             center
             of
             the
             earth
             ,
             by
             the
             center
             of
             the
             Moones
             Epicycle
             ,
             vnto
             the
             Zodiack
             .
          
           
             2.
             
             This
             line
             sheweth
             the
             middle
             place
             of
             the
             Moon
             in
             the
             Zodiack
             .
          
           
             3.
             
             And
             the
             middle
             motion
             of
             the
             Moone
             ,
             is
             the
             arch
             of
             the
             Zodiack
             ,
             from
             the
             beginning
             of
             Aries
             ,
             vnto
             the
             same
             line
             .
          
           
             4.
             
             So
             likewise
             the
             line
             of
             the
             true
             motion
             ,
             or
             of
             the
             true
             place
             of
             the
             Moone
             ,
             is
             drawne
             from
             the
             center
             of
             the
             world
             ,
             by
             the
             center
             of
             the
             Moone
             ,
             to
             the
             Zodiack
             .
          
           
             5.
             
             This
             line
             therefore
             sheweth
             the
             true
             place
             of
             the
             Moone
             in
             the
             Zodiack
             .
          
           
             6.
             
             And
             the
             true
             motion
             of
             the
             Moone
             ,
             is
             the
             arch
             of
             the
             Zodiack
             ,
             from
             the
             beginning
             of
             Aries
             ,
             vnto
             the
             true
             place
             of
             the
             Moone
             .
          
           
             7.
             
             The
             middle
             longitude
             of
             the
             Moone
             from
             the
             Sunne
             ,
             is
             the
             arch
             of
             the
             Zodiack
             ,
             from
             the
             middle
             place
             of
             the
             Sunne
             Eastwards
             vnto
             the
             middle
             place
             of
             the
             Moone
             .
          
           
             8.
             
             And
             this
             arch
             doubled
             ,
             is
             called
             the
             doubled
             longitude
             of
             the
             Moone
             from
             the
             Sunne
             ,
             or
             the
             center
             of
             the
             Moone
             (
             as
             the
             Alphonsines
             call
             it
             )
             which
             is
             nothing
             else
             but
             the
             arch
             of
             the
             Zodiack
             ,
             betweene
             the
             place
             of
             the
             Apogaeum
             of
             the
             Eccentrick
             and
             the
             
             middle
             place
             of
             the
             Moone
             .
             It
             is
             called
             the
             doubled
             longitude
             of
             the
             Moone
             from
             the
             Sunne
             ,
             because
             it
             is
             alwayes
             twice
             so
             much
             ,
             as
             is
             the
             middle
             longitude
             of
             the
             Moone
             from
             the
             Sunne
             .
          
           
             9.
             
             And
             it
             is
             called
             the
             center
             of
             the
             Moone
             ,
             because
             it
             sheweth
             the
             distance
             of
             the
             center
             of
             the
             Moones
             Epicycle
             from
             the
             Apogaeum
             .
          
           
             10.
             
             The
             equation
             ,
             or
             Prosthaphaeresis
             of
             the
             center
             ,
             is
             the
             arch
             of
             the
             Epicycle
             ,
             betweene
             the
             middle
             and
             true
             Apogaeum
             of
             the
             Epicycle
             .
          
           
             This
             equation
             or
             Prosthaphaeresis
             is
             nothing
             at
             all
             ,
             when
             the
             center
             of
             the
             Epicycle
             is
             in
             the
             Apogaeum
             ,
             or
             Perigaeum
             of
             the
             Eccentrick
             .
             But
             the
             Epicycle
             being
             in
             any
             other
             part
             of
             the
             Eccentricke
             there
             is
             alwaies
             some
             equation
             of
             the
             center
             ;
             yea
             in
             some
             parts
             thereof
             ,
             where
             it
             groweth
             greatest
             ,
             it
             is
             13.
             degr
             .
             9.
             minutes
             :
             and
             so
             long
             as
             the
             center
             of
             the
             Epicycle
             ,
             is
             in
             the
             halfe
             of
             the
             Eccentrick
             descending
             from
             the
             Apogaeum
             to
             the
             Perigaeum
             ,
             that
             equation
             is
             to
             be
             added
             to
             the
             motion
             of
             the
             Epicycle
             ;
             but
             in
             the
             other
             halle
             of
             the
             Eccentricke
             ascending
             ;
             ,
             it
             must
             be
             subtracted
             ;
             that
             so
             the
             true
             Argument
             〈…〉
             the
             Epicycle
             may
             be
             had
             .
          
           
             11.
             
             The
             Argument
             ,
             or
             Anamalie
             of
             the
             Moone
             is
             nothing
             els
             ,
             but
             the
             motion
             of
             the
             Moones
             Epicycle
             .
          
           
             12.
             
             The
             true
             or
             middle
             argument
             ,
             〈…〉
             is
             the
             arch
             of
             the
             Epicycle
             from
             the
             true
             or
             middle
             Apogaeum
             of
             the
             Epicycle
             ,
             vnto
             the
             center
             of
             the
             body
             of
             the
             Moone
             ,
             reckoned
             that
             way
             ,
             which
             the
             epicycle
             moueth
             .
          
