Speculum nauticum A looking-glasse for sea-men. Wherein they may behold, how by a small instrument, called the plain-scale, all nautical questions, and astronomical propositions, are very easily and demonstratively performed. First set down by John Aspley, student in physick, and practitioner of the mathematicks in London. The sixth edition. Whereunto are added, many new propositions in navigation and astronomy, and also a third book, shewing a new way of dialling. By H.P. and W.L.
         Aspley, John.
      
       
         
           1662
        
      
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             Speculum nauticum A looking-glasse for sea-men. Wherein they may behold, how by a small instrument, called the plain-scale, all nautical questions, and astronomical propositions, are very easily and demonstratively performed. First set down by John Aspley, student in physick, and practitioner of the mathematicks in London. The sixth edition. Whereunto are added, many new propositions in navigation and astronomy, and also a third book, shewing a new way of dialling. By H.P. and W.L.
             Aspley, John.
             H. P.
             W. L., 17th cent.
          
           [4], 64 [i.e. 72] p. : ill., charts
           
             printed by W. Leybourn, for George Harlock, and are to be sold at his shop at Magnus Church-Corner, in Thames Street, near London-Bridge,
             London :
             1662.
          
           
             Page 72 misnumbered 64.
             Reproduction of original in the British Library.
          
        
      
    
     
       
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         eng
      
       
         
           Dialing -- Early works to 1800.
           Navigation -- Early works to 1800.
           Nautical astronomy -- Early works to 1800.
        
      
    
     
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           Speculum
           Nauticum
           .
        
         
           A
           Looking-Glasse
           FOR
           SEA-MEN
           .
        
         
           Wherein
           they
           may
           behold
           ,
           how
           by
           a
           small
           Instrument
           ,
           called
           the
           PLAIN
           SCALE
           ,
           all
           Nautical
           Questions
           ,
           and
           Astronomical
           Propositions
           ,
           are
           very
           easily
           and
           demonstratively
           performed
           .
        
         
           First
           set
           forth
           by
           
             John
             Aspley
             ,
          
           Student
           in
           Physick
           ,
           and
           Practitioner
           of
           the
           Mathematicks
           in
           
             London
             .
          
        
         
           The
           Sixth
           Edition
           .
        
         
           Whereunto
           are
           added
           ,
           many
           new
           Propositions
           in
           Navigation
           and
           Astronomy
           ,
           and
           also
           a
           third
           Book
           ,
           shewing
           a
           new
           way
           of
           Dialling
           .
        
         
           
             By
          
           H.
           P.
           
             and
          
           W.
           L.
           
        
         
           
             LONDON
             ,
          
           Printed
           by
           
             W.
             Leybourn
             ,
          
           for
           
             George
             Hurlock
             ,
          
           and
           are
           to
           be
           sold
           at
           his
           Shop
           at
           
             Magnus
          
           Church-Corner
           ,
           in
           
           Thames-Street
           ,
           near
           
           London-Bridge
           ,
           1662.
           
        
      
       
         
         
         
           TO
           THE
           WORSHIPFVLL
           ,
           THE
           MASTER
           ,
           WARDENS
           ,
           &
           ASSISTANTS
           OF
           THE
           TRINITY
           HOVSE
           ;
           
             JOHN
             ASPLEY
             ,
          
           IN
           TESTIMONY
           OF
           THE
           HONOUR
           HE
           BEARS
           TO
           THE
           GOVERNOURS
           &
           PRACTISERS
           OF
           THE
           ART
           OF
           NAVIGATION
           ,
           DEDICATES
           THESE
           HIS
           FIRST
           LABOURS
           .
        
      
       
         
         
           The
           Printer
           to
           the
           Reader
           .
        
         
           THis
           little
           book
           having
           been
           well
           accepted
           of
           among
           Sea-men
           ,
           being
           the
           first
           fruites
           of
           Mr.
           
             Aspley's
          
           Mathematical
           Studies
           ,
           hath
           passed
           five
           Impressions
           ,
           without
           any
           alteration
           ;
           and
           so
           I
           doubt
           not
           might
           have
           done
           still
           :
           But
           because
           since
           that
           time
           there
           have
           been
           severall
           bookes
           put
           out
           of
           this
           nature
           ,
           I
           have
           procured
           this
           to
           be
           revised
           ,
           and
           severall
           alterations
           and
           additions
           to
           be
           made
           therein
           ,
           So
           that
           here
           you
           have
           both
           the
           old
           ,
           and
           a
           new
           booke
           intermingled
           all
           in
           one
           ,
           with
           a
           third
           part
           added
           thereto
           ,
           concerning
           Dialling
           ▪
           by
           a
           way
           not
           formerly
           published
           by
           any
           .
           All
           which
           I
           doubt
           not
           you
           will
           kindly
           accept
           of
           ,
           and
           receive
           much
           delight
           and
           profit
           thereby
           .
        
         
           
             Your
             .
             G.
             H.
             
          
        
      
       
         
           ERRATA
           .
        
         
           PAge
           34
           line
           26
           read
           360.
           
           Page
           .
           45.
           l.
           8.
           r.
           Distance
           I
           M.
           Page
           50.
           line
           13.
           for
           14
           &c.
           〈…〉
           which
           is
           just
           the
           length
           of
           the
           Gnomon
           .
           Page
           .
           50
           line
           .
           28.
           for
           increase
           ,
           read
           decrease
           ,
           Page
           52
           line
           4.
           r.
           H
           A
           I.
           line
           18.
           r.
           point
           O.
           Page
           57
           line
           11
           r.
           point
           L.
           
        
         
           Also
           for
           some
           lite●all
           faults
           we
           shall
           desire
           your
           Pardon
           ▪
        
      
    
     
       
         
         
           
             Speculum
             Nauticum
             ,
          
           OR
           THE
           SEA-MANS
           GLASSE
           .
        
         
           The
           First
           Book
           .
        
         
           
             CHAP.
             I.
             
          
           
             The
             Explanation
             of
             certain
             Terms
             of
             Geometry
             .
          
           
             BEing
             intended
             in
             this
             Treatise
             of
             the
             plain
             Scale
             ,
             to
             declare
             the
             manner
             of
             projection
             of
             the
             Sphere
             ,
             
               in
               plano
               ,
            
             I
             have
             thought
             fitting
             first
             ,
             to
             shew
             unto
             you
             some
             tearms
             of
             Geometry
             which
             are
             necessary
             for
             the
             unlearned
             to
             know
             ,
             (
             for
             whose
             sake
             chiefly
             I
             write
             this
             Treatise
             )
             before
             they
             enter
             into
             the
             definition
             of
             the
             Sphere
             .
             First
             therefore
             I
             intend
             to
             relate
             unto
             you
             ,
             what
             a
             point
             or
             prick
             is
             ,
             
             and
             afterward
             a
             Line
             both
             right
             and
             crooked
             ,
             and
             such
             sorts
             thereof
             as
             are
             appertinent
             unto
             the
             operations
             and
             use
             of
             this
             Scale
             .
          
           
             
               Punctum
               ,
            
             or
             a
             point
             ,
             is
             the
             beginning
             of
             things
             ,
             or
             a
             prick
             supposed
             indivisible
             ,
             void
             of
             length
             ,
             breadth
             ,
             and
             depth
             :
             as
             in
             the
             Figure
             following
             is
             noted
             by
             the
             point
             ,
             or
             prick
             A.
             
          
           
             
               Linea
               ,
            
             or
             a
             Line
             ,
             is
             a
             supposed
             length
             ,
             or
             a
             thing
             extending
             it self
             in
             length
             ,
             not
             having
             breadth
             nor
             thickness
             ,
             as
             is
             set
             forth
             unto
             you
             by
             the
             Line
             BAD
             .
          
           
           
             
               Parallela
               ,
            
             or
             a
             Parallel
             Line
             ,
             is
             a
             line
             drawn
             by
             the
             side
             of
             another
             line
             ,
             in
             such
             sort
             that
             they
             may
             be
             equidistant
             in
             all
             places
             .
             And
             of
             such
             parallels
             ,
             two
             only
             belong
             unto
             this
             work
             of
             the
             plain
             Scale
             ,
             that
             is
             to
             say
             ,
             the
             right
             lined
             Parallel
             ,
             and
             the
             circular
             Parallel
             .
          
           
             Right
             lined
             Parallels
             are
             two
             right
             lines
             equidistant
             one
             from
             another
             ,
             which
             being
             drawn
             forth
             infinitely
             ,
             would
             never
             touch
             or
             meet
             one
             another
             ,
             as
             you
             may
             see
             in
             the
             Figure
             ,
             where
             the
             line
             H
             I
             is
             Parallel
             unto
             the
             line
             CE
             ,
             and
             the
             line
             GF
             is
             Parallel
             unto
             them
             both
             .
          
           
           
             A
             circular
             Parallel
             is
             a
             circle
             drawn
             either
             within
             or
             without
             another
             circle
             upon
             the
             same
             center
             ,
             as
             you
             may
             plainly
             see
             by
             the
             two
             circles
             BCDE
             ,
             and
             XVYW
             .
             These
             circles
             are
             both
             drawn
             upon
             the
             center
             A
             ,
             and
             therefore
             are
             parallel
             the
             one
             unto
             the
             other
             .
             There
             is
             another
             kind
             of
             Parallel
             also
             ,
             which
             is
             called
             a
             Serpentine
             Parallel
             ,
             but
             because
             it
             is
             not
             belonging
             unto
             the
             use
             of
             this
             Scale
             ,
             I
             will
             omit
             it
             ,
             and
             so
             proceed
             unto
             the
             rest
             .
          
           
             
               Perpendiculum
               ,
            
             or
             a
             Perpendicular
             is
             a
             line
             raised
             from
             ,
             or
             let
             fall
             upon
             ,
             another
             line
             ,
             making
             equal
             Angles
             on
             both
             sides
             ,
             as
             you
             may
             see
             declared
             in
             the
             figure
             ,
             where
             in
             the
             line
             AC
             is
             perpendicular
             unto
             the
             line
             BAD
             ,
             making
             equal
             ●ngles
             in
             the
             point
             A.
             
          
           
             
               Diameter
               circuli
               ,
            
             or
             the
             Diameter
             of
             a
             Circle
             ,
             is
             a
             right
             line
             drawn
             thorow
             the
             center
             of
             any
             circle
             ,
             in
             such
             sort
             that
             it
             may
             divide
             the
             circle
             into
             two
             equal
             parts
             ,
             as
             you
             may
             see
             the
             line
             BAD
             is
             the
             Diameter
             of
             the
             circle
             BCDE
             ,
             because
             it
             passeth
             thorow
             the
             center
             A
             ,
             and
             the
             two
             ends
             thereof
             do
             divide
             the
             circle
             into
             two
             equal
             parts
             ,
             in
             the
             two
             extreams
             B
             and
             D
             ,
             making
             the
             semicircle
             BCD
             equal
             unto
             the
             semicircle
             DEB
             .
          
           
             
               Semidiameter
               circuli
               ,
            
             or
             the
             semidiameter
             of
             a
             circle
             is
             half
             of
             the
             Diameter
             ,
             and
             is
             contained
             betwixt
             the
             center
             ,
             and
             the
             one
             side
             of
             the
             circle
             ,
             as
             the
             line
             AD
             is
             the
             Semidiameter
             of
             the
             circle
             BCDE
             .
             This
             Semidiameter
             contains
             60
             degrees
             of
             the
             line
             of
             Chords
             ,
             which
             we
             sometimes
             call
             the
             Radius
             .
          
           
             
               Semicirculus
               ,
            
             or
             a
             Semicircle
             ,
             is
             the
             one
             half
             of
             a
             circle
             ,
             drawn
             upon
             his
             Diameter
             ,
             and
             is
             contained
             upon
             the
             Superficies
             ,
             or
             Surface
             ,
             of
             the
             Diameter
             ,
             as
             the
             Semicircle
             BCD
             which
             is
             half
             of
             the
             circle
             BCDE
             ,
             and
             is
             contained
             above
             the
             Diameter
             BAD
             .
          
           
             
               Quadrans
               circuli
               ,
            
             is
             the
             fourth
             part
             of
             a
             circle
             ,
             and
             is
             contained
             betwixt
             the
             Semidiameter
             of
             the
             circle
             ,
             and
             a
             line
             drawn
             Perpendicular
             ,
             unto
             the
             Diameter
             of
             the
             same
             circle
             ,
             from
             the
             Center
             thereof
             ,
             dividing
             the
             Semicircle
             into
             two
             equal
             parts
             ,
             of
             the
             which
             parts
             ,
             the
             one
             is
             the
             Quadrant
             ,
             or
             fourth
             part
             of
             the
             same
             circle
             .
             As
             for
             example
             ,
             the
             Diameter
             of
             the
             circle
             BCDE
             is
             the
             line
             BAD
             ,
             dividing
             the
             circle
             into
             two
             equal
             parts
             :
             then
             from
             the
             center
             A
             raise
             the
             Perpendicular
             AC
             ,
             dividing
             the
             Semicircle
             likewise
             into
             two
             equal
             parts
             ;
             so
             is
             ABC
             ,
             or
             ACD
             ,
             the
             Quadrant
             of
             the
             circle
             BCDE
             ,
             which
             was
             desired
             .
          
        
         
           
           
             CHAP.
             II.
             
          
           
             The
             manner
             how
             to
             raise
             a
             Perpendicular
             from
             the
             middle
             of
             a
             line
             given
             .
          
           
             〈◊〉
             first
             a
             ground
             line
             whereupon
             you
             would
             have
             a
             Perpendicular
             raised
             ,
             then
             open
             your
             Compasses
             unto
             any
             distance
             (
             so
             it
             exceed
             not
             the
             end
             of
             your
             line
             ,
             )
             placing
             one
             foot
             of
             the
             said
             Compasses
             in
             the
             point
             from
             whence
             the
             Perpendicular
             is
             ●o
             be
             raised
             ,
             and
             with
             the
             other
             foot
             make
             a
             mark
             in
             the
             line
             on
             〈…〉
             removing
             your
             Compasses
             unto
             any
             other
             distance
             that
             〈…〉
             set
             one
             foot
             thereof
             in
             one
             of
             the
             marks
             ,
             and
             with
             the
             〈◊〉
             foot
             make
             an
             Arch
             over
             the
             middle
             point
             ,
             then
             with
             the
             same
             distance
             of
             your
             Compasses
             set
             one
             foot
             in
             the
             other
             mark
             upon
             the
             line
             ,
             and
             with
             the
             other
             foot
             make
             another
             Arch
             of
             a
             Circle
             over
             the
             middle
             Point
             ,
             so
             that
             it
             may
             cross
             the
             first
             Arch
             ,
             and
             from
             the
             meeting
             of
             these
             two
             Arches
             ,
             draw
             a
             right
             line
             unto
             the
             middle
             Point
             ,
             from
             which
             the
             Perpendicular
             was
             to
             be
             raised
             ,
             which
             line
             shall
             be
             the
             Perpendicular
             desired
             .
          
           
           
             Example
             ,
             suppose
             your
             Base
             or
             ground
             line
             whereupon
             a
             Perpendicular
             is
             to
             be
             raised
             be
             the
             line
             FLK
             ,
             and
             from
             L
             the
             Perpendicular
             is
             to
             be
             raised
             ,
             set
             one
             foot
             of
             your
             Compasses
             in
             the
             Point
             L
             ,
             and
             with
             the
             other
             ,
             make
             the
             marks
             G
             and
             M
             on
             both
             sides
             of
             the
             point
             L
             ,
             the●
             opening
             your
             Compasses
             wider
             ,
             set
             one
             foot
             in
             the
             point
             M
             ,
             and
             with
             the
             other
             draw
             the
             Arch
             S
             over
             the
             point
             L
             ,
             
             then
             with
             the
             same
             distance
             of
             your
             Compasses
             ,
             set
             one
             foot
             in
             G
             ,
             and
             with
             the
             other
             make
             the
             Arch
             R
             ,
             crossing
             the
             Arch
             S
             in
             the
             point
             T
             ,
             then
             from
             T
             draw
             the
             line
             TL
             ,
             which
             line
             is
             perpendicular
             unto
             the
             line
             FLK
             from
             the
             point
             L
             ,
             which
             is
             the
             perpendicular
             desired
             .
          
        
         
           
             CHAP.
             III.
             
          
           
             To
             let
             a
             Perpendicular
             fall
             from
             any
             Point
             assigned
             ,
             unto
             the
             middle
             of
             a
             line
             .
          
           
             LET
             the
             line
             whereupon
             you
             would
             have
             a
             Perpendicular
             let
             fall
             be
             the
             line
             LFK
             ,
             and
             the
             point
             assigned
             to
             be
             the
             point
             T
             ,
             from
             whence
             you
             would
             have
             a
             Perpendicular
             let
             fall
             upon
             the
             line
             FLK
             ,
             first
             set
             one
             foot
             of
             your
             Compasses
             in
             T
             ,
             and
             open
             your
             Compasses
             unto
             any
             distance
             so
             that
             it
             be
             more
             than
             the
             distance
             TL
             ,
             which
             here
             we
             suppose
             to
             be
             the
             distance
             TM
             ;
             then
             make
             in
             the
             line
             FLK
             the
             marks
             G
             and
             M
             ,
             then
             with
             your
             Compasses
             take
             the
             one
             half
             of
             GM
             ,
             which
             is
             the
             point
             L
             ,
             then
             from
             L
             draw
             a
             line
             unto
             the
             point
             T
             ,
             so
             the
             line
             TL
             shall
             be
             the
             Perpendicular
             ,
             which
             was
             desired
             to
             be
             let
             fall
             from
             the
             assigned
             point
             T
             unto
             the
             middle
             of
             the
             line
             FLK
             .
          
        
         
           
             CHAP.
             IV.
             
          
           
             To
             raise
             a
             Perpendicular
             upon
             the
             end
             of
             a
             Line
             .
          
           
             SUppose
             the
             line
             whereupon
             you
             would
             have
             a
             Perpendicular
             raised
             ,
             be
             the
             line
             FLK
             ,
             and
             from
             the
             point
             F
             a
             Perpendicular
             is
             to
             be
             raised
             :
             first
             open
             your
             Compasses
             unto
             any
             distance
             ,
             which
             here
             we
             put
             to
             be
             the
             distance
             FG
             ,
             and
             set
             one
             foot
             of
             your
             Compasses
             in
             the
             point
             F
             ,
             and
             with
             the
             other
             draw
             the
             Arch
             DEG
             ,
             then
             set
             one
             foot
             of
             your
             Compasses
             in
             the
             point
             G
             ,
             and
             with
             the
             other
             draw
             the
             Arch
             E
             ;
             then
             placing
             one
             point
             of
             your
             Compasses
             in
             E
             ,
             with
             the
             other
             draw
             the
             Arch
             DB
             ;
             then
             place
             your
             
             Compasses
             in
             D
             ,
             and
             with
             the
             same
             distance
             draw
             the
             Arch
             A
             ,
             cutting
             the
             Arch
             DB
             in
             C
             ,
             then
             draw
             a
             line
             from
             C
             unto
             the
             end
             of
             the
             line
             FLK
             ,
             unto
             the
             assigned
             point
             F
             ,
             so
             shall
             the
             line
             CF
             be
             a
             Perpendicular
             raised
             from
             the
             end
             of
             the
             line
             FLK
             ,
             and
             from
             the
             assigned
             point
             F.
             
          
        
         
           
             CHAP.
             V.
             
          
           
             To
             let
             a
             Perpendicular
             fall
             from
             any
             point
             assigned
             unto
             the
             end
             of
             a
             Line
             .
          
           
             LET
             the
             line
             FLK
             be
             the
             Base
             or
             ground
             line
             ,
             and
             from
             the
             point
             I
             a
             Perpendicular
             is
             to
             be
             let
             fall
             upon
             the
             end
             of
             the
             line
             at
             K
             ,
             first
             from
             the
             assigned
             point
             I
             ,
             draw
             a
             line
             unto
             any
             part
             of
             the
             Base
             ,
             which
             shall
             be
             the
             line
             IHM
             ,
             then
             find
             the
             middle
             of
             the
             line
             IM
             ,
             which
             is
             at
             H
             ;
             place
             therefore
             one
             foot
             
             of
             your
             Compasses
             in
             the
             point
             H
             ,
             and
             extend
             the
             other
             unto
             I
             ,
             with
             which
             distance
             draw
             the
             Arch
             INK
             upon
             the
             Center
             H
             ,
             cutting
             the
             Base
             or
             ground-line
             in
             the
             point
             K
             ,
             then
             draw
             the
             line
             KI
             ,
             which
             line
             shall
             be
             the
             Perpendicular
             desired
             .
          
        
         
           
           
             CHAP.
             VI.
             
          
           
             A
             right
             Line
             being
             given
             ,
             how
             to
             draw
             another
             parallel
             there
             unto
             at
             any
             distance
             required
             .
          
           
             LEt
             the
             line
             given
             be
             AB
             ,
             unto
             which
             it
             is
             required
             to
             draw
             another
             right
             line
             CD
             which
             shall
             be
             parallel
             to
             the
             former
             line
             AB
             ,
             and
             at
             the
             distance
             AC
             .
          
           
             First
             open
             your
             Compasses
             to
             the
             distance
             AC
             ,
             then
             set
             one
             foot
             in
             the
             point
             A
             ,
             with
             the
             
             other
             describe
             the
             Arch
             C
             ;
             again
             ,
             place
             one
             foot
             in
             B
             ,
             and
             with
             the
             other
             describe
             the
             Arch
             D
             ;
             Then
             draw
             the
             line
             CD
             ,
             so
             that
             it
             may
             only
             touch
             the
             two
             Arches
             C
             and
             D
             ,
             so
             shall
             the
             line
             CD
             ,
             so
             drawn
             ,
             be
             parallel
             to
             AB
             ,
             and
             at
             the
             distance
             required
             .
          
        
         
           
             CHAP.
             VII
             .
          
           
             A
             right
             line
             being
             given
             ,
             how
             to
             draw
             another
             parallel
             thereunto
             ,
             which
             shall
             also
             pass
             through
             a
             point
             assigned
             .
          
           
             LEt
             AB
             be
             a
             line
             given
             ,
             and
             the
             point
             assigned
             be
             C
             :
             and
             let
             it
             be
             required
             to
             draw
             another
             line
             parallel
             thereunto
             ,
             which
             shall
             pass
             through
             the
             given
             point
             C.
             
          
           
           
             NOw
             I
             doubt
             not
             but
             you
             understand
             the
             way
             to
             let
             fal
             ,
             or
             to
             raise
             any
             manner
             of
             Perpendicular
             line
             ,
             either
             from
             ,
             or
             upon
             any
             part
             of
             a
             line
             :
             as
             also
             to
             draw
             lines
             parallel
             one
             to
             another
             at
             any
             distance
             required
             ,
             therefore
             now
             I
             intend
             to
             proceed
             unto
             the
             main
             point
             here
             aimed
             at
             ,
             which
             is
             ,
             to
             declare
             ,
             and
             make
             known
             unto
             you
             the
             several
             operations
             performed
             by
             the
             plain
             Scale
             ,
             which
             though
             it
             be
             in
             use
             with
             very
             few
             ,
             yet
             it
             is
             most
             necessary
             for
             Sea-men
             ,
             because
             all
             questions
             in
             Navigation
             are
             thereby
             easily
             and
             plainly
             wrought
             .
             And
             also
             all
             questions
             in
             Astronomy
             (
             belonging
             unto
             the
             expert
             ,
             and
             industrious
             Sea-men
             )
             may
             both
             speedily
             and
             easily
             be
             wrought
             by
             the
             same
             Scale
             :
             in
             regard
             whereof
             I
             have
             declared
             in
             this
             little
             Book
             ,
             that
             knowledge
             (
             which
             God
             hath
             been
             pleased
             to
             bestow
             upon
             me
             )
             concerning
             the
             necessary
             use
             and
             practice
             thereof
             ;
             hoping
             that
             you
             will
             as
             kindly
             accept
             it
             ,
             as
             it
             is
             freely
             offered
             unto
             your
             courteous
             considerations
             .
          
        
         
           
           
             CHAP.
             VIII
             .
          
           
             Of
             the
             description
             of
             the
             Scale
             .
          
           
             
               The
               figure
               of
               the
               plane
               Scale
               .
            
          
           
             The
             second
             part
             of
             the
             Scale
             ,
             is
             the
             single
             Chorde
             of
             a
             circle
             ,
             or
             the
             Chord
             of
             90
             ,
             and
             is
             divided
             into
             90
             unequal
             divisions
             ,
             representing
             the
             90
             degrees
             of
             the
             Quadrant
             :
             and
             are
             numbred
             with
             10
             ,
             20
             ,
             30
             ,
             40
             ,
             &c.
             unto
             90.
             
             This
             Ghord
             is
             in
             use
             to
             measure
             any
             part
             or
             Arch
             of
             a
             circle
             ,
             not
             surmounting
             90
             degrees
             :
             The
             number
             of
             these
             degrees
             from
             1
             unto
             60
             is
             called
             the
             Radius
             of
             the
             Scale
             ,
             upon
             which
             distance
             all
             circles
             are
             to
             be
             drawn
             ,
             whereupon
             60
             of
             th●se
             Degrees
             are
             the
             Semidiameter
             of
             any
             Circle
             that
             is
             drawn
             upon
             that
             Radius
             .
          
           
             The
             third
             part
             of
             the
             Scale
             is
             divided
             into
             eight
             parts
             ,
             representing
             the
             Points
             or
             Rumbes
             of
             the
             Mariners
             Compass
             ;
             which
             in
             all
             
             are
             32
             points
             :
             but
             upon
             the
             Scale
             there
             are
             only
             S
             reckoned
             ,
             which
             is
             but
             one
             Quadrant
             or
             quarter
             of
             them
             ,
             being
             to
             be
             reckoned
             from
             the
             Meridian
             of
             North
             and
             South
             both
             wayes
             ,
             as
             you
             may
             see
             more
             plainly
             by
             this
             figure
             ,
             representing
             the
             order
             of
             the
             points
             of
             the
             Compasse
             .
          
