Mathematicall recreations. Or, A collection of many problemes, extracted out of the ancient and modern philosophers as secrets and experiments in arithmetick, geometry, cosmographie, horologiographie, astronomie, navigation, musick, opticks, architecture, statick, mechanicks, chemistry, water-works, fire-works, &c. Not vulgarly manifest till now. Written first in Greeke and Latin, lately compi'ld in French, by Henry Van Etten, and now in English, with the examinations and augmentations of divers modern mathematicians whereunto is added the description and use of the generall horologicall ring: and the double horizontall diall. Invented and written by William Oughtred.
         Récréation mathématique. English.
      
       
         
           1653
        
      
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         A48262
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         ESTC R217635
         99829293
         99829293
         33730
         
           
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         Images scanned from microfilm: (Early English books, 1641-1700 ; 1992:7)
      
       
         
           
             Mathematicall recreations. Or, A collection of many problemes, extracted out of the ancient and modern philosophers as secrets and experiments in arithmetick, geometry, cosmographie, horologiographie, astronomie, navigation, musick, opticks, architecture, statick, mechanicks, chemistry, water-works, fire-works, &c. Not vulgarly manifest till now. Written first in Greeke and Latin, lately compi'ld in French, by Henry Van Etten, and now in English, with the examinations and augmentations of divers modern mathematicians whereunto is added the description and use of the generall horologicall ring: and the double horizontall diall. Invented and written by William Oughtred.
             Récréation mathématique. English.
             Oughtred, William, 1575-1660. aut
          
           [40], 286, [17] p. : ill.
           
             printed for William Leake, at the signe of the Crown in Fleetstreet, between the two Temple Gates,
             London :
             M D C LIII. [1653]
          
           
             Translation of: Jean Leurechon. Recreation mathematique.
             Henry Van Etten is a pseudonym of Jean Leurechon.
             With an added engraved title page reading: Mathematicall recreations or a collection of sundrie excellent problemes out of ancient and moderne phylosophers.
             "The description and use of the double horizontall dyall" has separate title page dated 1652; register is continuous.
             Running title reads: Mathematicall recreation.
             Reproduction of the original in the British Library.
          
        
      
    
     
       
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         eng
      
       
         
           Science -- Problems, exercises, etx. -- Early works to 1800.
           Mathematics -- Problems, exercises, etc. -- Early works to 1800.
           Fireworks -- Early works to 1800.
           Scientific recreations -- Early works to 1800.
           Sundials -- Early works to 1800.
        
      
    
     
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           Mathematicall
           RECREATIONS
           .
           OR
           ,
           A
           Collection
           of
           many
           Problemes
           ,
           extracted
           out
           of
           the
           Ancient
           and
           Modern
           Philosophers
           ,
           as
           Secrets
           and
           Experiments
           in
           
             Arithmetick
             ,
             Geometry
             ,
             Cosmographie
             ,
             Horologiographie
             ,
             Astronomie
             ,
             Navigation
             ,
             Musick
             ,
             Opticks
             ,
             Architecture
             ,
             Stati●k
             ,
             Mechanicks
             ,
             Chemistry
             ,
             Water-works
             ,
             Fire-works
             ,
             &c.
             
          
           Not
           vulgarly
           manifest
           till
           now
           .
        
         
           Written
           first
           in
           Greeke
           and
           Latin
           ,
           lately
           compi'ld
           in
           French
           ,
           by
           
             Henry
             Van
             Etten
          
           ,
           and
           now
           in
           English
           ,
           with
           the
           Examinations
           and
           Augmentations
           of
           divers
           
             Modern
             Mathematicians
          
        
         
           Whereunto
           is
           added
           the
           Description
           and
           Use
           of
           the
           
             Generall
             Horologicall
             Ring
          
           :
           And
           The
           
             Double
             Horizontall
             Diall
          
           .
           Invented
           and
           written
           by
           WILLIAM
           OUGHTRED
           .
        
         
           LONDON
           :
           Printed
           for
           
             William
             Leake
          
           ,
           at
           the
           Signe
           of
           the
           Crown
           in
           Fleetstreet
           ,
           between
           the
           two
           Temple
           Gates
           ,
           MDCLIII
           .
        
      
       
         
         
           On
           the
           Frontispice
           and
           Booke
           .
        
         
           ALL
           Recreations
           do
           delight
           the
           minde
           ,
        
         
           But
           these
           are
           best
           being
           of
           a
           learned
           kinde
           :
        
         
           Here
           Art
           and
           Nature
           strive
           to
           give
           content
           ,
        
         
           In
           shewing
           many
           a
           rare
           experiment
           ,
        
         
           Which
           you
           may
           read
           ,
           &
           on
           their
           Schemes
           here
           look
        
         
           Both
           in
           the
           Frontispice
           ,
           and
           in
           the
           Book
           .
        
         
           Upon
           whose
           table
           new
           conceits
           are
           set
           ,
        
         
           Like
           dainty
           dishes
           ,
           thereby
           for
           to
           whet
        
         
           And
           winne
           your
           judgement
           ,
           with
           your
           appetite
        
         
           To
           taste
           them
           ,
           and
           therein
           to
           taka
           delight
           .
        
         
           The
           Senses
           objects
           are
           but
           dull
           at
           best
           ,
        
         
           But
           Art
           doth
           give
           the
           Intellect
           a
           feast
           .
        
         
           Come
           hither
           then
           ,
           and
           here
           I
           will
           describe
           ,
        
         
           What
           this
           same
           Table
           doth
           for
           you
           provide
           .
        
         
           Here
           Questions
           of
           Arithmetick
           are
           wrought
           ,
        
         
           And
           hidden
           secrets
           unto
           light
           are
           brought
           ,
        
         
           The
           like
           it
           in
           Geometrie
           doth
           unfold
           ,
        
         
           And
           some
           too
           in
           Cosmographie
           are
           told
           :
        
         
           It
           divers
           pretty
           Dyals
           doth
           descrie
           ,
        
         
           With
           strange
           experiments
           in
           Astronomie
           ,
        
         
           And
           Navigation
           ,
           with
           each
           severall
           Picture
           ,
        
         
           In
           
             Musick
             ,
             Opticks
          
           ,
           and
           in
           Architecture
           :
        
         
           In
           
             Statick
             ,
             Machanicks
          
           ,
           and
           Chymistrie
           ,
        
         
           In
           Water-works
           ,
           and
           to
           ascend
           more
           hie
           ,
        
         
           In
           Fire-works
           ,
           like
           to
           
             Joves
             Artillerie
          
           .
        
         
           All
           this
           I
           know
           thou
           in
           this
           Book
           shalt
           finde
           ,
        
         
           And
           here
           's
           enough
           for
           to
           content
           thy
           minde
           .
        
         
           For
           from
           good
           Authors
           ,
           this
           our
           Author
           drew
        
         
           These
           Recreations
           ,
           which
           are
           strange
           ,
           and
           true
        
         
           So
           that
           this
           Book
           's
           a
           Centre
           ,
           and
           t
           is
           fit
           ,
        
         
           That
           in
           this
           Centre
           ;
           lines
           of
           praise
           should
           meet
        
         
           
             W.
             
          
        
      
    
     
       
         
           
             
             
               
                 
                   MATHEMATICALL
                   Recreations
                   Or
                   a
                   Collection
                   of
                   sundrie
                   excellent
                   Problemes
                   out
                   of
                   ancient
                   &
                   moderne
                   Phylosophers
                   Both
                   vsefull
                   and
                   Recreatiue
                   Printed
                   for
                   
                     William
                     Leake
                  
                   and
                   are
                   to
                   be
                   solde
                   at
                   the
                   Crowne
                   in
                   fleet
                   streete
                   betweene
                   the
                   two
                   Temple
                   gates
                   .
                
              
            
             
             
             
          
           
             
             
             
               TO
               The
               thrice
               Noble
               and
               most
               generous
               Lo.
               the
               Lo.
               Lambert
               Verreyken
               ,
               Lo.
               of
               Hinden
               ,
               Wolverthem
               ,
               &c.
               
            
             
               
                 My
                 honourable
                 Lo.
                 
              
            
             
               AMongst
               the
               rare
               and
               curious
               Propositions
               which
               I
               have
               learned
               out
               of
               the
               studies
               of
               the
               Mathematicks
               in
               the
               famous
               University
               of
               
                 Pont
                 a
                 Mousson
              
               ,
               I
               have
               taken
               singular
               pleasure
               in
               certaine
               Problemes
               no
               lesse
               ingenious
               than
               recreative
               ,
               which
               drew
               me
               unto
               the
               search
               of
               demonstrations
               more
               difficult
               and
               serious
               ;
               some
               of
               which
               I
               have
               amassed
               and
               caused
               to
               passe
               the
               Presse
               ,
               and
               here
               dedicate
               them
               now
               unto
               your
               Honour
               ;
               not
               that
               I
               account
               them
               worthy
               of
               your
               view
               ,
               but
               in
               part
               to
               
               testifie
               my
               affectionate
               desires
               to
               serve
               you
               ,
               and
               to
               satisfie
               the
               curious
               ,
               who
               delight
               themselves
               in
               these
               pleasant
               studies
               ,
               knowing
               well
               that
               the
               Nobilitie
               ,
               and
               Gentrie
               rather
               studie
               the
               
                 Mathematicall
                 Arts
              
               ,
               to
               content
               and
               satisfie
               their
               affections
               ,
               in
               the
               speculation
               of
               such
               admirable
               experiments
               as
               are
               extracted
               from
               them
               ,
               than
               in
               hope
               of
               gaine
               to
               fill
               their
               Purses
               .
               All
               which
               studies
               ,
               and
               others
               ,
               with
               my
               whole
               indevours
               ,
               I
               shall
               alwayes
               dedicate
               unto
               your
               Honour
               ,
               with
               an
               ardent
               desire
               to
               be
               accounted
               ever
               ,
            
             
               
                 Your
                 most
                 humble
                 and
                 obedient
                 Nephew
                 and
                 Servant
                 ,
                 
                   H.
                   VAN
                   ETTEN
                
                 .
              
            
          
           
             
             
               By
               vvay
               of
               advertisement
               .
               Five
               or
               six
               things
               I
               have
               thought
               worthy
               to
               declare
               before
               I
               passe
               further
               .
            
             
               FIrst
               ,
               that
               I
               place
               not
               the
               speculative
               demonstrations
               with
               all
               these
               Problems
               ,
               but
               content
               my self
               to
               shew
               them
               as
               at
               the
               fingers
               end
               :
               which
               was
               my
               plot
               and
               intention
               ,
               because
               those
               which
               understand
               the
               Mathematicks
               can
               conceive
               them
               easily
               ;
               others
               for
               the
               most
               part
               will
               content
               themselves
               onely
               with
               the
               knowledge
               of
               them
               ,
               without
               seeking
               the
               reason
               .
            
             
               Secondly
               ,
               to
               give
               a
               greater
               grace
               to
               the
               practice
               of
               these
               things
               ,
               they
               ought
               to
               be
               concealed
               as
               much
               as
               they
               may
               ,
               in
               the
               subtiltie
               of
               the
               way
               ;
               for
               that
               which
               doth
               ravish
               the
               spirits
               is
               ,
               
                 an
                 admirable
                 effect
                 ,
                 whose
                 cause
                 is
                 unknowne
                 :
              
               which
               if
               it
               were
               discovered
               ,
               halfe
               the
               pleasure
               is
               l●st
               ;
               therefore
               all
               the
               finenesse
               consists
               in
               the
               
               dexterity
               of
               the
               Act
               ,
               concealing
               the
               meanes
               ,
               and
               changing
               often
               the
               streame
               .
            
             
               Thirdly
               ,
               great
               care
               ought
               to
               be
               had
               that
               one
               deceive
               not
               himselfe
               ,
               that
               would
               declare
               by
               way
               of
               Art
               to
               deceive
               another
               :
               this
               will
               make
               the
               matter
               contemptible
               to
               ignorant
               Persons
               ,
               which
               will
               rather
               cast
               the
               fault
               upon
               the
               Science
               ,
               than
               upon
               him
               that
               shewes
               it
               :
               when
               the
               cause
               is
               not
               in
               the
               Mathematicall
               principles
               ,
               but
               in
               him
               that
               failes
               in
               the
               acting
               of
               it
               .
            
             
               Fourthly
               ,
               in
               certaine
               Arithmeticall
               propositions
               they
               have
               onely
               their
               answers
               as
               I
               found
               them
               in
               sundry
               Authors
               ,
               which
               any
               one
               being
               studious
               of
               Mathematicall
               learning
               ,
               may
               finde
               their
               originall
               ,
               and
               also
               the
               way
               of
               their
               operation
               .
            
             
               Fifthly
               ,
               because
               the
               number
               of
               these
               Problemes
               ,
               and
               their
               dependances
               are
               many
               ,
               and
               intermixed
               ,
               I
               thought
               it
               convenient
               to
               gather
               them
               into
               a
               Table
               :
               that
               so
               each
               one
               according
               to
               his
               fancie
               ,
               might
               make
               best
               choise
               of
               that
               which
               might
               best
               please
               his
               palate
               ,
               the
               matter
               being
               not
               of
               one
               nature
               ,
               nor
               of
               like
               subtiltie
               :
               But
               whosoever
               will
               have
               patience
               to
               read
               on
               ,
               shall
               finde
               the
               end
               better
               than
               the
               beginning
               .
            
          
           
             
             
               To
               the
               Reader
               .
            