           
             13.
             
             The
             equation
             of
             the
             argument
             ,
             or
             Prosthaphaeresis
             of
             the
             epicycle
             ,
             is
             the
             arch
             of
             the
             Zodiack
             ,
             
             〈…〉
             the
             middle
             ,
             and
             〈◊〉
             place
             of
             the
             Moone
             .
             This
             equation
             is
             〈◊〉
             ,
             when
             the
             Moone
             is
             in
             the
             true
             Apogaeum
             ,
             or
             Perigaeum
             of
             her
             epicycle
             .
             But
             it
             is
             greatest
             ,
             when
             the
             center
             of
             the
             Moone
             commeth
             〈…〉
             of
             the
             world
             ,
             and
             touching
             the
             epicycle
             ,
             when
             it
             is
             in
             the
             Perigaeum
             of
             the
             eccentrick
             .
          
           
             And
             the
             Moone
             being
             in
             the
             first
             ,
             that
             is
             in
             the
             〈…〉
             of
             the
             Epicycle
             ,
             〈…〉
             from
             the
             true
             Apogaeum
             thereof
             ,
             the
             middle
             place
             of
             the
             Moone
             goe
             〈◊〉
             before
             the
             true
             place
             ,
             and
             the
             equation
             of
             the
             argument
             must
             therefore
             be
             subtracted
             :
             but
             when
             the
             Moone
             is
             〈…〉
             semicircle
             of
             the
             epicycle
             ,
             〈…〉
             before
             the
             middle
             place
             ,
             and
             to
             that
             equation
             must
             be
             added
             to
             the
             Moones
             〈◊〉
             middle
             motion
             ,
             that
             the
             true
             motion
             and
             place
             of
             the
             〈…〉
             may
             be
             found
             .
          
        
         
           
             CHAP.
             XV.
             The
             reason
             of
             the
             variety
             of
             the
             Moones
             equation
             ,
             &c.
             
          
           
             THis
             equation
             becommeth
             lesser
             or
             greater
             ,
             according
             as
             the
             epicycle
             〈…〉
             or
             nearer
             to
             the
             center
             of
             the
             world
             .
             The
             least
             equations
             are
             ,
             when
             the
             epicycle
             is
             in
             the
             Apogaeum
             of
             the
             eccentrick
             ,
             and
             contrarywise
             ,
             the
             greatest
             must
             happen
             ,
             the
             epicycle
             being
             in
             the
             Perigaeum
             of
             the
             eccentrick
             .
          
           
             The
             difference
             between
             these
             greatest
             ,
             and
             least
             Equations
             ,
             Ptolemee
             and
             Copernicus
             call
             the
             excesse
             :
             but
             〈◊〉
             ,
             and
             the
             Alphonsines
             call
             it
             the
             diuersitie
             of
             the
             Diameter
             ;
             because
             that
             difference
             of
             the
             equations
             ariseth
             by
             reason
             of
             the
             diuerse
             apparent
             hignesse
             of
             the
             diameter
             of
             the
             Epicycle
             ,
             according
             
             as
             it
             is
             nearer
             to
             vs
             ,
             or
             further
             from
             vs.
             
          
           
             Therefore
             in
             the
             Astronomicall
             tables
             ,
             they
             vse
             to
             set
             downe
             those
             equations
             onely
             ,
             which
             happen
             when
             the
             Epicycle
             is
             in
             the
             Apogaeum
             of
             the
             eccentrick
             ,
             which
             are
             the
             least
             equations
             ,
             whereto
             they
             also
             adioyne
             the
             excesse
             ,
             or
             diuersity
             of
             diameter
             ,
             shewing
             how
             much
             those
             equations
             ,
             which
             happen
             when
             the
             Epicycle
             is
             in
             the
             Perigaeum
             of
             the
             Eccentrick
             ,
             exceed
             those
             which
             happen
             ,
             the
             epicycle
             being
             in
             the
             Apogaeum
             of
             the
             eccentrick
             .
             Moreouer
             ,
             there
             are
             annexed
             certaine
             min.
             which
             they
             call
             Scrupula
             ,
             or
             
               minuta
               proportion●alia
            
             :
             that
             is
             ,
             proportionall
             minutes
             :
             whereby
             is
             found
             ,
             how
             much
             of
             the
             sayd
             excesse
             ,
             is
             to
             be
             added
             to
             the
             foresayd
             equations
             ,
             when
             the
             epicycle
             is
             in
             any
             other
             part
             of
             the
             eccentrick
             ,
             then
             in
             the
             Apogaeum
             :
             that
             so
             the
             true
             equation
             of
             the
             argument
             ,
             for
             the
             same
             part
             of
             the
             eccentrick
             might
             at
             any
             time
             be
             found
             .
             For
             then
             onely
             is
             that
             whole
             excesse
             to
             be
             added
             ,
             when
             the
             epicycle
             is
             in
             the
             Perigaeum
             of
             the
             eccentrick
             .
             But
             if
             the
             epicycle
             be
             in
             any
             other
             part
             of
             the
             eccentrick
             ;
             then
             looke
             what
             proportion
             60.
             hath
             to
             the
             whole
             excesse
             ,
             the
             same
             proportion
             haue
             the
             proportionall
             minutes
             ,
             answerable
             to
             that
             part
             of
             the
             eccentrick
             ,
             wherein
             the
             epicycle
             is
             ,
             vnto
             the
             part
             proportional
             of
             the
             excesse
             ,
             which
             (
             part
             proportionall
             )
             being
             added
             to
             the
             equation
             before
             found
             ,
             shall
             giue
             you
             the
             true
             equation
             .
          