           
           
             It
             is
             usuall
             also
             to
             have
             another
             line
             placed
             upon
             your
             Scale
             ,
             to
             she●
             you
             how
             many
             leagues
             make
             a
             degree
             of
             longitude
             in
             every
             latitude
             ,
             concerning
             which
             you
             shall
             have
             directions
             in
             the
             14
             Chapter
             following
             .
          
        
         
           
           
             CHAP.
             IX
             .
          
           
             Knowing
             the
             course
             any
             ship
             hath
             made
             ,
             and
             the
             leagues
             she
             hath
             sailed
             :
             to
             find
             how
             much
             she
             hath
             raised
             or
             depressed
             the
             Pole
             ;
             and
             likewise
             how
             much
             she
             is
             departed
             from
             her
             first
             Meridian
             .
          
           
             The
             Course
             is
             South-west
             and
             by
             South
             ,
             the
             leagues
             sailed
             are
             
               100
               ,
            
             the
             difference
             of
             the
             Latitude
             ,
             and
             the
             distance
             of
             the
             Meridians
             is
             required
             .
          
           
           
             Now
             you
             must
             heedfully
             observe
             this
             point
             D
             ,
             for
             this
             represents
             the
             place
             where
             your
             Ship
             is
             ,
             and
             doth
             shew
             both
             the
             differencefo
             the
             latitude
             of
             the
             place
             you
             are
             in
             ,
             and
             also
             your
             distance
             or
             departure
             from
             your
             first
             meridian
             .
          
           
             First
             for
             the
             latitude
             ,
             you
             see
             the
             line
             DF
             ,
             being
             paralel
             to
             the
             
             line
             AB
             ,
             cuts
             the
             Meridian
             line
             AF
             in
             the
             point
             F
             :
             So
             that
             if
             you
             take
             the
             distance
             FA
             with
             your
             Compasses
             ,
             and
             apply
             it
             to
             the
             scale
             of
             equal
             leagues
             ,
             you
             shall
             find
             it
             is
             just
             83
             leagues
             ,
             which
             counting
             20
             leagues
             to
             a
             degree
             ,
             makes
             4
             degrees
             9
             min.
             and
             so
             much
             you
             have
             altered
             your
             latitude
             by
             the
             said
             course
             ,
             which
             degrees
             and
             minutes
             being
             added
             to
             ,
             or
             substracted
             from
             the
             latitude
             of
             the
             place
             you
             came
             from
             ,
             according
             as
             your
             course
             requires
             ,
             shews
             you
             alwaies
             the
             true
             latitude
             you
             are
             in
             .
          
           
             Likewise
             from
             this
             point
             D
             ,
             take
             with
             your
             Compasses
             the
             distance
             DF
             ,
             and
             you
             shall
             find
             it
             by
             your
             scale
             of
             equal
             leagues
             to
             be
             56
             leagues
             ,
             and
             so
             much
             you
             are
             departed
             from
             your
             first
             Meridian
             to
             the
             West-ward
             ;
             which
             when
             you
             are
             near
             the
             Equinoctial
             ,
             where
             the
             degrees
             of
             longitude
             are
             equal
             to
             the
             degrees
             of
             latitude
             ,
             would
             shew
             the
             longitude
             ,
             by
             taking
             20
             leagues
             for
             one
             degree
             ,
             &c.
             so
             it
             would
             be
             two
             degrees
             ,
             and
             48
             min.
             for
             your
             difference
             of
             longitude
             ,
             from
             y●ur
             first
             Meridian
             AF.
             But
             in
             other
             places
             ,
             you
             must
             first
             〈◊〉
             howmany
             leagues
             make
             a
             degree
             of
             longitude
             about
             that
             latitude
             where
             you
             are
             ,
             and
             so
             turn
             your
             leagues
             of
             distance
             from
             the
             Meridian
             ,
             into
             degrees
             and
             minutes
             of
             longitude
             ,
             of
             which
             more
             hereafter
             ,
             Chap.
             14.
             
          
           
             I
             have
             been
             the
             larger
             in
             these
             two
             Propositions
             ,
             because
             they
             are
             ●he
             first
             ,
             for
             the
             better
             understanding
             of
             all
             the
             rest
             ;
             and
             because
             they
             are
             most
             necessary
             ,
             for
             thereupon
             depends
             the
             knowledge
             of
             the
             true
             Traverse
             point
             ,
             and
             the
             keeping
             of
             your
             dead
             reckoning
             .
             Now
             because
             this
             cannot
             alwaies
             be
             kept
             exactly
             ,
             it
             is
             to
             be
             corrected
             by
             the
             observation
             of
             the
             latitude
             ,
             according
             to
             this
             following
             proposition
             .
          
        
         
           
           
             CHAP.
             X.
             
          
           
             Knowi
             g
             the
             difference
             of
             latitude
             of
             two
             places
             ,
             and
             the
             Rumb
             you
             have
             sailed
             upon
             ,
             to
             find
             the
             leagues
             you
             have
             sailed
             ,
             and
             the
             difference
             of
             Meridians
             .
          
           
             The
             Pole
             depressed
             four
             degrees
             and
             the
             Rumb
             South-West
             by
             South
             or
             the
             third
             from
             the
             Meridian
             ,
             to
             find
             your
             true
             Traverse
             point
             ,
             
               viz.
            
             how
             far
             you
             have
             sailed
             ,
             and
             how
             much
             you
             are
             departed
             from
             your
             first
             Meridian
             .
          
           
             In
             the
             first
             figure
          
           
             DRaw
             the
             lines
             as
             in
             the
             former
             Chapter
             ,
             so
             that
             AKF
             may
             represent
             the
             Meridian
             line
             ,
             and
             ACD
             may
             represent
             the
             third
             Rumb
             from
             the
             meridian
             ;
             then
             because
             you
             have
             altered
             your
             latitude
             4
             degrees
             ,
             which
             make
             80
             leagues
             ,
             take
             80
             leagues
             with
             your
             Compasses
             out
             of
             your
             Scale
             ,
             and
             set
             them
             upon
             the
             
             meridian
             line
             AF
             ,
             from
             A
             to
             L
             :
             Then
             keeping
             the
             same
             distance
             of
             your
             Compasses
             ,
             draw
             the
             line
             LM
             parallel
             to
             AB
             ,
             (
             or
             else
             you
             may
             erect
             LM
             perpendicular
             to
             the
             line
             AF
             ,
             in
             the
             point
             L
             )
             and
             mark
             where
             the
             said
             LM
             crosseth
             the
             Rumb
             line
             ACD
             ,
             which
             is
             in
             the
             point
             M.
             This
             point
             M
             is
             the
             true
             Traverse
             point
             ,
             the
             leagues
             sailed
             are
             shewed
             by
             the
             line
             AM
             ,
             which
             being
             measured
             in
             the
             Scale
             ,
             will
             be
             found
             to
             be
             96
             leagues
             and
             an
             half
             ,
             and
             the
             departure
             from
             the
             Meridian
             is
             LM
             ,
             which
             is
             54
             leagues
             .
          
           
             Now
             by
             this
             Proposition
             (
             as
             I
             said
             )
             you
             may
             correct
             your
             dead
             reckoning
             ;
             for
             suppose
             by
             the
             former
             proposition
             you
             reckon
             you
             had
             sailed
             100
             leagues
             upon
             the
             ●hird
             Rumb
             ,
             then
             as
             you
             see
             there
             ,
             you
             should
             have
             been
             at
             the
             point
             D
             ,
             and
             have
             altered
             your
             latitude
             
             83
             leagues
             ,
             and
             departed
             from
             your
             Meridian
             56
             leagues
             ;
             but
             now
             suppose
             that
             by
             a
             good
             observation
             of
             the
             latitude
             ,
             you
             find
             that
             you
             have
             altered
             the
             latitude
             onely
             80
             leagues
             ,
             from
             A
             to
             L
             ,
             by
             drawing
             this
             line
             LM
             ,
             which
             crosseth
             the
             Rumb
             or
             Ships
             way
             in
             M
             ,
             you
             may
             conclude
             your
             true
             Traverse
             point
             to
             be
             at
             M
             ,
             so
             that
             you
             have
             sailed
             only
             from
             A
             to
             M
             ,
             which
             is
             96
             leagues
             ½
             ,
             and
             departed
             from
             your
             Meridian
             54
             leagues
             .
             So
             that
             as
             you
             are
             short
             of
             the
             latitude
             you
             reckoned
             for
             3
             leagues
             or
             9
             min.
             you
             are
             also
             short
             of
             your
             way
             you
             reckoned
             3
             leagues
             ½
             ,
             and
             two
             leagues
             less
             in
             your
             departure
             from
             the
             Meridian
             .
             And
             this
             you
             must
             account
             for
             your
             true
             reckoning
             ,
             being
             thus
             corrected
             .
          
        
         
           
             CHAP.
             XI
             .
          
           
             By
             the
             difference
             of
             the
             latitudes
             of
             two
             places
             and
             the
             distance
             between
             their
             Meridians
             ,
             to
             find
             the
             Rumb
             by
             which
             you
             must
             sail
             from
             the
             one
             place
             to
             the
             other
             ,
             and
             how
             far
             it
             is
             from
             the
             one
             place
             to
             the
             other
             ?
          
           
             The
             difference
             of
             latitude
             between
             the
             two
             places
             is
             
               4
            
             deg
             .
             
               9
            
             min.
             and
             the
             distance
             between
             the
             two
             Meridians
             is
             
               56
            
             leagues
             ,
             and
             it
             is
             required
             to
             find
             the
             Rumb
             from
             the
             one
             place
             to
             the
             other
             .
          
           
             IN
             the
             former
             figure
             draw
             the
             quadrant
             AKCB
             ,
             then
             turn
             your
             four
             degrees
             9
             min.
             of
             latitude
             into
             leagues
             ,
             it
             maketh
             83
             leagues
             ,
             which
             you
             must
             place
             upon
             the
             meridian
             line
             from
             A
             to
             F.
             And
             from
             the
             point
             F
             draw
             the
             line
             FD
             parallel
             to
             the
             line
             AB
             .
             Then
             open
             your
             Compasses
             to
             the
             distance
             of
             the
             meridians
             which
             is
             56
             leagues
             ,
             and
             set
             it
             on
             the
             line
             FD
             ,
             from
             F
             to
             D.
             Then
             lay
             your
             Ruler
             by
             this
             mark
             D
             and
             the
             Centre
             A
             ,
             and
             draw
             the
             line
             ACD
             .
             Then
             mark
             where
             this
             line
             cuts
             the
             quadrant
             ,
             which
             is
             in
             the
             point
             C
             ,
             and
             setting
             one
             foot
             of
             your
             Compasses
             in
             the
             point
             C
             ,
             open
             the
             other
             to
             K
             ,
             and
             keeping
             your
             Compasses
             at
             that
             distance
             CK
             ,
             measure
             it
             upon
             your
             Scale
             ,
             either
             in
             the
             line
             of
             Chords
             ,
             or
             in
             the
             line
             of
             Rumbs
             ,
             you
             sh
             ll
             find
             it
             to
             be
             in
             the
             one
             33
             deg
             .
             45
             min.
             and
             in
             the
             other
             just
             the
             third
             Rumb
             from
             the
             meridian
             .
             So
             that
             the
             Rumb
             from
             A
             〈◊〉
             D
             ●s
             South-west
             and
             by
             South
             ,
             and
             the
             Rumb
             from
             D
             to
             A
             is
             the
             Rumb
             opposite
             thereunto
             ,
             which
             is
             North-east
             and
             by
             North.
             
          
           
           
             Then
             for
             the
             distance
             between
             the
             two
             places
             in
             the
             Rumb
             ,
             ●et
             one
             foot
             of
             your
             Compasses
             in
             the
             one
             place
             at
             A
             ,
             and
             open
             the
             other
             to
             the
             other
             place
             at
             D
             ,
             and
             the
             length
             of
             the
             line
             A
             D
             ineasured
             in
             the
             Scale
             of
             leagues
             ,
             shews
             the
             distance
             between
             them
             to
             be
             just
             100
             leagues
             .
          
           
             These
             three
             (
             or
             rather
             these
             six
             )
             Propositions
             ,
             (
             for
             they
             are
             each
             of
             them
             double
             )
             are
             the
             most
             usefull
             and
             necessary
             in
             the
             art
             of
             Navigation
             .
             By
             the
             first
             of
             these
             ,
             knowing
             the
             point
             of
             the
             Compass
             you
             ●ail
             upon
             ,
             and
             judging
             howmany
             leagues
             you
             have
             sailed
             thereon
             ,
             you
             know
             and
             are
             able
             to
             give
             a
             reasonable
             account
             where
             you
             are
             ,
             both
             in
             respect
             of
             latitude
             and
             longitude
             .
             By
             the
             second
             having
             a
             fair
             observation
             of
             the
             latitude
             at
             any
             time
             ,
             you
             may
             more
             perfectly
             know
             where
             you
             are
             ;
             and
             thereby
             correct
             your
             former
             account
             .
             And
             by
             this
             third
             you
             may
             know
             how
             to
             direct
             your
             course
             from
             any
             place
             to
             your
             desired
             haven
             .
             So
             that
             in
             effect
             you
             need
             no
             more
             ,
             but
             yet
             for
             your
             better
             instruction
             by
             variety
             of
             cases
             and
             examples
             ,
             I
             shall
             proceed
             .
          
        
         
           
             CHAP.
             XII
             .
          
           
             The
             difference
             of
             Latitude
             and
             the
             lea●●es
             sailed
             being
             given
             ,
             to
             find
             the
             distanee
             from
             the
             Meridian
             ,
             and
             the
             Rumb
             you
             have
             sailed
             upon
             .
          
           
             Sailing
             
               100
            
             leagues
             between
             South
             and
             West
             ,
             untill
             the
             Pole
             be
             depressed
             
               4
            
             deg
             .
             
               9
            
             min.
             the
             distance
             from
             the
             Meridian
             is
             demanded
             ,
             and
             what
             Rumb
             you
             have
             sailed
             upon
             ?
          
           
             IN
             the
             first
             figure
             draw
             the
             Quadrant
             AKCB
             ,
             as
             in
             the
             former
             Chapters
             ,
             and
             then
             reduce
             your
             degrees
             of
             latitude
             into
             leagues
             ,
             so
             4
             deg
             .
             9
             min.
             make
             83
             leagues
             ,
             which
             you
             must
             take
             with
             your
             Compasses
             out
             of
             your
             Scale
             of
             leagues
             ,
             and
             set
             them
             off
             in
             this
             Meridian
             line
             from
             A
             to
             F.
             Then
             from
             the
             point
             F
             draw
             the
             line
             FD
             ,
             parallel
             to
             the
             line
             AB
             ,
             which
             you
             may
             do
             with
             the
             foresaid
             distance
             of
             your
             Compasses
             .
             Then
             open
             your
             Compasses
             unto
             your
             distance
             failed
             ,
             which
             is
             100
             leagues
             ,
             and
             setting
             one
             foot
             of
             your
             Compasses
             in
             the
             point
             A
             ,
             with
             the
             other
             draw
             the
             little
             
             Arch
             HG
             ,
             cutting
             the
             line
             FD
             in
             the
             point
             D.
             So
             the
             line
             FD
             measured
             in
             the
             Scale
             of
             leagues
             ,
             shall
             shew
             you
             the
             distance
             from
             the
             M
             ridian
             ,
             which
             is
             56
             leagues
             ,
             and
             if
             you
             draw
             the
             line
             ACD
             ,
             it
             i●
             the
             Rumb
             line
             upon
             which
             you
             have
             sailed
             ,
             and
             the
             Arch
             KC
             〈◊〉
             ed
             in
             the
             Scale
             of
             Rumbs
             ,
             shews
             it
             to
             be
             the
             third
             Rumb
             from
             the
             Meridian
             ,
             or
             South-west
             by
             South
             .
          
        
         
           
             CHAP.
             XIII
             .
          
           
             To
             find
             the
             distance
             of
             any
             Island
             from
             you
             ,
             that
             you
             may
             discern
             at
             two
             stati
             n●
             ,
             knowing
             the
             po●ut
             of
             the
             Compasse
             ,
             the
             Island
             beareth
             unto
             each
             of
             the
             stations
             .
          
           
             Suppose
             ,
             being
             at
             Sea
             you
             discover
             an
             Island
             bearing
             North-east
             off
             you
             ,
             which
             place
             let
             it
             be
             your
             first
             station
             ,
             and
             then
             sailing
             seven
             leagues
             full
             North
             you
             observe
             the
             Island
             to
             bear
             full
             East
             off
             you
             ,
             which
             let
             be
             the
             second
             station
             ;
             the
             aemand
             is
             to
             find
             the
             distance
             of
             the
             said
             Island
             from
             both
             the
             said
             stations
             ?
          
           
             
             IN
             the
             second
             figure
             ,
             or
             demonstration
             ,
             let
             A
             be
             the
             first
             Station
             ,
             and
             upon
             the
             Center
             A
             draw
             the
             Quadrant
             ABDE
             ;
             Then
             in
             regard
             you
             found
             the
             Island
             to
             bear
             North-East
             from
             you
             ,
             take
             4
             of
             your
             8
             points
             of
             the
             Compass
             our
             of
             the
             Scale
             ,
             and
             place
             them
             upon
             your
             Quadrant
             from
             B
             to
             D
             ,
             then
             from
             the
             Center
             A
             by
             the
             point
             D
             ,
             draw
             the
             line
             ADF
             ,
             representing
             the
             visuall
             line
             passing
             between
             your
             sight
             and
             the
             Island
             ,
             being
             at
             the
             first
             station
             A.
             Then
             seeng
             when
             y●●
             had
             sailed
             7
             leagues
             North
             ,
             you
             observed
             the
             Island
             to
             bear
             full
             East
             off
             you
             ,
             set
             off
             the
             said
             7
             leagues
             from
             A
             to
             C
             ,
             (
             reckoning
             every
             10
             leag●
             s
             of
             your
             Scale
             to
             be
             but
             on●
             )
             and
             from
             this
             point
             C
             ,
             which
             is
             the
             second
             station
             ,
             draw
             the
             line
             C
             F
             parallel
             
             to
             AE
             ,
             and
             it
             will
             cut
             the
             line
             ADF
             in
             the
             point
             F
             :
             So
             shall
             the
             point
             F
             ,
             be
             the
             place
             of
             the
             Island
             desired
             ,
             and
             the
             distance
             AF
             ,
             is
             the
             distance
             of
             the
             Island
             from
             the
             first
             station
             ,
             viz.
             9
             leagues
             90
             parts
             or
             almost
             10
             leagues
             :
             Likewise
             the
             distance
             from
             C
             ,
             to
             F
             ,
             is
             the
             distance
             of
             the
             Island
             from
             the
             second
             station
             ,
             which
             is
             just
             seven
             leagues
             .
             And
             by
             this
             manner
             of
             work
             ,
             you
             may
             find
             the
             ▪
             distance
             of
             any
             Island
             or
             head
             land
             from
             you
             ,
             or
             you
             may
             take
             the
             distances
             of
             as
             many
             places
             as
             you
             will
             or
             can
             see
             at
             any
             two
             such
             stations
             ,
             and
             by
             the
             crossing
             of
             their
             visuall
             lines
             ,
             find
             their
             position
             and
             distances
             each
             from
             other
             .
          
        
         
           
             CHAP.
             XIV
             .
          
           
             To
             find
             how
             many
             leagues
             ,
             miles
             ,
             and
             parts
             do
             make
             one
             degree
             of
             longitude
             in
             every
             latitude
             .
          
           
             
               Note
               ,
            
             All
             this
             while
             we
             have
             been
             sailing
             according
             to
             the
             Rules
             of
             the
             plain
             Chart
             ,
             which
             supposith
             the
             degrees
             of
             longitude
             to
             be
             equal
             to
             the
             degrees
             of
             latitude
             ,
             in
             all
             latitudes
             ,
             but
             that
             is
             very
             false
             and
             erroneous
             ;
             it
             being
             true
             onely
             in
             places
             near
             the
             Equinoctiall
             ,
             where
             every
             degree
             of
             longitude
             contains
             
               20
            
             leagues
             ,
             as
             the
             degrees
             of
             latitude
             do
             ;
             But
             in
             places
             neer
             the
             Poles
             it
             alt●rs
             very
             much
             ,
             so
             that
             in
             the
             latitude
             of
             
               60
            
             degrees
             ,
             
               10
            
             leagues
             make
             a
             degree
             of
             longitude
             :
             and
             in
             other
             latitudes
             the
             degrees
             of
             longitude
             alter
             ,
             as
             in
             this
             little
             Table
             ,
             which
             shews
             at
             what
             degree
             and
             minute
             of
             latitude
             ,
             any
             nnmber
             of
             leagues
             make
             a
             degree
             of
             longitude
             ,
             by
             which
             you
             may
             divide
             a
             Line
             upon
             your
             Scale
             for
             your
             ready
             use
             .
          
           
             
               
                 Leagues
                 in
                 one
                 Degree
                 .
              
               
                 
                   20
                
                 
                   00
                   d
                
                 
                   00
                   m
                
              
               
                 
                   19
                
                 
                   18
                
                 
                   11
                
              
               
                 
                   18
                
                 
                   25
                
                 
                   50
                
              
               
                 
                   17
                
                 
                   31
                
                 
                   47
                
              
               
                 
                   16
                
                 
                   36
                
                 
                   52
                
              
               
                 
                   15
                
                 
                   41
                
                 
                   25
                
              
               
                 
                   14
                
                 
                   45
                
                 
                   34
                
              
               
                 
                   13
                
                 
                   49
                
                 
                   27
                
              
               
                 
                   12
                
                 
                   53
                
                 
                   08
                
              
               
                 
                   11
                
                 
                   56
                
                 
                   38
                
              
               
                 
                   10
                
                 
                   60
                   d
                
                 
                   00
                   m
                
              
               
                 
                   9
                
                 
                   63
                
                 
                   15
                
              
               
                 
                   8
                
                 
                   66
                
                 
                   25
                
              
               
                 
                   7
                
                 
                   69
                
                 
                   31
                
              
               
                 
                   6
                
                 
                   72
                
                 
                   32
                
              
               
                 
                   5
                
                 
                   75
                
                 
                   31
                
              
               
                 
                   4
                
                 
                   78
                
                 
                   28
                
              
               
                 
                   3
                
                 
                   81
                
                 
                   22
                
              
               
                 
                   2
                
                 
                   84
                
                 
                   16
                
              
               
                 
                   1
                
                 
                   87
                
                 
                   08
                
              
            
          
           
             
             
               Now
               to
               return
               to
               the
               Question
               ,
               and
               shew
               you
               by
               demonstration
               how
               to
               find
               how
               many
               leagues
               ,
               miles
               ,
               and
               parts
               ,
               make
               a
               degree
               of
               longitude
               in
               any
               degree
               of
               latitude
               ?
            
             
             
               The
               larger
               you
               make
               your
               Quadrant
               ,
               the
               more
               exact
               will
               the
               work
               be
               ,
               and
               shew
               the
               leagues
               and
               miles
               more
               exactly
               ,
               which
               you
               may
               make
               into
               a
               Table
               ,
               as
               this
               following
               .
            
             
             
               
                 
                   A
                   Table
                   shewing
                   how
                   many
                   leagues
                   ,
                   miles
                   ,
                   and
                   hundred
                   parts
                   of
                   a
                   mile
                   make
                   one
                   degree
                   of
                   longitude
                   in
                   any
                   latitude
                   .
                