             
               IT
               hath
               been
               observed
               by
               many
               ,
               that
               sundry
               fine
               wits
               as
               well
               amongst
               the
               Ancient
               as
               Moderne
               ,
               have
               sported
               and
               delighted
               themselves
               upon
               severall
               things
               of
               small
               consequence
               ,
               as
               upon
               the
               foot
               of
               a
               fly
               ,
               upon
               a
               straw
               ,
               upon
               a
               point
               ,
               nay
               upon
               nothing
               ;
               striving
               as
               it
               were
               to
               shew
               the
               greatnesse
               of
               their
               glory
               in
               the
               smalnesse
               of
               the
               subject
               :
               And
               have
               amongst
               most
               solid
               and
               artificiall
               conclusions
               ,
               composed
               and
               produced
               sundry
               Inventions
               both
               Philosophicall
               and
               Mathematicall
               ,
               to
               solace
               the
               minde
               ,
               and
               recreate
               the
               spirits
               ,
               which
               the
               succeeding
               ages
               have
               imbraced
               ,
               and
               from
               them
               gleaned
               and
               extracted
               many
               admirable
               ,
               and
               rare
               conclusions
               ;
               judging
               that
               borrowed
               matter
               often-times
               yeelds
               praise
               to
               the
               industry
               of
               its
               author
               .
               Hence
               for
               thy
               use
               (
               Courteous
               Reader
               )
               I
               have
               with
               
               great
               search
               and
               labour
               collected
               also
               ,
               and
               heaped
               up
               together
               in
               a
               body
               of
               these
               pleasant
               and
               fine
               experiments
               to
               stirre
               up
               and
               delight
               the
               affectionate
               ,
               (
               out
               of
               the
               writings
               of
               
                 Socrates
                 ,
                 Plato
                 ,
                 Aristotle
                 ,
                 Demosthenes
                 ,
                 Pythagoras
                 ,
                 Democrates
                 ,
                 Plinie
                 ,
                 Hyparchus
                 ,
                 Euclides
                 ,
                 Vitruvius
                 ,
                 Diaphantus
                 ,
                 Pergaeus
                 ,
                 Archimedes
                 ,
                 Papus
                 Alexandrinus
                 ,
                 Vitellius
                 ,
                 Ptolomaeus
                 ,
                 Copernicus
                 ,
                 Proclus
                 ,
                 Mauralicus
                 ,
                 Cardanus
                 ,
                 Valalpandus
                 ,
                 Kepleirus
                 ,
                 Gilbertus
                 ,
                 Tychonius
                 ,
                 Dureirus
                 ,
                 Josephus
                 ,
                 Clavius
                 ,
                 Gallileus
                 Maginus
                 ,
                 Euphanus
                 Tyberill
                 ,
              
               and
               others
               )
               knowing
               Art
               imitating
               Nature
               that
               glories
               alwayes
               in
               the
               variety
               of
               things
               ,
               which
               she
               produceth
               to
               satisfie
               the
               minde
               of
               curious
               inquisitors
               .
               And
               though
               perhaps
               these
               labours
               to
               some
               humourous
               persons
               may
               seeme
               vaine
               ,
               and
               ridiculous
               ,
               for
               such
               it
               was
               not
               undertaken
               :
               But
               for
               those
               which
               intentively
               have
               desired
               and
               ●ought
               after
               the
               knowledge
               of
               those
               things
               ,
               it
               being
               an
               invitation
               and
               motive
               to
               the
               search
               of
               greater
               matters
               ,
               and
               to
               imploy
               the
               minde
               in
               usefull
               knowledge
               ,
               rather
               than
               to
               be
               busied
               in
               vaine
               
                 Pamphlets
                 ,
                 Play-books
              
               ,
               fruitlesse
               Legends
               ,
               and
               prodigious
               Histories
               that
               are
               invented
               out
               of
               fancie
               ,
               which
               abuse
               many
               
                 Noble
                 spirits
              
               ,
               dull
               their
               wits
               ,
               &
               alienate
               
               their
               thoughts
               from
               laudable
               and
               honourable
               Studies
               .
               In
               this
               Tractate
               thou
               maist
               therefore
               make
               choise
               of
               such
               
                 Mathematicall
                 Problemes
              
               and
               Conclusions
               as
               may
               delight
               thee
               ,
               which
               kinde
               of
               learning
               doth
               excellently
               adorne
               a
               man
               ;
               seeing
               the
               usefulnesse
               thereof
               ,
               and
               the
               manly
               accomplishments
               it
               doth
               produce
               ,
               is
               profitable
               and
               delightfull
               for
               all
               sorts
               of
               people
               ,
               who
               may
               furnish
               and
               adorne
               themselves
               with
               abundance
               of
               matter
               in
               that
               kinde
               ,
               to
               help
               them
               by
               way
               of
               use
               ,
               and
               discourse
               .
               And
               to
               this
               we
               have
               also
               added
               our
               Pyrotechnie
               ,
               knowing
               that
               Beasts
               have
               for
               their
               object
               only
               the
               surface
               of
               the
               earth
               ;
               but
               hoping
               that
               thy
               spirit
               which
               followeth
               the
               motion
               of
               fire
               ,
               will
               abandon
               the
               lower
               Elements
               ,
               and
               cause
               thee
               to
               lift
               up
               thine
               eyes
               to
               soare
               in
               an
               higher
               Contemplation
               ,
               having
               so
               glittering
               a
               Canopie
               to
               behold
               ,
               and
               these
               pleasant
               and
               recreative
               fires
               ascending
               may
               cause
               thy
               affections
               also
               to
               ascend
               .
               The
               Whole
               whereof
               we
               send
               forth
               to
               thee
               ,
               that
               desirest
               the
               scrutability
               of
               things
               ;
               Nature
               having
               furnished
               us
               with
               matter
               ,
               thy
               spirit
               may
               easily
               digest
               them
               ,
               and
               put
               them
               finely
               in
               order
               ,
               though
               now
               in
               disorder
               .
            
          
           
             
             
               A
               Table
               of
               the
               particular
               heads
               of
               this
               Book
               ,
               contracted
               according
               to
               the
               severall
               Arts
               specified
               in
               the
               Title-page
               .
            
             
               
                 Experiments
                 of
                 Arithmetick
                 .
              
               
                 PAge
                 1
                 ,
                 2
                 ,
                 3
                 ,
                 16
                 ,
                 19
                 ,
                 22
                 ,
                 28
                 ,
                 33
                 ,
                 39
                 ,
                 40
                 ,
                 44
                 ,
                 45
                 ,
                 51
                 ,
                 52
                 ,
                 53
                 ,
                 59
                 ,
                 60
                 ,
                 69
                 ,
                 71
                 ,
                 77
                 ,
                 83
                 ,
                 85
                 ,
                 86
                 ,
                 89
                 ,
                 90
                 ,
                 91
                 ,
                 124
                 ,
                 134
                 ,
                 135
                 ,
                 136
                 ▪
                 137
                 ,
                 138
                 ,
                 139
                 ,
                 140
                 ,
                 178
                 179
                 ,
                 181
                 ,
                 182
                 ,
                 183
                 ,
                 184
                 ,
                 185
                 ,
                 188
                 ,
                 208
                 ,
                 210
                 ,
                 213.
                 
              
               
                 
                   Experiments
                   ●n
                   Geometrie
                
                 .
              
               
                 Pag.
                 12
                 ,
                 15
                 ,
                 24
                 ,
                 26
                 ,
                 27
                 ,
                 30
                 ,
                 35
                 ,
                 37
                 ,
                 41
                 ,
                 42
                 ,
                 47
                 ,
                 48
                 ,
                 49
                 ,
                 62
                 ,
                 65
                 ,
                 72
                 ,
                 79
                 ,
                 82
                 ,
                 113
                 ,
                 117
                 ,
                 118
                 ,
                 119
                 ,
                 214
                 ,
                 215
                 ,
                 217
                 ,
                 218
                 ,
                 234
                 ,
                 235
                 ,
                 236
                 ,
                 239
                 ,
                 240.
                 
              
               
                 Experiments
                 in
                 Cosmographie
                 .
              
               
                 Pag.
                 14
                 ,
                 43
                 ,
                 75
                 ,
                 106
                 ,
                 107
                 ,
                 219
                 ,
                 220
                 ,
                 225
                 ,
                 227
                 ,
                 228
                 ,
                 229
                 ,
                 230
                 ,
                 232.
                 
              
               
                 Experiments
                 in
                 Horologiographie
                 .
              
               
                 Pag.
                 137
                 ,
                 166
                 ,
                 167
                 ,
                 168
                 ,
                 169
                 ,
                 171
                 ,
                 234.
                 
              
               
                 Experiments
                 in
                 Astronomie
                 .
              
               
                 Pag.
                 220
                 ,
                 221
                 ,
                 222
                 ,
                 223
                 ,
                 224.
                 
              
               
                 Experiments
                 in
                 Navigation
                 .
              
               
                 Pag.
                 105
                 ,
                 233
                 ,
                 234
                 ,
                 237
                 ,
                 238.
                 
              
               
                 Experiments
                 in
                 Musick
                 .
              
               
                 Pag.
                 78
                 ,
                 87
                 ,
                 126.
                 
              
               
                 
                 
                   Experiments
                   in
                   Opticks
                
                 .
              
               
                 Pag.
                 6
                 ,
                 66
                 ,
                 98
                 ,
                 99
                 ,
                 100
                 ,
                 102
                 ,
                 129
                 ,
                 131
                 ,
                 141
                 ,
                 142
                 ,
                 143
                 ,
                 144
                 ,
                 146
                 ,
                 149
                 ,
                 151
                 ,
                 152
                 ,
                 153
                 ,
                 155
                 ,
                 156
                 ,
                 157
                 ,
                 158
                 ,
                 160
                 ,
                 161
                 ,
                 162
                 ,
                 163
                 ,
                 164
                 ,
                 165.
                 
              
               
                 Experiments
                 in
                 Architecture
                 .
              
               
                 Pag.
                 16
                 ,
                 242
                 ,
                 243.
                 
              
               
                 Experiments
                 in
                 Staticke
                 .
              
               
                 Pag.
                 27
                 ,
                 30
                 ,
                 32
                 ,
                 71
                 ,
                 199
                 ,
                 200
                 ,
                 201
                 ,
                 283
                 ,
                 204
                 ,
                 205
                 ,
                 207.
                 
              
               
                 Experiments
                 in
                 Machanicks
                 .
              
               
                 Pag.
                 56
                 ,
                 58
                 ,
                 68
                 ,
                 88
                 ,
                 95
                 ,
                 108
                 ,
                 110
                 ,
                 128
                 ,
                 173
                 ,
                 174
                 ,
                 176
                 ,
                 246
                 ,
                 248
                 ,
                 258
                 ,
                 259.
                 
              
               
                 Experiments
                 in
                 Chymistrie
                 .
              
               
                 Pag.
                 198
                 ,
                 255
                 ,
                 256
                 ,
                 257
                 ,
                 260
                 ,
                 262
                 ,
                 263
                 ,
                 264.
                 
              
               
                 Experiments
                 in
                 Water-workes
                 .
              
               
                 Pag.
                 190
                 ,
                 191
                 ,
                 192
                 ,
                 193
                 ,
                 194
                 ,
                 196
                 ,
                 247
                 ,
                 249
                 ,
                 250
                 ,
                 252
                 ,
                 253.
                 
              
               
                 Experiments
                 in
                 Fireworkes
                 .
              
               
                 From
                 page
                 ,
                 265.
                 to
                 the
                 end
                 .
              
            
             
               FINIS
               .
            
          
           
             
             
             
               A
               Table
               of
               the
               Contents
               ,
               and
               chiefe
               points
               conteined
               in
               this
               Book
               .
               PROBLEM
               .
               II.
               
            
             
               
                 HOw
                 visible
                 objects
                 that
                 are
                 without
                 ,
                 and
                 things
                 that
                 passe
                 by
                 ,
                 are
                 most
                 lively
                 represented
                 to
                 those
                 that
                 are
                 within
                 .
                 
                   Page
                   6
                
              
               
                 
                   Prob.
                   1
                
                 Of
                 finding
                 of
                 numbers
                 conceived
                 in
                 the
                 minde
                 .
                 
                   1
                   ,
                   2
                   ,
                   3
                
              
               
                 
                   Prob.
                   5
                
                 Of
                 a
                 Geographicall
                 Garden-plot
                 fit
                 for
                 a
                 Prince
                 or
                 some
                 great
                 personage
                 .
                 14
              
               
                 
                   Prob.
                   37
                
                 Any
                 liquid
                 substance
                 ,
                 as
                 water
                 or
                 wine
                 ,
                 placed
                 in
                 a
                 Glasse
                 ,
                 may
                 be
                 made
                 to
                 boile
                 by
                 the
                 motion
                 of
                 the
                 finger
                 ,
                 and
                 yet
                 not
                 touching
                 it
                 .
                 54
              
               
                 
                   Prob.
                   3
                
                 How
                 to
                 weigh
                 the
                 blow
                 of
                 ones
                 fist
                 ,
                 of
                 a
                 Mallet
                 ,
                 a
                 Hatchet
                 or
                 such
                 like
                 .
                 9.
                 
              
               
                 
                   Prob.
                   30
                
                 Two
                 severall
                 numbers
                 being
                 taken
                 by
                 two
                 sundry
                 persons
                 ,
                 how
                 subtilly
                 to
                 discover
                 which
                 of
                 those
                 numbers
                 each
                 of
                 them
                 took
                 .
                 46
              
               
                 
                   Prob.
                   4
                
                 That
                 a
                 staffe
                 may
                 be
                 broken
                 ▪
                 placed
                 upon
                 two
                 Glasses
                 ,
                 without
                 hurting
                 of
                 the
                 
                   Glasses
                   .
                   12
                
              
               
                 
                   Prob.
                   7
                
                 How
                 to
                 dispose
                 Lots
                 that
                 the
                 
                   5
                   ,
                   6
                   ,
                   9
                
                 ,
                 &c.
                 of
                 any
                 number
                 of
                 persons
                 may
                 escape
                 .
                 16
              
               
                 
                 
                   Prob.
                   13
                
                 How
                 the
                 weight
                 of
                 smoke
                 of
                 a
                 combustible
                 body
                 ,
                 which
                 is
                 exhaled
                 ,
                 may
                 be
                 weighed
                 .
                 27
              
               
                 
                   Prob.
                   12
                
                 Of
                 three
                 knives
                 which
                 may
                 be
                 so
                 disposed
                 to
                 hang
                 in
                 the
                 aire
                 ,
                 and
                 move
                 upon
                 the
                 Point
                 of
                 a
                 needle
                 .
                 27
              
               
                 
                   Prob.
                   17
                
                 Of
                 a
                 deceitfull
                 bowle
                 ,
                 to
                 bowle
                 withall
                 .
                 32
              
               
                 
                   Prob.
                   16
                
                 A
                 ponderous
                 or
                 heavy
                 body
                 may
                 be
                 supported
                 in
                 the
                 aire
                 without
                 any
                 one
                 touching
                 it
                 .
                 30
              
               
                 
                   Prob.
                   18
                
                 How
                 a
                 Peare
                 ,
                 or
                 Apple
                 ,
                 may
                 be
                 parted
                 into
                 any
                 parts
                 ,
                 without
                 breaking
                 the
                 rinde
                 thereof
                 .
                 33
              
               
                 
                   Prob.
                   15
                
                 Of
                 a
                 fine
                 kinde
                 of
                 dore
                 which
                 opens
                 and
                 shuts
                 on
                 both
                 sides
                 .
                 30
              
               
                 
                   Prob.
                   9
                
                 How
                 the
                 halfe
                 of
                 a
                 Vessell
                 which
                 containes
                 8
                 measures
                 may
                 be
                 taken
                 ,
                 being
                 but
                 onely
                 two
                 other
                 measures
                 ,
                 the
                 one
                 being
                 3
                 ,
                 and
                 the
                 other
                 8
                 measures
                 .
                 22
              
               
                 
                   Prob.
                   8
                
                 Three
                 persons
                 having
                 taken
                 each
                 of
                 them
                 severall
                 things
                 ,
                 to
                 finde
                 which
                 each
                 of
                 them
                 hath
                 taken
                 .
                 19
              
               
                 
                   Prob.
                   6
                
                 How
                 to
                 dispose
                 three
                 staves
                 which
                 may
                 support
                 each
                 other
                 in
                 the
                 aire
                 .
                 15
              
               
                 
                   Prob.
                   14
                
                 Many
                 things
                 being
                 disposed
                 Circular
                 (
                 or
                 otherwise
                 )
                 to
                 finde
                 which
                 of
                 them
                 any
                 one
                 thinks
                 upon
                 .
                 28
              
               
                 
                   Prob.
                   19
                
                 To
                 finde
                 a
                 number
                 thought
                 upon
                 
                 without
                 asking
                 questions
                 .
                 33
              
               
                 
                   Prob.
                   11
                
                 How
                 a
                 Milstone
                 or
                 other
                 ponderosity
                 may
                 hang
                 upon
                 the
                 point
                 of
                 a
                 Needle
                 without
                 bowing
                 ,
                 or
                 any
                 wise
                 breaking
                 of
                 it
                 .
                 26
              
               
                 
                   Prob.
                   20
                   and
                   21
                
                 How
                 a
                 body
                 that
                 is
                 uniforme
                 and
                 inflexible
                 may
                 passe
                 through
                 a
                 hole
                 which
                 is
                 round
                 ,
                 square
                 and
                 Triangular
                 ;
                 or
                 round
                 ,
                 square
                 and
                 ovall-wise
                 ,
                 and
                 exactly
                 fill
                 those
                 severall
                 holes
                 .
                 