        
         
           
             CHAP.
             XVI
             .
             The
             reason
             〈◊〉
             Moones
             proportionall
             minutes
             ,
             &c.
             
          
           
             THe
             reason
             of
             those
             proportionall
             minutes
             ,
             may
             in
             some
             sort
             be
             shewed
             ,
             by
             those
             concentricall
             
             arches
             of
             circles
             ,
             which
             you
             see
             drawne
             vppon
             the
             Moones
             eccentricall
             Orbe
             ,
             in
             this
             Sphaere
             :
             but
             indeed
             all
             those
             arches
             must
             bee
             vnderstood
             ,
             to
             haue
             alwayes
             the
             same
             center
             with
             the
             world
             ,
             and
             not
             to
             be
             moued
             about
             togither
             with
             the
             Eccentrick
             .
             The
             vppermost
             of
             them
             is
             to
             be
             drawne
             by
             the
             center
             of
             the
             Epicycle
             being
             in
             the
             Apogaeum
             of
             the
             Eccentrick
             ,
             and
             the
             nethermost
             is
             drawne
             by
             the
             same
             center
             when
             it
             is
             in
             the
             Perigaeum
             of
             the
             Eccentrick
             :
             so
             as
             the
             distance
             of
             these
             two
             arches
             ,
             or
             Peripheryes
             ,
             is
             iust
             twise
             so
             much
             as
             the
             eccentricitie
             ;
             that
             is
             the
             distance
             of
             the
             center
             of
             the
             Eccentrick
             ,
             from
             the
             center
             of
             the
             world
             ,
             shewed
             by
             the
             distance
             of
             the
             short
             lines
             NO
             ,
             or
             FF
             ,
             vppon
             the
             Orbe
             carying
             the
             Apogaeum
             ;
             or
             of
             PQ
             ,
             or
             GH
             ,
             vpon
             the
             caryer
             of
             the
             Perigaeum
             of
             the
             Moone
             .
          
           
             The
             whole
             distance
             ,
             between
             these
             two
             peripheries
             ,
             from
             the
             vttermost
             to
             the
             innermost
             ,
             is
             vnderstood
             to
             be
             deuided
             into
             60.
             equall
             parts
             ,
             imagining
             euery
             one
             of
             these
             to
             contayne
             10.
             as
             may
             appeare
             by
             the
             figures
             set
             to
             euery
             one
             of
             them
             ,
             from
             the
             vppermost
             to
             the
             nethermost
             ,
             in
             this
             order
             :
             10.
             20.
             30.
             40.
             50.
             60.
             
          
           
             Now
             the
             intersections
             of
             these
             Peripheries
             with
             the
             Eccentrick
             (
             that
             is
             )
             with
             the
             vppermost
             of
             the
             two
             deuided
             Peripheries
             ,
             which
             are
             drawne
             round
             about
             through
             the
             midst
             of
             the
             Moones
             eccentricall
             Orbe
             )
             do
             shew
             what
             proportionable
             min.
             answer
             to
             any
             part
             of
             the
             eccentrick
             ,
             
             after
             this
             manner
             :
             In
             the
             vppermost
             of
             the
             two
             foresaid
             graduated
             Peripheries
             ,
             looke
             that
             distance
             of
             the
             center
             of
             the
             moones
             Epicycle
             from
             the
             Apogaeum
             of
             the
             Eccentrick
             ,
             (
             that
             is
             to
             say
             )
             that
             doubled
             longitude
             of
             the
             Moone
             as
             the
             Alphonsines
             
             call
             it
             )
             which
             you
             desire
             :
             Then
             looke
             which
             of
             the
             consentricall
             arches
             before
             mentioned
             passeth
             by
             the
             the
             terme
             ,
             or
             end
             of
             that
             distance
             or
             doubled
             longitude
             :
             And
             thirdly
             ,
             looke
             about
             in
             the
             same
             arch
             ,
             what
             number
             is
             set
             thereuppon
             ,
             for
             that
             sheweth
             you
             the
             number
             of
             the
             proportionall
             minut
             .
             answerable
             to
             the
             scituation
             of
             the
             Epicycle
             ,
             at
             that
             distance
             from
             the
             Apogaeum
             of
             the
             Eccentrick
             .
          
           
             These
             proportionall
             min.
             therefore
             may
             be
             defined
             to
             be
             nothing
             else
             ,
             
             but
             the
             sixtieth
             parts
             of
             the
             diuersity
             of
             diameter
             ,
             or
             of
             the
             excesse
             wherwith
             the
             equations
             of
             the
             argument
             ,
             or
             Prostaphaeresis
             ,
             of
             the
             Epicycle
             are
             to
             be
             augmented
             when
             the
             Epicycle
             is
             any
             other
             part
             of
             the
             Eccentrick
             ,
             then
             in
             the
             Apogaeum
             .
          