                 
                   
                     Latitude
                  
                   
                     Leagues
                  
                   
                     Miles
                  
                   
                     Parts
                  
                   
                     Difference
                  
                   
                      
                  
                   
                     Latitude
                  
                   
                     Leagues
                  
                   
                     Miles
                  
                   
                     Parts
                  
                   
                     Diffe
                     ence
                  
                   
                      
                  
                   
                     Latitude
                  
                   
                     Leagues
                  
                   
                     Miles
                  
                   
                     Parts
                  
                   
                     Diff●rence
                  
                
                 
                   
                     0
                  
                   
                     20
                  
                   
                     0
                  
                   
                     0
                  
                   
                     —
                  
                   
                      
                  
                   
                     30
                  
                   
                     17
                  
                   
                     0
                  
                   
                     96
                  
                   
                     —
                  
                   
                      
                  
                   
                     60
                  
                   
                     10
                  
                   
                     0
                  
                   
                     0
                  
                   
                     —
                  
                
                 
                   
                     1
                  
                   
                     19
                  
                   
                     2
                  
                   
                     99
                  
                   
                     1
                  
                   
                      
                  
                   
                     31
                  
                   
                     17
                  
                   
                     0
                  
                   
                     43
                  
                   
                     53
                  
                   
                      
                  
                   
                     61
                  
                   
                     9
                  
                   
                     2
                  
                   
                     09
                  
                   
                     91
                  
                
                 
                   
                     2
                  
                   
                     19
                  
                   
                     2
                  
                   
                     96
                  
                   
                     3
                  
                   
                      
                  
                   
                     32
                  
                   
                     16
                  
                   
                     2
                  
                   
                     88
                  
                   
                     55
                  
                   
                      
                  
                   
                     62
                  
                   
                     9
                  
                   
                     1
                  
                   
                     17
                  
                   
                     92
                  
                
                 
                   
                     3
                  
                   
                     19
                  
                   
                     2
                  
                   
                     92
                  
                   
                     4
                  
                   
                      
                  
                   
                     33
                  
                   
                     16
                  
                   
                     2
                  
                   
                     32
                  
                   
                     56
                  
                   
                      
                  
                   
                     63
                  
                   
                     9
                  
                   
                     0
                  
                   
                     24
                  
                   
                     93
                  
                
                 
                   
                     4
                  
                   
                     19
                  
                   
                     2
                  
                   
                     85
                  
                   
                     7
                  
                   
                      
                  
                   
                     34
                  
                   
                     16
                  
                   
                     1
                  
                   
                     74
                  
                   
                     58
                  
                   
                      
                  
                   
                     64
                  
                   
                     8
                  
                   
                     2
                  
                   
                     30
                  
                   
                     94
                  
                
                 
                   
                     5
                  
                   
                     19
                  
                   
                     2
                  
                   
                     77
                  
                   
                     8
                  
                   
                      
                  
                   
                     35
                  
                   
                     16
                  
                   
                     1
                  
                   
                     15
                  
                   
                     59
                  
                   
                      
                  
                   
                     65
                  
                   
                     8
                  
                   
                     1
                  
                   
                     36
                  
                   
                     94
                  
                
                 
                   
                     6
                  
                   
                     19
                  
                   
                     2
                  
                   
                     67
                  
                   
                     10
                  
                   
                      
                  
                   
                     36
                  
                   
                     16
                  
                   
                     0
                  
                   
                     54
                  
                   
                     61
                  
                   
                      
                  
                   
                     66
                  
                   
                     8
                  
                   
                     0
                  
                   
                     40
                  
                   
                     96
                  
                
                 
                   
                     7
                  
                   
                     19
                  
                   
                     2
                  
                   
                     55
                  
                   
                     12
                  
                   
                      
                  
                   
                     37
                  
                   
                     15
                  
                   
                     2
                  
                   
                     92
                  
                   
                     62
                  
                   
                      
                  
                   
                     67
                  
                   
                     7
                  
                   
                     2
                  
                   
                     44
                  
                   
                     96
                  
                
                 
                   
                     8
                  
                   
                     19
                  
                   
                     2
                  
                   
                     42
                  
                   
                     13
                  
                   
                      
                  
                   
                     38
                  
                   
                     15
                  
                   
                     2
                  
                   
                     28
                  
                   
                     64
                  
                   
                      
                  
                   
                     68
                  
                   
                     7
                  
                   
                     1
                  
                   
                     47
                  
                   
                     97
                  
                
                 
                   
                     9
                  
                   
                     19
                  
                   
                     2
                  
                   
                     26
                  
                   
                     16
                  
                   
                      
                  
                   
                     39
                  
                   
                     15
                  
                   
                     1
                  
                   
                     63
                  
                   
                     65
                  
                   
                      
                  
                   
                     69
                  
                   
                     7
                  
                   
                     0
                  
                   
                     50
                  
                   
                     97
                  
                
                 
                   
                     10
                  
                   
                     19
                  
                   
                     2
                  
                   
                     09
                  
                   
                     17
                  
                   
                      
                  
                   
                     40
                  
                   
                     15
                  
                   
                     0
                  
                   
                     96
                  
                   
                     67
                  
                   
                      
                  
                   
                     70
                  
                   
                     6
                  
                   
                     2
                  
                   
                     52
                  
                   
                     98
                  
                
                 
                   
                     11
                  
                   
                     19
                  
                   
                     1
                  
                   
                     90
                  
                   
                     19
                  
                   
                      
                  
                   
                     41
                  
                   
                     15
                  
                   
                     0
                  
                   
                     28
                  
                   
                     68
                  
                   
                      
                  
                   
                     71
                  
                   
                     6
                  
                   
                     1
                  
                   
                     53
                  
                   
                     99
                  
                
                 
                   
                     12
                  
                   
                     19
                  
                   
                     1
                  
                   
                     69
                  
                   
                     21
                  
                   
                      
                  
                   
                     42
                  
                   
                     14
                  
                   
                     2
                  
                   
                     59
                  
                   
                     69
                  
                   
                      
                  
                   
                     72
                  
                   
                     6
                  
                   
                     0
                  
                   
                     54
                  
                   
                     99
                  
                
                 
                   
                     13
                  
                   
                     19
                  
                   
                     1
                  
                   
                     46
                  
                   
                     23
                  
                   
                      
                  
                   
                     43
                  
                   
                     14
                  
                   
                     1
                  
                   
                     88
                  
                   
                     71
                  
                   
                      
                  
                   
                     73
                  
                   
                     5
                  
                   
                     2
                  
                   
                     54
                  
                   
                     100
                  
                
                 
                   
                     14
                  
                   
                     19
                  
                   
                     1
                  
                   
                     22
                  
                   
                     24
                  
                   
                      
                  
                   
                     44
                  
                   
                     14
                  
                   
                     1
                  
                   
                     16
                  
                   
                     72
                  
                   
                      
                  
                   
                     74
                  
                   
                     5
                  
                   
                     1
                  
                   
                     54
                  
                   
                     100
                  
                
                 
                   
                     15
                  
                   
                     19
                  
                   
                     0
                  
                   
                     96
                  
                   
                     26
                  
                   
                      
                  
                   
                     45
                  
                   
                     14
                  
                   
                     0
                  
                   
                     43
                  
                   
                     73
                  
                   
                      
                  
                   
                     75
                  
                   
                     5
                  
                   
                     0
                  
                   
                     53
                  
                   
                     101
                  
                
                 
                   
                     16
                  
                   
                     19
                  
                   
                     0
                  
                   
                     68
                  
                   
                     28
                  
                   
                      
                  
                   
                     46
                  
                   
                     13
                  
                   
                     2
                  
                   
                     68
                  
                   
                     75
                  
                   
                      
                  
                   
                     76
                  
                   
                     4
                  
                   
                     2
                  
                   
                     52
                  
                   
                     101
                  
                
                 
                   
                     17
                  
                   
                     19
                  
                   
                     0
                  
                   
                     38
                  
                   
                     30
                  
                   
                      
                  
                   
                     47
                  
                   
                     13
                  
                   
                     1
                  
                   
                     92
                  
                   
                     76
                  
                   
                      
                  
                   
                     77
                  
                   
                     4
                  
                   
                     1
                  
                   
                     50
                  
                   
                     102
                  
                
                 
                   
                     18
                  
                   
                     19
                  
                   
                     0
                  
                   
                     06
                  
                   
                     32
                  
                   
                      
                  
                   
                     48
                  
                   
                     13
                  
                   
                     1
                  
                   
                     15
                  
                   
                     77
                  
                   
                      
                  
                   
                     78
                  
                   
                     4
                  
                   
                     0
                  
                   
                     48
                  
                   
                     102
                  
                
                 
                   
                     19
                  
                   
                     18
                  
                   
                     2
                  
                   
                     73
                  
                   
                     33
                  
                   
                      
                  
                   
                     49
                  
                   
                     13
                  
                   
                     0
                  
                   
                     36
                  
                   
                     79
                  
                   
                      
                  
                   
                     79
                  
                   
                     3
                  
                   
                     2
                  
                   
                     45
                  
                   
                     103
                  
                
                 
                   
                     20
                  
                   
                     18
                  
                   
                     2
                  
                   
                     38
                  
                   
                     35
                  
                   
                      
                  
                   
                     50
                  
                   
                     12
                  
                   
                     2
                  
                   
                     57
                  
                   
                     79
                  
                   
                      
                  
                   
                     80
                  
                   
                     3
                  
                   
                     1
                  
                   
                     42
                  
                   
                     103
                  
                
                 
                   
                     21
                  
                   
                     18
                  
                   
                     2
                  
                   
                     1
                  
                   
                     37
                  
                   
                      
                  
                   
                     51
                  
                   
                     12
                  
                   
                     1
                  
                   
                     76
                  
                   
                     81
                  
                   
                      
                  
                   
                     81
                  
                   
                     3
                  
                   
                     0
                  
                   
                     38
                  
                   
                     104
                  
                
                 
                   
                     22
                  
                   
                     18
                  
                   
                     1
                  
                   
                     63
                  
                   
                     38
                  
                   
                      
                  
                   
                     52
                  
                   
                     12
                  
                   
                     0
                  
                   
                     94
                  
                   
                     82
                  
                   
                      
                  
                   
                     82
                  
                   
                     2
                  
                   
                     2
                  
                   
                     35
                  
                   
                     103
                  
                
                 
                   
                     23
                  
                   
                     18
                  
                   
                     1
                  
                   
                     23
                  
                   
                     40
                  
                   
                      
                  
                   
                     53
                  
                   
                     12
                  
                   
                     0
                  
                   
                     11
                  
                   
                     83
                  
                   
                      
                  
                   
                     83
                  
                   
                     2
                  
                   
                     1
                  
                   
                     31
                  
                   
                     104
                  
                
                 
                   
                     24
                  
                   
                     18
                  
                   
                     0
                  
                   
                     81
                  
                   
                     42
                  
                   
                      
                  
                   
                     54
                  
                   
                     11
                  
                   
                     2
                  
                   
                     27
                  
                   
                     84
                  
                   
                      
                  
                   
                     84
                  
                   
                     2
                  
                   
                     0
                  
                   
                     27
                  
                   
                     104
                  
                
                 
                   
                     25
                  
                   
                     18
                  
                   
                     0
                  
                   
                     38
                  
                   
                     43
                  
                   
                      
                  
                   
                     55
                  
                   
                     11
                  
                   
                     1
                  
                   
                     41
                  
                   
                     86
                  
                   
                      
                  
                   
                     85
                  
                   
                     1
                  
                   
                     2
                  
                   
                     23
                  
                   
                     104
                  
                
                 
                   
                     26
                  
                   
                     17
                  
                   
                     2
                  
                   
                     93
                  
                   
                     45
                  
                   
                      
                  
                   
                     56
                  
                   
                     11
                  
                   
                     0
                  
                   
                     55
                  
                   
                     86
                  
                   
                      
                  
                   
                     86
                  
                   
                     1
                  
                   
                     1
                  
                   
                     18
                  
                   
                     105
                  
                
                 
                   
                     27
                  
                   
                     17
                  
                   
                     2
                  
                   
                     46
                  
                   
                     47
                  
                   
                      
                  
                   
                     57
                  
                   
                     10
                  
                   
                     2
                  
                   
                     68
                  
                   
                     87
                  
                   
                      
                  
                   
                     87
                  
                   
                     1
                  
                   
                     0
                  
                   
                     14
                  
                   
                     104
                  
                
                 
                   
                     28
                  
                   
                     17
                  
                   
                     1
                  
                   
                     98
                  
                   
                     48
                  
                   
                      
                  
                   
                     58
                  
                   
                     10
                  
                   
                     1
                  
                   
                     80
                  
                   
                     88
                  
                   
                      
                  
                   
                     88
                  
                   
                     0
                  
                   
                     2
                  
                   
                     09
                  
                   
                     105
                  
                
                 
                   
                     29
                  
                   
                     17
                  
                   
                     1
                  
                   
                     48
                  
                   
                     50
                  
                   
                      
                  
                   
                     59
                  
                   
                     10
                  
                   
                     0
                  
                   
                     90
                  
                   
                     90
                  
                   
                      
                  
                   
                     89
                  
                   
                     0
                  
                   
                     1
                  
                   
                     05
                  
                   
                     104
                  
                
                 
                   
                     30
                  
                   
                     17
                  
                   
                     0
                  
                   
                     96
                  
                   
                     52
                  
                   
                      
                  
                   
                     60
                  
                   
                     10
                  
                   
                     0
                  
                   
                     0
                  
                   
                     90
                  
                   
                      
                  
                   
                     90
                  
                   
                     0
                  
                   
                     0
                  
                   
                     0
                  
                   
                     105
                  
                
              
            
          
        
         
           
           
             CHAP.
             XV.
             
          
           
             The
             difference
             of
             latitude
             ,
             and
             the
             Rumb
             or
             distance
             sailed
             being
             known
             ,
             to
             find
             the
             distance
             of
             the
             Meridians
             ,
             and
             thereby
             to
             find
             the
             degrees
             and
             minutes
             of
             the
             difference
             of
             longitude
             in
             any
             latitude
             .
          
           
             Sailing
             from
             the
             North
             parallel
             of
             
               56
            
             degrees
             and
             
               5
            
             min.
             latitude
             ,
             
               100
            
             leagues
             upon
             the
             third
             Rumb
             from
             the
             Meridian
             ▪
             
               viz.
            
             South-west
             and
             by
             South
             untill
             
               I
            
             find
             the
             Pole
             is
             depressed
             
               4
            
             deg
             .
             
               9
            
             m.
             and
             the
             Meridional
             distance
             
               56
            
             leagues
             ;
             the
             longitude
             is
             desired
             thereby
             ?
          
           
             I●
             the
             first
             figure
          
           
           
             Now
             to
             reduce
             this
             56
             leagues
             into
             degrees
             of
             longitude
             ,
             you
             must
             consider
             from
             what
             latitude
             you
             have
             sailed
             ,
             and
             to
             what
             latitude
             you
             are
             come
             ,
             
               viz.
            
             from
             latitude
             56
             d.
             5
             m.
             to
             4
             deg
             .
             9
             min.
             lesse
             ,
             which
             is
             51
             d.
             56
             m.
             and
             take
             the
             middle
             latitude
             (
             or
             somewhat
             more
             )
             between
             the
             two
             places
             ,
             which
             in
             this
             example
             falls
             out
             to
             be
             54d
             .
             01
             m.
             Then
             by
             the
             Table
             in
             the
             former
             Chapter
             ,
             find
             out
             howmany
             leagues
             and
             miles
             in
             the
             said
             middle
             latitude
             make
             one
             
             degree
             of
             longitude
             ,
             and
             you
             shall
             find
             in
             that
             Table
             ,
             that
             in
             the
             latitude
             of
             54
             d.
             there
             is
             but
             11
             leagues
             ,
             and
             2
             miles
             ,
             and
             27
             parts
             in
             one
             degree
             of
             longitude
             ;
             Therefore
             open
             your
             Compasses
             upon
             your
             Scale
             of
             leagues
             ,
             to
             this
             11
             leagues
             ,
             2
             miles
             ,
             27
             parts
             ,
             and
             keeping
             your
             Compasses
             at
             that
             distance
             ,
             set
             one
             foot
             of
             them
             at
             56
             leagues
             in
             your
             Scale
             of
             leagues
             ,
             or
             in
             the
             line
             DF
             in
             the
             figure
             ,
             (
             or
             upon
             the
             like
             line
             in
             your
             Chart
             at
             any
             time
             )
             either
             at
             F
             or
             D
             ,
             and
             measure
             howmany
             times
             you
             find
             that
             distance
             either
             to
             the
             end
             of
             your
             Scale
             coming
             backward
             ,
             or
             in
             the
             line
             DF
             ,
             for
             so
             many
             degrees
             is
             the
             difference
             o●
             longitude
             ,
             and
             if
             any
             odde
             part
             remain
             ,
             you
             may
             proportion
             i●
             by
             your
             eye
             ,
             judging
             it
             to
             be
             a
             quarter
             ,
             a
             third
             ,
             an
             half
             ,
             or
             any
             part
             more
             or
             lesse
             of
             a
             degree
             ,
             which
             you
             may
             either
             reckon
             by
             parts
             ,
             or
             15
             ,
             20
             ,
             30
             &c.
             minutes
             ,
          
           
             Thus
             this
             line
             DF
             being
             56
             leagues
             ,
             opening
             your
             Compasses
             to
             11
             leagues
             2
             miles
             27
             parts
             ,
             you
             will
             find
             this
             distance
             in
             it
             ,
             4
             times
             and
             3
             quarters
             ;
             so
             that
             the
             difference
             of
             longitude
             is
             4
             deg
             .
             45
             min.
             
          
           
             Or
             you
             may
             reduce
             it
             into
             miles
             and
             work
             by
             the
             rule
             of
             proportion
             ,
             so
             you
             shall
             find
             
               
                 
                   As
                   11
                   leagues
                   ,
                   2
                   miles
                   ,
                   27
                   parts
                   ,
                   that
                   is
                   35
                   miles
                   27
                   parts
                   .
                
                 
                   35,27
                
              
               
                 
                   To
                   one
                   degree
                   of
                   longitude
                   in
                   the
                   latitude
                   of
                   54
                   d.
                   
                
                 
                   01,00
                
              
               
                 
                   So
                   is
                   56
                   leagues
                   ,
                   or
                   168
                   miles
                   .
                
                 
                   168,00
                
              
               
                 
                   To
                   4
                   degrees
                   ,
                   76
                   parts
                   .
                
                 
                   04
                   76
                
              
            
          
           
             But
             if
             your
             Scale
             be
             large
             ,
             the
             other
             way
             with
             your
             Compasses
             will
             give
             you
             the
             degrees
             and
             parts
             of
             longitude
             as
             exactly
             as
             you
             need
             for
             most
             uses
             .
          
           
             Also
             if
             the
             latitude
             fall
             not
             out
             in
             equal
             parts
             ,
             you
             may
             find
             out
             for
             your
             odde
             minutes
             by
             proportion
             ,
             for
             which
             purpose
             I
             have
             set
             the
             differences
             between
             each
             degree
             in
             the
             Table
             .
          
           
             So
             that
             as
             one
             hundred
             parts
             or
             60
             minutes
             being
             one
             degree
             ,
             to
             the
             difference
             in
             the
             Table
             between
             the
             two
             next
             degrees
             ;
          
           
             So
             the
             odde
             hundred
             parts
             or
             minutes
             of
             latitude
             ,
             to
             the
             parts
             and
             minutes
             proportional
             to
             be
             allowed
             .
          
        
         
           
           
             CHAP.
             XVI
             .
          
           
             Sailing
             from
             the
             South
             latitude
             of
             
               60
            
             degrees
             ,
             
               51
            
             min.
             and
             from
             longitude
             
               25
            
             degrees
             ,
             
               24
            
             min.
             
               99
            
             leagues
             ,
             upon
             a
             South-west
             course
             :
             the
             latitude
             and
             longitude
             of
             the
             second
             place
             is
             demanded
             .
          
           
             IN
             the
             second
             demonstration
             ,
             draw
             the
             Quadrant
             ABCDE
             ,
             as
             is
             formerly
             taught
             ,
             then
             in
             regard
             you
             sail
             South-west
             ,
             take
             4
             points
             of
             the
             Compasse
             from
             your
             Scale
             ,
             and
             place
             them
             from
             B
             unto
             D
             ,
             then
             by
             the
             point
             D
             draw
             the
             line
             ADF
             ,
             then
             place
             your
             
             ninety
             nine
             leagues
             upon
             the
             line
             ADF
             ,
             from
             A
             unto
             F
             ,
             so
             shall
             F
             be
             the
             place
             of
             your
             Ship.
             Then
             from
             F
             draw
             the
             line
             FC
             parallel
             unto
             AE
             ,
             cutting
             the
             line
             ABC
             in
             C
             ,
             so
             shall
             the
             distance
             CA
             be
             the
             leagues
             you
             have
             run
             South
             ,
             which
             is
             seventy
             leagues
             ,
             or
             3
             deg
             .
             30
             minutes
             ,
             which
             being
             added
             to
             the
             latitude
             from
             whence
             you
             dearted
             ,
             makes
             64
             deg
             .
             and
             21
             minutes
             for
             the
             latitude
             of
             the
             second
             place
             :
             then
             take
             the
             distance
             CF
             ,
             and
             apply
             it
             unto
             the
             line
             of
             equal
             parts
             ,
             and
             you
             shall
             find
             it
             likewise
             70
             leagues
             :
             Then
             finding
             the
             middle
             latitude
             62
             degrees
             36
             minutes
             in
             the
             Table
             ,
             Chap.
             14.
             you
             shall
             find
             that
             9
             leagues
             and
             0
             miles
             ,
             and
             61
             parts
             ,
             do
             alter
             a
             degree
             of
             longitude
             in
             that
             latitude
             .
             Then
             opening
             the
             feet
             of
             your
             Compasses
             to
             9
             leagues
             0
             miles
             61
             parts
             ,
             in
             the
             Scale
             of
             equall
             leagues
             ,
             and
             keeping
             the
             Compasses
             at
             that
             distance
             ,
             see
             howmany
             times
             that
             distance
             is
             in
             the
             line
             CF
             ,
             which
             is
             seven
             times
             and
             somewhat
             above
             an
             half
             ,
             the
             true
             difference
             of
             longitude
             being
             7
             deg
             .
             36
             m.
             which
             being
             substracted
             from
             the
             longitude
             from
             whence
             you
             departed
             ,
             leaves
             17
             degrees
             and
             48
             minutes
             for
             the
             longitudeof
             the
             second
             place
             .
          
        
         
           
           
             CHAP.
             XVII
             .
          
           
             A
             Ship
             sayling
             from
             the
             North
             Parallel
             of
             fifty
             degrees
             ,
             having
             an
             hundred
             leagues
             to
             sail
             South-west
             ,
             and
             by
             West
             ,
             by
             the
             way
             is
             enforced
             by
             contrary
             winds
             to
             sail
             upon
             several
             points
             of
             the
             Compasse
             ,
             first
             sailing
             thirty
             leagues
             upon
             a
             direct
             course
             ,
             then
             West
             North-west
             twenty
             leagues
             ,
             then
             South
             sixty
             leagues
             ,
             the
             question
             is
             to
             find
             the
             latitude
             of
             the
             second
             place
             ,
             how
             far
             it
             is
             to
             the
             place
             whereuuto
             you
             are
             bound
             ,
             the
             distance
             of
             the
             Rumb
             that
             is
             betwixt
             them
             ,
             the
             distance
             that
             you
             are
             from
             your
             first
             Meridian
             ,
             and
             thereby
             the
             difference
             of
             longitude
             .
          
           
             IN
             the
             third
             demonstration
             ,
             draw
             the
             line
             AD
             ,
             and
             from
             the
             point
             A
             ,
             raise
             the
             perpendicular
             AB
             ,
             then
             open
             your
             Compass
             unto
             the
             Radius
             of
             your
             Scale
             ,
             and
             place
             one
             foot
             thereof
             in
             the
             center
             A.
             and
             with
             
             the
             other
             draw
             the
             Quadrant
             BCD
             ,
             then
             take
             three
             points
             of
             the
             compasse
             &
             place
             them
             upon
             the
             Quadrant
             from
             D.
             unto
             C
             ,
             then
             from
             the
             Center
             A
             ,
             by
             the
             point
             C
             ,
             draw
             the
             line
             ACL
             ,
             100
             Leagues
             in
             length
             ,
             which
             is
             the
             true
             course
             you
             are
             to
             saile
             ,
             Then
             in
             regard
             you
             sayled
             thirtie
             leagues
             direct
             ,
             take
             thirtie
             leagues
             from
             your
             Scale
             of
             equall
             parts
             ,
             and
             place
             them
             upon
             the
             line
             AEC
             ,
             it
             extends
             from
             A
             unto
             E
             :
             then
             in
             regard
             you
             turned
             your
             Course
             ,
             West
             ,
             Northwest
             ,
             from
             the
             Center
             E
             ,
             draw
             the
             Line
             EG
             parallell
             unto
             A.
             D.
             and
             again
             from
             the
             center
             E
             draw
             the
             line
             EH
             perpendicular
             to
             EG
             ,
             and
             parallell
             to
             AB
             ,
             then
             
             witn
             the
             distance
             of
             the
             Radius
             ,
             set
             one
             foot
             of
             your
             compasses
             in
             the
             center
             E
             ,
             and
             with
             the
             other
             draw
             the
             Quadrant
             GMH
             ,
             and
             in
             regard
             you
             sayled
             West
             ,
             Northwest
             ,
             which
             is
             two
             points
             from
             the
             West
             Northward
             ,
             take
             from
             your
             Scale
             two
             points
             of
             the
             Compass
             ,
             and
             place
             them
             upon
             the
             Quadrant
             GMH
             ,
             from
             G
             unto
             M
             ,
             then
             from
             the
             center
             E
             unto
             the
             point
             M
             ,
             draw
             the
             line
             EFM
             ,
             then
             take
             20
             Leagues
             with
             your
             Compasses
             from
             the
             Scale
             of
             equall
             parts
             ,
             and
             place
             them
             upon
             the
             line
             EFM
             ,
             from
             E
             unto
             F
             ,
             then
             is
             your
             Ship
             in
             the
             point
             F.
             Lastly
             ,
             in
             regard
             you
             run
             South
             60
             Leagues
             from
             F
             ,
             draw
             a
             Line
             Parallell
             unto
             the
             Meridian
             AB
             ,
             which
             is
             the
             line
             FI
             ,
             then
             take
             from
             your
             Scale
             of
             equall
             parts
             sixtie
             Leagues
             ,
             and
             place
             them
             from
             F
             ,
             unto
             I
             ,
             then
             is
             your
             Ship
             in
             the
             point
             I
             :
             then
             last
             of
             all
             is
             to
             be
             found
             how
             far
             it
             is
             to
             the
             place
             where
             unto
             you
             were
             bound
             ,
             the
             distance
             of
             the
             Rumb
             that
             is
             betwixt
             you
             ,
             the
             degrees
             and
             minutes
             you
             have
             raised
             the
             Pole
             ,
             the
             distance
             of
             departure
             from
             the
             first
             Meridian
             ,
             and
             thereby
             t●e
             difference
             of
             Longitude
             :
             and
             that
             you
             may
             so
             doe
             ,
             first
             draw
             the
             line
             OIK
             ,
             Perpendicular
             unto
             the
             line
             IF
             in
             the
             point
             I
             ,
             and
             with
             your
             Compasses
             opened
             unto
             the
             distance
             of
             the
             Radius
             ,
             set
             one
             foot
             of
             your
             Compasses
             in
             the
             Center
             I
             ,
             and
             with
             the
             other
             draw
             the
             Quadrant
             KNF
             ,
             then
             in
             regard
             your
             ship
             is
             in
             the
             point
             I
             ,
             and
             the
             place
             whereunto
             you
             are
             bound
             is
             the
             point
             L
             ,
             therefore
             from
             I
             ,
             thorow
             the
             point
             L
             draw
             the
             line
             ILN
             ,
             cutting
             the
             Arch
             KNF
             ,
             in
             the
             point
             N
             ,
             therefore
             let
             IL
             ,
             be
             the
             Leagues
             you
             have
             unto
             the
             place
             whereunto
             you
             are
             bound
             ,
             which
             is
             fortie
             one
             Leagues
             and
             a
             halfe
             ,
             and
             the
             Rumb
             the
             distance
             KN
             ,
             which
             is
             West
             ,
             and
             by
             North
             ,
             and
             three
             degrees
             unto
             the
             Northward
             ,
             so
             likewise
             is
             the
             line
             AO
             ,
             the
             number
             of
             Leagues
             you
             have
             run
             due
             South
             ,
             which
             is
             sixtie
             eight
             Leagues
             and
             one
             mile
             ,
             or
             three
             degrees
             and
             twenty
             five
             minutes
             ,
             which
             being
             taken
             from
             fiftie
             degrees
             ,
             the
             parallell
             from
             which
             you
             departed
             ,
             leaves
             fortie
             six
             degrees
             and
             thirtie
             five
             minutes
             for
             the
             Parallel
             you
             are
             in
             .
             Last
             of
             all
             ,
             shall
             the
             line
             IO
             ,
             be
             the
             Leagues
             that
             you
             have
             departed
             your
             first
             Meridian
             ,
             which
             are
             fortie
             two
             leagues
             and
             one
             mile
             ,
             Then
             take
             the
             middle
             latitude
             which
             is
             fortie
             eight
             degrees
             seventeen
             minutes
             and
             in
             the
             Table
             chap.
             14
             you
             shall
             find
             that
             thirteen
             Leagues
             0.
             mile
             ,
             92
             parts
             ,
             do
             answer
             unto
             a
             degree
             of
             Longitude
             in
             that
             Parallell
             ;
             then
             setting
             one
             foot
             of
             your
             Compasses
             
             in
             thirteen
             Leagues
             ,
             and
             ninety
             two
             parts
             ,
             
             extending
             the
             other
             to
             the
             beginning
             of
             the
             Scale
             ,
             keeping
             the
             Compasses
             at
             that
             distance
             ,
             turn
             them
             over
             the
             line
             I
             O
             ,
             and
             you
             shall
             find
             it
             contains
             that
             distance
             three
             times
             and
             almost
             a
             quarter
             ,
             So
             the
             difference
             of
             longitude
             is
             three
             degrees
             eleven
             minutes
             .
          