                   35
                   ,
                   37
                
              
               
                 
                   Prob.
                   10
                
                 How
                 a
                 stick
                 may
                 stand
                 upon
                 ones
                 finger
                 ,
                 or
                 a
                 Pike
                 in
                 the
                 middle
                 of
                 a
                 Court
                 without
                 falling
                 .
                 24
              
               
                 
                   Prob.
                   22
                
                 To
                 finde
                 a
                 number
                 thought
                 upon
                 after
                 another
                 manner
                 than
                 those
                 which
                 are
                 formerly
                 delivered
                 .
                 39
              
               
                 
                   Prob.
                   23
                
                 To
                 finde
                 out
                 many
                 numbers
                 that
                 sundry
                 persons
                 or
                 any
                 one
                 hath
                 thought
                 upon
                 .
                 40
              
               
                 
                   Prob.
                   24
                
                 How
                 is
                 it
                 that
                 a
                 man
                 in
                 one
                 &
                 the
                 same
                 time
                 may
                 have
                 his
                 head
                 upward
                 ,
                 and
                 his
                 feet
                 upward
                 ,
                 being
                 in
                 one
                 and
                 the
                 same
                 place
                 ?
                 4●
              
               
                 
                   Prob.
                   25
                
                 Of
                 a
                 Ladder
                 by
                 which
                 two
                 men
                 ascending
                 at
                 one
                 time
                 ,
                 the
                 more
                 they
                 ascend
                 ,
                 the
                 more
                 they
                 shal
                 be
                 asunder
                 ,
                 notwith
                 standing
                 the
                 one
                 be
                 as
                 high
                 as
                 the
                 other
                 .
                 42
              
               
                 
                   Prob.
                   26
                
                 How
                 is
                 it
                 that
                 a
                 man
                 having
                 but
                 a
                 Rod
                 or
                 Pole
                 of
                 land
                 ,
                 doth
                 brag
                 that
                 he
                 
                 may
                 in
                 a
                 right
                 line
                 passe
                 from
                 place
                 to
                 place
                 3000
                 miles
                 .
                 42
              
               
                 
                   Prob.
                   27
                
                 How
                 is
                 it
                 that
                 a
                 man
                 standing
                 upright
                 ,
                 and
                 looking
                 which
                 way
                 he
                 will
                 ,
                 he
                 looketh
                 true
                 North
                 or
                 
                   South
                   .
                   43
                
              
               
                 
                   Prob.
                   28
                
                 To
                 tell
                 any
                 one
                 what
                 number
                 remaines
                 after
                 certaine
                 operations
                 being
                 ended
                 ,
                 without
                 asking
                 any
                 question
                 .
                 44
              
               
                 
                   Prob.
                   29
                
                 Of
                 the
                 play
                 with
                 two
                 severall
                 things
                 .
                 45
              
               
                 
                   Prob.
                   31
                
                 How
                 to
                 describe
                 a
                 circle
                 that
                 shall
                 touch
                 3
                 points
                 placed
                 howsoever
                 upon
                 a
                 plaine
                 ,
                 if
                 they
                 be
                 not
                 in
                 a
                 right
                 line
                 .
                 47
              
               
                 
                   Prob.
                   32
                
                 How
                 to
                 change
                 a
                 circle
                 into
                 a
                 square
                 forme
                 .
                 48
              
               
                 
                   Prob.
                   33
                
                 With
                 one
                 and
                 the
                 same
                 compasses
                 ,
                 and
                 at
                 one
                 and
                 the
                 same
                 extent
                 or
                 opening
                 ,
                 how
                 to
                 describe
                 many
                 circles
                 concentricall
                 ,
                 that
                 is
                 ,
                 greater
                 or
                 lesser
                 one
                 than
                 another
                 .
                 49
              
               
                 
                   Prob.
                   34
                
                 Any
                 number
                 under
                 10.
                 being
                 thought
                 upon
                 ,
                 to
                 finde
                 what
                 numbers
                 they
                 were
                 .
                 51
              
               
                 
                   Prob
                   ,
                   35
                
                 Of
                 the
                 play
                 with
                 the
                 
                   Ring
                   .
                   52
                
              
               
                 
                   Prob.
                   36
                
                 The
                 play
                 of
                 
                   3
                   ,
                   4
                
                 ,
                 or
                 more
                 
                   Dice
                   .
                   53
                
              
               
                 
                   Prob.
                   38
                
                 Of
                 a
                 fine
                 Vessell
                 which
                 holds
                 Wine
                 or
                 Water
                 being
                 cast
                 into
                 it
                 at
                 a
                 certain
                 height
                 ,
                 but
                 being
                 filled
                 higher
                 it
                 will
                 runne
                 all
                 out
                 of
                 its
                 owne
                 accord
                 .
                 56
              
               
                 
                 
                   Prob.
                   39
                
                 Of
                 a
                 Glasse
                 very
                 pleasant
                 .
                 58
              
               
                 
                   Prob.
                   40.
                
                 
                 If
                 any
                 one
                 should
                 hold
                 in
                 each
                 hand
                 as
                 many
                 pieces
                 of
                 money
                 as
                 in
                 the
                 other
                 ,
                 how
                 to
                 finde
                 how
                 much
                 there
                 is
                 .
                 59
              
               
                 
                   Prob.
                   41
                
                 Many
                 Dice
                 being
                 cast
                 ,
                 how
                 artificially
                 to
                 discover
                 the
                 number
                 of
                 the
                 points
                 that
                 may
                 arise
                 .
                 60
              
               
                 
                   Prob.
                   42
                
                 Two
                 metals
                 as
                 Gold
                 and
                 Silver
                 or
                 of
                 other
                 kinde
                 ,
                 weighing
                 alike
                 ,
                 being
                 privately
                 placed
                 into
                 two
                 like
                 boxes
                 ,
                 to
                 finde
                 in
                 which
                 of
                 them
                 the
                 Gold
                 or
                 Silver
                 is
                 .
                 62
              
               
                 
                   Prob.
                   43
                
                 Two
                 Globes
                 of
                 divers
                 metals
                 (
                 as
                 one
                 Gold
                 the
                 other
                 Copper
                 )
                 yet
                 of
                 equall
                 weight
                 ,
                 being
                 put
                 in
                 a
                 Box
                 as
                 B.G.
                 to
                 finde
                 in
                 which
                 end
                 the
                 Gold
                 or
                 Copper
                 is
                 .
                 65
              
               
                 
                   Prob.
                   44
                
                 How
                 to
                 represent
                 divers
                 sorts
                 of
                 Rainbowes
                 here
                 below
                 .
                 66
              
               
                 
                   Prob.
                   45
                
                 How
                 that
                 if
                 all
                 the
                 powder
                 in
                 the
                 World
                 were
                 inclosed
                 in
                 a
                 bowle
                 of
                 paper
                 or
                 glasse
                 ,
                 and
                 being
                 fired
                 on
                 all
                 parts
                 ,
                 it
                 could
                 not
                 break
                 that
                 bowle
                 .
                 68
              
               
                 
                   Prob.
                   46
                
                 To
                 finde
                 a
                 number
                 which
                 being
                 divided
                 by
                 2.
                 there
                 will
                 remaine
                 1.
                 being
                 divided
                 by
                 3.
                 there
                 will
                 remaine
                 1.
                 and
                 so
                 likewise
                 being
                 divided
                 by
                 
                   4
                   ,
                   5
                
                 ,
                 or
                 6.
                 there
                 will
                 still
                 remaine
                 one
                 ,
                 but
                 being
                 divided
                 by
                 7
                 will
                 remaine
                 nothing
                 .
                 69
              
               
                 
                   Prob.
                   47
                
                 One
                 had
                 a
                 certaine
                 number
                 of
                 Crownes
                 ,
                 and
                 counting
                 them
                 by
                 2
                 and
                 2
                 ,
                 
                 there
                 rested
                 1.
                 counting
                 them
                 by
                 3
                 ,
                 and
                 3
                 ,
                 there
                 rested
                 2.
                 counting
                 them
                 by
                 4
                 ,
                 and
                 4
                 ,
                 there
                 rested
                 3.
                 counting
                 them
                 by
                 5
                 ,
                 and
                 5
                 ,
                 there
                 rested
                 4.
                 counting
                 them
                 by
                 6
                 ,
                 and
                 6
                 ,
                 there
                 rested
                 5.
                 but
                 counting
                 them
                 by
                 7
                 and
                 7
                 ,
                 there
                 rested
                 nothing
                 ,
                 how
                 many
                 Crownes
                 might
                 he
                 have
                 ?
                 71
              
               
                 
                   Prob.
                   48
                
                 How
                 many
                 sorts
                 of
                 weights
                 in
                 the
                 least
                 manner
                 must
                 there
                 be
                 to
                 weigh
                 all
                 sorts
                 of
                 things
                 betweene
                 one
                 pound
                 and
                 121
                 pound
                 ,
                 and
                 so
                 unto
                 364
                 pound
                 ?
                 71
              
               
                 
                   Prob.
                   49
                
                 Of
                 a
                 deceitfull
                 balance
                 which
                 being
                 empty
                 seems
                 to
                 be
                 just
                 ,
                 because
                 it
                 hangs
                 in
                 Aequilibrio
                 ,
                 notwithstanding
                 putting
                 12
                 pound
                 in
                 one
                 ballance
                 ,
                 and
                 11
                 in
                 the
                 other
                 ,
                 it
                 will
                 remaine
                 in
                 
                   Aequilibrio
                   .
                   72
                
              
               
                 
                   Prob.
                   50
                
                 To
                 heave
                 or
                 lift
                 up
                 a
                 bottle
                 with
                 a
                 straw
                 .
                 74
              
               
                 
                   Prob.
                   51
                
                 How
                 in
                 the
                 middle
                 of
                 a
                 wood
                 or
                 desert
                 ,
                 without
                 the
                 sight
                 of
                 the
                 Sun
                 ,
                 starres
                 ,
                 shadow
                 ,
                 or
                 compasse
                 ,
                 to
                 finde
                 out
                 the
                 North
                 ,
                 or
                 South
                 ,
                 or
                 the
                 
                   4
                   Cardinal
                
                 points
                 of
                 the
                 World
                 ,
                 
                   East
                   ,
                   West
                   ,
                   &c.
                   75
                
              
               
                 
                   Prob.
                   52
                
                 Three
                 persons
                 having
                 taken
                 
                   Counters
                   ,
                   Cards
                
                 ,
                 or
                 other
                 things
                 ,
                 to
                 finde
                 how
                 much
                 each
                 one
                 hath
                 taken
                 .
                 7●
              
               
                 
                   Prob.
                   53
                
                 How
                 to
                 make
                 a
                 consort
                 of
                 Musick
                 of
                 many
                 parts
                 with
                 one
                 voice
                 or
                 one
                 instrument
                 onely
                 .
                 78
              
               
                 
                   Prob.
                   54
                
                 To
                 make
                 or
                 describe
                 an
                 oval
                 form
                 ,
                 
                 or
                 that
                 which
                 is
                 neare
                 resembled
                 unto
                 it
                 at
                 one
                 turning
                 ,
                 with
                 a
                 paire
                 of
                 common
                 
                   Compasses
                   .
                   79
                
              
               
                 
                   Prob.
                   55
                
                 Of
                 a
                 purse
                 difficult
                 to
                 be
                 opened
                 .
                 80
              
               
                 
                   Prob.
                   56
                
                 Whether
                 is
                 it
                 more
                 hard
                 and
                 admirable
                 without
                 Compasses
                 to
                 make
                 a
                 perfect
                 circle
                 ,
                 or
                 being
                 made
                 to
                 finde
                 out
                 the
                 Centre
                 of
                 it
                 ?
                 82
              
               
                 
                   Prob.
                   56
                
                 Any
                 one
                 having
                 taken
                 
                   3
                   Cards
                
                 ,
                 to
                 finde
                 how
                 many
                 points
                 they
                 containe
                 .
                 83
              
               
                 
                   Prob.
                   57
                
                 Many
                 Cards
                 placed
                 in
                 divers
                 ranks
                 ,
                 to
                 finde
                 which
                 of
                 those
                 Cards
                 any
                 one
                 hath
                 thought
                 .
                 85
              
               
                 
                   Prob.
                   58
                
                 Many
                 Cards
                 being
                 offered
                 to
                 sundry
                 persons
                 to
                 finde
                 which
                 of
                 those
                 Cards
                 any
                 one
                 thinketh
                 upon
                 .
                 86
              
               
                 
                   Prob.
                   59
                
                 How
                 to
                 make
                 an
                 instrument
                 that
                 helps
                 to
                 heare
                 ,
                 as
                 Gallileus
                 made
                 to
                 help
                 to
                 see
                 .
                 87
              
               
                 
                   Prob.
                   60
                
                 Of
                 a
                 fine
                 Lamp
                 which
                 goeth
                 not
                 out
                 ,
                 though
                 one
                 carries
                 it
                 in
                 ones
                 pocket
                 ,
                 or
                 being
                 rolled
                 on
                 the
                 ground
                 will
                 still
                 burne
                 .
                 88
              
               
                 
                   Prob.
                   61
                
                 Any
                 one
                 having
                 thought
                 a
                 Card
                 amongst
                 many
                 Cards
                 ,
                 how
                 artificially
                 to
                 discover
                 it
                 out
                 .
                 89
              
               
                 
                 
                   Prob.
                   62
                
                 Three
                 Women
                 
                   A
                   ,
                   B
                   ,
                   C.
                
                 carried
                 Apples
                 to
                 a
                 Market
                 to
                 sell
                 :
                 A
                 had
                 
                   20.
                   
                   B
                
                 had
                 
                   30.
                   
                   C
                   40.
                
                 they
                 sold
                 as
                 many
                 for
                 a
                 penny
                 one
                 as
                 the
                 other
                 ,
                 and
                 brought
                 home
                 one
                 as
                 much
                 money
                 as
                 another
                 ,
                 how
                 could
                 this
                 be
                 ?
                 90
              
               
                 
                   Prob.
                   63
                
                 Of
                 the
                 properties
                 of
                 some
                 numbers
                 .
                 91
              
               
                 
                   Prob.
                   64
                
                 Of
                 an
                 excellent
                 Lamp
                 which
                 serves
                 or
                 furnisheth
                 it selfe
                 with
                 Oile
                 ,
                 and
                 burnes
                 a
                 long
                 time
                 .
                 95
              
               
                 
                   Prob.
                   65
                
                 Of
                 the
                 play
                 at
                 Keyles
                 or
                 
                   Nine-pins
                   .
                   97
                
              
               
                 
                   Prob.
                   66
                
                 Of
                 Spectacles
                 of
                 pleasure
              
               
                 Of
                 Spectacles
                 which
                 give
                 severall
                 colours
                 to
                 the
                 visage
                 .
                 98
              
               
                 Of
                 Spectacles
                 which
                 make
                 a
                 Towne
                 seeme
                 to
                 be
                 a
                 City
                 ,
                 one
                 armed
                 man
                 as
                 a
                 Company
                 ,
                 and
                 a
                 piece
                 of
                 Gold
                 as
                 many
                 pieces
                 .
                 99
              
               
                 How
                 out
                 of
                 a
                 Chamber
                 to
                 see
                 the
                 objects
                 which
                 passe
                 by
                 according
                 to
                 the
                 lively
                 perspective
                 .
                 100
              
               
                 Of
                 Gallileus
                 admirable
                 Optick-Glasse
                 ,
                 which
                 helps
                 one
                 to
                 see
                 the
                 beginning
                 and
                 ending
                 of
                 Eclipses
                 ,
                 the
                 spots
                 in
                 the
                 Sunne
                 ,
                 the
                 Starres
                 which
                 move
                 about
                 the
                 Planets
                 ,
                 and
                 perspicuously
                 things
                 far
                 remote
                 .
              