           
             Otherwise
             also
             ,
             these
             proportionall
             min.
             may
             be
             defined
             ,
             to
             be
             sixtieth
             parts
             of
             the
             excesse
             ,
             wherewith
             the
             line
             drawne
             from
             the
             center
             of
             the
             earth
             ,
             to
             the
             Apogaeum
             of
             the
             Moones
             Eccentrick
             ,
             exceedeth
             the
             line
             drawne
             from
             the
             same
             center
             to
             the
             Perigaeum
             of
             the
             Eccentrick
             :
             For
             these
             sixtieth
             parts
             also
             may
             not
             vnfitly
             be
             called
             proportionall
             min.
             because
             that
             alwaies
             looke
             how
             many
             of
             these
             parts
             there
             are
             left
             without
             the
             circumference
             of
             the
             Eccentrick
             ,
             or
             beyond
             the
             center
             of
             the
             Epicycle
             ;
             so
             many
             of
             the
             former
             sixtieth
             parts
             of
             the
             diuersity
             of
             diameter
             ,
             or
             of
             the
             excesse
             of
             the
             Prostaphaerses
             of
             the
             Epicycle
             ,
             must
             be
             added
             to
             the
             Equation
             of
             the
             argument
             ,
             that
             the
             true
             equation
             of
             the
             argument
             may
             bee
             had
             ,
             for
             that
             position
             ,
             or
             scituation
             of
             the
             Epicycle
             ,
             in
             the
             Eccentrick
             .
          
        
         
           
           
             CHAP.
             XVII
             .
             The
             reason
             of
             the
             Eclipses
             of
             the
             Sunne
             and
             Moone
             ,
             &c.
             
          
           
             NOw
             by
             this
             Sphere
             ,
             it
             may
             easily
             be
             conceiued
             ,
             why
             there
             is
             not
             an
             Eclipse
             ,
             in
             euery
             coniunction
             or
             opposition
             of
             the
             Sunne
             and
             Moone
             .
             For
             seeing
             that
             the
             Moone
             hath
             for
             the
             most
             part
             a
             greater
             apparent
             latitude
             ,
             then
             the
             visible
             or
             apparent
             conioyned
             semediameters
             of
             the
             Sunne
             and
             Moone
             in
             the
             coniunction
             :
             and
             because
             the
             true
             latitude
             of
             the
             Moone
             ,
             is
             also
             for
             the
             most
             part
             greater
             then
             the
             apparent
             semediameters
             of
             the
             Moone
             and
             shadow
             of
             the
             earth
             (
             at
             that
             place
             where
             the
             Moone
             should
             passe
             through
             that
             shadow
             )
             in
             the
             oppossition
             ,
             to
             make
             an
             Eclipse
             :
             it
             commeth
             to
             passe
             ,
             that
             in
             most
             coniunctions
             and
             oppositions
             of
             the
             Sunne
             and
             Moone
             ,
             there
             is
             no
             Eclipse
             .
             And
             the
             reason
             hereof
             is
             this
             ,
             because
             that
             the
             Moone
             commeth
             vnder
             the
             way
             of
             the
             Sunne
             (
             which
             wee
             call
             the
             Ecliptick
             line
             )
             onely
             twise
             in
             a
             moneth
             ,
             and
             those
             2.
             points
             (
             wherin
             the
             wayes
             of
             the
             Sunne
             and
             Moone
             crosse
             each
             other
             )
             onely
             twise
             in
             a
             synodicall
             moneth
             ,
             which
             two
             points
             wee
             called
             the
             Dragons
             head
             and
             taile
             ;
             whereof
             wee
             haue
             also
             spoken
             before
             ,
             )
             Wherfore
             ,
             seeing
             the
             Sunne
             (
             going
             but
             once
             only
             through
             the
             compasse
             of
             the
             Ecliptick
             in
             a
             yeare
             )
             can
             come
             but
             once
             in
             a
             yeare
             to
             eyther
             of
             those
             points
             ;
             the
             Moone
             for
             the
             most
             part
             ,
             when
             she
             cōmeth
             to
             bee
             in
             opposition
             ,
             or
             coniunction
             with
             the
             Sun
             ,
             must
             needs
             be
             fo
             farre
             wide
             from
             the
             Ecliptick
             line
             ,
             or
             way
             of
             the
             Sunne
             ,
             either
             towards
             the
             North
             or
             South
             :
             that
             she
             can
             neither
             come
             betwixt
             vs
             and
             the
             Sun
             in
             the
             coniunction
             ,
             nor
             yet
             within
             the
             compasse
             of
             the
             shadow
             of
             the
             earth
             in
             the
             opposition
             .
          
           
           
             But
             when
             the
             Sunne
             commeth
             neare
             eyther
             of
             those
             points
             (
             which
             hapneth
             once
             in
             six
             moneths
             (
             there
             must
             needs
             for
             the
             most
             part
             be
             some
             Eclipse
             ,
             eyther
             of
             the
             Sunne
             or
             Moone
             ,
             or
             both
             .
          