        
         
           
             CHAP.
             XVIII
             .
          
           
             Two
             Ships
             departing
             from
             one
             Parallel
             ,
             and
             Port
             ,
             the
             one
             in
             sayling
             eight
             Leagues
             betwixt
             the
             North
             ,
             and
             the
             West
             ,
             hath
             raised
             the
             Pole
             two
             degrees
             ,
             the
             other
             in
             sailing
             a
             hundred
             Leagues
             betwixt
             the
             North
             ,
             and
             West
             ,
             hath
             raised
             the
             Pole
             four
             degrees
             ,
             I
             demand
             by
             what
             Rhumbs
             the
             said
             Ships
             have
             sailed
             ,
             and
             the
             Rhumb
             and
             distance
             that
             is
             betwixt
             them
             ?
          
           
             IN
             the
             fourth
             Demonstration
             ,
             draw
             the
             Quadrant
             ABCDE
             ,
             then
             in
             regard
             the
             first
             Ship
             hath
             raised
             the
             Pole
             two
             degrees
             ,
             which
             is
             fortie
             leagues
             ,
             take
             fortie
             Leagues
             off
             your
             Scale
             ,
             and
             applie
             them
             unto
             the
             Meridian
             line
             AGL
             ,
             from
             A
             unto
             G
             :
             then
             from
             the
             point
             G
             ,
             draw
             the
             line
             GF
             ,
             parallel
             unto
             AB
             ,
             then
             opening
             your
             compasses
             unto
             80
             Leagues
             ,
             set
             one
             foot
             in
             the
             Center
             A
             ,
             with
             the
             other
             make
             a
             marke
             in
             the
             line
             GF
             ,
             which
             will
             be
             at
             F
             ,
             so
             shall
             F
             be
             the
             place
             of
             the
             first
             ship
             ;
             the
             second
             Ship
             hath
             raised
             the
             Pole
             four
             degrees
             ,
             which
             is
             80
             Leagues
             ,
             therefore
             place
             80
             leagues
             upon
             the
             Meridian
             line
             AGL
             ,
             from
             A
             unto
             L
             ,
             and
             from
             the
             
             point
             L
             draw
             the
             line
             LM
             ,
             parallel
             unto
             GHF
             ,
             then
             open
             your
             Compasses
             unto
             the
             distance
             of
             a
             hundred
             leagues
             ,
             which
             are
             the
             Leagues
             the
             second
             ship
             did
             run
             ,
             and
             set
             the
             foot
             of
             your
             Compasses
             in
             the
             Center
             A
             ,
             and
             with
             the
             other
             make
             a
             mark
             in
             the
             line
             LM
             ,
             which
             will
             be
             at
             M
             ,
             then
             draw
             the
             line
             MA
             ,
             which
             is
             the
             course
             of
             the
             second
             Ship
             ,
             and
             the
             line
             FA
             ,
             is
             the
             course
             of
             the
             first
             ship
             ,
             then
             from
             F
             let
             a
             Perpendicular
             fall
             ,
             being
             Perpendicular
             to
             the
             line
             GF
             ,
             which
             is
             the
             line
             FK
             ,
             then
             opening
             your
             Compasses
             unto
             the
             Radius
             of
             your
             Scale
             ,
             set
             one
             foot
             in
             the
             Center
             F
             ,
             and
             with
             the
             other
             draw
             the
             Quadrant
             HIK
             ,
             likewise
             from
             F
             ,
             the
             place
             of
             the
             first
             Ship
             ,
             draw
             a
             line
             by
             the
             point
             M
             ,
             the
             place
             of
             the
             second
             ,
             cutting
             the
             Quadrant
             KHI
             ,
             in
             I
             ,
             so
             let
             IK
             ,
             be
             the
             course
             that
             is
             betwixt
             them
             ,
             that
             is
             ,
             if
             you
             will
             saile
             from
             the
             first
             ship
             unto
             the
             second
             ,
             you
             must
             saile
             North
             and
             by
             East
             ,
             and
             one
             and
             fortie
             minutes
             to
             the
             Eastward
             ,
             likewise
             let
             F
             
               M
               ,
            
             be
             the
             distance
             that
             is
             betwixt
             them
             ,
             which
             in
             this
             Demonstration
             is
             fortie
             Leagues
             ,
             two
             miles
             ,
             so
             shall
             BC
             ,
             be
             the
             course
             of
             the
             first
             ship
             from
             the
             West
             Northward
             ,
             wh
             ch
             here
             is
             found
             to
             be
             thirtie
             degrees
             and
             one
             minut
             from
             the
             West
             Northward
             ,
             or
             Northwest
             by
             West
             ,
             and
             three
             degrees
             and
             fortie
             four
             minutes
             to
             the
             west
             ward
             .
             Lastly
             the
             Arch
             ED
             ,
             is
             in
             the
             distance
             of
             the
             course
             that
             the
             second
             Ship
             made
             from
             the
             North
             Westward
             ,
             which
             is
             found
             by
             this
             Demonstration
             to
             be
             Northwest
             and
             by
             North
             ,
             and
             three
             degrees
             five
             minutes
             to
             the
             Westward
             .
          
        
         
           
             CHAP.
             X●X
             .
          
           
             Two
             Ships
             departing
             from
             one
             Parallell
             and
             Port
             in
             the
             Parallell
             of
             
               47
            
             deg
             .
             
               56
            
             min.
             the
             first
             in
             sayling
             
               80
            
             leag
             .
             betwixt
             the
             North
             and
             West
             ,
             hath
             raised
             the
             Pole
             two
             degrees
             ,
             I
             demand
             by
             what
             course
             the
             second
             ship
             must
             runne
             ,
             and
             how
             much
             she
             shall
             alter
             in
             her
             first
             Meridian
             or
             longitude
             ,
             to
             bring
             her selfe
             
               40.
            
             leagues
             and
             two
             miles
             North
             and
             by
             East
             ,
             and
             
               41.
            
             minutes
             to
             the
             Eastward
             of
             the
             first
             ship
             ?
          
           
             IN
             the
             fourth
             Demonstration
             draw
             the
             Quadrant
             ABCDE
             ,
             then
             multiplie
             your
             two
             degrees
             you
             have
             altered
             your
             latitude
             by
             twentie
             and
             it
             maketh
             fourtie
             Leagues
             ;
             which
             fourtie
             Leagues
             
             set
             upon
             the
             line
             AEL
             ,
             from
             A
             unto
             G
             ,
             then
             from
             the
             point
             G
             draw
             the
             line
             GF
             ,
             parallel
             unto
             AB
             ,
             then
             open
             your
             Compasses
             unto
             the
             distance
             of
             80
             Leagues
             ,
             which
             are
             the
             Leagues
             your
             first
             ship
             did
             runne
             ,
             and
             place
             one
             foot
             of
             your
             Compasses
             in
             the
             Center
             A
             ,
             and
             with
             the
             other
             make
             a
             marke
             in
             the
             line
             GF
             ,
             which
             will
             be
             at
             the
             point
             F
             ,
             then
             from
             the
             Center
             A
             unto
             the
             point
             F
             draw
             the
             line
             AF
             ,
             representing
             the
             distance
             of
             the
             Course
             of
             the
             first
             Ship
             80
             leagues
             :
             Then
             from
             F
             let
             fall
             a
             Perpendicular
             FK
             ,
             and
             upon
             the
             Center
             F
             ,
             
             with
             the
             Radius
             of
             the
             Scale
             draw
             the
             Arch
             HIK
             ,
             Then
             in
             regard
             you
             must
             bring
             the
             second
             ship
             North
             and
             by
             East
             ,
             and
             41
             minutes
             Eastward
             of
             the
             first
             ship
             ,
             take
             11
             degrees
             56
             minutes
             from
             your
             Scale
             of
             Chords
             ,
             and
             place
             them
             from
             Kunto
             I
             ,
             upon
             the
             quadrant
             KIH
             .
             Then
             from
             F
             draw
             the
             line
             IF
             ,
             and
             upon
             the
             line
             ,
             FI
             ,
             place
             the
             distance
             that
             you
             must
             bring
             the
             second
             ship
             from
             the
             first
             (
             which
             is
             fourty
             leagues
             and
             two
             miles
             )
             from
             F
             unto
             M.
             So
             is
             M
             the
             place
             of
             your
             second
             ship
             .
             Then
             from
             M
             draw
             the
             line
             ML
             parallel
             unto
             FG
             ,
             cutting
             the
             line
             AGL
             in
             L
             ,
             then
             draw
             the
             line
             MA
             ,
             cutting
             the
             Quadrant
             BDE
             in
             D.
             So
             shall
             the
             Arch
             DE
             be
             the
             course
             that
             the
             second
             ship
             must
             run
             ,
             to
             bring
             her self
             fourty
             leagues
             and
             two
             miles
             North
             and
             by
             East
             ,
             and
             41
             minutes
             East
             of
             the
             first
             ship
             .
             Then
             to
             know
             what
             you
             have
             altered
             the
             latitude
             ,
             first
             take
             the
             distance
             LA
             and
             apply
             it
             unto
             the
             Scale
             of
             equall
             parts
             ,
             and
             you
             shall
             find
             it
             to
             be
             80
             leagues
             ,
             which
             is
             just
             4
             degrees
             ,
             which
             you
             have
             altered
             your
             latitude
             ,
             or
             Poles
             elevation
             :
             which
             4
             degrees
             added
             unto
             the
             latitude
             you
             depar
             ed
             from
             ,
             it
             makes
             51
             degrees
             56
             min.
             for
             the
             latitude
             that
             your
             second
             Ship
             is
             in
             ,
             then
             take
             the
             distance
             LM
             and
             apply
             it
             to
             the
             Scale
             ,
             it
             gives
             60
             leagues
             ;
             then
             open
             your
             Compasses
             unto
             the
             distance
             of
             the
             middle
             latitude
             ,
             which
             is
             40
             deg
             .
             5●
             min.
             of
             the
             Chord
             ,
             and
             apply
             it
             unto
             the
             Table
             of
             longitudes
             ,
             and
             it
             gives
             12
             
             leagues
             ,
             and
             2
             miles
             ,
             and
             62
             parts
             ,
             to
             alter
             one
             degree
             of
             longitude
             in
             that
             Parallel
             :
             Then
             set
             one
             foot
             of
             your
             Compasses
             in
             12
             leagues
             2
             miles
             ,
             and
             62
             parts
             ,
             and
             open
             the
             other
             to
             the
             beginning
             of
             the
             line
             ,
             and
             with
             that
             distance
             measure
             the
             line
             
               L
            
             M
             ,
             being
             60
             leagues
             ,
             and
             you
             shall
             find
             that
             it
             is
             contained
             there
             in
             four
             times
             and
             two
             thirds
             ,
             so
             the
             longitude
             is
             4
             degrees
             40
             minutes
             .
          
        
         
           
             CHAP.
             XXI
             .
          
           
             Of
             the
             Ebbing
             and
             Flowing
             of
             the
             Sea
             ,
             aud
             of
             the
             Tides
             ,
             and
             how
             to
             find
             them
             in
             all
             places
             .
          
           
             
               
                 A
                 generall
                 Table
                 for
                 the
                 Tides
                 in
                 all
                 places
                 .
              
               
                 
                   The
                   Moons
                   age
                   .
                
                 
                   Hours
                   and
                   minutes
                   to
                   be
                   added
                   .
                
                 
                   Hours
                   and
                   minutes
                   to
                   be
                   added
                   .
                
                 
                    
                
                 
                   The
                   Moons
                   age
                   .
                
                 
                   Hours
                   and
                   minutes
                   to
                   be
                   added
                   :
                
                 
                   Hours
                   and
                   minutes
                   to
                   be
                   added
                   :
                
              
               
                 
                   Daies
                   .
                
                 
                   Degrees
                   :
                
                 
                   Minutes
                   :
                
                 
                    
                
                 
                   Daies
                   .
                
                 
                   Degrees
                   :
                
                 
                   Minutes
                   :
                
              
               
                 
                   1
                
                 
                   0
                
                 
                   48
                
                 
                    
                
                 
                   16
                
                 
                   0
                
                 
                   48
                
              
               
                 
                   2
                
                 
                   1
                
                 
                   36
                
                 
                    
                
                 
                   17
                
                 
                   1
                
                 
                   36
                
              
               
                 
                   3
                
                 
                   2
                
                 
                   24
                
                 
                    
                
                 
                   18
                
                 
                   2
                
                 
                   24
                
              
               
                 
                   4
                
                 
                   3
                
                 
                   21
                
                 
                    
                
                 
                   19
                
                 
                   3
                
                 
                   12
                
              
               
                 
                   5
                
                 
                   4
                
                 
                   0
                
                 
                    
                
                 
                   20
                
                 
                   4
                
                 
                   0
                
              
               
                 
                   6
                
                 
                   4
                
                 
                   48
                
                 
                    
                
                 
                   21
                
                 
                   4
                
                 
                   48
                
              
               
                 
                   7
                
                 
                   5
                
                 
                   36
                
                 
                    
                
                 
                   22
                
                 
                   5
                
                 
                   36
                
              
               
                 
                   8
                
                 
                   6
                
                 
                   24
                
                 
                    
                
                 
                   23
                
                 
                   6
                
                 
                   24
                
              
               
                 
                   9
                
                 
                   7
                
                 
                   12
                
                 
                    
                
                 
                   24
                
                 
                   7
                
                 
                   12
                
              
               
                 
                   10
                
                 
                   8
                
                 
                   0
                
                 
                    
                
                 
                   25
                
                 
                   8
                
                 
                   0
                
              
               
                 
                   11
                
                 
                   8
                
                 
                   48
                
                 
                    
                
                 
                   26
                
                 
                   8
                
                 
                   48
                
              
               
                 
                   12
                
                 
                   9
                
                 
                   36
                
                 
                    
                
                 
                   27
                
                 
                   9
                
                 
                   36
                
              
               
                 
                   13
                
                 
                   10
                
                 
                   24
                
                 
                    
                
                 
                   28
                
                 
                   10
                
                 
                   24
                
              
               
                 
                   14
                
                 
                   11
                
                 
                   12
                
                 
                    
                
                 
                   29
                
                 
                   11
                
                 
                   12
                
              
               
                 
                   15
                
                 
                   0
                
                 
                   0
                
                 
                    
                
                 
                   30
                
                 
                   0
                
                 
                   0
                
              
            
          
           
             
             
               The
               use
               of
               the
               Table
               of
               the
               Tides
               .
            
             
               FIrst
               it
               is
               to
               be
               understood
               ,
               that
               by
               the
               swift
               motion
               of
               the
               first
               Mover
               ,
               the
               Moon
               and
               all
               the
               rest
               of
               the
               Stars
               and
               Planets
               ,
               are
               turned
               about
               the
               World
               in
               four
               and
               twenty
               hours
               ,
               upon
               which
               swift
               motion
               of
               the
               Moon
               ,
               the
               daily
               motions
               of
               the
               Sea
               ,
               do
               depend
               ,
               which
               motion
               of
               the
               Sea
               falleth
               not
               out
               alwaies
               at
               one
               hour
               ,
               the
               reason
               thereof
               is
               ,
               because
               of
               the
               swift
               motion
               of
               the
               Moon
               in
               regard
               she
               goeth
               almost
               thirteen
               degrees
               in
               four
               and
               twenty
               hours
               ,
               and
               the
               Sun
               moveth
               scarce
               one
               degree
               ,
               which
               gives
               every
               day
               twelve
               degrees
               ,
               that
               the
               Moon
               cometh
               slower
               to
               any
               point
               in
               the
               Heaven
               than
               the
               Sun
               :
               which
               twelve
               degrees
               makes
               fourty
               eight
               minutes
               of
               time
               for
               the
               difference
               of
               every
               full
               Sea
               ,
               according
               unto
               the
               middle
               motion
               of
               the
               Moon
               ,
               which
               difference
               is
               here
               set
               down
               in
               this
               Table
               for
               every
               day
               of
               the
               Moons
               age
               .
               Therefore
               if
               you
               would
               know
               the
               full
               Sea
               at
               any
               place
               in
               the
               World
               ,
               first
               you
               must
               know
               at
               what
               hour
               it
               is
               full
               Sea
               at
               the
               new
               or
               full
               Moon
               ;
               which
               hours
               and
               minutes
               keep
               in
               mind
               ,
               then
               seek
               the
               age
               of
               the
               Moon
               as
               is
               before
               taught
               ,
               and
               with
               the
               number
               of
               her
               age
               enter
               this
               Table
               ,
               under
               the
               Title
               of
               the
               Moons
               age
               ,
               and
               having
               found
               her
               age
               in
               the
               Table
               ,
               against
               it
               you
               shall
               find
               the
               hours
               and
               minutes
               which
               are
               to
               be
               added
               unto
               the
               time
               that
               the
               Moon
               maketh
               full
               Sea
               in
               any
               place
               ,
               and
               the
               whole
               number
               of
               hours
               and
               minutes
               is
               the
               time
               that
               the
               Moon
               maketh
               full
               Sea
               in
               that
               place
               upon
               the
               day
               desired
               .
               As
               for
               example
               ,
               I
               desire
               to
               know
               the
               full
               Sea
               at
               
                 London
              
               Bridge
               upon
               the
               13
               of
               
                 July
              
               1624.
               the
               age
               of
               the
               Moon
               being
               found
               as
               before
               ,
               is
               eight
               daies
               ,
               then
               in
               the
               Table
               I
               find
               eight
               daies
               ,
               and
               against
               it
               6
               hours
               ,
               and
               24
               minutes
               ,
               which
               being
               added
               unto
               3
               hours
               ,
               the
               full
               Sea
               upon
               the
               change
               day
               gives
               9
               a
               clock
               24
               minutes
               for
               the
               time
               at
               the
               full
               Sea
               upon
               the
               13
               day
               of
               
                 July
              
               1624.
               
            
          
        
      
       
         
         
           THE
           SEA-MANS
           GLASSE
           .
        
         
           The
           Second
           Book
           .
        
         
           VVherein
           is
           declared
           the
           Definition
           of
           the
           Sphear
           ,
           a
           Description
           of
           the
           six
           great
           Circles
           ,
           and
           also
           of
           the
           four
           lesser
           Circles
           ,
           last
           of
           all
           ,
           certain
           Questions
           Astronomicall
           ,
           performed
           by
           the
           said
           Scale
           .
        
         
           
             CHAP.
             I.
             
          
           
             Of
             a
             Sphear
             ,
             and
             the
             Circles
             thereof
             .
          
           
             
               The
               figure
               of
               the
               plaine
               Scale
               .
            
          
           
             A
             
               Sphear
            
             according
             to
             the
             Description
             of
             
               Theodosius
               ,
            
             is
             a
             certain
             solid
             Sup●
             ficies
             ,
             in
             whose
             middle
             is
             a
             Point
             ,
             from
             which
             all
             lines
             drawn
             unto
             the
             Circumference
             are
             equall
             ;
             which
             Poi●●
             is
             called
             the
             Center
             of
             the
             Sphear
             ,
             by
             which
             C●●●er
             a
             right
             Line
             being
             drawn
             ,
             and
             excending
             himself
             on
             either
             side
             unto
             that
             part
             of
             the
             Circumference
             whereupon
             the
             Sphear
             is
             turned
             ,
             is
             called
             
               Axis
               Spherae
               ,
            
             or
             the
             Axle-tree
             of
             the
             World.
             
          
           
           
             A
             
               Sphear
            
             accidentally
             is
             divided
             into
             two
             parts
             ,
             that
             is
             to
             say
             ,
             
               in
               Sphaeram
               rectam
               &
               Sphaeram
               obliquam
               .
            
          
           
             
               Sphaera
               recta
               ,
            
             or
             a
             right
             Sphear
             ,
             is
             onely
             unto
             those
             that
             dwell
             under
             the
             
               Equinoctiall
               ,
               Quibus
               neuter
               Polorum
               magis
               altero
               elevatur
               :
            
             that
             is
             ,
             to
             whom
             neither
             of
             the
             Poles
             of
             the
             World
             are
             seen
             ,
             but
             lie
             hid
             in
             the
             
               Horizon
               .
            
          
           
             
               Sphaera
               obliqua
               ,
            
             or
             an
             oblique
             Sphear
             ,
             is
             unto
             those
             that
             inhabit
             on
             either
             side
             of
             the
             
               Equinoctial
               ,
            
             unto
             whom
             one
             of
             the
             Poles
             is
             ever
             seen
             ,
             and
             the
             other
             hid
             under
             the
             
               Horizon
               .
            
          
           
             The
             Circles
             whereupon
             the
             Sphear
             is
             composed
             are
             divided
             into
             two
             sorts
             :
             that
             is
             to
             say
             ,
             
               in
               Circulos
               majores
               &
               minores
               .
            
          
           
             
               Circuli
               majores
               ,
            
             or
             the
             greater
             Circles
             ,
             are
             those
             that
             divide
             the
             Sphear
             into
             two
             equall
             parts
             :
             and
             they
             are
             in
             number
             six
             ,
             
               viz.
            
             the
             
               Equinoctial
               ,
            
             the
             middle
             of
             the
             
               Zodiack
               ,
            
             or
             the
             
               Ecliptique
            
             line
             ,
             the
             two
             
               Colures
               ,
            
             the
             
               Meridian
               ,
            
             and
             the
             
               Horizon
               .
            
          
           
             
               Minores
               vero
               Circuli
               ,
            
             or
             the
             lesser
             Circles
             ,
             are
             such
             as
             divide
             the
             Sphear
             into
             two
             parts
             ,
             unequally
             ,
             and
             they
             are
             four
             in
             number
             ;
             as
             the
             Tropick
             of
             
               Cancer
               ,
            
             the
             Tropick
             of
             
               Capricorn
               ,
            
             the
             Circle
             
               Artike
            
             and
             the
             Circle
             
               Antartike
               .
            
          
        
         
           
             CHAP.
             II.
             
          
           
             Of
             the
             six
             greater
             Circles
             .
          
           
             I.
             THE
             
               Equinoctial
            
             is
             a
             Circle
             that
             crosseth
             the
             Poles
             of
             the
             World
             at
             right
             Angles
             ,
             and
             divideth
             the
             Sphear
             into
             two
             equall
             parts
             ,
             and
             is
             called
             the
             
               Equinoctial
               ,
            
             because
             when
             the
             Sun
             cometh
             unto
             it
             ,
             (
             which
             is
             twice
             in
             the
             year
             ,
             viz.
             
               In
               principio
               Arietis
               ,
               &
               Librae
               ,
            
             that
             is
             ,
             in
             
               March
            
             and
             
               September
               )
            
             the
             daies
             and
             nights
             are
             equal
             thoroughout
             the
             whole
             World
             ,
             whereupon
             it
             is
             called
             
               Equator
               diei
               &
               noctis
               ,
            
             the
             equall
             proportioner
             of
             the
             day
             and
             night
             artificiall
             :
             and
             in
             the
             figure
             is
             described
             by
             the
             line
             CAE
             .
          
           
             II.
             The
             
               Meridian
            
             is
             a
             great
             Circle
             passing
             thorow
             the
             Poles
             of
             the
             World
             ,
             and
             the
             Poles
             of
             the
             
               Horizon
               ,
            
             or
             
               Zenith
            
             point
             over
             our
             heads
             ;
             and
             is
             so
             called
             ,
             because
             that
             in
             any
             time
             of
             the
             year
             ,
             or
             in
             
             any
             place
             of
             the
             World
             ,
             when
             the
             Sun
             (
             by
             the
             motion
             of
             the
             Heavens
             )
             cometh
             unto
             that
             Circle
             ,
             it
             is
             noon
             ,
             or
             twelve
             of
             the
             Clock
             .
             And
             it
             is
             to
             be
             understood
             ,
             that
             all
             Towns
             and
             places
             that
             lie
             East
             and
             VVest
             one
             of
             another
             ,
             have
             every
             one
             a
             severall
             Meridian
             :
             but
             all
             places
             that
             lie
             North
             and
             South
             one
             of
             another
             ,
             have
             one
             and
             the
             same
             meridian
             .
             This
             Circle
             is
             declared
             in
             the
             figure
             following
             by
             the
             Circle
             BCDE
             .
          