               
                 Of
                 the
                 parts
                 of
                 Gallileus
                 his
                 
                   Glasse
                   .
                   102
                
              
               
                 
                   Prob.
                   67
                
                 Of
                 the
                 Magnes
                 and
                 Needles
                 touched
                 therewith
                 .
              
               
                 
                 How
                 Rings
                 of
                 Iron
                 may
                 hang
                 one
                 by
                 another
                 in
                 the
                 
                   aire
                   .
                   103
                
              
               
                 Of
                 Mahomets
                 Tombe
                 which
                 hangs
                 in
                 the
                 aire
                 by
                 the
                 touch
                 of
                 the
                 
                   Magnes
                   .
                   104
                
              
               
                 How
                 by
                 the
                 Magnes
                 only
                 to
                 finde
                 out
                 North
                 and
                 
                   South
                   105
                
              
               
                 Of
                 a
                 secrecie
                 in
                 the
                 Magnes
                 ,
                 for
                 discovering
                 things
                 farre
                 remote
                 .
                 106
              
               
                 Of
                 finding
                 the
                 Poles
                 by
                 the
                 
                   Magnes
                   107
                
              
               
                 
                   Prob.
                   68
                
                 Of
                 the
                 properties
                 of
                 Aeolipiles
                 or
                 Bowles
                 to
                 blow
                 the
                 
                   fire
                   .
                   108
                
              
               
                 
                   Prob.
                   69
                
                 Of
                 the
                 Thermometer
                 ,
                 or
                 that
                 which
                 measures
                 the
                 degrees
                 of
                 heat
                 and
                 cold
                 by
                 the
                 
                   aire
                   .
                   110
                
              
               
                 
                   Of
                   the
                   proportion
                   of
                   humane
                   bodies
                   ,
                   of
                   statues
                   ,
                   of
                   Colosses
                   ,
                   or
                   huge
                   Jmages
                   and
                   monstrous
                   Giants
                   .
                   113
                
              
               
                 Of
                 the
                 commensuration
                 of
                 the
                 parts
                 of
                 the
                 bodie
                 the
                 one
                 to
                 the
                 other
                 in
                 particular
                 ,
                 by
                 which
                 the
                 Lion
                 was
                 measured
                 by
                 his
                 claw
                 ,
                 the
                 Giant
                 by
                 his
                 thumbe
                 ,
                 and
                 Hercules
                 by
                 his
                 foot
                 .
                 
                   115
                   ,
                   116
                
              
               
                 Of
                 Statues
                 or
                 Colosses
                 ,
                 or
                 huge
                 Images
                 ;
                 that
                 mount
                 Athos
                 metamorphosed
                 by
                 Dynocrites
                 into
                 a
                 statue
                 ,
                 in
                 whose
                 hand
                 was
                 a
                 Towne
                 able
                 to
                 receive
                 ten
                 thousand
                 men
                 .
                 117
              
               
                 Of
                 the
                 famous
                 Colossus
                 at
                 Rhodes
                 which
                 bad
                 70
                 cubits
                 in
                 height
                 ,
                 and
                 loaded
                 
                   900.
                   
                   Camels
                
                 ,
                 which
                 weighed
                 
                   1080000
                   l.
                   118
                
              
               
                 
                 Of
                 Nero
                 his
                 great
                 Colossus
                 which
                 had
                 a
                 face
                 of
                 12
                 foot
                 large
                 .
                 119
              
               
                 Of
                 monstrous
                 Giants
              
               
                 Of
                 the
                 Giant
                 Og
                 and
                 
                   Goliah
                   .
                   119
                   ,
                   120
                
              
               
                 Of
                 the
                 Carkasse
                 of
                 a
                 man
                 found
                 which
                 was
                 in
                 length
                 49
                 foot
                 ;
                 and
                 of
                 that
                 monster
                 found
                 in
                 Creet
                 ,
                 which
                 had
                 46.
                 
                 Cubits
                 of
                 height
                 .
                 120
              
               
                 Of
                 Campesius
                 his
                 relation
                 of
                 a
                 monster
                 of
                 300
                 foot
                 found
                 in
                 Sicile
                 ,
                 whose
                 face
                 according
                 to
                 the
                 former
                 proportion
                 should
                 be
                 30
                 foot
                 in
                 length
                 .
                 121
              
               
                 
                   Prob.
                   71
                
                 Of
                 the
                 game
                 at
                 the
                 Palme
                 ,
                 at
                 Trap
                 ,
                 at
                 Bowles
                 ,
                 Paile-maile
                 ,
                 and
                 others
                 .
                 122
              
               
                 
                   Prob.
                   72
                
                 Of
                 the
                 game
                 of
                 square
                 formes
                 .
                 124
              
               
                 
                   Prob.
                   73
                
                 How
                 to
                 make
                 the
                 string
                 of
                 a
                 Viol
                 sensibly
                 shake
                 without
                 any
                 one
                 touching
                 it
                 .
                 126
              
               
                 
                   Prob.
                   74
                
                 Of
                 a
                 Vessell
                 which
                 containes
                 3
                 severall
                 kindes
                 of
                 liquor
                 ,
                 all
                 put
                 in
                 at
                 one
                 bung-hole
                 ,
                 and
                 drawne
                 out
                 at
                 one
                 Tap
                 severally
                 without
                 mixture
                 .
                 128
              
               
                 
                   Prob.
                   75
                   Of
                   burning-Glasses
                
                 .
              
               
                 Archimedes
                 his
                 way
                 of
                 burning
                 the
                 ships
                 of
                 
                   Syracuse
                   .
                   129
                
              
               
                 Of
                 Proclus
                 his
                 way
                 ,
                 and
                 of
                 concave
                 and
                 sphericall
                 Glasses
                 which
                 burne
                 ,
                 the
                 cause
                 and
                 demonstration
                 of
                 burning
                 with
                 Glasses
                 .
                 131
              
               
                 Of
                 Maginus
                 his
                 way
                 of
                 setting
                 fire
                 to
                 Powder
                 in
                 a
                 Mine
                 by
                 Glasses
                 .
                 131
              
               
                 
                 Of
                 the
                 examination
                 of
                 burning
                 by
                 Glasses
                 .
                 133
              
               
                 
                   Prob.
                   76
                   Of
                   pleasant
                   questions
                   by
                   way
                   of
                   Arithmetick
                   .
                
              
               
                 Of
                 the
                 Asse
                 and
                 the
                 Mule.
                 134
              
               
                 Of
                 the
                 number
                 of
                 Souldiers
                 that
                 fought
                 before
                 old
                 
                   Troy.
                   135
                
              
               
                 Of
                 the
                 number
                 of
                 Crownes
                 that
                 two
                 men
                 had
                 .
                 136
              
               
                 About
                 the
                 houre
                 of
                 the
                 day
                 .
                 137
              
               
                 Of
                 Pythagoras
                 Schollers
                 .
                 137
              
               
                 Of
                 the
                 number
                 of
                 Apples
                 given
                 amongst
                 the
                 Graces
                 and
                 the
                 Muses
                 .
                 138
              
               
                 Of
                 the
                 testament
                 or
                 last
                 will
                 of
                 a
                 dying
                 Father
                 .
                 138
              
               
                 Of
                 the
                 cups
                 of
                 
                   Croesus
                   .
                   139
                
              
               
                 Of
                 Cupids
                 Apples
                 .
                 139
              
               
                 Of
                 a
                 Mans
                 Age.
                 140
              
               
                 Of
                 the
                 Lion
                 of
                 Bronze
                 placed
                 upon
                 a
                 fountaine
                 with
                 his
                 Epigram
                 .
                 ibid.
                 
              
               
                 
                   Prob.
                   77
                   In
                   Opticks
                   ,
                   excellent
                   experiments
                   .
                
              
               
                 Principles
                 touching
                 reflections
                 .
                 141
              
               
                 Experiments
                 upon
                 flat
                 and
                 plaine
                 Glasses
                 .
                 142
              
               
                 How
                 the
                 Images
                 seeme
                 to
                 sink
                 into
                 a
                 plaine
                 Glasse
                 ,
                 and
                 alwayes
                 are
                 seene
                 perpendicular
                 to
                 the
                 Glasse
                 ,
                 an●
                 also
                 inversed
                 .
                 143
              
               
                 
                 The
                 things
                 which
                 passe
                 by
                 in
                 a
                 street
                 may
                 by
                 help
                 of
                 a
                 plaine
                 glasse
                 be
                 seen
                 in
                 a
                 Chamber
                 ,
                 and
                 the
                 height
                 of
                 a
                 tower
                 or
                 tree
                 observed
                 .
                 143
              
               
                 How
                 severall
                 Candles
                 from
                 one
                 Candle
                 are
                 represented
                 in
                 a
                 plaine
                 Glasse
                 ,
                 and
                 Glasses
                 alternately
                 may
                 be
                 seene
                 one
                 within
                 another
                 ,
                 as
                 also
                 the
                 back-parts
                 of
                 the
                 body
                 as
                 well
                 as
                 the
                 fore-parts
                 are
                 evidently
                 represented
                 .
                 144
              
               
                 How
                 an
                 Image
                 may
                 be
                 seene
                 to
                 hang
                 in
                 the
                 aire
                 by
                 help
                 of
                 a
                 Glasse
                 :
                 and
                 writing
                 read
                 or
                 easily
                 understood
                 .
                 146
              
               
                 
                   Experiments
                   upon
                
                 Gibbous
                 ,
                 
                   or
                   convex
                   Sphericall
                   Glasses
                
                 .
              
               
                 How
                 lively
                 to
                 represent
                 a
                 whole
                 City
                 ,
                 fortification
                 ,
                 or
                 Army
                 ,
                 by
                 a
                 Gibbous
                 Glasse
                 .
                 147
              
               
                 How
                 the
                 Images
                 are
                 seen
                 in
                 Concave
                 Glasses
                 .
                 149
              
               
                 How
                 the
                 Images
                 are
                 transformed
                 by
                 approaching
                 to
                 the
                 centre
                 of
                 the
                 Glasse
                 ,
                 or
                 point
                 of
                 concourse
                 ;
                 and
                 of
                 an
                 exceeding
                 light
                 that
                 a
                 Concave
                 Glasse
                 gives
                 by
                 help
                 of
                 a
                 Candle
                 .
                 151
              
               
                 How
                 the
                 Images
                 ,
                 as
                 a
                 man
                 ,
                 a
                 sword
                 ,
                 or
                 hand
                 ,
                 doth
                 come
                 forth
                 out
                 of
                 the
                 Glasse
                 .
                 
                   152
                   ,
                   153
                
              
               
                 Of
                 strange
                 apparitions
                 of
                 Images
                 in
                 the
                 aire
                 ,
                 by
                 help
                 of
                 sundry
                 Glasses
                 .
                 
                   152
                   ,
                   154
                
              
               
                 Of
                 the
                 wonderfull
                 augmentation
                 of
                 the
                 parts
                 of
                 mans
                 body
                 comming
                 neare
                 the
                 point
                 of
                 inflammation
                 ,
                 or
                 centre
                 of
                 the
                 Glasse
                 .
                 155
              
               
                 How
                 writing
                 may
                 be
                 reverberated
                 from
                 a
                 Glasse
                 upon
                 a
                 VVall
                 ,
                 and
                 Read.
                 156
              
               
                 How
                 by
                 help
                 of
                 a
                 Concave
                 Glasse
                 to
                 cast
                 light
                 into
                 a
                 Campe
                 ,
                 or
                 to
                 give
                 a
                 perspective
                 light
                 to
                 Pyoneers
                 in
                 a
                 Mine
                 ,
                 by
                 one
                 Candle
                 only
                 .
                 156
              
               
                 How
                 excellently
                 by
                 help
                 of
                 a
                 Concave
                 Glasse
                 and
                 a
                 
                 Candle
                 placed
                 in
                 the
                 centre
                 ,
                 to
                 give
                 light
                 to
                 read
                 by
                 .
                 157
              
               
                 Of
                 other
                 Glasses
                 of
                 pleasure
                 .
                 158
              
               
                 Of
                 strange
                 deformed
                 representations
                 by
                 Glasses
                 ;
                 causing
                 a
                 man
                 to
                 have
                 foure
                 eyes
                 ,
                 two
                 Mouthes
                 ,
                 two
                 Noses
                 ,
                 two
                 heads
                 .
              
               
                 Of
                 Glasses
                 which
                 give
                 a
                 colour
                 to
                 the
                 visage
                 ,
                 and
                 make
                 the
                 face
                 seeme
                 faire
                 and
                 foule
                 .
                 160
              
               
                 
                   Prob.
                   78
                
                 How
                 to
                 shew
                 one
                 that
                 is
                 suspicious
                 ,
                 what
                 is
                 in
                 another
                 Chamber
                 or
                 Roome
                 ,
                 notwithstanding
                 the
                 interposition
                 of
                 that
                 wall
                 .
                 160
              
               
                 Corolary
                 ,
                 1.
                 
                 To
                 see
                 the
                 Besiegers
                 of
                 a
                 place
                 ,
                 upon
                 the
                 Rampa●●t
                 of
                 a
                 fortification
                 161
              
               
                 Corolary
                 2.
                 and
                 3.
                 
                 Notwithstanding
                 the
                 interposition
                 of
                 VValls
                 and
                 Chambers
                 ,
                 by
                 help
                 of
                 a
                 Glasse
                 things
                 may
                 be
                 seen
                 ,
                 which
                 passe
                 by
                 .
                 162
              
               
                 
                   Prob.
                   79
                
                 How
                 with
                 a
                 Musket
                 to
                 strike
                 a
                 marke
                 not
                 looking
                 towards
                 it
                 ,
                 as
                 exactly
                 as
                 one
                 aimed
                 at
                 it
                 .
                 162
              
               
                 How
                 exactly
                 to
                 shoot
                 out
                 of
                 a
                 Mu●ket
                 to
                 a
                 place
                 which
                 is
                 not
                 seene
                 ,
                 being
                 hindred
                 by
                 some
                 obstacle
                 or
                 other
                 interposition
                 .
                 163
              
               
                 
                   Prob.
                   80
                
                 How
                 to
                 make
                 an
                 Image
                 to
                 be
                 seen
                 hanging
                 in
                 the
                 aire
                 ,
                 having
                 his
                 head
                 downward
                 .
                 164
              
               
                 
                   Prob.
                   81.
                
                 
                 How
                 to
                 make
                 a
                 company
                 of
                 representative
                 souldiers
                 seeme
                 to
                 be
                 as
                 a
                 regiment
                 ,
                 or
                 how
                 few
                 in
                 number
                 may
                 be
                 multiplyed
                 to
                 seem
                 to
                 be
                 many
                 in
                 number
                 .
                 165
              
               
                 COROLARIE
                 .
                 Of
                 an
                 excellent
                 delightfull
                 Cabinet
                 made
                 of
                 plaine
                 Glasses
                 .
                 165
              
               
                 
                   Prob.
                   82
                   Of
                   fine
                   and
                   pleasant
                   Dyalls
                   in
                   Horologiographie
                   .
                
              
               
                 Of
                 a
                 Dyall
                 of
                 herbs
                 for
                 a
                 Garden
                 .
                 166
              
               
                 Of
                 the
                 Dyall
                 upon
                 the
                 finger
                 and
                 hand
                 ,
                 to
                 finde
                 what
                 
                 of
                 the
                 Clock
                 it
                 is
                 .
                 167
              
               
                 Of
                 a
                 Dyall
                 which
                 was
                 about
                 an
                 Obelisk
                 at
                 
                   Rome
                   .
                   168
                
              
               
                 Of
                 Dyals
                 with
                 Glasses
                 .
                 168
              
               
                 Of
                 a
                 Dyall
                 which
                 hath
                 a
                 Glasse
                 in
                 the
                 place
                 of
                 the
                 stile
                 .
                 169
              
               
                 Of
                 Dyals
                 with
                 water
                 ,
                 which
                 the
                 Ancients
                 use●
                 171
              
               
                 
                   Prob.
                   83
                   Of
                   shooting
                   out
                   of
                   Cannons
                   or
                   great
                   Artillery
                   .
                