        
         
           
             CHAP.
             XVIII
             .
             Of
             the
             diuersity
             of
             the
             bounds
             or
             spaces
             ,
             within
             which
             an
             Eclipse
             may
             happen
             :
             and
             the
             reason
             of
             that
             diuersity
             .
          
           
             THe
             bounds
             or
             distances
             from
             the
             Dragons
             head
             or
             taile
             ,
             within
             which
             there
             may
             happen
             an
             Eclipse
             of
             the
             Moone
             ,
             are
             sometimes
             greater
             and
             sometimes
             lesse
             ,
             by
             reason
             of
             the
             diuers
             distances
             of
             the
             Sunne
             ,
             or
             Moone
             ,
             or
             both
             of
             them
             ,
             from
             the
             earth
             .
             For
             seeing
             the
             body
             of
             the
             Sunne
             is
             greater
             then
             the
             globe
             of
             the
             whole
             earth
             (
             as
             it
             is
             manifestly
             demonstrated
             by
             Ptolemee
             and
             Copernicus
             )
             it
             must
             needs
             be
             ,
             that
             the
             greater
             distance
             the
             Sun
             hath
             from
             the
             earth
             ,
             the
             greater
             shadow
             must
             the
             earth
             haue
             ;
             and
             the
             nearer
             the
             Sunne
             is
             to
             the
             earth
             ,
             the
             lesse
             shadow
             shall
             the
             earth
             haue
             ,
             at
             the
             place
             of
             the
             Moons
             passage
             through
             the
             shadow
             ,
             at
             equall
             distances
             from
             the
             earth
             .
          
           
             Contrariwise
             ,
             the
             further
             that
             the
             Moone
             is
             from
             the
             earth
             ,
             the
             lesse
             shall
             the
             shadow
             of
             the
             earth
             be
             ,
             and
             the
             nearer
             the
             Moone
             is
             to
             the
             earth
             ,
             the
             greater
             shall
             the
             shadow
             be
             ,
             at
             the
             place
             where
             the
             Moone
             is
             to
             passe
             through
             the
             shadow
             .
          
           
             The
             greatest
             distance
             therefore
             from
             the
             Dragons
             head
             or
             taile
             ,
             wherein
             there
             can
             at
             any
             time
             happen
             any
             Eclipse
             of
             the
             Moone
             ,
             is
             about
             13.
             degrees
             .
             And
             the
             least
             distance
             at
             which
             it
             is
             possible
             for
             the
             Moone
             to
             auoid
             an
             Eclipse
             ,
             is
             about
             10.
             degr
             .
             and
             one
             third
             part
             of
             a
             degree
             ;
             which
             hapneth
             when
             
             the
             Moone
             is
             in
             the
             Apogaeum
             of
             her
             Epicycle
             ,
             in
             her
             greatest
             distance
             from
             the
             earth
             ,
             and
             the
             Sunne
             in
             his
             Perigaeum
             ,
             in
             the
             time
             of
             his
             greatest
             eccentricity
             ,
             for
             then
             the
             Sunne
             commeth
             nearest
             to
             the
             earth
             and
             maketh
             the
             least
             shadow
             :
             as
             contrarywise
             at
             the
             same
             time
             of
             his
             greatest
             eccentricity
             ,
             beeing
             in
             his
             Apogaeum
             ,
             he
             hath
             his
             greatest
             distance
             from
             the
             earth
             ,
             and
             so
             maketh
             the
             earth
             cast
             forth
             her
             greatest
             shadow
             .
             At
             which
             time
             ,
             if
             the
             Moone
             also
             chance
             to
             be
             in
             the
             Perigaeum
             of
             her
             Epicycle
             ,
             and
             so
             in
             her
             nearest
             distance
             from
             the
             earth
             ,
             she
             may
             be
             something
             Eclipsed
             ,
             although
             she
             be
             full
             13.
             degrees
             or
             something
             more
             from
             the
             Dragons
             head
             or
             taile
             .
          
        
         
           
             CHAP.
             XIX
             .
             How
             to
             find
             the
             place
             of
             the
             Dragons
             head
             and
             taile
             for
             any
             time
             .
          
           
             NOw
             the
             place
             ,
             and
             time
             of
             the
             full
             Moone
             ,
             being
             easily
             knowne
             by
             some
             Almanack
             ,
             or
             Prognostication
             ;
             it
             shall
             not
             be
             hard
             ,
             to
             giue
             a
             reasonable
             neare
             estimate
             ,
             and
             to
             foretell
             both
             the
             time
             ,
             and
             quantity
             of
             the
             Eclipse
             of
             the
             Moone
             ,
             the
             place
             of
             the
             Dragons
             head
             and
             taile
             ,
             being
             first
             knowne
             after
             this
             manner
             .
          