           
           
             IV.
             The
             two
             Colures
             ,
             
               Colurus
               Solstitiorum
               ,
            
             or
             the
             Summer
             Colure
             ,
             is
             a
             Circle
             passing
             by
             the
             Poles
             of
             the
             World
             ,
             and
             by
             the
             Poles
             of
             the
             Ecliptick
             ,
             and
             by
             the
             head
             of
             
               Cancer
            
             and
             
               Capricorn
               ,
            
             whereupon
             ,
             the
             first
             scruple
             of
             
               Cancer
               ,
            
             where
             the
             Colure
             crosseth
             the
             Ecliptick
             Line
             ,
             is
             called
             
               Punctus
               solstitiae
               aestivalis
               ,
            
             or
             the
             point
             of
             the
             Summer
             Solstice
             :
             to
             which
             place
             when
             the
             Sun
             cometh
             ,
             he
             can
             approach
             no
             nearer
             unto
             our
             
               Zenith
               ,
            
             but
             returneth
             unto
             the
             
               Equator
            
             again
             .
             
               Arcus
               vero
               Coluri
               ,
            
             The
             Ark
             of
             the
             Colure
             contained
             betwixt
             the
             Summer
             Solstice
             and
             the
             
               Equator
               ,
            
             is
             called
             the
             greatest
             declination
             of
             the
             Sun
             ,
             which
             
               Ptolomy
            
             found
             to
             be
             23
             degrees
             ,
             31
             minutes
             :
             
               but
               by
               the
               observation
               of
            
             Copernicus
             
               it
               was
               found
               to
               vary
               ,
               for
               ●e
               found
               the
               declination
               sometimes
               to
               be
            
             23
             
               degrees
            
             52
             
               minutes
               ,
               and
               in
               the
               processe
               of
               time
               to
               be
               but
            
             23
             
               degrees
            
             28
             
               minutes
               .
               And
               in
               these
               our
               daies
               (
               by
               the
               observation
               of
            
             Ticho
             de
             Brahe
             ,
             
               and
               that
               late
               famous
               Mathematician
               ,
               Mr.
            
             Edward
             Right
             )
             
               it
               is
               found
               distant
               from
               the
            
             Equinoctiall
             23
             
               degrees
               ,
            
             31
             
               minutes
               ,
            
             30
             
               seconds
               .
            
          
           
             V.
             The
             other
             Colure
             passeth
             by
             the
             Poles
             of
             the
             World
             ,
             &
             by
             the
             first
             point
             of
             
               Aries
            
             and
             
               Libra
               ,
            
             whereupon
             it
             is
             called
             
               Colurus
               distinguens
               Equinoxia
               .
            
             These
             two
             Colures
             do
             crosse
             each
             other
             at
             right
             Angles
             in
             the
             Poles
             of
             the
             world
             ,
             
               whereupon
               these
               ,
               verses
               were
               made
               .
            
             
               
                 Haec
                 duo
                 Solstitia
                 faciunt
                 
                   Cancer
                   Capricornus
                   ,
                
              
               
                 Sed
                 noctes
                 aequant
                 
                   Aries
                   &
                   Libra
                
                 diebus
                 .
              
            
          
           
        
         
           
           
             CHAP.
             III.
             
          
           
             Of
             the
             four
             lesser
             Circles
             .
          
           
             THe
             Sun
             having
             ascended
             unto
             his
             highest
             Solstitial
             Point
             doth
             describe
             a
             Circle
             ,
             which
             is
             the
             nearest
             that
             he
             can
             approach
             unto
             the
             North
             Pole
             ,
             whereupon
             it
             is
             called
             
               Circulus
               Solstitii
               aestivalis
               ,
            
             the
             Circle
             of
             the
             Summer
             Solstice
             ,
             or
             the
             Tropick
             of
             
               Cancer
               ,
            
             and
             is
             noted
             in
             the
             figure
             before
             ,
             by
             the
             line
             H
             Y
             I.
             
          
           
             The
             Sun
             also
             approaching
             unto
             the
             first
             scruple
             of
             
               Capricornus
               ,
            
             or
             the
             Winter
             Solstice
             ,
             describeth
             another
             Circle
             ,
             which
             is
             the
             utmost
             bounds
             that
             the
             Sun
             can
             depart
             from
             the
             Equinoctiall
             Line
             towards
             the
             Antartike
             Pole
             ,
             whereupon
             it
             is
             called
             
               Circulus
               solstitii
               hyemalis
               ,
               sive
               Tropicus
               hyemalis
               ,
               vel
               Capricorni
               :
            
             the
             Circle
             of
             the
             Winter
             Solstice
             ,
             the
             VVinter
             Tropick
             ,
             or
             the
             Tropick
             of
             
               Capricorn
               ,
            
             and
             is
             described
             in
             the
             figure
             by
             the
             line
             GXF.
             
          
           
             So
             much
             as
             the
             Ecliptick
             declineth
             from
             the
             Equinoctiall
             ,
             so
             much
             doth
             the
             Poles
             of
             the
             Ecliptick
             decline
             from
             the
             Poles
             of
             the
             VVorld
             ,
             whereupon
             the
             Pole
             of
             the
             Ecliptick
             ,
             which
             is
             by
             the
             North
             Pole
             of
             the
             VVorld
             ,
             describeth
             a
             certain
             Circle
             as
             it
             passeth
             about
             the
             Pole
             of
             the
             VVorld
             ,
             being
             just
             so
             far
             from
             the
             Pole
             as
             the
             Tropick
             of
             
               Cancer
            
             is
             from
             the
             Equator
             ,
             and
             it
             is
             the
             third
             of
             the
             lesser
             Circles
             ,
             and
             is
             called
             
               Circulus
               Arcticus
               ,
            
             or
             the
             Circle
             of
             the
             North
             Pole
             ,
             and
             is
             described
             in
             the
             
               Diagram
               ,
            
             in
             the
             second
             Chapter
             by
             the
             line
             PO.
             
          
           
             The
             fourth
             and
             last
             of
             the
             lesser
             Circles
             is
             described
             in
             like
             manner
             ,
             by
             the
             other
             Pole
             of
             the
             Ecliptick
             ,
             about
             the
             South
             Pole
             of
             the
             world
             ,
             and
             therefore
             called
             
               Circulus
               Antarcticus
               ,
            
             the
             Antarctick
             Circle
             ,
             or
             the
             Circle
             of
             the
             Antarctick
             or
             South
             Pole
             ,
             and
             is
             demonstrated
             in
             the
             former
             figure
             ,
             by
             the
             line
             NM
             .
          
        
         
           
           
             CHAP.
             IV.
             
          
           
             Definitions
             of
             some
             peculiar
             terms
             fit
             to
             be
             known
             by
             such
             as
             intend
             to
             practice
             the
             Art
             of
             Navigation
             or
             Astronomy
             .
          
           
             THe
             Zenith
             is
             an
             imaginary
             point
             in
             the
             Heavens
             over
             our
             heads
             ,
             making
             right
             Angles
             with
             the
             Horizon
             ,
             as
             the
             Equinoctiall
             maketh
             with
             the
             Pole.
             
          
           
             The
             
               Nadir
            
             is
             a
             prick
             in
             the
             heavens
             under
             our
             feet
             ,
             making
             right
             Angles
             with
             the
             Horizon
             under
             the
             earth
             ,
             as
             the
             Zenith
             doth
             above
             ,
             and
             therefore
             is
             opposite
             unto
             the
             Zenith
             .
          
           
             The
             declination
             of
             the
             Sun
             is
             the
             Ark
             of
             a
             Circle
             contained
             betwixt
             the
             place
             of
             the
             Sun
             in
             the
             Ecliptick
             ,
             and
             the
             Equinoctiall
             ,
             making
             right
             Angles
             with
             the
             Equinoctiall
             .
             But
             the
             declination
             of
             a
             Star
             is
             the
             Ark
             of
             a
             Circle
             let
             fall
             from
             the
             Center
             of
             a
             Star
             ,
             perpendicularly
             unto
             the
             Equinoctiall
             .
          
           
             The
             Latitude
             is
             the
             Ark
             of
             a
             Circle
             contained
             betwixt
             the
             Center
             of
             any
             Star
             ,
             and
             the
             Ecliptick
             Line
             ,
             making
             right
             Angles
             with
             the
             Ecliptick
             ,
             and
             counted
             either
             Northward
             ,
             or
             Southward
             ,
             according
             to
             the
             scituation
             of
             the
             Star
             ,
             whether
             it
             be
             nearer
             unto
             the
             North
             or
             South
             Pole
             of
             the
             Ecliptick
             .
          
           
             The
             Latitude
             of
             a
             Town
             or
             Countrey
             ,
             is
             the
             height
             of
             the
             Pole
             above
             the
             Horizon
             ,
             or
             the
             distance
             betwixt
             the
             Zenith
             and
             the
             Equinoctiall
             .
          
           
             The
             Longitude
             of
             a
             Star
             is
             that
             part
             of
             the
             Ecliptick
             which
             is
             contained
             betwixt
             the
             Stars
             place
             in
             the
             Ecliptick
             ,
             and
             the
             beginning
             of
             
               Aries
               ,
            
             counting
             them
             from
             
               Aries
            
             according
             to
             the
             succession
             or
             order
             of
             the
             signes
             .
          
           
             The
             Longitude
             of
             a
             Town
             or
             Countrey
             are
             the
             number
             of
             degrees
             ,
             which
             are
             contained
             in
             the
             Equinoctiall
             ,
             betwixt
             the
             Meridian
             that
             passeth
             over
             the
             Isles
             of
             
               Azores
               ,
            
             (
             from
             whence
             the
             beginning
             of
             longitude
             is
             accounted
             )
             East
             wards
             ,
             and
             the
             Meridian
             that
             passeth
             over
             the
             Town
             or
             Country
             desired
             .
          
           
             The
             Altitude
             of
             the
             Sun
             or
             Star
             is
             the
             Arch
             of
             a
             Circle
             ,
             contained
             betwixt
             the
             Center
             of
             the
             Sun
             ,
             or
             any
             Star
             ,
             and
             the
             Horizon
             .
          
           
           
             The
             Amplitude
             is
             that
             part
             of
             the
             Horizon
             which
             is
             betwixt
             the
             true
             East
             or
             West
             points
             ,
             and
             the
             point
             of
             the
             Compasse
             that
             the
             Sun
             or
             any
             Star
             doth
             rise
             or
             set
             upon
             .
          
           
             Azimuth's
             are
             Circles
             ,
             which
             meet
             together
             in
             the
             Zenith
             ,
             and
             crosse
             the
             Horizon
             at
             right
             Angles
             ,
             and
             serve
             to
             find
             the
             point
             of
             the
             Compasse
             ,
             which
             the
             Sun
             is
             upon
             at
             any
             hour
             of
             the
             day
             ,
             or
             the
             Azimuth
             of
             the
             Sun
             or
             Star
             ,
             is
             a
             part
             of
             the
             Horizon
             contained
             betwixt
             the
             true
             East
             or
             West
             point
             ,
             and
             that
             Azimuth
             which
             passeth
             by
             the
             Center
             of
             the
             same
             Star
             to
             the
             Horizon
             .
          
           
             The
             right
             ascension
             of
             a
             Star
             is
             that
             part
             of
             the
             Equinoctiall
             that
             riseth
             or
             setteth
             with
             the
             Star
             ,
             in
             a
             right
             Sphere
             :
             or
             in
             an
             oblique
             Sphere
             ,
             it
             is
             that
             portion
             of
             the
             Equinoctiall
             ,
             contained
             betwixt
             the
             beginning
             of
             
               Aries
               ,
            
             and
             that
             place
             of
             the
             Equinoctiall
             ,
             which
             passeth
             by
             the
             Meridian
             with
             the
             Center
             of
             the
             Star.
             
          
           
             The
             oblique
             ascension
             is
             a
             part
             of
             the
             Equinoctiall
             ,
             contained
             betwixt
             the
             beginning
             of
             
               Aries
               ,
            
             and
             that
             part
             of
             the
             Equinoctiall
             that
             riseth
             with
             the
             Center
             of
             a
             Star
             ,
             in
             an
             oblique
             Sphere
             .
          
           
             The
             difference
             ascensionall
             ,
             is
             the
             difference
             betwixt
             the
             right
             and
             oblique
             ascension
             :
             or
             it
             is
             the
             number
             of
             degrees
             contained
             betwixt
             that
             place
             of
             the
             Equinoctiall
             that
             riseth
             with
             the
             Center
             of
             a
             Star
             ,
             and
             that
             place
             of
             the
             Equinoctiall
             that
             cometh
             unto
             the
             Meridian
             ,
             with
             the
             Center
             of
             the
             same
             Star.
             
          
           
             
               Almicanterahs
            
             are
             Circles
             drawn
             parallel
             unto
             the
             Horizon
             ,
             one
             over
             another
             ,
             untill
             you
             come
             unto
             the
             Zenith
             :
             these
             are
             Circles
             that
             do
             measure
             the
             elevation
             of
             the
             Pole
             ,
             or
             height
             of
             the
             Sun
             ,
             Moon
             ,
             or
             Stars
             above
             the
             Horizon
             ,
             which
             is
             called
             the
             Almicanter
             of
             the
             Sun
             ,
             Moon
             ,
             or
             Star
             :
             the
             Ark
             of
             the
             Sun
             or
             Stars
             Almicanter
             ,
             is
             a
             portion
             of
             an
             Azimuth
             contained
             betwixt
             that
             Almicanter
             which
             passeth
             thorow
             the
             Center
             of
             the
             Star
             ,
             and
             the
             Horizon
             .
          
        
         
           
           
             QUESTIONS
             ASTRONOMICAL
             ,
             performed
             by
             the
             plain
             Scale
             .
          
           
             CHAP.
             V.
             
          
           
             The
             true
             place
             of
             the
             Sun
             being
             given
             ,
             to
             find
             his
             declination
             .
             The
             Sun
             being
             in
             the
             head
             of
             
               Taurus
               ,
            
             his
             declination
             is
             desired
             .
          
           
             BY
             the
             seventh
             Demonstration
             ,
             draw
             the
             line
             AD
             ,
             then
             upon
             the
             Center
             A
             raise
             the
             Perpendicular
             AB
             ,
             then
             opening
             your
             Compasses
             to
             the
             Radius
             of
             your
             Scale
             ,
             place
             one
             foot
             in
             the
             Center
             A
             ,
             and
             with
             the
             other
             draw
             the
             Quadrant
             BCD
             ,
             then
             opening
             your
             Compasses
             unto
             the
             greatest
             declination
             of
             the
             Sun
             ,
             place
             it
             upon
             the
             Quadrant
             ,
             from
             D
             unto
             K
             ,
             then
             from
             the
             point
             K
             draw
             the
             line
             KH
             ,
             parallel
             to
             DA
             ,
             cutting
             the
             line
             AB
             in
             H
             ,
             then
             with
             the
             distance
             AH
             draw
             the
             small
             Quadrant
             GEH
             ,
             and
             in
             regard
             the
             Sun
             is
             in
             
             the
             head
             of
             
               Taurus
               ,
            
             which
             is
             30
             degrees
             from
             the
             beginning
             of
             
               Aries
               ,
            
             let
             AD
             be
             the
             Equator
             ,
             and
             D
             the
             beginning
             of
             
               Aries
               ,
            
             DC
             30
             degrees
             ,
             or
             longitude
             of
             the
             Sun
             ,
             then
             from
             the
             point
             C
             draw
             the
             line
             CA
             ,
             cutting
             the
             Quadrant
             GEH
             in
             E
             ,
             then
             from
             E
             draw
             the
             line
             EI
             parallel
             to
             AD
             ,
             cutting
             the
             Quadrant
             BCD
             in
             I
             ,
             so
             shall
             the
             Arch
             ID
             be
             the
             declination
             of
             the
             Sun
             desired
             ,
             which
             in
             this
             demonstration
             is
             found
             to
             be
             eleven
             degrees
             ,
             and
             thirty
             one
             minutes
             .
          
        
         
           
           
             CHAP.
             VI.
             
          
           
             The
             declination
             of
             the
             Sun
             ,
             and
             quarter
             of
             the
             Ecliptick
             that
             he
             possesseth
             ,
             being
             given
             ,
             it
             is
             desired
             to
             find
             his
             true
             place
             .
          
           
             The
             Declination
             is
             
               10
            
             deg
             .
             
               31
            
             min.
             the
             first
             quarter
             that
             he
             possesseth
             ,
             is
             betwixt
             the
             head
             of
             
               Aries
            
             and
             
               Cancer
               .
            
          
           
             FIrst
             ,
             by
             the
             seventh
             Demonstration
             ,
             draw
             the
             Quadrant
             ABCD
             ,
             as
             is
             taught
             in
             the
             former
             Chapter
             ,
             then
             set
             the
             greatest
             declination
             of
             the
             Sun
             upon
             the
             Chord
             from
             D
             unto
             K
             ,
             which
             is
             23
             deg
             .
             and
             31
             min.
             then
             from
             K
             draw
             the
             line
             KH
             parallel
             unto
             the
             
               Equator
            
             DA
             ,
             cutting
             the
             line
             BA
             in
             the
             point
             H.
             So
             shall
             HA
             be
             the
             sign
             of
             the
             Suns
             greatest
             declination
             ,
             then
             with
             the
             distance
             AH
             draw
             the
             Quadrant
             GEH
             ,
             then
             from
             D
             upon
             the
             Quadrant
             DBC
             set
             the
             declination
             of
             the
             Sun
             ,
             which
             is
             11
             degrees
             31
             minutes
             from
             D
             unto
             I
             ,
             then
             draw
             the
             line
             IE
             parallel
             unto
             AD
             ,
             cutting
             the
             Quadrant
             GEH
             in
             E.
             Then
             from
             the
             Center
             A
             by
             the
             point
             E
             ,
             draw
             the
             line
             AEC
             ,
             cutting
             the
             Quadrant
             BCD
             in
             C.
             So
             shall
             the
             Ark
             CD
             be
             the
             distance
             of
             the
             sun
             from
             the
             head
             of
             
               Aries
               ,
            
             which
             is
             here
             found
             to
             be
             just
             30
             degrees
             ,
             which
             is
             in
             the
             beginning
             of
             
               Taurus
               .
            
          
        
         
           
             CHAP.
             VII
             .
          
           
             By
             the
             elevation
             of
             the
             Pole
             ,
             and
             declination
             of
             the
             sun
             ,
             to
             find
             the
             amplitude
             of
             the
             sun
             ,
             or
             his
             distance
             of
             rising
             ,
             or
             setting
             from
             the
             true
             East
             or
             West
             point
             .
          
           
             The
             elevation
             of
             the
             Pole
             is
             
               51
            
             deg
             .
             
               32
            
             min.
             the
             declination
             of
             the
             sun
             is
             
               14
            
             deg
             .
             
               52
            
             min.
             North.
             
          
           
             BY
             the
             eight
             Demonstration
             ,
             first
             draw
             the
             line
             BD
             ,
             then
             upon
             the
             Center
             A
             draw
             the
             Circle
             BCDE
             ,
             then
             from
             A
             raise
             the
             Perpendicular
             CAE
             ,
             then
             is
             your
             Circle
             divided
             into
             four
             equall
             parts
             :
             then
             suppose
             the
             elevation
             of
             the
             Pole
             to
             
             be
             51
             degrees
             ,
             32
             minutes
             ,
             which
             must
             be
             placed
             upon
             the
             Circle
             ,
             from
             D
             unto
             F
             ,
             then
             from
             the
             point
             F
             ,
             by
             the
             Center
             A
             ,
             draw
             the
             line
             FAG
             ,
             representing
             the
             Pole
             of
             the
             World
             ,
             F
             being
             the
             North
             Pole
             ,
             and
             G
             the
             South
             Pole
             ,
             then
             substract
             51
             deg
             .
             32
             min.
             from
             90
             deg
             .
             and
             the
             remainder
             is
             the
             height
             of
             the
             Equinoctiall
             ,
             which
             is
             38
             deg
             .
             28
             min.
             which
             must
             be
             placed
             upon
             the
             Circle
             from
             the
             
             Horizon
             B
             ,
             unto
             the
             point
             I
             ,
             then
             from
             I
             ,
             by
             the
             Center
             A
             ,
             draw
             the
             line
             IAH
             ,
             representing
             the
             Equinoctiall
             Circle
             .
             Then
             from
             I
             unto
             M
             set
             the
             declination
             of
             the
             Sun
             ,
             being
             here
             supposed
             14
             deg
             .
             52
             minutes
             North
             ,
             then
             from
             the
             point
             M
             draw
             the
             line
             ,
             or
             Parallel
             of
             declination
             MTN
             ,
             parallel
             unto
             the
             Equator
             I
             A
             H
             ,
             cutting
             the
             Horizon
             BD
             in
             T
             ,
             then
             from
             T
             raise
             the
             perpendicular
             TV
             ,
             cutting
             the
             Circle
             BCDE
             in
             V
             ,
             so
             shall
             the
             distance
             CV
             be
             the
             true
             amplitude
             of
             the
             sun
             desired
             ,
             which
             here
             is
             found
             to
             be
             24
             deg
             ,
             21
             minutes
             North.
             
          
        
         
           
           
             CHAP.
             VIII
             .
          
           
             By
             the
             Amplitude
             of
             the
             Sun
             ,
             to
             find
             the
             variation
             of
             the
             Compasse
             .
          
           
             HAving
             found
             the
             Amplitude
             of
             the
             Sun
             by
             the
             last
             Chapter
             ,
             first
             observe
             with
             a
             Compasse
             ,
             or
             rather
             with
             a
             Semicircle
             ,
             upon
             what
             degree
             and
             minute
             the
             Sun
             riseth
             or
             setteth
             ,
             beginning
             to
             reckon
             from
             the
             East
             or
             West
             ,
             and
             ending
             at
             the
             North
             or
             South
             at
             90
             degrees
             :
             and
             when
             you
             have
             diligently
             observed
             the
             Magneticall
             rising
             or
             setting
             ,
             by
             the
             Semicircle
             ,
             or
             by
             some
             other
             like
             fitting
             Instrument
             :
             and
             also
             the
             true
             Amplitude
             found
             ,
             as
             is
             declared
             in
             the
             last
             Chapter
             ,
             the
             difference
             of
             these
             two
             Amplitudes
             ,
             is
             the
             variation
             of
             the
             Compasse
             :
             But
             when
             the
             Sun
             riseth
             upon
             the
             same
             Degree
             of
             the
             Compasse
             ,
             as
             is
             found
             by
             the
             Scale
             ,
             the
             variation
             is
             nothing
             ,
             but
             the
             Needle
             pointeth
             directly
             unto
             the
             Poles
             of
             the
             World
             ,
             which
             by
             M.
             
               Mulinux
            
             was
             affirmed
             to
             be
             at
             the
             Westernmost
             part
             of
             
               S.
               Michaels
               ,
            
             one
             of
             the
             Islands
             of
             the
             
               Azores
               ,
            
             from
             whence
             he
             will
             have
             the
             Longitude
             reckoned
             .
             Secondly
             ,
             when
             the
             Sun
             is
             in
             the
             Equinoctial
             Circle
             ,
             where
             he
             hat●
             no
             Amplitude
             ,
             look
             what
             distance
             the
             Compasse
             maketh
             the
             Sun
             to
             rise
             from
             the
             East
             or
             West
             of
             the
             Compasse
             ,
             the
             same
             distance
             is
             the
             Compasses
             variation
             ,
             from
             the
             North
             or
             South
             .
             Thirdly
             ,
             if
             the
             Sun
             rise
             more
             to
             the
             South
             of
             the
             Compasse
             ,
             or
             setteth
             more
             to
             the
             North
             of
             the
             Compasse
             ,
             than
             is
             shewed
             by
             the
             Scale
             ,
             the
             difference
             betwixt
             the
             Amplitude
             given
             by
             the
             Scale
             ,
             and
             the
             Amplitude
             given
             by
             the
             Needle
             ,
             is
             the
             variation
             of
             the
             Compasse
             from
             the
             North
             Westward
             .
             Fourthly
             ,
             if
             the
             Compasse
             sheweth
             the
             Sun
             to
             rise
             more
             Northward
             ,
             or
             set
             more
             Southward
             ,
             than
             is
             shewed
             by
             the
             Scale
             ,
             the
             difference
             is
             the
             variation
             of
             the
             Compasse
             ,
             from
             the
             North
             Eastward
             .
             Fifthly
             ,
             if
             the
             Scale
             shew
             the
             Amplitude
             of
             the
             Sun
             rising
             Southerly
             ,
             and
             the
             Compasse
             shew
             it
             to
             be
             Northerly
             ,
             adde
             both
             the
             Amplitudes
             together
             ,
             and
             they
             shew
             you
             the
             variation
             Westernly
             .
          
        
         
           
           
             CHAP.
             IX
             .
          
           
             The
             place
             of
             the
             sun
             being
             given
             ,
             to
             find
             his
             declination
             ,
             by
             a
             whole
             Circle
             .
          
           
             The
             suns
             place
             is
             the
             tenth
             degree
             of
             
               Taurus
               .
            