              
               
                 How
                 to
                 charge
                 a
                 Cannon
                 without
                 powder
                 .
                 173
              
               
                 To
                 finde
                 how
                 much
                 time
                 the
                 Bullet
                 of
                 a
                 Cannon
                 spends
                 in
                 the
                 Aire
                 before
                 it
                 falls
                 to
                 the
                 ground
                 .
                 174
              
               
                 How
                 it
                 is
                 that
                 a
                 Cannon
                 shooting
                 upward
                 ,
                 the
                 Bullet
                 flies
                 with
                 more
                 violence
                 ,
                 than
                 being
                 shot
                 point
                 blanke
                 ,
                 or
                 shooting
                 downeward
                 .
                 174
              
               
                 VVhether
                 is
                 the
                 discharge
                 of
                 a
                 Cannon
                 so
                 much
                 the
                 more
                 violent
                 ,
                 by
                 how
                 much
                 it
                 hath
                 the
                 more
                 length
                 ?
                 176
              
               
                 
                   Prob.
                   84
                   Of
                   prodigious
                   progressions
                   ,
                   and
                   multiplications
                   of
                   creatures
                   ,
                   plants
                   ,
                   fruits
                   ,
                   numbers
                   ,
                   gold
                   ,
                   silver
                   ,
                   &c.
                   
                
              
               
                 Of
                 graines
                 of
                 Mustardseed
                 ,
                 and
                 that
                 one
                 graine
                 being
                 sowne
                 ,
                 with
                 the
                 increase
                 thereof
                 for
                 20
                 yeares
                 will
                 produce
                 a
                 heap
                 greater
                 than
                 all
                 the
                 earth
                 a
                 hundred
                 thousand
                 times
                 .
                 178
              
               
                 Of
                 Pigges
                 ,
                 and
                 that
                 the
                 great
                 Turke
                 with
                 all
                 his
                 Revenne
                 ,
                 is
                 not
                 able
                 to
                 maintaine
                 for
                 one
                 yeare
                 ,
                 a
                 Sow
                 with
                 all
                 her
                 increase
                 for
                 12
                 yeares
                 .
                 179
              
               
                 
                 Of
                 graines
                 of
                 Corne
                 ,
                 and
                 that
                 1
                 graine
                 with
                 all
                 its
                 increase
                 for
                 12
                 yeares
                 ,
                 will
                 amount
                 to
                 244140625000000000000
                 graines
                 ,
                 which
                 exceeds
                 in
                 value
                 all
                 the
                 treasures
                 in
                 the
                 World.
                 183
              
               
                 Of
                 the
                 wonderfull
                 increase
                 af
                 Sheepe
                 .
                 182
              
               
                 Of
                 the
                 increase
                 of
                 Cod-fish
                 .
                 182
              
               
                 Of
                 the
                 Progressive
                 Multiplication
                 of
                 soules
                 ;
                 that
                 from
                 one
                 of
                 Noahs
                 Sonnes
                 ,
                 from
                 the
                 flood
                 unto
                 Nimrods
                 Monarchie
                 ,
                 should
                 be
                 produced
                 111350
                 soules
                 .
                 183
              
               
                 Of
                 the
                 increase
                 of
                 Numbers
                 in
                 double
                 proportion
                 ,
                 and
                 that
                 a
                 pin
                 being
                 doubled
                 as
                 often
                 as
                 there
                 are
                 weekes
                 in
                 the
                 yeare
                 ,
                 the
                 number
                 of
                 pinnes
                 that
                 should
                 arise
                 is
                 able
                 to
                 load
                 45930
                 ships
                 of
                 a
                 thousand
                 Tunne
                 apiece
                 ,
                 which
                 are
                 worth
                 more
                 than
                 tenne
                 hundred
                 thousand
                 pounds
                 a
                 day
                 .
                 
                   183
                   ,
                   184
                
              
               
                 Of
                 a
                 man
                 that
                 gathered
                 Apples
                 ,
                 stones
                 ,
                 or
                 such
                 like
                 upon
                 a
                 condition
                 .
                 185
              
               
                 Of
                 the
                 changes
                 in
                 Bells
                 ,
                 in
                 musicall
                 instruments
                 ,
                 transmutation
                 of
                 Places
                 ,
                 in
                 Numbers
                 ,
                 Letters
                 ,
                 Men
                 and
                 such
                 like
                 ▪
                 185
              
               
                 
                 Of
                 the
                 wonderfull
                 interchange
                 of
                 the
                 Letters
                 in
                 the
                 Alphabet
                 :
                 the
                 exceeding
                 number
                 of
                 men
                 ,
                 and
                 time
                 to
                 expresse
                 the
                 words
                 that
                 may
                 be
                 made
                 with
                 these
                 letters
                 ,
                 and
                 the
                 number
                 of
                 Books
                 to
                 comprehend
                 them
                 .
                 
                   187
                   ,
                   188
                
              
               
                 Of
                 a
                 servant
                 hired
                 upon
                 certaine
                 condition
                 ,
                 that
                 he
                 might
                 have
                 land
                 lent
                 him
                 to
                 sowe
                 one
                 graine
                 of
                 Corne
                 with
                 its
                 increase
                 for
                 8
                 yeares
                 time
                 ,
                 which
                 amounted
                 to
                 more
                 than
                 four
                 hundred
                 thousand
                 Acres
                 of
                 Land.
                 188
              
               
                 
                   Prob.
                   85
                   Of
                   Fountaines
                   ,
                   Hydriatiques
                   ;
                   Stepticks
                   ,
                   Machinecks
                   ,
                   and
                   other
                   experiments
                   upon
                   water
                   ,
                   or
                   other
                   liquor
                   .
                
              
               
                 First
                 ,
                 how
                 water
                 at
                 the
                 foot
                 of
                 a
                 Mountaine
                 may
                 be
                 made
                 to
                 ascend
                 to
                 the
                 top
                 of
                 it
                 ,
                 and
                 so
                 to
                 descend
                 on
                 the
                 other
                 side
                 of
                 it
                 190
              
               
                 Secondly
                 ,
                 to
                 finde
                 how
                 much
                 Liquor
                 is
                 in
                 a
                 Vessell
                 ,
                 onely
                 by
                 using
                 the
                 tap-hole
                 .
                 191
              
               
                 Thirdly
                 ,
                 how
                 is
                 it
                 ,
                 that
                 a
                 Vessell
                 is
                 said
                 to
                 hold
                 more
                 water
                 at
                 the
                 foot
                 of
                 a
                 Mountaine
                 ,
                 then
                 at
                 the
                 top
                 of
                 it
                 191
              
               
                 4
                 How
                 to
                 conduct
                 water
                 from
                 the
                 top
                 of
                 one
                 Mountaine
                 to
                 the
                 top
                 of
                 another
                 192
              
               
                 5
                 Of
                 a
                 fine
                 Fountaine
                 which
                 spouts
                 water
                 very
                 high
                 and
                 with
                 great
                 violence
                 ,
                 by
                 turning
                 of
                 a
                 Cock
                 193
              
               
                 6
                 Of
                 Archimedes
                 screw
                 which
                 makes
                 water
                 ascend
                 by
                 descending
                 .
                 194
              
               
                 7
                 Of
                 a
                 fine
                 Fountaine
                 of
                 pleasure
                 .
                 196
              
               
                 
                 8
                 Of
                 a
                 fine
                 watering
                 pot
                 for
                 Gardens
                 .
                 197
              
               
                 9
                 How
                 easily
                 to
                 take
                 Wine
                 out
                 of
                 a
                 Vessell
                 at
                 the
                 bung
                 hole
                 without
                 piercing
                 a
                 hole
                 in
                 the
                 Vessell
                 .
                 198
              
               
                 10
                 How
                 to
                 measure
                 irregular
                 bodies
                 by
                 help
                 of
                 water
                 .
                 198
              
               
                 11
                 To
                 finde
                 the
                 weight
                 of
                 water
                 .
                 199
              
               
                 12
                 To
                 finde
                 the
                 charge
                 that
                 a
                 vessell
                 may
                 carry
                 ,
                 as
                 Ships
                 ,
                 Boats
                 or
                 such
                 like
                 .
                 200
              
               
                 13
                 How
                 comes
                 it
                 that
                 a
                 ship
                 having
                 safely
                 sailed
                 in
                 the
                 vast
                 Ocean
                 ,
                 and
                 being
                 come
                 into
                 the
                 port
                 or
                 harbour
                 ,
                 will
                 sinke
                 down
                 right
                 .
                 200
              
               
                 14
                 How
                 a
                 grosse
                 body
                 of
                 metall
                 may
                 swim
                 upon
                 the
                 water
                 .
                 201
              
               
                 15
                 How
                 to
                 weigh
                 the
                 lightnesse
                 of
                 the
                 aire
                 .
                 203
              
               
                 16
                 Being
                 given
                 a
                 body
                 ,
                 to
                 mark
                 it
                 about
                 ,
                 and
                 shew
                 how
                 much
                 of
                 it
                 will
                 sink
                 in
                 the
                 water
                 ,
                 or
                 swim
                 above
                 the
                 water
                 .
                 204
              
               
                 17
                 To
                 finde
                 how
                 much
                 severall
                 metalls
                 or
                 other
                 bodies
                 do
                 weigh
                 lesse
                 in
                 the
                 water
                 than
                 in
                 the
                 aire
                 .
                 204
              
               
                 18
                 How
                 is
                 it
                 that
                 a
                 ballance
                 having
                 like
                 weight
                 in
                 each
                 scale
                 ,
                 and
                 hanging
                 
                   in
                   Aequilibrio
                
                 in
                 the
                 aire
                 ,
                 being
                 removed
                 from
                 that
                 place
                 (
                 without
                 diminishing
                 the
                 weights
                 in
                 each
                 balance
                 ,
                 or
                 adding
                 to
                 it
                 )
                 it
                 shall
                 cease
                 to
                 hang
                 
                   in
                   Aequilibrio
                
                 sensibly
                 ,
                 yea
                 by
                 a
                 great
                 difference
                 of
                 weight
                 .
                 205
              
               
                 
                 19
                 To
                 shew
                 what
                 waters
                 are
                 heavier
                 one
                 than
                 another
                 ,
                 and
                 how
                 much
                 .
                 206
              
               
                 20
                 How
                 to
                 make
                 a
                 pound
                 of
                 water
                 weigh
                 as
                 much
                 as
                 
                   10
                   ,
                   20
                   ,
                   30
                
                 ,
                 or
                 a
                 hundred
                 pound
                 of
                 Lead
                 ,
                 nay
                 as
                 much
                 as
                 a
                 thousand
                 or
                 ten
                 thousand
                 pound
                 weight
                 .
                 207
              
               
                 
                   Prob.
                   86.
                   
                   Of
                   sundry
                   questions
                   of
                   Arithmetick
                   ,
                   and
                   first
                   of
                   the
                   number
                   of
                   sands
                   calculated
                   by
                
                 Archimedes
                 and
                 Clavius
                 .
                 208
              
               
                 2
                 Divers
                 metalls
                 being
                 melted
                 together
                 in
                 one
                 body
                 ,
                 to
                 finde
                 the
                 mixture
                 of
                 them
                 .
                 210
              
               
                 3
                 A
                 subtile
                 question
                 of
                 three
                 partners
                 about
                 equality
                 of
                 Wine
                 and
                 Vessels
                 .
                 213
              
               
                 4
                 Of
                 a
                 Ladder
                 which
                 standing
                 upright
                 against
                 a
                 wall
                 of
                 10
                 foot
                 high
                 ,
                 the
                 foot
                 of
                 it
                 is
                 pulled
                 out
                 6
                 foot
                 from
                 the
                 wall
                 upon
                 the
                 pavement
                 ,
                 how
                 much
                 hath
                 the
                 top
                 of
                 the
                 Ladder
                 descended
                 .
                 214
              
               
                 
                   Prob.
                   87
                
                 Witty
                 suits
                 or
                 debates
                 between
                 Caius
                 and
                 Sempronius
                 ,
                 upon
                 the
                 forme
                 of
                 figures
                 ,
                 which
                 Geometricians
                 call
                 Isoperimeter
                 ,
                 or
                 equall
                 in
                 circuit
                 ,
                 or
                 Compasse
                 .
                 214
              
               
                 1
                 Incident
                 :
                 of
                 changing
                 a
                 field
                 of
                 6
                 measures
                 square
                 ,
                 for
                 a
                 long
                 rectrangled
                 fiel
                 of
                 9
                 measures
                 in
                 length
                 and
                 3
                 in
                 breadth
                 :
                 both
                 equall
                 in
                 circuit
                 but
                 not
                 in
                 quantity
                 .
                 215
              
               
                 2
                 Incident
                 :
                 about
                 two
                 sacks
                 each
                 of
                 them
                 ho●ding
                 but
                 a
                 bushell
                 ,
                 and
                 yet
                 were
                 able
                 to
                 hold
                 4
                 bushels
                 .
                 217
              
               
                 
                 3
                 Incident
                 :
                 sheweth
                 the
                 deceit
                 of
                 pipes
                 which
                 conveygh
                 water
                 ,
                 that
                 a
                 pipe
                 of
                 two
                 inches
                 diameter
                 ,
                 doth
                 cast
                 out
                 foure
                 times
                 as
                 much
                 water
                 as
                 a
                 pipe
                 of
                 one
                 such
                 diameter
                 .
                 218
              
               
                 7
                 Heapes
                 of
                 Corne
                 of
                 10
                 foot
                 every
                 way
                 ,
                 is
                 not
                 as
                 much
                 as
                 one
                 heap
                 of
                 Corne
                 of
                 20
                 foot
                 every
                 way
                 .
                 218
              
               
                 
                   Prob.
                   88
                   Of
                   sundry
                   questions
                   in
                   matter
                   of
                   Cosmographie
                   ,
                   and
                   Astronomy
                   .
                