           
             The
             place
             of
             the
             Dragans
             head
             ,
             being
             first
             giuen
             for
             any
             time
             ,
             for
             euery
             yeare
             before
             the
             same
             time
             ,
             adde
             to
             the
             same
             place
             :
             and
             for
             euery
             yeare
             after
             the
             same
             time
             subtract
             19.
             degrees
             and
             one
             third
             part
             of
             a
             degree
             and
             for
             euery
             moneth
             a
             degree
             and
             an
             halfe
             and
             a
             tenth
             part
             of
             a
             degree
             and
             for
             euery
             day
             3.
             minutes
             and
             the
             remainder
             shall
             shew
             you
             the
             place
             of
             the
             Dragons
             head
             after
             the
             same
             time
             :
             or
             the
             summe
             before
             
             that
             time
             without
             any
             great
             errour
             .
          
           
             As
             for
             example
             ,
             The
             30.
             of
             Iune
             this
             present
             yeare
             1600.
             suppose
             you
             would
             know
             the
             place
             of
             the
             Dragons
             head
             :
             The
             place
             therefore
             of
             the
             Dragons
             head
             being
             first
             giuen
             ,
             for
             the
             beginning
             of
             the
             same
             yeare
             ,
             in
             0.
             degree
             45.
             minutes
             ,
             of
             Aquarius
             :
             and
             six
             moneths
             onely
             of
             that
             yeare
             being
             passed
             ,
             I
             take
             for
             those
             six
             moneths
             6.
             degrees
             and
             6.
             halfe
             degrees
             that
             is
             9.
             degrees
             and
             sixteenth
             parts
             of
             a
             degree
             that
             is
             36.
             min.
             the
             summe
             of
             all
             which
             is
             9.
             degrees
             and
             36.
             minutes
             .
          
           
             Which
             being
             subtracted
             out
             of
             0.
             degree
             ,
             45.
             minutes
             of
             Aquarius
             ,
             there
             remaine
             21.
             degrees
             9.
             min.
             of
             Capricorne
             ,
             for
             the
             place
             of
             the
             Dragons
             head
             at
             that
             time
             .
          
        
         
           
             CHAP.
             XX.
             A
             table
             for
             finding
             the
             place
             of
             the
             Dragons
             head
             and
             taile
             more
             exactly
             and
             the
             declaration
             thereof
             .
          
           
             BVt
             if
             you
             would
             haue
             the
             place
             of
             the
             Dragons
             head
             more
             exactly
             ,
             you
             may
             find
             the
             same
             most
             easily
             ,
             by
             meanes
             of
             the
             table
             following
             ,
             for
             any
             time
             within
             the
             space
             of
             these
             20.
             yeares
             ,
             yet
             to
             come
             .
          
           
             This
             table
             conteyneth
             three
             principall
             parts
             or
             columnes
             ,
             the
             first
             part
             sheweth
             you
             in
             what
             signe
             ,
             degr
             .
             and
             min.
             the
             Dragons
             head
             is
             ,
             at
             the
             beginning
             of
             any
             yeare
             ;
             from
             this
             present
             yeare
             1600.
             till
             the
             yere
             1620.
             
             The
             second
             part
             sheweth
             how
             much
             the
             Dragons
             head
             moueth
             ,
             in
             any
             number
             of
             moneths
             of
             the
             yeare
             :
             the
             third
             part
             giueth
             you
             the
             motion
             of
             the
             Dragons
             head
             ,
             in
             any
             number
             of
             dayes
             of
             the
             moneth
             .
          
           
           
             
               
                 
                   The
                   place
                   of
                   the
                   Dragons
                   head
                   .
                
                 
                    
                
              
               
                 
                   Yeare
                
                 
                   Sign
                   .
                
                 
                   Deg.
                   
                
                 
                   Mt.
                   
                
                 
                   Moneths
                   Complete
                   .
                
                 
                   De.
                   Mi.
                   
                
                 
                   Da.
                   
                
                 
                   De.
                   Mi.
                   
                
              
               
                 
                   1600
                
                 
                   Aquarius
                
                 
                   0
                
                 
                   45
                
                 
                   Ianuary
                
                 
                   1
                   38
                
                 
                   1
                
                 
                   0
                   3
                
              
               
                 
                   1601
                
                 
                   Capricorn
                
                 
                   11
                
                 
                   21
                
                 
                   February
                
                 
                   3
                   8
                
                 
                   2
                
                 
                   0
                   6
                
              
               
                 
                   1602
                
                 
                   Sagittar
                   .
                
                 
                   22
                
                 
                   2
                
                 
                   March
                
                 
                   4
                   46
                
                 
                   3
                
                 
                   0
                   10
                
              
               
                 
                   1603
                
                 
                   Sagittar
                   .
                
                 
                   2
                
                 
                   42
                
                 
                   Aprill
                
                 
                   6
                   22
                
                 
                   4
                
                 
                   0
                   13
                
              
               
                 
                   1604
                
                 
                   Scorpio
                
                 
                   13
                
                 
                   22
                
                 
                   May
                
                 
                   8
                   0
                
                 
                   5
                
                 
                   0
                   16
                
              
               
                 
                   1605
                
                 
                   Libra
                
                 
                   23
                
                 
                   59
                
                 
                   Iune
                
                 
                   9
                   36
                
                 
                   6
                
                 
                   0
                   19
                
              
               
                 
                   1606
                
                 
                   Libra
                
                 
                   4
                
                 
                   39
                
                 
                   Iuly
                
                 
                   11
                   14
                
                 
                   7
                
                 
                   0
                   22
                
              
               
                 
                   1607
                
                 
                   Virgo
                
                 
                   15
                
                 
                   19
                
                 
                   August
                
                 
                   12
                   53
                
                 
                   8
                
                 
                   0
                   25
                
              
               
                 
                   1608
                
                 
                   Leo
                
                 
                   25
                
                 
                   59
                
                 
                   Septemb.
                   