          
           
             ACcording
             unto
             the
             eighth
             Demonstration
             ,
             first
             draw
             the
             Circle
             BCDE
             ,
             then
             draw
             the
             Horizon
             BAD
             ,
             and
             then
             the
             Equinoctial
             IAH
             ,
             as
             is
             before
             taught
             :
             and
             then
             the
             Tropick
             of
             
               Cancer
            
             KL
             ,
             twenty
             three
             degrees
             and
             a
             half
             from
             the
             Equinoctial
             :
             then
             draw
             the
             Tropick
             of
             
               Capricorn
            
             PO
             ,
             
             of
             like
             distance
             from
             the
             Equinoctial
             ,
             and
             after
             from
             K
             to
             O
             draw
             the
             Ecliptick
             line
             KAO.
             And
             when
             you
             have
             thus
             laid
             down
             the
             Sphere
             ,
             suppose
             the
             Sun
             to
             be
             in
             the
             tenth
             degree
             of
             
               Taurus
               ,
            
             at
             which
             time
             his
             declination
             is
             desired
             .
             And
             in
             regard
             the
             Sun
             is
             more
             near
             unto
             the
             Tropical
             point
             
               Cancer
               ,
            
             than
             unto
             
               Capricorn
               ;
            
             first
             find
             how
             
             many
             degrees
             he
             is
             from
             the
             Tropick
             of
             
               Cancer
               ,
            
             and
             you
             shall
             find
             him
             to
             be
             50
             degrees
             ;
             therefore
             take
             with
             your
             Compasses
             50
             degrees
             from
             the
             Chord
             ,
             and
             apply
             it
             from
             the
             Tropical
             point
             
               Cancer
            
             at
             K
             ,
             unto
             V
             ,
             upon
             one
             side
             ,
             and
             unto
             P
             on
             the
             other
             side
             :
             then
             draw
             the
             Line
             VP
             ,
             cutting
             the
             Ecliptick
             KO
             in
             the
             point
             R
             ,
             then
             from
             R
             draw
             the
             Line
             MRN
             parallel
             unto
             the
             Equinoctial
             IAH
             ,
             and
             cutting
             the
             Quadrant
             BC
             in
             the
             point
             M.
             So
             shall
             the
             arke
             MI
             be
             the
             declination
             of
             the
             Sun
             desired
             ,
             which
             being
             applyed
             unto
             your
             Scale
             ,
             gives
             you
             14
             deg
             .
             and
             52
             minutes
             .
          
        
         
           
             CHAP.
             X.
             
          
           
             The
             elevation
             of
             the
             Pole
             ,
             and
             declination
             of
             the
             sun
             given
             ,
             to
             find
             his
             height
             in
             the
             vertical
             Circle
             .
          
           
             The
             Pole
             is
             elevated
             
               51
            
             degrees
             
               32
            
             minutes
             ,
             the
             declination
             of
             the
             sun
             is
             
               14
            
             degrees
             
               52
            
             minutes
             North
             ,
             his
             height
             in
             the
             Verticall
             Circle
             is
             found
             as
             followeth
             .
          
           
             FIrst
             ,
             according
             unto
             the
             former
             Chapter
             ,
             draw
             the
             Circle
             BCDE
             ,
             then
             the
             Horizon
             BAD
             ,
             and
             after
             the
             verticall
             line
             CAE
             ,
             then
             the
             Axis
             of
             the
             World
             FG
             ,
             and
             likewise
             the
             Equator
             IAH
             ,
             this
             being
             done
             ,
             place
             the
             declination
             of
             the
             Sun
             14
             degrees
             52
             minutes
             ,
             upon
             the
             Circle
             from
             I
             unto
             M
             ,
             and
             also
             from
             H
             unto
             N
             ,
             then
             draw
             the
             line
             MN
             ,
             cutting
             the
             line
             CAE
             in
             S
             ,
             then
             from
             S
             draw
             the
             line
             SVV
             ,
             parallel
             unto
             the
             Horizon
             BAD
             ,
             cutting
             the
             Meridian
             Circle
             BCDE
             in
             VV
             :
             so
             shall
             the
             distance
             DVV
             be
             the
             height
             of
             the
             Sun
             in
             the
             vertical
             Circle
             ,
             for
             the
             time
             demanded
             ,
             which
             by
             this
             proposition
             is
             found
             to
             be
             19
             degrees
             and
             8
             minutes
             .
          
        
         
           
           
             CHAP.
             XI
             .
          
           
             The
             elevation
             of
             the
             Pole
             ,
             and
             the
             Amplitude
             of
             the
             sun
             ,
             being
             given
             ,
             to
             find
             the
             declination
             .
          
           
             The
             elevation
             of
             the
             Pole
             is
             
               51
            
             degrees
             
               32
            
             minutes
             ,
             the
             suns
             amplitude
             is
             
               24
            
             degrees
             
               21
            
             minutes
             ,
             the
             declination
             is
             found
             as
             followeth
             .
          
           
             
          
           
             FIrst
             ,
             as
             in
             the
             eight
             demonstration
             ,
             upon
             the
             Center
             A
             ,
             draw
             the
             Circle
             BCDE
             ,
             then
             draw
             the
             Line
             BAD
             ,
             representing
             the
             Horizon
             :
             dividing
             the
             circle
             into
             two
             equall
             parts
             then
             draw
             the
             Line
             CAE
             ,
             perpendicular
             to
             BAD
             ,
             representing
             the
             East
             and
             VVest
             points
             of
             the
             Compasse
             ,
             then
             placing
             the
             elevation
             of
             the
             Pole
             51
             degrees
             and
             32
             minutes
             ,
             from
             D
             unto
             F
             ,
             from
             F
             ,
             by
             the
             center
             A
             ▪
             draw
             the
             Line
             FAG
             ,
             which
             let
             be
             the
             Pole
             or
             Axletree
             of
             the
             world
             ,
             then
             from
             B
             unto
             I
             ,
             and
             from
             D
             unto
             H
             ,
             
             set
             the
             complement
             of
             the
             Poles
             elevation
             :
             which
             shall
             represent
             the
             Equinoctiall
             ,
             in
             regard
             it
             maketh
             right
             Angles
             with
             the
             Pole
             of
             the
             world
             ,
             in
             the
             center
             A.
             Then
             from
             
               C
            
             unto
             V
             place
             the
             amplitude
             of
             the
             Sun
             ,
             which
             is
             24
             degrees
             and
             21
             minutes
             :
             then
             from
             V
             let
             fall
             the
             perpendicular
             VT
             ,
             cutting
             the
             Horizon
             BAD
             in
             the
             point
             T
             ,
             then
             from
             the
             point
             T
             ,
             draw
             the
             Line
             MTN
             parallel
             unto
             the
             Equinoctiall
             IAH
             ,
             and
             cutting
             the
             Circle
             BCDE
             in
             the
             points
             ,
             M
             and
             N
             ,
             so
             shall
             the
             distance
             ,
             M
             ,
             or
             HN
             ,
             be
             the
             declination
             of
             the
             Sun
             ,
             which
             was
             desired
             :
             which
             being
             applied
             unto
             your
             Scale
             ,
             gives
             you
             fourteen
             degrees
             and
             fifty
             two
             minutes
             .
          
        
         
           
             CHAP.
             XII
             .
          
           
             The
             elevation
             of
             the
             Pole
             ,
             the
             declination
             of
             the
             Sun
             ,
             and
             hour
             of
             the
             day
             being
             given
             ▪
             to
             find
             the
             Almicanter
             .
          
           
             The
             elevation
             of
             the
             Pole
             is
             thirty
             degrees
             ,
             the
             declination
             of
             the
             Sun
             is
             twenty
             degrees
             North
             ,
             the
             hour
             is
             nine
             in
             the
             morning
             ,
             at
             which
             time
             the
             Almicanter
             is
             found
             ,
             as
             followeth
             .
          
           
             BY
             the
             ninth
             demonstration
             ,
             first
             upon
             the
             Center
             A
             ,
             draw
             the
             Circle
             BCDE
             ,
             then
             draw
             the
             line
             BD
             for
             the
             Horizon
             ,
             then
             place
             your
             Poles
             elevation
             ,
             which
             is
             thirty
             degrees
             ,
             upon
             the
             Circle
             from
             D
             unto
             R
             ,
             then
             from
             R
             by
             the
             center
             A
             ,
             draw
             the
             Line
             RAS
             ,
             representing
             the
             Axis
             of
             the
             World
             ,
             then
             from
             B
             unto
             F
             place
             the
             complement
             of
             the
             Poles
             elevation
             ,
             which
             is
             ●0
             degrees
             ,
             and
             from
             the
             point
             F
             ,
             by
             the
             Center
             A
             ,
             draw
             the
             line
             FAH
             ,
             representing
             the
             Equinoctial
             line
             ,
             and
             then
             set
             the
             declination
             of
             the
             Sun
             from
             F
             unto
             L
             ▪
             and
             from
             L
             draw
             the
             Line
             LPO
             parallel
             unto
             the
             Equator
             FAH
             ,
             cutting
             the
             Axis
             of
             the
             World
             in
             the
             point
             P
             ,
             then
             set
             one
             foot
             of
             your
             Compasses
             in
             the
             point
             P
             ,
             and
             extend
             the
             other
             either
             unto
             L
             or
             unto
             O
             ,
             and
             with
             the
             same
             distance
             of
             your
             Compasses
             ,
             upon
             the
             Center
             P
             ,
             draw
             the
             circle
             LNOQ
             ,
             which
             is
             called
             the
             hour
             circle
             :
             so
             shall
             L
             be
             the
             point
             of
             twelve
             a
             clock
             at
             noon
             ,
             N
             the
             place
             of
             six
             a
             clock
             after
             noon
             ,
             O
             the
             place
             of
             twelve
             a
             clock
             or
             midnight
             ,
             and
             Q
             the
             place
             of
             six
             a
             clock
             
             in
             the
             morning
             :
             Every
             one
             of
             the
             four
             quarters
             must
             be
             divided
             into
             six
             equall
             parts
             ,
             or
             hours
             ,
             making
             the
             whole
             Circle
             to
             contain
             twenty
             four
             parts
             ,
             representing
             the
             twenty
             four
             hours
             of
             the
             day
             and
             night
             ,
             then
             in
             regard
             the
             hour
             of
             the
             day
             was
             nine
             of
             the
             clock
             ,
             which
             is
             three
             hours
             before
             noon
             ,
             take
             three
             of
             those
             twenty
             four
             
             hours
             ,
             and
             place
             them
             upon
             the
             circle
             LNOQ
             ,
             from
             the
             Meridian
             point
             L
             unto
             K
             ,
             the
             nine
             a
             clock
             point
             in
             the
             morning
             ,
             and
             unto
             M
             the
             point
             of
             three
             a
             clock
             after
             noon
             ,
             then
             draw
             the
             line
             MK
             ,
             cutting
             the
             parallel
             of
             the
             Sun
             LO
             in
             the
             point
             I
             ,
             then
             from
             I
             draw
             the
             line
             IG
             parallel
             unto
             the
             Horizon
             BAD
             ,
             which
             shall
             cut
             the
             Meridian
             Circle
             BCDE
             in
             the
             point
             G
             ,
             so
             shall
             the
             distance
             of
             G
             and
             B
             be
             the
             Almicanter
             the
             Sun
             ,
             which
             was
             desired
             ,
             which
             in
             this
             demonstration
             is
             found
             to
             be
             fourty
             eight
             degrees
             and
             eighteen
             minutes
             .
          
        
         
           
           
             CHAP.
             XIII
          
           
             The
             elevation
             of
             the
             Pole
             ,
             the
             Almicanter
             ,
             and
             declination
             of
             the
             Sunne
             ,
             being
             given
             ,
             to
             finde
             the
             houre
             of
             the
             day
             .
          
           
             The
             elevation
             of
             the
             Pole
             is
             thirty
             degrees
             ,
             the
             declination
             of
             the
             Sun
             ,
             is
             twentie
             degrees
             ,
             the
             Almicanter
             of
             the
             Sun
             ,
             is
             fortie
             eight
             degrees
             ,
             and
             eighteene
             minutes
             ,
             the
             houre
             of
             the
             day
             is
             found
             as
             followeth
             .
          
           
             FIrst
             ,
             as
             in
             the
             ninth
             demonstration
             ,
             upon
             the
             Center
             A
             ,
             draw
             the
             Circle
             BCDE
             ,
             then
             draw
             the
             Diameter
             BD
             ,
             representing
             the
             Horizon
             ,
             then
             from
             D
             unto
             R
             ,
             set
             30
             degrees
             ,
             the
             elevation
             of
             the
             Pole
             ,
             then
             from
             R
             unto
             the
             point
             A
             ,
             draw
             the
             line
             RAS
             ,
             representing
             the
             Pole
             of
             the
             World
             ,
             then
             draw
             the
             line
             FAH
             ,
             crossing
             the
             Pole
             in
             A
             ,
             at
             right
             Angles
             ,
             cutting
             the
             Meridian
             circle
             in
             F
             ,
             then
             from
             F
             ,
             set
             twenty
             degrees
             ,
             the
             declination
             of
             ●he
             Sun
             unto
             L
             ,
             and
             then
             from
             the
             point
             L
             ,
             draw
             the
             line
             LPO
             ,
             representing
             the
             parallell
             of
             the
             Sun
             ,
             and
             cutting
             the
             Pole
             of
             the
             World
             in
             P
             ,
             then
             placing
             one
             foot
             of
             your
             Compasses
             in
             P
             ,
             extend
             the
             other
             unto
             L
             ,
             with
             which
             distance
             of
             your
             Compasses
             ,
             draw
             the
             hour
             Circle
             LNOQ
             ,
             then
             from
             the
             Horizon
             at
             B
             ,
             place
             the
             Suns
             Almicanter
             :
             (
             which
             is
             fortie
             eight
             degrees
             ,
             and
             eighteen
             minutes
             ▪
             )
             upon
             the
             Quadrant
             BGL
             ,
             from
             B
             unto
             G
             ,
             then
             from
             the
             point
             G
             ,
             draw
             the
             line
             G●
             parallel
             unto
             the
             Horizon
             BAD
             ,
             cutting
             the
             Line
             LO
             ,
             in
             I
             ,
             then
             from
             the
             point
             I
             ,
             draw
             the
             line
             KIM
             ,
             parallell
             to
             the
             Pole
             of
             the
             World
             QAN
             ,
             cutting
             the
             Circle
             LNO
             ,
             in
             M
             ,
             then
             let
             LN
             ,
             be
             divided
             into
             six
             houres
             ,
             whereof
             LM
             ,
             are
             there
             :
             whereupon
             I
             conclude
             ,
             that
             is
             is
             three
             houres
             from
             noon
             ,
             that
             is
             ,
             at
             nine
             a
             clock
             in
             the
             morning
             ,
             or
             three
             in
             the
             after
             noon
             .
          
        
         
           
           
             CHAP.
             XIV
             .
          
           
             
               The
               Latitude
               of
               the
               place
               ,
               the
               Declination
               of
               the
               Sun
               ,
               and
               the
               Altitude
               of
               the
               Sun
               being
               given
               ,
               to
               finde
               the
               Hour
               of
               the
               day
               :
            
             By
             a
             n●w
             way
             differing
             from
             that
             in
             the
             former
             Chapter
             .
          
           
             
               
                 
                    
                
                 
                   deg
                   .
                
                 
                   min.
                   
                
                 
                    
                
                 
                   deg
                   .
                
                 
                   m
                
              
               
                 
                   The
                   Suns
                   Altitude
                   is
                
                 
                   48
                
                 
                   18
                
                 
                    
                
                 
                    
                
                 
                    
                
              
               
                 
                   The
                   Lat●ude
                   of
                   the
                   place
                   is
                
                 
                   30
                
                 
                   00
                
                 
                   its
                   Comple
                   .
                
                 
                   60
                
                 
                   00
                
              
               
                 
                   The
                   Suns
                   declination
                   is
                
                 
                   20
                
                 
                   00
                
                 
                   N.
                   
                
                 
                   70
                
                 
                   00
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   Sum
                
                 
                   130
                
                 
                   00
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   difference
                
                 
                   10
                
                 
                   00
                
              
            
          
        
         
           
             The
             Complement
             of
             any
             arch
             lesse
             then
             
               90
            
             degrees
             ,
             is
             so
             much
             as
             the
             arch
             wants
             of
             
               90
            
             degrees
             ,
             as
             the
             Complement
             of
             
               20
            
             degrees
             is
             
               70
            
             degrees
             ,
             &c.
             
          
           
             FIrst
             ,
             finde
             the
             sum
             and
             difference
             of
             the
             Complement
             of
             the
             Suns
             declination
             ,
             and
             the
             Complement
             of
             the
             Latitude
             ,
             as
             above
             is
             done
             ,
             where
             the
             sum
             is
             130
             deg
             .
             and
             the
             difference
             10
             deg
             .
             Then
             your
             Compasses
             being
             opened
             to
             the
             
               Radius
            
             of
             your
             line
             of
             Chords
             :
             describe
             the
             Semicircle
             ABC
             ,
             and
             divide
             it
             into
             two
             Quadrants
             by
             the
             perpendic●lar
             BD
             ,
             then
             out
             of
             your
             line
             of
             Chords
             ;
             take
             48
             deg
             .
             18
             min.
             the
             Suns
             Altitude
             ,
             and
             set
             it
             from
             B
             to
             E
             ,
             and
             draw
             E
             F
             parallel
             to
             B
             D
             :
             Then
             from
             your
             line
             of
             Chords
             take
             130
             deg
             .
             the
             sum
             ,
             and
             set
             it
             from
             A
             to
             G
             ,
             (
             or
             its
             Complement
             to
             180
             deg
             .
             which
             is
             50
             deg
             .
             from
             C
             to
             G
             )
             and
             draw
             the
             line
             GH
             also
             parallel
             to
             BD.
             Again
             ,
             out
             of
             your
             line
             of
             Chords
             ,
             take
             10
             deg
             .
             (
             which
             is
             the
             difference
             )
             and
             set
             that
             distance
             from
             A
             to
             K
             ,
             and
             draw
             K
             L
             parallel
             to
             EF
             or
             BD.
             
          
           
             This
             done
             ,
             take
             with
             your
             Compasses
             the
             distance
             from
             F
             to
             H
             ,
             and
             seting
             one
             foot
             in
             A
             ,
             with
             the
             other
             describe
             the
             Arch
             MP
             ,
             likewise
             take
             the
             distance
             from
             F
             to
             L
             ,
             and
             seting
             one
             foot
             in
             C
             ,
             
             with
             the
             other
             describe
             the
             arch
             NQ
             .
             Lastly
             draw
             the
             streight
             line
             PQ
             ▪
             which
             only
             touching
             the
             two
             former
             arkes
             will
             cut
             the
             line
             AC
             in
             O
             ,
             Upon
             the
             point
             O
             ,
             therefore
             ,
             erect
             the
             perpendicular
             OR
             ,
             
             cutting
             the
             Semicircle
             in
             R
             ,
             so
             will
             CR
             being
             measured
             upon
             your
             line
             of
             Chords
             ,
             give
             you
             the
             degrees
             of
             the
             Sun
             from
             the
             South
             part
             of
             the
             Meridian
             ,
             which
             here
             you
             will
             finde
             to
             be
             45
             degrees
             ,
             which
             make
             3
             hours
             ,
             allowing
             15
             degrees
             for
             an
             hour
             ,
             for
             15
             degrees
             make
             one
             hour
             ,
             and
             one
             degree
             makes
             4
             minuts
             of
             an
             hour
             ,
             so
             that
             it
             is
             either
             9
             of
             the
             clock
             in
             the
             morning
             ,
             or
             3
             in
             the
             afternoon
             .
          
        
         
           
             CHAP.
             XV.
             
          
           
             The
             Almicanter
             ,
             or
             height
             of
             the
             Sun
             being
             given
             ,
             to
             finde
             the
             length
             of
             the
             right
             shadow
             .
          
           
             The
             Almicanter
             is
             
               45
            
             degrees
             .
          
           
             ACcording
             unto
             the
             tenth
             Diagram
             ,
             draw
             the
             line
             AF
             ,
             and
             upon
             the
             center
             A
             ,
             raise
             the
             perpendicular
             AC
             ,
             then
             upon
             the
             center
             A
             ,
             draw
             the
             Quadrant
             CDF
             ,
             then
             suppose
             the
             
             height
             of
             your
             
               Gnomon
               ,
            
             or
             substance
             yelding
             shadow
             be
             the
             Line
             ,
             
             AB
             ,
             which
             is
             to
             be
             divided
             into
             12
             equall
             parts
             ,
             which
             
               Gnomon
               ,
            
             I
             have
             here
             made
             just
             12
             degrees
             of
             the
             equall
             Leagues
             of
             the
             Scale
             ,
             then
             from
             B
             ,
             to
             the
             top
             of
             the
             
               Gnomon
            
             draw
             the
             Line
             BE
             ,
             parallel
             unto
             AF
             ,
             then
             set
             the
             Almicanter
             which
             is
             fortie
             five
             degrees
             from
             F
             ,
             unto
             D
             ,
             and
             from
             the
             point
             D
             ,
             draw
             the
             Line
             DA
             ,
             cutting
             the
             Line
             BE
             in
             the
             point
             G
             ,
             so
             shall
             BG
             ,
             be
             the
             length
             of
             the
             right
             shadow
             desired
             ,
             which
             here
             is
             found
             to
             be
             fourteen
             degrees
             and
             eighteen
             minutes
             ,
             which
             is
             but
             just
             the
             length
             of
             your
             
               Gnomon
               ,
            
             and
             2
             /
             12
             and
             ⅓
             of
             a
             twelfe
             over
             :
             Note
             that
             the
             right
             shadow
             ,
             is
             the
             shadow
             of
             any
             poste
             ,
             staffe
             ,
             or
             steeple
             ,
             that
             standeth
             at
             right
             Angles
             with
             the
             Horizon
             ,
             the
             one
             end
             thereof
             respecting
             the
             Zenith
             of
             the
             place
             ,
             and
             the
             other
             the
             
               Naedir
               .
            
          
        
         
           
             CHAP.
             XVI
             .
          
           
             The
             Almicanter
             ,
             or
             height
             of
             the
             Sun
             being
             given
             ,
             to
             finde
             the
             length
             of
             the
             contrary
             shaddow
             .
          
           
             The
             Almicanter
             given
             is
             
               70
            
             deg
             .
          
           
             BY
             the
             verse
             or
             contrary
             shadow
             ,
             is
             understood
             the
             length
             of
             any
             shadow
             ,
             that
             is
             made
             by
             a
             staffe
             or
             
               Gnomon
               ,
            
             standing
             against
             any
             perpendicular
             wall
             ,
             in
             such
             a
             manner
             that
             it
             may
             l●e
             parallel
             unto
             the
             Horizon
             ,
             the
             length
             of
             the
             contrary
             shadow
             ,
             doth
             increase
             as
             the
             Sun
             riseth
             in
             height
             ,
             whereas
             contrariwise
             the
             right
             shadow
             doth
             increase
             in
             length
             ,
             as
             the
             Sun
             doth
             increase
             in
             height
             :
             the
             way
             to
             finde
             the
             verse
             shadow
             is
             as
             followeth
             .
             First
             ,
             draw
             your
             Quadrant
             as
             is
             taught
             in
             the
             last
             Chapter
             ,
             wherein
             let
             AB
             ,
             be
             the
             length
             of
             the
             
               Gnomon
               ,
            
             likewise
             from
             B
             ,
             draw
             the
             line
             BE
             ,
             parallel
             unto
             AF
             ,
             as
             before
             ,
             then
             set
             your
             Almicanter
             from
             C
             upon
             the
             Quadrant
             which
             is
             given
             to
             be
             seventie
             degrees
             and
             
             it
             will
             extend
             from
             C
             unto
             H
             ,
             then
             from
             the
             point
             H
             draw
             the
             line
             HA
             ,
             cutting
             the
             line
             BE
             ,
             in
             the
             point
             K
             ,
             so
             shall
             KB
             ,
             be
             the
             length
             of
             the
             contrary
             shadow
             ,
             which
             here
             is
             found
             to
             be
             thirtie
             four
             degrees
             and
             eight
             minutes
             ,
             or
             twice
             so
             long
             as
             your
             
               Gnomon
               ,
            
             and
             ●0
             /
             ●2
             about
             ½
             part
             of
             a
             twelfth
             more
             .
          
        
         
           
             CHAP.
             XVII
             .
          
           
             The
             latitude
             of
             the
             place
             ,
             the
             Almicanter
             ,
             and
             declination
             of
             the
             Sun
             being
             given
             ,
             to
             find
             the
             Azimuth
             .
          
           
             The
             latitude
             of
             the
             place
             is
             fiftie
             one
             degrees
             ,
             thirtie
             minutes
             ,
             the
             declination
             of
             the
             Sun
             twenty
             degrees
             North
             ,
             the
             Almicanter
             thirtie
             eight
             degrees
             thirtie
             minutes
             ,
             the
             true
             Azimuth
             of
             the
             Sun
             is
             desired
             .
          
           
             
          
           
             FIrst
             as
             in
             the
             eleventh
             Demonstration
             upon
             the
             Center
             A
             ,
             draw
             the
             Circle
             BCDE
             ,
             then
             draw
             the
             Diameter
             BAD
             ▪
             
             and
             from
             D
             unto
             F
             ,
             set
             the
             Elevation
             of
             the
             Pole
             ,
             which
             is
             one
             and
             fiftie
             degrees
             ,
             and
             thirtie
             minutes
             ,
             whose
             complement
             is
             eight
             and
             thirtie
             degrees
             and
             thirtie
             minutes
             ,
             which
             must
             be
             placed
             from
             B
             unto
             H
             ,
             then
             from
             H
             ,
             draw
             the
             line
             HAL
             ,
             representing
             the
             Equinoctial
             line
             ,
             and
             from
             F
             ,
             draw
             the
             line
             FAG
             ,
             representing
             the
             Pole
             of
             the
             World
             ,
             then
             from
             H
             unto
             P
             ,
             and
             from
             I
             unto
             Q
             ,
             set
             the
             declination
             of
             the
             Sun
             ,
             which
             is
             twentie
             degrees
             ,
             and
             by
             those
             two
             points
             draw
             the
             line
             PQ
             ,
             for
             the
             Parallel
             of
             the
             Suns
             declination
             ;
             then
             upon
             the
             Circle
             from
             B
             unto
             H
             ▪
             set
             the
             Suns
             Almicanter
             ,
             thirtie
             eight
             degrees
             ,
             and
             thirtie
             minutes
             ,
             then
             from
             H
             ,
             draw
             the
             line
             HR
             ▪
             parallel
             unto
             the
             Horizon
             cutting
             the
             Suns
             parallel
             POQ
             in
             O
             ,
             then
             draw
             the
             Line
             TVAE
             Perpendicular
             unto
             the
             line
             BAD
             ,
             in
             the
             Center
             A
             ,
             and
             cutting
             the
             line
             HVR
             ,
             in
             V
             ,
             then
             seting
             one
             foot
             of
             your
             Compasses
             in
             the
             point
             V
             ,
             extend
             the
             other
             unto
             R
             ,
             and
             with
             the
             same
             distance
             draw
             the
             Semicircle
             HLR
             ,
             then
             draw
             the
             Concentricke
             Circle
             upon
             the
             Radius
             of
             the
             Scale
             MTN
             ,
             and
             where
             the
             Line
             POQ
             ,
             and
             the
             line
             MON
             do
             meet
             in
             the
             point
             V
             ,
             raise
             the
             Perpendicular
             OL
             ,
             cutting
             the
             Semicircle
             HLR
             in
             
               L
               ,
            
             then
             lay
             the
             Scale
             from
             the
             Center
             A
             to
             the
             point
             L
             ,
             and
             draw
             the
             line
             LK
             ,
             cutting
             the
             Semicircle
             MTN
             ,
             in
             K
             ,
             so
             shall
             M
             K
             ,
             be
             the
             true
             distance
             of
             the
             Sun
             from
             the
             East
             ,
             or
             West
             point
             Southward
             ,
             or
             the
             Suns
             true
             Azimuth
             ,
             which
             is
             here
             found
             to
             be
             seventie
             two
             degrees
             ,
             and
             fortie
             minutes
             from
             the
             South
             part
             of
             the
             Meridian
             .
          