              
               
                 In
                 what
                 place
                 the
                 middle
                 of
                 the
                 earth
                 is
                 supposed
                 to
                 be
                 .
                 219
              
               
                 Of
                 the
                 depth
                 of
                 the
                 earth
                 ,
                 and
                 height
                 of
                 the
                 Heavens
                 ,
                 and
                 the
                 compasse
                 of
                 the
                 World
                 ,
                 how
                 much
                 .
                 219
              
               
                 How
                 much
                 the
                 starry
                 Firmament
                 ,
                 the
                 Sun
                 ,
                 and
                 the
                 Moone
                 are
                 distant
                 from
                 the
                 centre
                 of
                 the
                 earth
                 .
                 220
              
               
                 How
                 long
                 a
                 Mill-stone
                 would
                 be
                 in
                 falling
                 to
                 the
                 centre
                 of
                 the
                 earth
                 from
                 the
                 superficies
                 ,
                 if
                 it
                 might
                 have
                 passage
                 thither
                 .
                 220
              
               
                 How
                 long
                 time
                 a
                 man
                 or
                 a
                 bird
                 may
                 be
                 in
                 compassing
                 the
                 whole
                 earth
                 .
                 220
              
               
                 If
                 a
                 man
                 should
                 ascend
                 by
                 supposition
                 20
                 miles
                 every
                 day
                 :
                 how
                 long
                 it
                 would
                 be
                 before
                 he
                 approach
                 to
                 the
                 Moone
                 .
                 221
              
               
                 The
                 Sunne
                 moves
                 more
                 in
                 one
                 day
                 than
                 the
                 Moone
                 in
                 20
                 dayes
                 .
                 221
              
               
                 If
                 a
                 milstone
                 from
                 the
                 orbe
                 of
                 the
                 Sun
                 should
                 descend
                 a
                 thousand
                 miles
                 in
                 an
                 houre
                 how
                 long
                 
                 it
                 would
                 be
                 before
                 it
                 come
                 to
                 the
                 earth
                 .
                 221
              
               
                 Of
                 the
                 Sunnes
                 quick
                 motion
                 ,
                 of
                 more
                 than
                 7500
                 miles
                 in
                 one
                 minute
                 .
                 221
              
               
                 Of
                 the
                 rapt
                 and
                 violent
                 motion
                 of
                 the
                 starry
                 Firmament
                 ,
                 which
                 if
                 a
                 Horseman
                 should
                 ride
                 every
                 day
                 40
                 miles
                 ,
                 he
                 could
                 not
                 in
                 a
                 thousand
                 yeares
                 make
                 such
                 a
                 distance
                 as
                 it
                 moves
                 every
                 houre
                 .
                 221
              
               
                 To
                 finde
                 the
                 Circle
                 of
                 the
                 Sunne
                 by
                 the
                 fingers
                 .
                 223
              
               
                 
                   Prob.
                   93
                
                 Of
                 finding
                 the
                 new
                 and
                 full
                 Moone
                 in
                 each
                 moneth
                 .
                 224
              
               
                 
                   Prob.
                   94
                
                 To
                 finde
                 the
                 latitude
                 of
                 Countreys
                 .
                 225
              
               
                 
                   Prob.
                   95
                
                 Of
                 the
                 Climates
                 of
                 Countreys
                 ,
                 and
                 how
                 to
                 finde
                 them
                 .
                 225
              
               
                 
                   Prob.
                   96
                   Of
                   longitude
                   and
                   latitude
                   of
                   the
                   places
                   of
                   the
                   earth
                   ,
                   and
                   of
                   the
                   Starres
                   of
                   the
                   Heavens
                   .
                   227
                
              
               
                 To
                 finde
                 the
                 Longitude
                 of
                 a
                 Countrey
                 .
                 228
              
               
                 Of
                 the
                 Latitude
                 of
                 a
                 Countrey
                 .
                 229
              
               
                 To
                 finde
                 the
                 Latitude
                 of
                 a
                 Countrey
                 .
                 230
              
               
                 To
                 finde
                 the
                 distance
                 of
                 places
                 .
                 230
              
               
                 Of
                 the
                 Longitude
                 ,
                 Latitude
                 ,
                 Declination
                 ,
                 and
                 distance
                 of
                 the
                 starres
                 .
                 231
              
               
                 How
                 is
                 it
                 that
                 two
                 Horses
                 or
                 other
                 creatures
                 comming
                 into
                 the
                 World
                 at
                 one
                 time
                 ,
                 and
                 dying
                 at
                 one
                 and
                 the
                 same
                 instant
                 ,
                 yet
                 the
                 one
                 of
                 them
                 to
                 be
                 a
                 day
                 older
                 than
                 the
                 other
                 ?
                 232
              
               
                 
                 
                   Certaine
                   fine
                   Observations
                
                 .
              
               
                 In
                 what
                 places
                 of
                 the
                 World
                 is
                 it
                 that
                 the
                 needle
                 hangs
                 
                   in
                   Aequilibrio
                
                 ,
                 and
                 verticall
                 ?
                 233
              
               
                 In
                 what
                 place
                 of
                 the
                 world
                 is
                 it
                 the
                 sun
                 is
                 East
                 or
                 West
                 but
                 twice
                 in
                 the
                 yeare
                 ?
                 233
              
               
                 In
                 what
                 place
                 of
                 the
                 World
                 is
                 it
                 that
                 the
                 Sunnes
                 Longitude
                 from
                 the
                 Equinoctiall
                 paints
                 and
                 Altitude
                 ,
                 being
                 equall
                 ,
                 the
                 Sunne
                 is
                 due
                 East
                 or
                 West
                 ?
              
               
                 That
                 the
                 sunne
                 comes
                 twice
                 to
                 one
                 point
                 of
                 the
                 Compasse
                 in
                 the
                 forenoone
                 or
                 afternoone
                 .
                 233
              
               
                 That
                 in
                 some
                 place
                 of
                 the
                 World
                 there
                 are
                 but
                 two
                 kindes
                 of
                 winde
                 all
                 the
                 yeare
                 .
                 233
              
               
                 Two
                 ships
                 may
                 be
                 two
                 leagues
                 asunder
                 under
                 the
                 equinoctiall
                 ,
                 and
                 sayling
                 North
                 at
                 a
                 certaine
                 parallell
                 they
                 will
                 be
                 but
                 just
                 halfe
                 so
                 much
                 .
                 233
              
               
                 To
                 what
                 inhabitants
                 ,
                 and
                 at
                 what
                 time
                 the
                 sunne
                 will
                 touch
                 the
                 north-part
                 of
                 the
                 Horizon
                 at
                 midnight
                 .
                 234
              
               
                 How
                 a
                 man
                 may
                 know
                 in
                 his
                 Navigation
                 when
                 he
                 is
                 under
                 the
                 Equinoctiall
                 .
                 234
              
               
                 At
                 what
                 day
                 in
                 the
                 yeare
                 the
                 extremitie
                 of
                 the
                 styles
                 shadow
                 in
                 a
                 Dyall
                 makes
                 a
                 right
                 line
                 .
                 234
              
               
                 What
                 height
                 the
                 Sunne
                 is
                 of
                 ,
                 and
                 how
                 far
                 from
                 the
                 Zenith
                 ,
                 or
                 Horizon
                 ,
                 when
                 a
                 mans
                 
                 shadow
                 is
                 as
                 long
                 as
                 his
                 height
                 .
                 234
              
               
                 
                   Prob.
                   97
                
                 To
                 make
                 a
                 Triangle
                 that
                 shall
                 have
                 three
                 right
                 Angles
                 .
                 234
              
               
                 
                   Prob.
                   98
                
                 To
                 divide
                 a
                 line
                 in
                 as
                 many
                 parts
                 as
                 one
                 will
                 ,
                 without
                 compasses
                 or
                 without
                 seeing
                 of
                 it
                 .
                 235
              
               
                 
                   Prob.
                   99
                
                 To
                 draw
                 a
                 line
                 which
                 shall
                 incline
                 to
                 another
                 line
                 ,
                 yet
                 never
                 meet
                 against
                 the
                 Axiome
                 of
                 Parallells
                 .
                 236
              
               
                 
                   Prob.
                   100
                
                 To
                 finde
                 the
                 variation
                 of
                 the
                 Compasse
                 by
                 the
                 Sunne
                 shining
                 .
                 237
              
               
                 
                   Prob.
                   101
                
                 To
                 know
                 which
                 way
                 the
                 winde
                 is
                 in
                 ones
                 Chamber
                 without
                 going
                 abroad
                 .
                 238
              
               
                 
                   Prob.
                   102
                
                 How
                 to
                 draw
                 a
                 parallel
                 sphaericall
                 line
                 with
                 great
                 ease
                 .
                 239
              
               
                 
                   Prob.
                   103
                
                 To
                 measure
                 an
                 height
                 onely
                 by
                 help
                 of
                 ones
                 Hat.
                 240
              
               
                 
                   Prob.
                   104
                
                 To
                 take
                 an
                 height
                 with
                 two
                 strawes
                 .
                 240
              
               
                 In
                 Architecture
                 how
                 statues
                 or
                 other
                 things
                 in
                 high
                 buildings
                 shall
                 beare
                 a
                 proportion
                 to
                 the
                 eye
                 below
                 either
                 equall
                 ,
                 double
                 ,
                 &c.
                 242
              
               
                 
                   Prob.
                   106
                
                 Of
                 deformed
                 figures
                 which
                 have
                 no
                 exact
                 proportion
                 ,
                 where
                 to
                 place
                 the
                 eye
                 to
                 see
                 them
                 direct
                 .
                 243
              
               
                 
                   Prob.
                   107
                
                 How
                 a
                 Cannon
                 that
                 hath
                 shot
                 may
                 be
                 covered
                 from
                 the
                 battery
                 of
                 the
                 Enemy
                 .
                 244
              
               
                 
                   Prob.
                   108
                
                 Of
                 a
                 fine
                 Lever
                 ,
                 by
                 which
                 one
                 
                 man
                 alone
                 may
                 place
                 a
                 Cannon
                 upon
                 his
                 Carriage
                 .
                 245
              
               
                 
                   Prob.
                   109
                
                 How
                 to
                 make
                 a
                 Clock
                 with
                 one
                 wheele
                 246
              
               
                 
                   Of
                   Water-workes
                
                 .
              
               
                 
                   Prob.
                   110
                
                 How
                 a
                 childe
                 may
                 draw
                 up
                 a
                 Hogshead
                 of
                 water
                 with
                 ease
                 .
                 247
              
               
                 
                   Prob.
                   111
                
                 Of
                 a
                 Ladder
                 of
                 Cords
                 to
                 cary
                 in
                 ones
                 pocket
                 ,
                 by
                 which
                 he
                 may
                 mount
                 a
                 wall
                 or
                 Tower
                 alone
                 .
                 248
              
               
                 
                   Prob.
                   112
                
                 Of
                 a
                 marvelous
                 Pump
                 which
                 drawes
                 up
                 great
                 quantity
                 of
                 water
                 .
                 249
              
               
                 
                   Prob.
                   113
                
                 How
                 naturally
                 to
                 cause
                 water
                 to
                 ascend
                 out
                 of
                 a
                 Pit.
                 250
              
               
                 
                   Prob.
                   114
                
                 How
                 to
                 cast
                 water
                 out
                 of
                 a
                 fountaine
                 very
                 high
                 .
                 252
              
               
                 
                   Prob.
                   115
                
                 How
                 to
                 empty
                 the
                 water
                 of
                 a
                 Pit
                 by
                 help
                 of
                 a
                 Cisterne
                 .
                 253
              
               
                 
                   Prob.
                   116
                
                 How
                 to
                 spout
                 out
                 water
                 very
                 high
                 .
                 253
              
               
                 
                   Prob.
                   117
                
                 How
                 to
                 re-animate
                 simples
                 though
                 brought
                 a
                 thousand
                 miles
                 .
                 255
              
               
                 
                   Prob.
                   118
                
                 How
                 to
                 make
                 a
                 perpetuall
                 motion
                 .
                 255
              
               
                 
                   Prob.
                   119
                
                 Of
                 the
                 admirable
                 invention
                 of
                 making
                 the
                 Philosophers
                 Tree
                 ,
                 which
                 one
                 may
                 see
                 to
                 grow
                 by
                 little
                 and
                 little
                 .
                 256
              
               
                 
                   Prob.
                   120
                
                 How
                 to
                 make
                 the
                 representation
                 of
                 the
                 great
                 world
                 257
              
               
                 
                   Prob.
                   121
                
                 Of
                 a
                 Cone
                 ,
                 or
                 Pyramidall
                 figure
                 that
                 moves
                 upon
                 a
                 Table
                 258
              
               
                 
                   Prob.
                   122
                
                 How
                 an
                 Anvill
                 may
                 be
                 cleaved
                 by
                 the
                 blow
                 of
                 a
                 Pistoll
                 .
                 258
              
               
                 
                   Prob.
                   123
                
                 How
                 a
                 Capon
                 may
                 be
                 rosted
                 in
                 a
                 mans
                 travells
                 at
                 his
                 sa●●le-bowe
                 .
                 259
              
               
                 
                   Prob.
                   124
                
                 How
                 a
                 Candle
                 may
                 be
                 made
                 to
                 burne
                 three
                 times
                 longer
                 than
                 usually
                 it
                 doth
                 259
              
               
                 
                   Prob.
                   125
                
                 How
                 to
                 draw
                 Wine
                 out
                 of
                 water
                 260
              
               
                 
                 
                   Prob.
                   126
                
                 Of
                 two
                 Marmouzets
                 ,
                 the
                 one
                 of
                 which
                 lights
                 a
                 Candle
                 ,
                 and
                 the
                 other
                 blowes
                 it
                 out
                 .
                 261
              
               
                 
                   Prob.
                   127
                
                 How
                 to
                 make
                 Wine
                 fresh
                 without
                 Ice
                 or
                 Snow
                 in
                 the
                 height
                 of
                 Summer
                 .
                 262
              
               
                 
                   Prob.
                   128
                
                 To
                 make
                 a
                 Cement
                 which
                 lastes
                 as
                 marble
                 ,
                 resisting
                 aire
                 and
                 water
                 .
                 262
              
               
                 
                   Prob.
                   129
                
                 How
                 to
                 melt
                 metall
                 upon
                 a
                 shell
                 with
                 little
                 fire
                 .
                 263
              
               
                 
                   Prob.
                   130
                
                 Of
                 the
                 hardning
                 of
                 Iron
                 and
                 steele
                 .
                 263
              
               
                 
                   Prob.
                   131
                
                 To
                 preserve
                 fire
                 as
                 long
                 as
                 you
                 will
                 ,
                 imitating
                 the
                 inextinguible
                 fire
                 of
                 the
                 Vestales
                 .
                 264
              
            
             
               FINIS
               .
            
          
           
             
               Ad
               Authorem
               D.D.
               
                 Henricum
                 Van
                 Etenium
              
               ,
               Alumnum
               Academiae
               Ponta
               Mousson
               .
            
             
               ARdua
               Walkeri
               sileant
               secreta
               profundi
               ,
            
             
               Desinat
               occultam
               carpere
               Porta
               viam
               .
            
             
               Itala
               Cardani
               mirata
               est
               Lampada
               docti
            
             
               Terra
               ,
               Syracusium
               Graecia
               tota
               senem
               :
            
             
               Orbi
               terrarum
               ,
               Ptolemaei
               Clepsydra
               toti
               ,
            
             
               Rara
               dioptra
               Procli
               ,
               mira
               fuêre
               duo
               ,
            
             
               Anglia
               te
               foveat
               doctus
               Pont-Mousson
               alumnum
               :
            
             
               Quidquid
               naturae
               ,
               qui
               legis
               ,
               hortus
               habet
               .
            
             
               Docta
               ,
               coronet
               opus
               doctum
               ,
               te
               sit
               tua
               docto
            
             
               Digna
               ,
               Syracusii
               ,
               arca
               ,
               corona
               ,
               viri
               .
            
             
               Arca
               Syracusiis
               utinam
               sit
               plumbea
               servis
               ,
            
             
               Aurea
               sed
               dominis
               ,
               aurea
               tota
               suis.
               
            
          
        
         
           
             
             MATHEMATICAL
             RECREATION
             .
          
           
             
               PROBLEM
               I.
               To
               finde
               a
               number
               thought
               upon
               .
            
             
               BId
               him
               that
               he
               Quadruple
               the
               Number
               thought
               upon
               ,
               that
               is
               ,
               multiply
               it
               by
               4
               ,
               and
               unto
               it
               bid
               him
               to
               adde
               6
               ,
               8
               ,
               10
               ,
               or
               any
               Number
               at
               pleasure
               :
               and
               let
               him
               take
               the
               halfe
               of
               the
               sum
               ,
               then
               ask
               how
               much
               it
               coms
               to
               ,
               for
               then
               if
               you
               take
               away
               half
               the
               number
               from
               it
               which
               you
               willed
               him
               at
               first
               to
               add
               to
               it
               ,
               there
               shall
               remain
               the
               double
               of
               the
               number
               thought
               upon
               .
            