                
                 
                   14
                   28
                
                 
                   9
                
                 
                   0
                   29
                
              
               
                 
                   1609
                
                 
                   Leo
                
                 
                   6
                
                 
                   35
                
                 
                   October
                
                 
                   16
                   7
                
                 
                   10
                
                 
                   0
                   32
                
              
               
                 
                   1610
                
                 
                   Cancer
                
                 
                   17
                
                 
                   15
                
                 
                   Nouemb.
                   
                
                 
                   17
                   42
                
                 
                   11
                
                 
                   0
                   35
                   
                
              
               
                 
                   1611
                
                 
                   Gemini
                
                 
                   27
                
                 
                   55
                
                 
                   Decemb.
                   
                
                 
                   19
                   21
                
                 
                   12
                
                 
                   0
                   38
                
              
               
                 
                   1612
                
                 
                   Gemini
                
                 
                   8
                
                 
                   35
                
                 
                    
                
                 
                    
                
                 
                   13
                
                 
                   0
                   41
                
              
               
                 
                   1613
                
                 
                   Taurus
                
                 
                   19
                
                 
                   12
                
                 
                    
                
                 
                    
                
                 
                   14
                
                 
                   0
                   44
                
              
               
                 
                   1614
                
                 
                   Aries
                
                 
                   29
                
                 
                   52
                
                 
                    
                
                 
                    
                
                 
                   15
                
                 
                   0
                   48
                
              
               
                 
                   1615
                
                 
                   Aries
                
                 
                   10
                
                 
                   32
                
                 
                    
                
                 
                    
                
                 
                   16
                
                 
                   0
                   51
                
              
               
                 
                   1616
                
                 
                   Pisces
                
                 
                   21
                
                 
                   12
                
                 
                    
                
                 
                    
                
                 
                   17
                
                 
                   0
                   54
                
              
               
                 
                   1617
                
                 
                   Pisces
                
                 
                   1
                
                 
                   49
                
                 
                    
                
                 
                    
                
                 
                   18
                
                 
                   0
                   57
                
              
               
                 
                   1618
                
                 
                   Aquarius
                
                 
                   12
                
                 
                   29
                
                 
                    
                
                 
                    
                
                 
                   19
                
                 
                   1
                   0
                
              
               
                 
                   1619
                
                 
                   Capricorn
                
                 
                   23
                
                 
                   9
                
                 
                    
                
                 
                    
                
                 
                   20
                
                 
                   1
                   4
                
              
               
                 
                   1620
                
                 
                   Capricorn
                
                 
                   3
                
                 
                   49
                
                 
                    
                
                 
                    
                
                 
                   21
                
                 
                   1
                   7
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   22
                
                 
                   1
                   10
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   23
                
                 
                   1
                   13
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   24
                
                 
                   1
                   16
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   25
                
                 
                   1
                   19
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   26
                
                 
                   1
                   13
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   27
                
                 
                   1
                   26
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   28
                
                 
                   1
                   29
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   29
                
                 
                   1
                   32
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   30
                
                 
                   1
                   35
                
              
            
          
        
         
           
           
             CHAP.
             XXI
             .
             To
             finde
             the
             place
             of
             the
             Dragons
             head
             or
             tayle
             ,
             by
             the
             former
             table
             .
          
           
             FInde
             out
             in
             the
             former
             table
             ,
             the
             moneth
             next
             going
             before
             the
             moneth
             giuen
             ;
             finde
             out
             also
             the
             day
             of
             the
             moneth
             ,
             Adde
             together
             the
             numbers
             of
             degrees
             and
             minutes
             answerable
             to
             that
             moneth
             and
             day
             of
             the
             moneth
             ,
             and
             subtract
             the
             same
             out
             of
             the
             place
             of
             the
             Dragons
             head
             at
             the
             beginning
             of
             the
             yeare
             ,
             adding
             thereto
             30.
             degr
             .
             (
             ●●at
             is
             the
             whole
             signe
             next
             going
             before
             resolued
             in
             to
             degr
             .
             )
             if
             the
             Sunne
             aforesayd
             be
             greater
             then
             the
             number
             of
             degr
             .
             shewing
             the
             place
             of
             the
             Dragons
             head
             at
             the
             beginning
             of
             the
             yeare
             :
             so
             shall
             you
             haue
             the
             place
             of
             the
             Dragons
             head
             for
             the
             time
             giuen
             .
             And
             the
             point
             of
             the
             Zodiack
             opposite
             to
             this
             ,
             is
             the
             place
             of
             the
             Dragons
             taile
             .
          
           
             Take
             for
             example
             ,
             The
             29.
             of
             Nouember
             1601.
             