        
         
           
           
             CHAP.
             XVIII
             .
          
           
             The
             Latitde
             of
             the
             place
             ,
             the
             Declination
             of
             the
             Sun
             ,
             and
             the
             Altitude
             of
             the
             Sun
             being
             given
             to
             finde
             the
             
               Azimuth
               :
               By
               a
               new
               way
               differing
               from
               that
               in
               the
               former
               Chapter
               .
            
          
           
             
               
                 
                    
                
                 
                   deg
                   .
                
                 
                   min.
                   
                
                 
                   S.
                   
                
                 
                   deg
                   .
                
                 
                   m.
                   
                
              
               
                 
                   The
                   Suns
                   Declination
                   is
                
                 
                   20
                
                 
                   00
                
                 
                    
                
                 
                    
                
                 
                    
                
              
               
                 
                   The
                   Latitude
                   of
                   the
                   place
                   is
                
                 
                   51
                
                 
                   30
                
                 
                   its
                   Comple
                   .
                
                 
                   38
                
                 
                   30
                
              
               
                 
                   The
                   Suns
                   Altitude
                   is
                
                 
                   12
                
                 
                   00
                
                 
                    
                
                 
                   78
                
                 
                   00
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   Sum
                
                 
                   116
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   difference
                
                 
                   39
                
                 
                   30
                
              
            
          
           
             HAving
             found
             the
             sum
             and
             the
             difference
             of
             the
             complement
             of
             the
             Suns
             Altitude
             ,
             and
             the
             complement
             of
             the
             Latitude
             as
             above
             is
             expressed
             where
             you
             finde
             the
             Sum
             of
             them
             to
             be
             116
             deg
             .
             30
             min.
             and
             their
             difference
             39
             deg
             .
             30
             min.
             
          
           
           
             Secondly
             ,
             take
             116
             deg
             .
             30
             min.
             the
             sum
             out
             of
             your
             line
             of
             Chords
             ,
             and
             set
             it
             from
             C
             to
             G
             ,
             and
             draw
             the
             line
             GK
             parallell
             D
             to
             B
             ,
          
           
             Thirdly
             take
             39
             deg
             .
             30
             min.
             the
             difference
             ,
             out
             of
             your
             line
             of
             Chords
             ,
             and
             set
             it
             from
             C
             to
             H
             ,
             and
             draw
             the
             line
             HL
             parallell
             also
             to
             BD.
             
          
           
             Fourthly
             Take
             in
             your
             compasses
             the
             distance
             from
             F
             to
             K
             ,
             and
             setting
             one
             foot
             in
             A
             ,
             with
             the
             other
             describe
             the
             arch
             
               S.
               
            
          
           
             Fifthly
             ,
             Take
             the
             distance
             from
             F
             ,
             to
             L
             ,
             and
             setting
             one
             foot
             in
             C
             ,
             with
             the
             other
             describe
             the
             arch
             R.
             
          
           
             Sixthly
             ,
             Lay
             a
             rular
             ,
             that
             it
             may
             only
             touch
             these
             two
             arches
             ,
             
               S
               ,
            
             and
             R
             ,
             and
             by
             it
             draw
             a
             line
             as
             SR
             ,
             cutting
             the
             line
             AC
             in
             N.
             
          
           
             Lastly
             ,
             upon
             the
             point
             N
             ,
             erect
             the
             perpendicular
             NM
             ,
             then
             the
             distance
             AM
             ,
             measured
             upon
             your
             Line
             of
             Chords
             ,
             is
             the
             Azimuth
             from
             the
             South
             part
             of
             the
             Meridian
             ,
             which
             in
             this
             example
             will
             be
             found
             to
             be
             34
             deg
             .
             MC
             the
             Azimuth
             from
             the
             North
             146
             deg
             .
             And
             MD
             ,
             the
             Azimuth
             from
             the
             East
             or
             West
             ,
             56
             deg
             .
          
        
         
           
             CHAP.
             XIX
             ,
          
           
             The
             place
             of
             the
             Sun
             being
             given
             ,
             to
             find
             the
             right
             ascension
             ,
             Suppose
             the
             Sun
             be
             in
             the
             twentieth
             degree
             of
             Taurus
             ,
             his
             right
             ascention
             is
             found
             as
             followeth
             .
          
           
             FIrst
             ,
             as
             in
             the
             12
             demostrastion
             ,
             draw
             the
             line
             BAF
             ,
             for
             the
             Pole
             of
             the
             World
             ,
             the
             ●
             upon
             the
             Center
             A
             draw
             the
             Circle
             BCDE
             ,
             then
             from
             the
             Center
             A
             ,
             raise
             the
             Perpendicular
             CAE
             ,
             for
             the
             Equator
             ,
             then
             place
             your
             greatest
             declination
             from
             C
             unto
             Q
             ,
             and
             from
             E
             unto
             P
             ,
             then
             daw
             the
             line
             QAP
             ,
             which
             doth
             represent
             the
             Eclipticke
             line
             ,
             then
             in
             regard
             the
             Sunne
             is
             in
             the
             twentieth
             degree
             of
             
               Taurus
               ,
            
             which
             is
             forty
             degrees
             ,
             from
             the
             head
             of
             
               Cancer
               ,
            
             which
             forty
             degrees
             ,
             place
             from
             Q
             unto
             L
             ,
             and
             unto
             K
             ,
             then
             draw
             the
             line
             KL
             ,
             cuting
             the
             Eclipticke
             in
             I
             ,
             then
             from
             the
             point
             I
             draw
             the
             line
             HI
             ,
             parallel
             unto
             CAE
             ,
             cuting
             
             the
             Pole
             of
             the
             World
             in
             
               O
            
             then
             set
             one
             foot
             of
             your
             Compasses
             in
             
               O
               ,
            
             and
             extend
             the
             other
             unto
             G
             ,
             with
             which
             distance
             draw
             the
             Semicircle
             HDG
             ,
             then
             opening
             your
             Compasses
             unto
             the
             Radius
             of
             the
             Scale
             ,
             and
             upon
             the
             Center
             O
             ,
             likewise
             draw
             the
             Circle
             HNFG
             ,
             
             then
             draw
             the
             line
             IM
             ,
             parallel
             unto
             AOD
             ,
             cutting
             the
             Semicircle
             HMDG
             ,
             in
             
               M
               ,
            
             then
             lay
             your
             Scale
             from
             the
             Center
             O
             ,
             unto
             the
             point
             M
             ,
             and
             draw
             the
             Line
             NM
             ,
             cutting
             the
             Concentricke
             Circle
             in
             N
             ,
             so
             shall
             the
             distance
             NF
             ,
             be
             the
             right
             ascention
             ,
             which
             is
             here
             found
             tobe
             two
             and
             fortie
             degrees
             ,
             seven
             and
             twentieminutes
             .
          
        
         
           
           
             CHAP.
             XX.
             
          
           
             The
             elevation
             of
             the
             Pole
             ,
             and
             declination
             of
             the
             Sunne
             given
             ,
             to
             finde
             the
             difference
             of
             the
             ascensions
             .
          
           
             The
             Poles
             elevation
             is
             
               51
            
             degrees
             ,
             
               32
            
             minutes
             ,
             the
             declination
             of
             the
             Sun
             is
             
               21.
            
             degrees
             .
          
           
             FIrst
             ,
             as
             in
             the
             13th
             .
             demonstration
             ,
             draw
             the
             Line
             BAK
             ,
             representing
             the
             Horizon
             ,
             then
             upon
             the
             Center
             A
             ,
             draw
             the
             Circle
             BCDEF
             ,
             Then
             from
             K
             unto
             D
             ,
             set
             the
             elevation
             of
             the
             Pole
             which
             is
             51
             degrees
             ,
             and
             thirty
             two
             minutes
             :
             then
             from
             the
             point
             D
             ,
             
             by
             the
             Center
             A
             ,
             draw
             the
             Line
             DAF
             ,
             representing
             the
             Pole
             of
             the
             World
             ,
             then
             from
             B
             unto
             C
             ,
             set
             the
             Complement
             of
             the
             Poles
             elevation
             which
             is
             thirty
             eight
             degrees
             ,
             and
             28
             minutes
             :
             then
             from
             C
             by
             the
             center
             A
             ,
             draw
             the
             line
             CAE
             ,
             representing
             the
             Equinoctiall
             
             Line
             ;
             then
             from
             
               C
            
             unto
             G
             ▪
             and
             likewise
             from
             E
             unto
             H
             ,
             for
             the
             declination
             of
             the
             Sunne
             ,
             which
             is
             21
             degrees
             ,
             then
             from
             G
             unto
             H
             ,
             draw
             the
             parallel
             of
             the
             Sunnes
             declination
             ,
             cutting
             the
             Pole
             of
             the
             world
             in
             L
             ,
             and
             he
             Horizon
             in
             I
             ,
             then
             set
             one
             foote
             of
             your
             Compasses
             in
             the
             point
             L
             ,
             and
             extend
             the
             other
             unto
             G
             ,
             then
             with
             that
             distance
             of
             your
             Compasses
             draw
             the
             Semicircle
             GMNH
             ,
             then
             opening
             your
             Compasses
             unto
             the
             Radius
             of
             your
             Scale
             ,
             upon
             the
             same
             Center
             draw
             the
             Concentricke
             Circle
             ,
             GXOH
             ,
             then
             from
             I
             ,
             where
             the
             declination
             of
             the
             Sunne
             doth
             cut
             the
             Horizon
             ,
             draw
             the
             Line
             IN
             ,
             parallell
             unto
             the
             Pole
             of
             the
             World
             AM
             ,
             cutting
             the
             Circle
             GMH
             in
             N
             ,
             then
             lay
             your
             Ruler
             from
             the
             point
             I
             unto
             the
             point
             N
             ,
             and
             so
             draw
             the
             line
             NO
             ,
             cutting
             the
             Concentricke
             Circle
             GXOH
             ,
             in
             O
             ,
             so
             shall
             the
             distance
             of
             O
             and
             X
             ,
             be
             the
             difference
             of
             the
             ascentions
             ,
             which
             is
             here
             found
             to
             bee
             eight
             and
             twentie
             degrees
             ,
             and
             foure
             and
             fiftie
             minutes
             .
          
        
         
           
             CHAP.
             XXI
             .
          
           
             The
             right
             ascention
             of
             the
             Sun
             or
             of
             a
             Star
             being
             given
             ,
             together
             with
             the
             difference
             of
             their
             ascention
             ,
             to
             finde
             the
             oblique
             ascention
             or
             descention
             .
          
           
             The
             Sun
             is
             in
             the
             
             4th
             .
             degree
             of
             
               Sagitarius
               ,
            
             his
             right
             ascention
             is
             
               242
            
             degrees
             ,
             or
             
               16
            
             hours
             
               8
            
             minutes
             ,
             the
             difference
             of
             ascention
             is
             
               1
            
             houre
             
               53
            
             min.
             or
             
               28
            
             deg
             .
             
               28
            
             min.
             the
             oblique
             ascention
             or
             desce●tion
             is
             required
             .
          
           
             THe
             right
             ascention
             of
             any
             point
             of
             the
             Heavens
             being
             known
             ,
             the
             difference
             of
             the
             ascention
             is
             either
             to
             bee
             added
             thereunto
             ,
             or
             else
             to
             bee
             substracted
             from
             it
             ,
             according
             as
             the
             Starre
             is
             situate
             in
             the
             Northern
             or
             Southerne
             Signes
             :
             As
             for
             example
             ,
             if
             the
             Sunne
             be
             in
             any
             of
             these
             sixe
             Signes
             ,
             
               Aries
               ,
               Taurus
               ,
               Gemini
               ,
               Cancer
               ,
               Leo
               ,
            
             or
             
               Virgo
               ,
            
             then
             the
             difference
             of
             the
             ascentions
             is
             to
             bee
             substracted
             from
             the
             right
             ascention
             ,
             and
             the
             remainder
             is
             the
             oblique
             ascention
             .
             Suppose
             therefore
             the
             Sunne
             to
             be
             in
             the
             fourth
             degree
             of
             
               Gemini
               ,
            
             where
             the
             right
             ascention
             is
             found
             to
             be
             foure
             houres
             ,
             and
             8
             minutes
             ,
             or
             62
             degrees
             ,
             and
             the
             difference
             of
             ascention
             where
             the
             Pole
             is
             elevated
             51
             degrees
             ,
             is
             found
             to
             be
             one
             houre
             53
             minutes
             ,
             otherwise
             28
             degrees
             50
             
             minutes
             ,
             which
             being
             taken
             from
             the
             right
             ascention
             ,
             leaves
             two
             houres
             and
             16
             minutes
             ,
             or
             33
             degrees
             and
             42
             minutes
             ,
             which
             is
             the
             oblique
             ascention
             of
             the
             Sunne
             in
             the
             fourth
             degree
             of
             
               Gemini
               .
            
             But
             if
             the
             Sun
             be
             upon
             the
             South
             side
             of
             the
             Equinoctiall
             ,
             either
             in
             
               Libra
               ,
               Scorpio
               ,
               Sagitarius
               Capricornus
               ,
               Aquarius
               ,
            
             or
             
               Pisces
               ,
            
             then
             the
             difference
             of
             the
             ascentions
             is
             to
             bee
             added
             unto
             the
             right
             ascention
             ,
             and
             the
             Product
             will
             be
             the
             oblique
             ascention
             .
             Suppose
             the
             fourth
             degree
             of
             
               Sagitarius
            
             is
             given
             ,
             for
             which
             Sign
             and
             degree
             the
             oblique
             ascention
             of
             the
             Sun
             is
             desired
             ,
             his
             right
             ascension
             being
             then
             found
             to
             be
             242
             degrees
             ,
             or
             16
             hours
             8.
             min.
             the
             difference
             of
             the
             ascensions
             is
             one
             hour
             ,
             53
             minutes
             ,
             or
             28
             degrees
             ,
             18
             minutes
             :
             which
             being
             added
             unto
             the
             right
             ascension
             ,
             makes
             18
             hours
             ,
             and
             one
             minute
             ;
             or
             in
             degrees
             270
             degrees
             ,
             and
             18.
             minutes
             :
             which
             is
             the
             oblique
             ascention
             of
             the
             Sunne
             ,
             when
             he
             is
             in
             the
             fourth
             degree
             of
             
               Sagitarius
               .
            
             And
             if
             you
             would
             finde
             the
             oblique
             descention
             ,
             you
             must
             adde
             the
             difference
             of
             the
             ascentions
             unto
             the
             right
             ascention
             ,
             when
             the
             Sunne
             is
             in
             these
             six
             Signes
             .
             
               Aries
               ,
               Taurus
               ,
               Gemini
               ,
               Cancer
               ,
               Leo
               ,
               Virgo
               :
            
             and
             contrariwise
             ,
             when
             the
             Su●n
             is
             in
             the
             other
             six
             Signes
             ,
             you
             mnst
             substract
             the
             difference
             from
             the
             right
             ascention
             ,
             and
             you
             shall
             have
             the
             oblike
             descention
             of
             the
             Sun
             or
             any
             Starre
             ,
             whose
             right
             ascention
             and
             difference
             of
             ascentions
             is
             knowne
             .
             But
             it
             is
             to
             be
             understood
             ,
             that
             this
             manner
             of
             operation
             ,
             doth
             serve
             no
             longer
             than
             you
             are
             upon
             the
             North
             side
             of
             the
             Equinoctiall
             .
             For
             if
             the
             South
             Pole
             be
             elevated
             ,
             the
             worke
             is
             contrary
             :
             for
             so
             long
             as
             the
             Sunne
             is
             in
             any
             of
             the
             Northerne
             Signes
             ,
             the
             difference
             of
             the
             ascentions
             is
             to
             be
             added
             unto
             the
             right
             ascention
             ,
             to
             find
             the
             oblique
             ascention
             .
             And
             contrariwise
             ,
             substracted
             to
             finde
             the
             oblique
             descention
             .
             Likewise
             if
             the
             Sunne
             or
             Star
             be
             in
             the
             South●rn
             Signes
             ,
             then
             is
             the
             difference
             of
             ascentions
             ,
             substracted
             from
             the
             right
             ascention
             ,
             to
             finde
             the
             oblique
             ascention
             ,
             and
             added
             ,
             to
             finde
             the
             oblique
             descention
             .
          
           
             The
             end
             of
             the
             Second
             Book
             .
          
        
      
       
         
         
           THE
           SEA-MANS
           GLASSE
           :
           
             The
             Third
             Book
             .
          
        
         
           Shewing
           how
           by
           the
           
             Plain-Scale
             ,
          
           to
           delineate
           Houre-lines
           upon
           all
           kinde
           of
           Upright
           Plains
           ,
           either
           Direct
           or
           Declining
           ,
           in
           any
           Latitude
           .
           
             
               The
               figure
               of
               the
               plaine
               Scale
               .
            
          
        
         
           
             CHAP.
             I
          
           
             How
             to
             draw
             hour
             lines
             upon
             an
             Horizontal
             Plain
             ,
             in
             any
             Latitude
             .
          
           
             VVith
             the
             Radius
             of
             your
             line
             of
             Chords
             ,
             upon
             E
             as
             a
             Center
             ,
             describe
             the
             Circle
             ABCD
             ,
             and
             crosse
             it
             with
             he
             diameters
             AB
             ,
             and
             CD
             .
             This
             done
             ,
             out
             of
             the
             line
             of
             Chords
             
             take
             the
             complement
             of
             the
             Latitude
             of
             your
             place
             (
             which
             we
             here
             suppose
             to
             be
             
               London
               ,
            
             whose
             latitude
             is
             51
             deg
             .
             30
             m.
             and
             its
             complement
             38.
             deg
             .
             30
             m.
             )
             which
             set
             from
             B
             to
             G
             ,
             from
             G
             to
             N
             ,
             and
             from
             D
             to
             M
             ;
             then
             lay
             a
             ruler
             from
             A
             to
             G
             ,
             and
             it
             will
             cut
             the
             line
             CD
             in
             H
             ,
             and
             from
             A
             to
             N
             it
             will
             cut
             
               C
            
             D
             in
             O
             ,
             and
             from
             A
             to
             M
             it
             will
             cut
             the
             same
             line
             in
             F.
             
          
           
             This
             done
             ,
             upon
             O
             (
             as
             a
             center
             )
             place
             one
             foot
             of
             your
             compasses
             ,
             and
             extend
             the
             other
             foot
             to
             F
             ,
             and
             with
             this
             distance
             describe
             an
             arch
             of
             a
             circle
             ,
             which
             (
             if
             the
             rest
             of
             your
             worke
             be
             true
             )
             will
             fall
             just
             in
             the
             points
             A
             and
             B
             ,
             and
             so
             constitute
             the
             arch
             AFB
             ,
             representing
             the
             Equinoctiall
             Circle
             ,
             and
             so
             we
             shall
             hereafter
             call
             it
             .
          
           
             Having
             drawn
             the
             Equinoctiall
             AFB
             ,
             divide
             the
             Semicircle
             ADB
             ,
             into
             12
             equall
             parts
             in
             the
             points
             ***
             ,
             &c.
             
             Then
             laying
             a
             ruler
             to
             the
             Center
             E
             ,
             and
             every
             one
             of
             these
             marks
             ***
             &c.
             it
             will
             divide
             the
             Equinoctiall
             circle
             into
             12
             unequall
             parts
             in
             the
             points
             ●●●●
             &c.
             
          
           
             Again
             ,
             Lay
             a
             ruler
             to
             H
             ,
             and
             every
             of
             these
             unequall
             parts
             ●●●●
             ,
             &c.
             it
             will
             cut
             the
             semicircle
             ADB
             in
             the
             points
             7
             ,
             8
             ,
             9
             ,
             10
             ,
             11
             ,
             12
             ,
             1
             ,
             2
             ,
             3
             ,
             4
             ,
             5
             and
             6.
             
          
           
             Lastly
             ,
             If
             you
             lay
             a
             ruler
             on
             the
             center
             E
             ,
             and
             from
             thence
             draw
             right
             lines
             to
             the
             severall
             points
             7
             ,
             8
             ,
             9
             ,
             10
             ,
             &c.
             they
             shall
             be
             12
             of
             the
             true
             houre-lines
             belonging
             to
             an
             horizontall
             diall
             for
             the
             latitude
             of
             51
             degrees
             ,
             30
             minutes
             .
          
           
             But
             for
             the
             houres
             before
             6
             in
             the
             morning
             ,
             and
             after
             6
             at
             night
             ,
             do
             thus
             ;
             draw
             the
             hour
             liues
             of
             4
             and
             5
             in
             the
             evening
             ,
             quite
             through
             the
             center
             E
             ,
             and
             they
             shall
             be
             the
             hours
             of
             4
             and
             5
             in
             the
             morning
             ;
             also
             ,
             7
             and
             8
             in
             the
             morning
             drawn
             through
             the
             center
             ,
             shall
             give
             the
             hours
             of
             7
             and
             8
             at
             night
             ,
             as
             in
             the
             figure
             .
          
           
             
          
        
         
           
             CHAP
             :
             II.
             
          
           
             Concerning
             direct
             South
             Dials
             .
          
           
             A
             Direct
             South
             diall
             is
             no
             other
             then
             an
             horizontall
             diall
             ,
             the
             makeing
             whereof
             is
             before
             described
             ,
             the
             difference
             consisting
             only
             in
             the
             numbring
             of
             the
             houres
             ,
             and
             in
             the
             placing
             of
             it
             ,
             the
             one
             being
             to
             be
             fixed
             on
             a
             poste
             or
             the
             like
             ,
             and
             the
             other
             to
             be
             fixed
             to
             a
             Wall
             which
             exactly
             beholds
             the
             South
             ,
             I
             say
             here
             is
             no
             other
             difference
             :
             for
             
             
               
                 
                    
                
                 
                   degrees
                
                 
                    
                
                 
                   degrees
                
              
               
                 
                   An
                   Horizontall
                   Diall
                   for
                   the
                   Latitude
                   of
                
                 
                   10
                
                 
                   Will
                   be
                   a
                   direct
                   South
                   Dial
                   in
                   the
                   Latitude
                   of
                
                 
                   80
                
              
               
                 
                   20
                
                 
                   70
                
              
               
                 
                   30
                
                 
                   60
                
              
               
                 
                   40
                
                 
                   50
                
              
               
                 
                   50
                
                 
                   40
                
              
               
                 
                   60
                
                 
                   30
                
              
               
                 
                   70
                
                 
                   20
                
              
               
                 
                   80
                
                 
                   10
                
              
            
          
           
             And
             the
             like
             in
             any
             other
             Latitude
             ,
             as
             15
             ,
             16
             ,
             33
             ,
             &c.
             
          
        
         
           
             CHAP.
             III.
             
          
           
             Of
             driect
             North
             dialls
             .
          
           
             A
             Direct
             North
             diall
             ,
             is
             the
             same
             with
             a
             direct
             South
             diall
             ;
             for
             ,
             i●
             you
             take
             a
             South
             diall
             and
             turn
             it
             upside
             down
             ,
             causing
             the
             Sc●le
             or
             cock
             to
             point
             upwards
             ,
             as
             the
             Cock
             of
             the
             South
             doth
             down
             wards
             ;
             and
             leaving
             out
             the
             hours
             neer
             the
             Meridian
             ,
             in
             these
             Northern
             Latitudes
             ;
             as
             the
             hours
             of
             9
             ,
             10
             ,
             11
             ,
             and
             12
             at
             night
             ,
             and
             1
             ,
             2
             and
             3
             in
             the
             morning
             ,
             all
             which
             time
             the
             Sunne
             is
             under
             the
             Horizon
             .
             I
             say
             a
             South
             diall
             so
             disposed
             ,
             and
             fixed
             against
             a
             direct
             North
             Wall
             ,
             shall
             give
             you
             the
             true
             houre
             of
             the
             day
             .
          
        
         
           
             CHAP.
             IV.
             
          
           
             How
             to
             draw
             the
             houre
             lines
             on
             a
             direct
             East
             or
             West
             plain
             .
          
           
           
           
             This
             done
             ,
             upon
             the
             point
             G
             ,
             with
             the
             radius
             of
             your
             Chord
             ,
             descirbe
             an
             occult
             arch
             of
             a
             Circle
             H
             I
             ,
             and
             set
             thereon
             15
             degrees
             fr
             om
             H
             to
             I
             ,
             then
             from
             G
             ,
             through
             I
             ,
             draw
             the
             line
             G
             K
             ,
             cutting
             N
             Min
             K
             ,
             On
             K
             ,
             as
             a
             center
             ,
             with
             the
             radius
             of
             your
             Chord
             ,
             describe
             the
             quadrant
             K
             
               S
            
             T
             ,
             which
             divide
             into
             6
             equall
             parts
             in
             the
             points
             ●●●●
             ,
             through
             which
             points
             and
             K
             ,
             draw
             the
             lines
             ,
             K●
             ,
             K●
             ,
             &c.
             cutting
             the
             Equinoctiall
             EB
             in
             ****
             &c.
             