             
               Example
            
             
               
                 The
                 Number
                 thought
                 upon
              
               
                 5
              
               
                 The
                 Quadruple
                 of
                 it
              
               
                 20
              
               
                 Put
                 8
                 unto
                 it
                 ,
                 makes
              
               
                 28
              
               
                 The
                 halfe
                 of
                 it
                 is
              
               
                 14
              
               
                 
                 Take
                 away
                 halfe
                 the
                 number
                 added
                 from
                 it
                 ,
                 viz
                 4
                 ,
                 the
                 rest
                 is
              
               
                 10
              
               
                 The
                 double
                 of
                 the
                 number
                 thought
                 upon
                 ,
                 viz.
                 
              
               
                 10
              
            
             
               
                 Another
                 way
                 to
                 finde
                 what
                 Number
                 was
                 thought
                 upon
                 .
              
               
                 BId
                 him
                 which
                 thinketh
                 double
                 his
                 Number
                 ,
                 and
                 unto
                 that
                 double
                 adde
                 4
                 ,
                 and
                 bid
                 him
                 multiply
                 that
                 same
                 product
                 by
                 5
                 ,
                 and
                 unto
                 that
                 product
                 bid
                 him
                 adde
                 12
                 ,
                 and
                 multiply
                 that
                 last
                 number
                 by
                 10
                 (
                 which
                 is
                 done
                 easily
                 by
                 setting
                 a
                 Cypher
                 at
                 the
                 end
                 of
                 the
                 number
                 )
                 then
                 ask
                 him
                 the
                 last
                 number
                 or
                 product
                 ,
                 and
                 from
                 it
                 secretly
                 subtract
                 320
                 ,
                 the
                 remainder
                 in
                 the
                 hundreth
                 place
                 ,
                 is
                 the
                 number
                 thought
                 upon
                 .
              
               
                 Example
                 .
              
               
                 
                   The
                   number
                   thought
                   upon
                
                 
                   7
                   For
                   which
                   700
                   account
                   onely
                   but
                   the
                   number
                   of
                   the
                   hundreds
                   viz.
                   7.
                   so
                   have
                   you
                   the
                   number
                   thought
                   upon
                   .
                
                 
                   His
                   double
                
                 
                   14
                   For
                   which
                   700
                   account
                   onely
                   but
                   the
                   number
                   of
                   the
                   hundreds
                   viz.
                   7.
                   so
                   have
                   you
                   the
                   number
                   thought
                   upon
                   .
                
                 
                   To
                   it
                   add
                   4
                   ,
                   makes
                
                 
                   18
                   For
                   which
                   700
                   account
                   onely
                   but
                   the
                   number
                   of
                   the
                   hundreds
                   viz.
                   7.
                   so
                   have
                   you
                   the
                   number
                   thought
                   upon
                   .
                
                 
                   Which
                   multiplyed
                   by
                   5
                   makes
                
                 
                   90
                   For
                   which
                   700
                   account
                   onely
                   but
                   the
                   number
                   of
                   the
                   hundreds
                   viz.
                   7.
                   so
                   have
                   you
                   the
                   number
                   thought
                   upon
                   .
                
                 
                   To
                   which
                   add
                   12
                   makes
                
                 
                   102
                   For
                   which
                   700
                   account
                   onely
                   but
                   the
                   number
                   of
                   the
                   hundreds
                   viz.
                   7.
                   so
                   have
                   you
                   the
                   number
                   thought
                   upon
                   .
                
                 
                   This
                   multiplyed
                   by
                   10
                   which
                   is
                   only
                   by
                   adding
                   a
                   Cypher
                   to
                   it
                   ,
                   makes
                
                 
                   1020
                   For
                   which
                   700
                   account
                   onely
                   but
                   the
                   number
                   of
                   the
                   hundreds
                   viz.
                   7.
                   so
                   have
                   you
                   the
                   number
                   thought
                   upon
                   .
                
                 
                   From
                   this
                   subtract
                
                 
                   320
                   For
                   which
                   700
                   account
                   onely
                   but
                   the
                   number
                   of
                   the
                   hundreds
                   viz.
                   7.
                   so
                   have
                   you
                   the
                   number
                   thought
                   upon
                   .
                
                 
                   Rest
                
                 
                   700
                   For
                   which
                   700
                   account
                   onely
                   but
                   the
                   number
                   of
                   the
                   hundreds
                   viz.
                   7.
                   so
                   have
                   you
                   the
                   number
                   thought
                   upon
                   .
                
              
            
             
               
               
                 To
                 finde
                 numbers
                 conceived
                 upon
                 ,
                 otherwise
                 than
                 the
                 former
                 .
              
               
                 BId
                 the
                 party
                 which
                 thinks
                 the
                 number
                 ,
                 that
                 he
                 triple
                 his
                 thought
                 ,
                 and
                 cause
                 him
                 to
                 take
                 the
                 half
                 of
                 it
                 :
                 (
                 if
                 it
                 be
                 odde
                 take
                 the
                 least
                 half
                 ,
                 and
                 put
                 one
                 unto
                 it
                 :
                 )
                 then
                 will
                 him
                 to
                 triple
                 the
                 half
                 ,
                 and
                 take
                 half
                 of
                 it
                 as
                 before
                 :
                 lastly
                 ,
                 ask
                 him
                 how
                 many
                 nines
                 there
                 is
                 in
                 the
                 last
                 half
                 ,
                 and
                 for
                 every
                 nine
                 ,
                 account
                 four
                 in
                 your
                 memory
                 ,
                 for
                 that
                 shall
                 shew
                 the
                 number
                 thought
                 upon
                 ,
                 if
                 both
                 the
                 triples
                 were
                 even
                 :
                 but
                 if
                 it
                 be
                 odde
                 at
                 the
                 first
                 triple
                 ,
                 and
                 ev●n
                 at
                 the
                 second
                 ,
                 for
                 the
                 one
                 added
                 unto
                 the
                 least
                 halfe
                 keep
                 one
                 in
                 memory
                 :
                 if
                 the
                 first
                 triple
                 be
                 even
                 ,
                 and
                 the
                 second
                 odde
                 ,
                 for
                 the
                 one
                 added
                 unto
                 the
                 least
                 halfe
                 keepe
                 two
                 in
                 memory
                 ;
                 lastly
                 ,
                 if
                 at
                 both
                 times
                 in
                 tripling
                 ,
                 the
                 numbers
                 be
                 odde
                 ,
                 for
                 the
                 two
                 added
                 unto
                 the
                 least
                 halfes
                 ,
                 keep
                 three
                 in
                 memory
                 ,
                 these
                 cautions
                 observed
                 ,
                 and
                 added
                 unto
                 as
                 many
                 fours
                 as
                 the
                 party
                 sayes
                 there
                 is
                 nines
                 contained
                 in
                 the
                 last
                 halfe
                 ,
                 shall
                 never
                 fail
                 you
                 to
                 declare
                 or
                 discern
                 truly
                 what
                 number
                 was
                 thought
                 upon
                 .
              
               
                 Example
                 .
              
               
                 
                   The
                   number
                   thought
                   upon
                
                 
                   4
                   or
                   7
                
                 
                   The
                   triple
                
                 
                   12
                   or
                   21
                
                 
                   The
                   half
                   thereof
                   6
                   or
                   10
                   ,
                   one
                   put
                   to
                   it
                   makes
                
                 
                   11
                
                 
                   The
                   triple
                   of
                   the
                   halfe
                
                 
                   18
                   or
                   33
                
                 
                   The
                   halfe
                   9
                   or
                   1●
                   ,
                   one
                   put
                   to
                   it
                   makes
                
                 
                   17
                
                 
                   The
                   number
                   of
                   nines
                   in
                   the
                   last
                   halfe
                
                 
                   1
                   or
                   1
                
              
               
               
                 The
                 first
                 1.
                 representeth
                 the
                 4.
                 number
                 thought
                 upon
                 ,
                 and
                 the
                 last
                 1.
                 with
                 the
                 caution
                 makes
                 7.
                 the
                 other
                 number
                 thought
                 upon
                 .
              
            
             
               
                 Note
                 .
              
               
                 Order
                 your
                 method
                 so
                 that
                 you
                 be
                 not
                 discovered
                 ,
                 which
                 to
                 help
                 ,
                 you
                 may
                 with
                 dexterity
                 and
                 industry
                 make
                 
                   Additions
                   ▪
                   Substractions
                   ,
                   Multiplications
                   ,
                   Divisions
                   ,
                   &c.
                
                 and
                 instead
                 of
                 asking
                 how
                 many
                 nines
                 there
                 is
                 ,
                 you
                 may
                 ask
                 how
                 many
                 eights
                 tens
                 ,
                 &c.
                 there
                 is
                 ,
                 or
                 subtract
                 8.10
                 .
                 &c.
                 from
                 the
                 Number
                 which
                 remains
                 ,
                 for
                 to
                 finde
                 out
                 the
                 number
                 thought
                 upon
                 .
              
               
                 Now
                 touching
                 the
                 Demonstrations
                 of
                 the
                 former
                 directions
                 ,
                 and
                 others
                 which
                 follow
                 ,
                 they
                 depend
                 upon
                 the
                 2
                 ,
                 7
                 ,
                 8
                 ,
                 and
                 9
                 ,
                 Books
                 of
                 the
                 Elements
                 of
                 Euclide
                 :
                 upon
                 which
                 2.
                 
                 Book
                 &
                 4.
                 proposition
                 this
                 may
                 bee
                 extracted
                 ,
                 for
                 these
                 which
                 are
                 more
                 learned
                 for
                 the
                 finding
                 of
                 any
                 number
                 that
                 any
                 one
                 thinketh
                 on
                 .
              
               
                 Bid
                 the
                 party
                 that
                 thinks
                 ,
                 that
                 he
                 break
                 the
                 number
                 thought
                 upon
                 into
                 any
                 two
                 parts
                 ,
                 and
                 unto
                 the
                 Squares
                 of
                 the
                 parts
                 ,
                 let
                 him
                 adde
                 the
                 double
                 product
                 of
                 the
                 parts
                 ,
                 then
                 ask
                 what
                 it
                 amounteth
                 unto
                 ,
                 so
                 the
                 
                   root
                   Quadrat
                
                 shall
                 be
                 the
                 number
                 thought
                 upon
                 .
              
               
                 
                   The
                   number
                   thought
                   upon
                   5
                   ,
                   the
                   parts
                   suppose
                   3
                   and
                   2.
                   
                
                 
                   
                   The
                   square
                   of
                   3
                   makes
                
                 
                   9
                   the
                   sum
                   of
                   these
                   three
                   nūbers
                   25
                   ,
                   the
                   
                     squa●e
                     Root
                  
                   of
                   which
                   is
                   5
                   ,
                   the
                   number
                   thought
                   upon
                
                 
                   The
                   square
                   of
                   2
                   makes
                
                 
                   4
                   the
                   sum
                   of
                   these
                   three
                   nūbers
                   25
                   ,
                   the
                   
                     squa●e
                     Root
                  
                   of
                   which
                   is
                   5
                   ,
                   the
                   number
                   thought
                   upon
                
                 
                   The
                   product
                   of
                   the
                   parts
                   .
                   viz.
                   3
                   by
                   2
                   makes
                   6
                   ,
                   which
                   6
                   doubled
                   makes
                
                 
                   12
                   the
                   sum
                   of
                   these
                   three
                   nūbers
                   25
                   ,
                   the
                   
                     squa●e
                     Root
                  
                   of
                   which
                   is
                   5
                   ,
                   the
                   number
                   thought
                   upon
                
              
               
                 Or
                 more
                 compendiously
                 it
                 may
                 be
                 delivered
                 thus
                 .
              
               
                 Break
                 the
                 number
                 into
                 two
                 parts
                 ,
                 and
                 to
                 the
                 product
                 of
                 the
                 parts
                 ,
                 adde
                 the
                 square
                 of
                 half
                 the
                 difference
                 of
                 the
                 parts
                 ,
                 then
                 the
                 Root
                 Quadrat
                 of
                 the
                 aggregate
                 is
                 halfe
                 the
                 number
                 conceived
                 .
              
            
             
               
                 EXAMINATION
                 .
              
               
                 THe
                 Problems
                 which
                 concern
                 Arithmetick
                 ,
                 we
                 examine
                 not
                 ,
                 for
                 these
                 are
                 easie
                 to
                 any
                 one
                 which
                 hath
                 read
                 the
                 grounds
                 and
                 principles
                 of
                 Arithmetick
                 ,
                 but
                 we
                 especially
                 touch
                 upon
                 that
                 ,
                 which
                 tends
                 to
                 the
                 speculations
                 of
                 
                   Physick
                   ,
                   Geometry
                
                 ,
                 and
                 Optickes
                 ,
                 and
                 such
                 others
                 which
                 are
                 of
                 more
                 difficulty
                 ,
                 and
                 more
                 principally
                 to
                 be
                 examined
                 and
                 considered
                 .
              
            
          
           
             
             
               PROBLEM
               II.
               How
               to
               represent
               to
               those
               which
               are
               in
               a
               Cham●er
               that
               which
               is
               without
               ,
               or
               all
               that
               which
               passeth
               by
               ,
            
             
             
               It
               is
               pleasant
               to
               see
               the
               beautifull
               and
               goodly
               representation
               of
               the
               heavens
               intermixed
               with
               clouds
               in
               the
               Horizon
               ,
               upon
               a
               woody
               scituation
               ,
               the
               motion
               of
               Birds
               in
               the
               Aire
               ,
               of
               men
               and
               other
               creatures
               upon
               the
               ground
               ,
               with
               the
               trembling
               of
               plants
               ,
               tops
               of
               trees
               ,
               and
               such
               like
               :
               for
               every
               thing
               will
               be
               seen
               within
               even
               to
               the
               life
               ,
               but
               inversed
               :
               notwithstanding
               ,
               this
               beautifull
               paint
               will
               so
               naturally
               represent
               it self
               in
               such
               a
               lively
               Perspective
               ,
               that
               hardly
               the
               most
               accurate
               Painter
               can
               represent
               the
               like
               .
            
             
             
               But
               here
               note
               ,
               that
               they
               may
               be
               represented
               right
               two
               manner
               of
               wayes
               ;
               first
               ,
               with
               a
               concave
               glasse
               :
               secondly
               ,
               by
               help
               of
               another
               convex
               glasse
               ,
               disposed
               or
               placed
               between
               the
               paper
               and
               the
               other
               Glasse
               :
               as
               may
               be
               seen
               here
               by
               the
               figure
               .
            
             
             
               Now
               I
               will
               add
               here
               only
               by
               passing
               by
               ,
               for
               such
               which
               affect
               Painting
               and
               portraiture
               ,
               that
               this
               experiment
               may
               excellently
               help
               them
               in
               the
               lively
               painting
               of
               things
               perspectivewise
               ,
               as
               
                 Topographicall
                 cards
                 ,
                 &c.
              
               and
               for
               Philosophers
               ,
               it
               is
               a
               fine
               secret
               to
               explain
               the
               Organ
               of
               the
               sight
               ,
               for
               the
               hollow
               of
               the
               eye
               is
               taken
               as
               the
               close
               Chamber
               ,
               the
               Ball
               of
               the
               Apple
               of
               the
               eye
               ,
               for
               the
               hole
               of
               the
               Chamber
               ,
               the
               Crystaline
               humor
               at
               the
               small
               of
               the
               Glasse
               ,
               and
               the
               bottome
               of
               the
               eye
               ,
               for
               the
               Wall
               or
               leafe
               of
               paper
               .
            
             
               
                 EXAMINATION
                 .
              