             I
             find
             therefore
             against
             October
             (
             the
             moneth
             going
             next
             before
             Nouember
             )
             16.
             degrees
             7.
             minutes
             and
             against
             the
             29.
             day
             1.
             degree
             32.
             minutes
             ,
             the
             summe
             of
             both
             these
             added
             together
             is
             17.
             degrees
             39.
             min.
             the
             place
             of
             the
             Dragons
             head
             for
             the
             beginning
             of
             the
             yeare
             1601.
             is
             11.
             deg
             .
             21.
             min.
             of
             Capricorne
             ,
             which
             because
             they
             be
             lesse
             then
             17.
             deg
             .
             39.
             min.
             I
             adde
             vnto
             them
             30.
             deg
             .
             that
             is
             the
             whole
             signe
             of
             Sagittarie
             ,
             and
             the
             summe
             of
             both
             is
             41.
             deg
             .
             12.
             min.
             out
             of
             which
             subtract
             17.
             deg
             .
             39.
             min.
             and
             there
             shall
             remaine
             23.
             deg
             .
             42.
             minutes
             of
             Sagittarie
             ;
             the
             place
             of
             the
             Dragons
             head
             at
             that
             time
             .
             And
             the
             point
             of
             the
             Zodiacke
             which
             is
             opposite
             hereto
             (
             that
             is
             the
             2●
             
             〈◊〉
             42.
             minutes
             of
             Gemini
             )
             is
             the
             place
             of
             the
             〈◊〉
             tayle
             .
          
        
         
           
             CHAP.
             XXII
             .
             To
             know
             at
             what
             time
             there
             shall
             be
             an
             Eclipse
             of
             the
             Moone
             .
          
           
             THe
             place
             of
             the
             Dragons
             head
             being
             thus
             knowne
             ,
             finde
             out
             the
             same
             place
             vpon
             the
             horizon
             of
             the
             Sphaere
             ,
             and
             see
             what
             day
             and
             moneth
             answereth
             thereto
             finde
             out
             also
             the
             place
             of
             the
             full
             Moone
             ,
             which
             hapneth
             next
             before
             or
             after
             that
             day
             ,
             which
             place
             if
             it
             chance
             to
             bee
             within
             11.
             or
             12.
             deg
             .
             eyther
             before
             or
             after
             that
             point
             of
             the
             Zodiack
             which
             is
             opposite
             to
             the
             Dragons
             head
             ,
             there
             must
             needs
             be
             for
             the
             most
             part
             in
             Eclipse
             of
             the
             Moone
             .
          
           
             Likewise
             if
             you
             finde
             what
             day
             and
             moneth
             is
             answerable
             to
             the
             place
             of
             the
             Dragons
             taile
             vpon
             the
             horizon
             of
             the
             Sphaere
             if
             the
             place
             of
             the
             full
             Moone
             which
             hapneth
             next
             before
             or
             after
             that
             day
             chance
             to
             be
             within
             11.
             or
             12.
             degrees
             of
             the
             Dragons
             head
             ,
             for
             the
             most
             part
             there
             shall
             bee
             an
             Eclipse
             of
             the
             Moone
             .
          
           
             As
             for
             example
             ,
             The
             20.
             of
             Ianuarie
             last
             this
             present
             yeare
             1600.
             the
             place
             of
             the
             Dragons
             head
             was
             found
             (
             by
             the
             former
             Chapter
             )
             to
             haue
             beene
             in
             29.
             deg
             .
             41.
             min.
             of
             Capricorne
             ;
             whereto
             there
             answereth
             in
             the
             horizon
             the
             10.
             day
             of
             Ianuarie
             the
             place
             of
             the
             full
             Moone
             hapning
             next
             after
             ,
             vpon
             the
             20.
             of
             the
             same
             moneth
             in
             the
             morning
             must
             needs
             be
             in
             the
             place
             opposite
             to
             the
             place
             of
             the
             Sunne
             the
             same
             20.
             
             〈◊〉
             Therefore
             because
             〈◊〉
             Sun
             that
             day
             is
             in
             9.
             deg
             .
             〈◊〉
             one
             halfe
             of
             Aquarius
             ,
             therefore
             the
             place
          
           
           
        
      
    
     
       
         Notes, typically marginal, from the original text
         
           Notes for div A15751-e720
           
             Why
             this
             Circle
             is
             called
             the
             Equinoctiall
             or
             Equator
             .
          
        
         
           Notes for div A15751-e5910
           
             The
             scituation
             of
             the
             Orbe
             carying
             the
             Dragons
             head
             and
             tayle
             .
          
           
             The
             scituation
             of
             the
             rest
             of
             the
             Orbes
             .
          
           
             Why
             the
             Moone
             seemeth
             sometimes
             to
             moue
             swifter
             ,
             sometimes
             slower
             .
          
           
             To
             finde
             the
             Moones
             proportionall
             minutes
             .
          
           
             What
             the
             proportionall
             minutes
             of
             the
             Moone
             are
             .
          
           
             ●t
             the
             begining
             of
             the
             〈◊〉
             of
             our
             ●●rd
             .