             Through
             these
             points
             ***
             ,
             &c.
             draw
             right
             lines
             quiet
             through
             your
             plain
             perpendicular
             to
             the
             equinoctial
             ,
             which
             will
             be
             parallel
             to
             your
             lines
             of
             VI
             ,
             and
             XI
             ,
             and
             will
             be
             the
             true
             hours
             of
             VII
             ,
             VIII
             ,
             IX
             ,
             and
             X
             ,
             then
             the
             like
             distances
             of
             VII
             and
             VIII
             ,
             set
             above
             VI
             ,
             on
             the
             other
             side
             ,
             and
             drawn
             parallel
             thereto
             ,
             shall
             be
             the
             true
             hours
             of
             IIII.
             and
             V.
             and
             thus
             have
             you
             all
             the
             hours
             of
             an
             East
             dial
             truly
             drawn
             ,
             which
             is
             from
             Four
             in
             the
             morning
             ,
             till
             Eleven
             at
             noon
             ,
             and
             is
             the
             same
             with
             a
             West
             diall
             only
             naming
             the
             hours
             contrary
             :
             for
             ,
             in
             the
             East
             diall
             4
             ,
             5
             ,
             6
             ,
             7
             ,
             8
             ,
             9
             ,
             10
             ,
             11
             ,
             in
             the
             morning
             ,
             are
             in
             the
             West
             diall
             8
             ,
             7
             ,
             6
             ,
             5
             ,
             4
             ,
             3
             ,
             2
             ,
             1
             ,
             h
             in
             the
             evening
             .
          
           
             The
             Stile
             of
             either
             of
             these
             dials
             ,
             is
             a
             t
             in
             plate
             of
             brasse
             ,
             made
             directly
             of
             the
             breadth
             of
             the
             distance
             between
             the
             hours
             of
             VI
             ,
             and
             IX
             ,
             and
             must
             be
             placed
             directly
             perpendicular
             upon
             the
             line
             of
             VI
             ,
             and
             so
             is
             your
             diall
             finished
             .
          
        
         
           
             CHAP.
             V.
             
          
           
             Of
             upright
             declining
             Plains
             .
          
           
             BEfore
             we
             come
             to
             draw
             the
             houre
             lines
             upon
             a
             declining
             plain
             ,
             two
             things
             are
             first
             to
             be
             discovered
             ,
             
               viz.
               
            
          
           
             First
             .
             
               The
               height
               of
               the
               pole
               above
               the
               plain
               ,
            
             which
             is
             the
             height
             of
             the
             Cock
             or
             Stile
             .
          
           
             Secondly
             ,
             
               The
               deflexion
               ,
            
             or
             distance
             of
             the
             substile
             from
             the
             Meridian
             or
             line
             of
             Twelve
             a
             Clock
             .
          
        
         
           
             
               1.
               
            
             To
             finde
             the
             height
             of
             the
             Pole
             above
             a
             declining
             Plain
             .
          
           
           
             VVIth
             the
             tadius
             of
             your
             line
             of
             Chords
             ,
             upon
             A
             ,
             as
             a
             center
             ,
             describe
             the
             Quadrant
             AB
             
               C
               ,
            
             then
             your
             Latitude
             being
             51
             deg
             .
             30
             min.
             take
             it
             out
             of
             your
             line
             of
             Chords
             ,
             and
             set
             it
             from
             B
             to
             F
             ,
             and
             draw
             the
             line
             ED
             parallel
             to
             AB
             ,
             cutting
             the
             line
             AC
             in
             D
             ,
             then
             with
             the
             distance
             DE
             ,
             on
             the
             center
             A
             ,
             describe
             the
             Quadrant
             GHR
             .
             Then
             supposing
             your
             plain
             to
             decline
             30
             deg
             .
             set
             30
             deg
             .
             from
             B
             to
             F
             ,
             in
             the
             Quadrant
             BEC
             ,
             and
             draw
             the
             line
             FA
             cutting
             the
             Quadrant
             GHR
             in
             H
             ,
             through
             which
             point
             H
             ,
             draw
             the
             line
             SHN
             parallel
             to
             CA
             ,
             and
             cutting
             the
             Quadrant
             BE
             
               C
            
             in
             N
             ,
             so
             shall
             the
             arch
             CN
             be
             the
             height
             of
             the
             Pole
             above
             the
             plain
             ,
             and
             in
             this
             example
             contains
             32
             deg
             .
             37
             min.
             
          
        
         
           
             
               2.
               
            
             To
             finde
             the
             Deflexion
             ,
             or
             the
             distance
             of
             the
             Substile
             from
             the
             Meridian
             .
          
           
             Out
             of
             this
             figure
             ,
             take
             the
             distance
             HS
             ,
             and
             set
             it
             in
             the
             line
             
             DE
             ,
             from
             D
             to
             K
             ;
             through
             which
             point
             K
             ,
             draw
             the
             line
             AKL
             ,
             cutting
             the
             Quad
             ant
             BC
             in
             L
             ;
             so
             shall
             the
             arch
             CL
             be
             the
             distance
             of
             the
             Substile
             from
             the
             Meridian
             :
             and
             in
             thls
             Example
             will
             be
             found
             to
             be
             21
             degrees
             42
             minutes
             .
          
        
         
           
             CHAP.
             VI.
             
          
           
             How
             to
             draw
             the
             Houre-lines
             upon
             an
             upright
             Plain
             declining
             from
             the
             Meridian
             towards
             the
             East
             or
             West
             .
          
           
             VVE
             will
             here
             take
             for
             Example
             a
             South
             erect
             plain
             ,
             declining
             Eastward
             30
             deg
             .
          
           
           
             Having
             (
             by
             the
             Fifth
             Chapter
             of
             this
             Book
             )
             found
             the
             Defl●xion
             of
             such
             a
             plain
             to
             be
             21
             deg
             .
             42
             min.
             And
             the
             height
             of
             ●he
             ●●ile
             (
             by
             the
             same
             Chapter
             )
             to
             be
             32
             deg
             .
             37
             min.
             we
             may
             proceed
             to
             draw
             the
             Diall
             in
             manner
             following
             .
          
           
             With
             the
             radius
             of
             your
             line
             of
             Chords
             ,
             on
             the
             Center
             C
             ,
             describe
             the
             Circle
             XNSW
             ;
             and
             in
             it
             ,
             draw
             SN
             through
             the
             Center
             C
             ,
             for
             the
             Meridian
             ,
             or
             line
             of
             12.
             
             Then
             the
             deflexion
             being
             found
             to
             be
             21
             deg
             .
             42
             min.
             set
             that
             from
             N
             to
             E
             ,
             and
             draw
             the
             line
             ●C
             through
             the
             center
             to
             G
             ▪
             This
             line
             representeth
             the
             Substilar
             line
             of
             your
             Diall
             ,
             upon
             which
             line
             the
             Stile
             or
             Co●k
             must
             stand
             ▪
             Also
             ,
             out
             from
             your
             line
             of
             Chords
             take
             32
             deg
             .
             37
             min.
             the
             height
             of
             the
             S●ile
             ,
             and
             set
             that
             distance
             from
             E
             to
             H
             ,
             and
             draw
             the
             line
             CH
             for
             the
             Stile
             of
             your
             Diall
             ;
             so
             shall
             the
             Triangle
             ECH
             ,
             be
             the
             true
             pattern
             for
             the
             Cock
             of
             your
             Diall
             .
          
           
             The
             Substilar
             line
             EG
             being
             〈◊〉
             ●●aw
             the
             line
             XW
             through
             the
             center
             C
             ,
             and
             perpendicular
             to
             EG
             .
             This
             done
             ,
             take
             the
             distance
             EH
             ,
             (
             which
             is
             equall
             to
             the
             Stiles
             height
             )
             and
             set
             that
             distance
             from
             A
             to
             B
             ,
             and
             from
             W
             to
             D.
             Likewise
             ,
             take
             the
             distance
             from
             W
             to
             B
             ,
             and
             set
             it
             from
             B
             to
             I.
             These
             three
             points
             I
             ,
             B
             and
             D
             ,
             being
             found
             in
             the
             circumference
             of
             the
             Circle
             XNSW
             ,
             lay
             a
             ruler
             from
             X
             to
             I
             and
             it
             will
             cut
             the
             substilar
             line
             EC
             being
             extended
             in
             the
             point
             G
             ,
             which
             is
             the
             center
             upon
             which
             the
             equinoctiall
             Circle
             must
             be
             described
             .
             Again
             ,
             a
             ruler
             laid
             from
             X
             to
             B
             ,
             will
             cut
             the
             substilar
             line
             in
             F
             ,
             and
             a
             ruler
             laid
             from
             X
             to
             D
             ,
             will
             cut
             the
             substilar
             in
             O.
             Now
             ,
             if
             you
             set
             one
             foot
             of
             your
             Compasses
             in
             G
             ,
             and
             extend
             the
             other
             to
             X
             or
             W
             ,
             you
             may
             describe
             the
             Equinoctial
             circle
             XOW
             ,
             which
             (
             if
             you
             have
             not
             erred
             in
             your
             former
             worke
             )
             will
             passe
             exactly
             through
             the
             point
             O
             in
             the
             substilar
             line
             before
             found
             .
             In
             the
             next
             place
             ,
             if
             you
             lay
             a
             Ruler
             from
             F
             to
             N
             ,
             it
             will
             cut
             the
             Equinoctiall
             circle
             in
             P
             ,
             and
             a
             ruler
             laid
             from
             C
             to
             P
             ,
             will
             cut
             the
             Diall
             circle
             in
             V.
             
          
           
             These
             things
             being
             performed
             ,
             the
             next
             thing
             is
             to
             draw
             the
             hour
             lines
             ,
             which
             will
             be
             easily
             effected
             if
             you
             〈◊〉
             the
             former
             directions
             .
          
           
             First
             ,
             from
             the
             point
             V
             last
             found
             ,
             begin
             to
             divide
             your
             houre
             circle
             into
             24
             equall
             parts
             (
             or
             only
             one
             halfe
             of
             it
             into
             12
             parts
             )
             which
             you
             may
             do
             by
             taking
             15
             deg
             .
             out
             of
             your
             line
             of
             Chords
             and
             
             set
             that
             distance
             on
             both
             sides
             of
             V
             at
             the
             marks
             ⚹
             ⚹
             ⚹
             &c.
             so
             many
             times
             as
             the
             plain
             is
             capable
             of
             hours
             .
          
           
           
             This
             done
             ,
             If
             you
             lay
             a
             ruler
             on
             the
             center
             C
             ,
             and
             every
             of
             these
             points
             ****
             &c.
             you
             shall
             divide
             the
             equinoctiall
             Circle
             into
             12
             unequall
             parts
             in
             the
             points
             ●●●●
             &c.
             
             Now
             a
             ruler
             laid
             from
             F
             to
             every
             of
             these
             unequall
             points
             ●●●●
             ,
             &c.
             will
             divide
             the
             houre
             circle
             into
             12
             other
             unequall
             parts
             marked
             with
             4.
             5.
             6.
             7.
             8.
             
             ▪
             9.
             10.
             11.
             12.
             1.
             on
             the
             one
             side
             of
             V
             ,
             and
             with
             2.
             3
             ▪
             ●n
             the
             other
             side
             of
             V.
             
          
           
           
             Lastly
             ,
             a
             ruler
             laid
             from
             C
             to
             the
             severall
             points
             4.
             5.
             6.
             7.
             8.
             9.
             10.
             11.
             12.
             1.
             2.
             3.
             and
             lines
             drawn
             by
             the
             side
             thereof
             they
             shall
             be
             the
             true
             houre
             lines
             belonging
             to
             such
             a
             declining
             plain
             of
             30
             deg
             .
             in
             the
             Latitude
             of
             51
             deg
             .
             30
             min.
             But
             if
             you
             desire
             more
             hours
             then
             12
             ,
             the
             equinoctiall
             may
             be
             divided
             into
             more
             unequall
             parts
             ,
             being
             continued
             beyond
             X
             and
             W
             ,
             and
             if
             you
             will
             ,
             quite
             round
             the
             whole
             Circle
             ,
             but
             that
             is
             needlesse
             without
             you
             would
             make
             4
             Dialls
             in
             the
             makeing
             of
             one
             as
             you
             may
             easily
             do
             .
             For
             ,
          
           
             The
             hours
             that
             are
             on
             the
             West
             side
             of
             the
             Meridian
             of
             a
             South
             East
             diall
             ,
             being
             drawn
             through
             the
             Center
             ,
             will
             make
             a
             North
             West
             diall
             of
             the
             same
             declination
             .
             And
             the
             hours
             on
             the
             east
             side
             of
             the
             Meridian
             of
             a
             South
             West
             diall
             ;
             being
             drawn
             through
             the
             center
             ,
             will
             produce
             a
             North
             East
             diall
             of
             the
             same
             declination
             .
             And
             Again
             ,
             the
             reall
             houre
             lines
             of
             a
             South
             East
             diall
             being
             drawn
             on
             the
             other
             side
             of
             the
             paper
             ,
             and
             the
             hours
             named
             by
             their
             Complements
             to
             12
             ,
             that
             is
             ,
             10
             for
             2
             ,
             9
             for
             3
             ,
             8
             for
             4
             ,
             &c.
             will
             make
             a
             South
             West
             diall
             of
             the
             same
             declination
             .
          
        
         
           
             CHAP.
             VII
             .
          
           
             How
             to
             place
             any
             upright
             diall
             truly
             .
          
           
             ALL
             upright
             dialls
             ,
             in
             what
             oblique
             latitude
             soever
             have
             the
             Meridian
             perpendicular
             to
             the
             horizon
             ,
             wherefore
             to
             set
             your
             diall
             exact
             ,
             hang
             a
             line
             with
             a
             plummet
             at
             the
             end
             thereof
             ,
             and
             with
             a
             nail
             fixed
             in
             the
             line
             of
             12
             towards
             the
             top
             thereof
             ,
             to
             hang
             the
             plummet
             upon
             ,
             apply
             the
             diall
             to
             the
             place
             where
             it
             is
             to
             be
             fixed
             ,
             so
             that
             the
             line
             and
             plummet
             may
             hang
             just
             down
             upon
             the
             line
             of
             12
             ,
             neither
             inclining
             on
             one
             side
             or
             the
             other
             ,
             the
             diall
             thus
             fixed
             if
             the
             declination
             were
             truly
             taken
             ,
             and
             the
             dial
             rightly
             made
             ,
             by
             the
             former
             directions
             ,
             shall
             at
             all
             times
             (
             the
             Sun
             shining
             upon
             it
             )
             give
             you
             the
             true
             hour
             of
             the
             day
             .
          
        
         
           
           
             CHAP.
             VIII
             .
          
           
             How
             to
             insert
             the
             halve
             and
             Quarters
             of
             hours
             in
             all
             dialls
             .
          
           
             THe
             halves
             and
             quarters
             of
             hours
             are
             drawn
             in
             all
             plaines
             by
             the
             same
             rules
             ,
             and
             the
             like
             reason
             ,
             that
             the
             hours
             are
             inserted
             .
             Therefore
             take
             notice
             that
             if
             you
             would
             insert
             the
             halfe
             hours
             into
             any
             diall
             ,
             you
             must
             divide
             your
             Equinoctiall
             Circle
             into
             24
             equall
             parts
             instead
             of
             12
             ,
             and
             if
             you
             would
             insert
             the
             quarters
             ,
             then
             you
             must
             divide
             it
             into
             48
             parts
             ,
             and
             then
             proceed
             in
             all
             respect
             ,
             as
             you
             did
             for
             the
             whole
             hours
             .
          
        
         
           
             CHAP.
             IX
             .
          
           
             How
             to
             finde
             the
             declinatioon
             of
             any
             upright
             Wall.
             
          
           
             THe
             declination
             of
             a
             plain
             is
             an
             arch
             of
             the
             horizon
             comprehended
             between
             the
             pole
             of
             the
             plains
             horizontall
             line
             ,
             and
             the
             meridian
             of
             the
             place
             .
          
           
             To
             finde
             this
             declination
             ,
             two
             observations
             must
             be
             made
             ,
             the
             Sun
             shining
             ,
             and
             both
             at
             one
             instant
             of
             time
             (
             as
             neer
             as
             may
             be
             .
             )
             The
             first
             is
             the
             horizontall
             distance
             of
             the
             Sun
             from
             the
             pole
             of
             the
             plain
             .
             The
             second
             is
             the
             Suns
             Altitude
             .
          
           
             First
             ,
             to
             finde
             the
             horizontall
             distance
             .
             Apply
             the
             side
             of
             a
             Quadrant
             to
             your
             plain
             ,
             holding
             it
             (
             as
             neer
             as
             may
             be
             )
             horizontall
             ,
             that
             is
             to
             say
             ,
             levell
             ,
             Then
             holding
             up
             a
             thrid
             and
             plummet
             ,
             which
             must
             hang
             at
             full
             liberty
             ,
             so
             that
             the
             shadow
             of
             the
             thrid
             may
             passe
             directly
             through
             the
             center
             of
             the
             Quadrant
             ,
             then
             diligently
             note
             ●
             through
             what
             degree
             of
             the
             Quadrant
             the
             shadow
             passed
             ,
             and
             count
             those
             degrees
             from
             the
             side
             of
             your
             Quadrant
             which
             is
             perpendi●cular
             to
             the
             plain
             ,
             for
             those
             degrees
             are
             the
             Horizontall
             distance
             .
          
           
             Secondly
             ,
             At
             the
             same
             instant
             ,
             take
             the
             Suns
             a●●itude
             ,
             these
             two
             being
             heedfully
             taken
             ,
             will
             help
             you
             to
             the
             plains
             declination
             by
             th
             rules
             following
             .
          
           
           
             By
             the
             17
             or
             18
             Chapters
             of
             the
             Second
             Book
             find
             the
             Suns
             Azimuth
             .
             Then
             observe
             whether
             the
             Sun
             be
             between
             the
             pole
             of
             the
             plains
             horizontall
             line
             and
             the
             North
             or
             South
             points
             ,
             or
             not
             .
          
           
             If
             the
             Sun
             be
             between
             them
             ,
             adde
             the
             Azimuth
             and
             horizontall
             distance
             together
             ,
             and
             the
             sum
             of
             them
             is
             the
             declination
             of
             the
             plain
             .
          
           
             If
             the
             Sun
             be
             not
             between
             them
             ,
             substract
             the
             lesser
             of
             them
             from
             the
             greater
             ,
             and
             the
             difference
             shall
             be
             the
             declination
             of
             the
             plain
             .
             These
             rules
             sh●w
             you
             the
             quantity
             of
             your
             plains
             declination
             .
             But
             ,
          
        
         
           
             CHAP.
             X.
             
          
           
             Shewing
             how
             to
             know
             whether
             your
             plain
             declin
             from
             the
             Meridian
             towards
             either
             the
             East
             or
             West
             .
          
           
             YOu
             must
             take
             notice
             in
             your
             observation
             ,
             that
             if
             the
             Meridian
             point
             fall
             between
             the
             Azimuth
             and
             the
             pole
             of
             the
             plains
             horizontall
             line
             ,
             then
             doth
             the
             plain
             decline
             to
             the
             Coast
             contrary
             to
             that
             wherein
             the
             Sun
             is
             ,
             that
             is
             to
             say
             ,
             if
             the
             Sun
             be
             to
             the
             Eastward
             of
             the
             Meridian
             ,
             the
             plain
             declines
             to
             the
             Westward
             ,
             But
             if
             the
             Meridian
             point
             be
             not
             between
             the
             forementioned
             distance
             and
             the
             pole
             of
             the
             plain
             ,
             then
             doth
             the
             plain
             decline
             to
             the
             same
             Coast
             in
             which
             the
             Sun
             was
             at
             the
             time
             of
             observation
             .
          
        
         
           
             CHAP.
             XI
             .
          
           
             Concerning
             Polar
             Dials
             .
          
           
             A
             Polar
             diall
             is
             made
             in
             all
             respects
             as
             an
             East
             or
             West
             Diall
             is
             made
             ,
             onely
             the
             line
             of
             6
             a
             clock
             in
             the
             East
             or
             West
             Diall
             ,
             is
             12
             a
             clock
             in
             the
             Polar
             Diall
             ,
             the
             houre
             of
             7
             is
             1
             ,
             of
             8
             is
             2
             ,
             of
             9
             is
             ●
             ,
             of
             10
             is
             4
             ,
             and
             of
             11
             is
             5.
             
             Also
             the
             houre
             of
             5
             in
             the
             East
             or
             West
             Diall
             ,
             is
             11
             in
             the
             Polar
             ,
             of
             4
             is
             10
             ,
             of
             3
             is
             9
             ,
             of
             2
             8
             ,
             of
             ●
             is
             7
             ,
             &c.
             
             The
             Cock
             of
             this
             Diall
             is
             a
             plate
             of
             Iron
             or
             Brasse
             made
             of
             the
             breadth
             between
             12
             and
             3
             a
             cloock
             ,
             and
             set
             perpendicular
             
             upon
             the
             line
             of
             12
             ,
             as
             in
             the
             East
             or
             West
             Diall
             it
             is
             upon
             the
             line
             of
             6.
             
             In
             these
             Dialls
             the
             Equinoctiall
             line
             is
             to
             lie
             parallel
             to
             the
             Horizon
             ,
             and
             not
             to
             be
             elevated
             according
             to
             the
             complement
             of
             the
             Latitude
             of
             the
             place
             ,
             as
             in
             the
             East
             or
             West
             Diall
             it
             is
             .
          
        
         
           
             CHAP.
             XII
             .
          
           
             Concerning
             Equinoctiall
             Dialls
             .
          
           
             AN
             Equinoctiall
             Diall
             is
             of
             all
             other
             Dialls
             ,
             the
             most
             easie
             to
             make
             ,
             for
             if
             you
             describe
             a
             Circle
             ,
             and
             divide
             it
             into
             24
             equall
             parts
             ,
             and
             draw
             lines
             from
             the
             center
             through
             eve●●
             one
             of
             those
             equall
             parts
             ,
             the
             lines
             so
             drawn
             shall
             be
             the
             true
             houre
             lines
             .
          
           
             For
             the
             Stile
             of
             these
             Dialls
             ,
             it
             is
             no
             other
             but
             a
             streight
             Wyre
             of
             any
             length
             set
             perpendicular
             in
             the
             Center
             of
             the
             Circle
             ,
             whose
             shadow
             shall
             give
             the
             true
             houre
             of
             the
             Day
             .
          
        
         
           
             CHAP.
             XIII
             .
          
           
             Of
             such
             Plains
             as
             decline
             very
             far
             from
             the
             East
             or
             West
             towards
             the
             Meridian
             as
             
               75
               ,
               80
               ,
            
             or
             
               85
               ,
            
             deg
             ▪
             above
             which
             plains
             the
             Pole
             hath
             small
             Elevation
             .
          
           
             SUch
             plains
             as
             decline
             above
             60
             degrees
             the
             houre
             lines
             will
             come
             very
             close
             together
             ,
             so
             that
             if
             they
             be
             ▪
             not
             extended
             very
             far
             from
             the
             center
             ,
             there
             will
             be
             no
             sensible
             distance
             between
             hour
             and
             hour
             ▪
          
           
             To
             remedie
             this
             inconvenience
             ,
             there
             are
             severall
             wayes
             ,
             I
             will
             instance
             only
             in
             one
             which
             is
             familiar
             and
             easie
             ,
             and
             that
             is
             this
             .
          
           
             When
             〈◊〉
             have
             〈…〉
             your
             diall
             on
             a
             large
             sheet
             of
             paper
             ,
             fix
             it
             on
             some
             large
             Table
             or
             smooth
             Floor
             of
             a
             Room
             ,
             if
             the
             Diall
             you
             are
             to
             make
             be
             very
             large
             ,
             as
             5
             ,
             6
             ,
             or
             7
             ▪
             foot
             square
             ,
             then
             by
             the
             side
             
             of
             a
             long
             Rular
             laid
             to
             the
             Center
             and
             every
             hour
             line
             ,
             as
             also
             to
             the
             Stile
             and
             Substile
             ,
             draw
             lines
             to
             the
             full
             extent
             of
             the
             Table
             or
             Flour
             ,
             and
             you
             shall
             finde
             them
             to
             be
             of
             a
             competent
             largnesse
             .
             Then
             according
             to
             the
             bignesse
             of
             your
             plain
             ,
             cut
             off
             the
             houres
             .
             Stile
             and
             Substile
             ,
             leaving
             the
             center
             quite
             ou●
             ,
             and
             yout
             work
             is
             finis●ed
             .
          
        
         
           
             CHAP
             :
             XIIII
          
           
             Concerning
             Declining
             Reclining
             and
             Inclining
             Dials
             .
          
           
             VVE
             should
             now
             shew
             the
             manner
             of
             drawing
             houre
             lines
             upon
             declining
             reclining
             and
             inclining
             plains
             ,
             of
             which
             there
             are
             severall
             varieties
             ,
             and
             many
             cautions
             ,
             which
             in
             this
             place
             and
             at
             this
             time
             ,
             would
             be
             too
             many
             to
             ennumerate
             :
             but
             if
             this
             which
             hath
             been
             already
             delivered
             concerning
             Upright
             decliners
             shall
             be
             kindly
             accepted
             ,
             it
             shall
             animate
             me
             to
             do
             the
             like
             for
             all
             other
             plains
             whatsoever
             .
          
           
             FINIS
             .
          
        
      
    
     
       
         
           ADVERTISEMENT
           .
        
         
           NOte
           ,
           that
           this
           Scale
           and
           all
           other
           Instruments
           for
           the
           Mathematicks
           ,
           are
           made
           by
           
             Walter
             Hayes
             ,
          
           at
           the
           Crosse
           dagers
           in
           Moore
           ,
           Fields
           next
           doore
           to
           the
           Popes
           head
           Tavern
           ,
           
             London
             .