               
                 THe
                 species
                 being
                 pressed
                 together
                 or
                 contracted
                 doth
                 not
                 perform
                 it
                 upon
                 a
                 wall
                 ,
                 for
                 the
                 species
                 of
                 any
                 thing
                 doth
                 represent
                 it selfe
                 not
                 only
                 in
                 one
                 hole
                 of
                 a
                 window
                 ,
                 but
                 in
                 infinite
                 holes
                 ,
                 even
                 unto
                 the
                 whole
                 Sphere
                 ,
                 or
                 at
                 least
                 unto
                 a
                 Hemisphere
                 (
                 intellectuall
                 in
                 a
                 free
                 medium
                 )
                 if
                 the
                 beams
                 or
                 reflections
                 be
                 not
                 interposed
                 ,
                 and
                 by
                 how
                 much
                 the
                 hole
                 is
                 made
                 less
                 to
                 give
                 passage
                 to
                 the
                 species
                 ,
                 by
                 so
                 much
                 the
                 more
                 lively
                 are
                 the
                 Images
                 formed
                 .
              
               
                 In
                 convexe
                 ,
                 or
                 concave
                 Glasses
                 the
                 Images
                 will
                 be
                 disproportionable
                 to
                 the
                 eye
                 ,
                 by
                 how
                 much
                 they
                 are
                 more
                 concave
                 ,
                 or
                 convexe
                 ,
                 &
                 by
                 how
                 much
                 the
                 parts
                 of
                 the
                 image
                 comes
                 
                 neer
                 to
                 the
                 Axis
                 ,
                 for
                 these
                 that
                 are
                 neer
                 are
                 better
                 proportioned
                 then
                 these
                 which
                 are
                 farther
                 off
                 .
              
               
                 But
                 to
                 have
                 them
                 more
                 lively
                 and
                 true
                 ,
                 according
                 to
                 the
                 imaginary
                 conicall
                 section
                 ,
                 let
                 the
                 hole
                 be
                 no
                 greater
                 than
                 a
                 pins
                 head
                 made
                 upon
                 a
                 piece
                 of
                 thin
                 brasse
                 ,
                 or
                 such
                 like
                 ,
                 which
                 hole
                 represents
                 the
                 top
                 of
                 the
                 Cone
                 ,
                 and
                 the
                 Base
                 thereof
                 the
                 term
                 of
                 the
                 species
                 :
                 this
                 practice
                 is
                 best
                 when
                 the
                 sun
                 shines
                 upon
                 the
                 hole
                 ,
                 for
                 then
                 the
                 objects
                 which
                 are
                 opposite
                 to
                 that
                 plaine
                 will
                 make
                 two
                 like
                 Cones
                 ,
                 and
                 will
                 lively
                 represent
                 the
                 things
                 without
                 in
                 a
                 perfect
                 inversed
                 perspective
                 ,
                 which
                 drawn
                 by
                 the
                 Pensill
                 of
                 some
                 artificiall
                 Painter
                 ,
                 turn
                 the
                 paper
                 upside
                 down
                 ,
                 and
                 it
                 will
                 be
                 direct
                 and
                 to
                 the
                 life
                 .
              
               
                 But
                 the
                 apparences
                 may
                 be
                 direct
                 ,
                 if
                 you
                 place
                 another
                 hole
                 opposite
                 unto
                 the
                 former
                 ,
                 so
                 that
                 the
                 spectator
                 be
                 under
                 it
                 ;
                 or
                 let
                 the
                 species
                 reflect
                 upon
                 a
                 concave
                 Glass
                 ,
                 and
                 let
                 that
                 glas
                 reflect
                 upon
                 a
                 paper
                 or
                 some
                 white
                 thing
                 .
              
            
          
           
             
               PROBLEM
               III.
               To
               tell
               how
               much
               waighs
               the
               blow
               of
               ones
               fist
               ,
               of
               a
               Mallet
               ,
               Hatchet
               ,
               or
               such
               like
               ,
               or
               resting
               without
               giving
               the
               blow
            
             
               SCaliger
               in
               his
               331
               exercise
               against
               Cardan
               ,
               relates
               that
               the
               Mathematicians
               of
               Maximillian
               
               the
               Emperour
               did
               propose
               upon
               a
               day
               this
               Question
               ,
               and
               promised
               to
               give
               the
               resolution
               ;
               notwithstanding
               ●caliger
               delivered
               it
               not
               ,
               and
               I
               conceive
               it
               to
               be
               thus
               .
               Take
               a
               Balance
               ,
               and
               let
               the
               Fist
               ,
               the
               Mallet
               ,
               or
               Hatchet
               rest
               upon
               the
               scale
               ,
               or
               upon
               the
               beam
               of
               the
               Balance
               ,
               and
               put
               into
               the
               other
               Scale
               as
               much
               weight
               as
               may
               counterpoyse
               it
               ;
               then
               charging
               or
               laying
               more
               waight
               into
               the
               Scale
               ,
               and
               striking
               upon
               the
               other
               end
               ,
               you
               may
               see
               how
               much
               one
               blow
               is
               heavier
               than
               another
               ,
               and
               so
               consequently
               how
               much
               it
               may
               waigh
               for
               as
               Aristotle
               saith
               ,
               
                 The
                 motion
                 that
                 is
                 made
                 in
                 striking
                 adds
                 great
                 waight
                 unto
                 it
                 ,
                 and
                 so
                 much
                 the
                 more
                 ,
                 by
                 how
                 much
                 it
                 is
                 quicker
                 :
              
               therefore
               
               in
               effect
               ,
               if
               there
               were
               placed
               a
               thousand
               mallets
               ,
               or
               a
               Thousand
               pounde
               waight
               upon
               a
               stone
               ,
               nay
               ,
               though
               it
               were
               exceedingly
               pressed
               down
               by
               way
               of
               a
               Vice
               ,
               by
               Levers
               ,
               or
               other
               Mechanick
               Engine
               ,
               it
               would
               be
               nothing
               to
               the
               rigor
               and
               violence
               of
               a
               blow
               .
            
             
               Is
               it
               not
               evident
               that
               the
               edge
               of
               a
               knife
               laid
               upon
               butter
               ,
               and
               a
               hatchet
               upon
               a
               leafe
               of
               paper
               ,
               without
               striking
               makes
               no
               impression
               ,
               or
               at
               least
               enters
               not
               ;
               but
               striking
               upon
               the
               wood
               a
               little
               ,
               you
               may
               presently
               see
               what
               effect
               it
               hath
               ,
               which
               is
               from
               the
               quicknesse
               of
               the
               motion
               ,
               which
               breaks
               and
               enters
               without
               resistance
               ,
               if
               it
               be
               extream
               quick
               ,
               as
               experience
               shews
               us
               in
               the
               
               blows
               of
               Arrows
               ,
               of
               Cannons
               ,
               Thunder-boults
               ,
               and
               such
               like
               .
            
             
               
                 EXAMINATION
                 .
              
               
                 THis
                 Problem
                 was
                 extracted
                 from
                 Scaliger
                 ,
                 who
                 had
                 it
                 from
                 Aristotle
                 ,
                 but
                 somwhat
                 refractory
                 compiled
                 ,
                 &
                 the
                 strength
                 of
                 the
                 effect
                 he
                 says
                 depends
                 only
                 in
                 the
                 violence
                 of
                 the
                 motion
                 ;
                 then
                 would
                 it
                 follow
                 that
                 a
                 little
                 light
                 hammer
                 upon
                 a
                 piece
                 of
                 wood
                 being
                 quickly
                 caused
                 to
                 smite
                 ,
                 would
                 give
                 a
                 greater
                 blow
                 ,
                 and
                 do
                 more
                 hurt
                 than
                 a
                 great
                 sledge
                 striking
                 soft
                 ;
                 this
                 is
                 absurd
                 ,
                 and
                 contrary
                 to
                 experience
                 :
                 therefore
                 it
                 consists
                 not
                 totally
                 in
                 the
                 motion
                 ,
                 for
                 if
                 two
                 severall
                 hammers
                 ,
                 the
                 one
                 being
                 20
                 times
                 heavier
                 than
                 the
                 other
                 ,
                 should
                 move
                 with
                 like
                 quickness
                 ,
                 the
                 effect
                 would
                 be
                 much
                 different
                 ,
                 there
                 is
                 then
                 some
                 thing
                 else
                 to
                 be
                 considered
                 besides
                 the
                 Motion
                 which
                 Scaliger
                 understood
                 not
                 ,
                 for
                 if
                 one
                 should
                 have
                 asked
                 him
                 ,
                 what
                 is
                 the
                 reason
                 that
                 a
                 stone
                 falling
                 from
                 a
                 window
                 to
                 a
                 place
                 neer
                 at
                 hand
                 ,
                 is
                 not
                 so
                 forceable
                 as
                 if
                 it
                 fell
                 farther
                 〈◊〉
                 when
                 a
                 bullet
                 flying
                 out
                 of
                 a
                 peece
                 and
                 striking
                 the
                 mark
                 neer
                 at
                 hand
                 〈◊〉
                 not
                 make
                 such
                 an
                 effect
                 as
                 striking
                 〈…〉
                 that
                 Scaliger
                 and
                 〈…〉
                 this
                 subiect
                 ▪
                 would
                 not
                 be
                 less
                 troubled
                 to
                 resolve
                 this
                 ,
                 than
                 they
                 have
                 been
                 in
                 that
                 .
              
            
          
           
             
             
               PROBLEM
               IV.
               How
               to
               break
               a
               staffe
               which
               is
               laid
               upon
               two
               Glasses
               full
               of
               water
               ,
               without
               breaking
               the
               Glasses
               ,
               spilling
               the
               water
               ,
               or
               upon
               two
               reeds
               or
               straws
               without
               breaking
               of
               them
               .
            
             
             
               In
               like
               manner
               may
               you
               doe
               upon
               two
               Reeds
               ,
               held
               with
               your
               hands
               in
               the
               aire
               without
               breaking
               them
               ▪
               thence
               Kitchin
               boyes
               often
               break
               bones
               of
               mutton
               upon
               their
               hand
               ,
               or
               with
               a
               napkin
               without
               any
               hurt
               ,
               in
               only
               striking
               upon
               the
               middle
               of
               the
               bone
               with
               a
               knife
               .
            
             
             
               Now
               in
               this
               act
               ,
               the
               two
               ends
               of
               the
               staffe
               in
               breaking
               slides
               away
               from
               the
               Glasses
               ,
               upon
               which
               they
               were
               placed
               ;
               hence
               it
               commeth
               that
               the
               Glasses
               are
               no
               wise
               indangered
               ,
               no
               more
               than
               the
               knee
               upon
               which
               a
               staffe
               is
               broken
               ,
               forasmuch
               as
               in
               breaking
               it
               presseth
               not
               :
               as
               Aristotle
               in
               his
               
                 Mechanick
                 Questions
              
               observeth
               .
            
             
               
                 EXAMINATION
                 .
              
               
                 IT
                 were
                 necessary
                 here
                 to
                 note
                 ,
                 that
                 this
                 thing
                 may
                 be
                 experimented
                 ,
                 first
                 ,
                 without
                 Glasses
                 ,
                 in
                 placing
                 a
                 small
                 slender
                 staffe
                 upon
                 two
                 props
                 ,
                 and
                 then
                 making
                 tryall
                 upon
                 it
                 ,
                 by
                 which
                 you
                 may
                 see
                 how
                 the
                 Staffe
                 will
                 either
                 break
                 ,
                 bow
                 ,
                 or
                 depart
                 from
                 his
                 props
                 ,
                 and
                 that
                 either
                 directly
                 or
                 obliquely
                 :
                 But
                 why
                 by
                 this
                 violence
                 ,
                 that
                 one
                 Staffe
                 striking
                 another
                 ,
                 (
                 which
                 is
                 supported
                 by
                 two
                 Glasses
                 )
                 will
                 be
                 broken
                 without
                 offending
                 the
                 Glasses
                 ,
                 is
                 as
                 great
                 a
                 difficulty
                 to
                 be
                 resolved
                 as
                 the
                 former
                 .
              
            
          
           
             
             
               PROBLEM
               V.
               How
               to
               make
               a
               faire
               Ge●graphic●ll
               Card
               in
               a
               Garden
               Plot
               ,
               fit
               for
               a
               Prince
               ,
               or
               great
               personage
               .
            
             
               IT
               is
               usuall
               amongst
               great
               men
               to
               have
               faire
               
                 Geographicall
                 Maps
              
               ▪
               large
               Cards
               ,
               and
               great
               Globes
               ,
               that
               by
               them
               they
               may
               as
               at
               once
               have
               a
               view
               of
               any
               place
               of
               the
               World
               ,
               and
               so
               furnish
               themselves
               with
               a
               generall
               knowledge
               ,
               not
               only
               of
               their
               own
               Kingdoms
               form
               ,
               scituation
               ,
               longitude
               ,
               latitude
               ,
               &c.
               but
               of
               all
               other
               places
               in
               the
               whole
               Universe
               ,
               with
               their
               magnitudes
               ,
               positions
               ,
               Climats
               ,
               and
               distances
               .
            
             
               Now
               I
               esteem
               that
               it
               is
               not
               unworthy
               for
               the
               meditations
               of
               a
               Prince
               ,
               seeing
               it
               carries
               with
               it
               many
               profitable
               and
               pleasant
               contentmen●s
               :
               if
               such
               a
               Card
               or
               Map
               by
               the
               advice
               and
               direction
               of
               an
               able
               Mathematician
               were
               Geographically
               described
               in
               a
               Garden
               plot
               form
               ,
               or
               in
               some
               other
               convenient
               place
               ,
               and
               instead
               of
               which
               generall
               description
               might
               particularly
               and
               artificially
               be
               prefigured
               his
               whole
               Kingdoms
               and
               Dominions
               ,
               the
               Mountains
               and
               hils
               being
               raised
               like
               small
               hillocks
               with
               turfs
               of
               earth
               ,
               the
               valleys
               somwhat
               concave
               ,
               which
               will
               be
               more
               agreeable
               and
               pleasing
               to
               the
               eye
               ,
               than
               the
               description
               in
               plain
               Maps
               and
               Cards
               ,
               within
               which
               may
               be
               presented
               the
               Towns
               ,
               Villages
               ,
               Castles
               ,
               or
               other
               remarkable
               edifices
               in
               small
               green
               mo●●e
               banks
               ,
               or
               spring-work
               proportionall
               to
               the
               pl●tform
               ,
               
               the
               Forrests
               and
               Woods
               represented
               according
               to
               their
               form
               and
               capacity
               ,
               with
               herbs
               and
               stoubs
               ,
               the
               great
               Rivers
               ,
               Lakes
               ,
               and
               Ponds
               to
               dilate
               themselves
               according
               to
               their
               course
               from
               some
               artificiall
               Fountain
               made
               in
               the
               Garden
               to
               passe
               through
               chanels
               ;
               then
               may
               there
               be
               composed
               walks
               of
               pleasure
               ,
               ascents
               ,
               places
               of
               repose
               ,
               adorned
               with
               all
               variety
               of
               delightfull
               herbs
               and
               flowers
               ,
               both
               to
               please
               the
               eye
               or
               other
               senses
               .
               A
               Garden
               thus
               accommodated
               shall
               farre
               exceed
               that
               of
               my
               Lord
               of
               Verulams
               specified
               in
               his
               ●ssayes
               ;
               that
               being
               only
               for
               delight
               and
               pleasure
               ,
               this
               may
               have
               all
               the
               properties
               of
               that
               ,
               and
               also
               for
               singular
               use
               ,
               by
               which
               a
               Prince
               may
               in
               little
               time
               personally
               visit
               his
               whole
               Kingdom
               ,
               and
               in
               short
               time
               know
               them
               distinctly
               :
               and
               so
               in
               like
               manner
               may
               any
               particular
               man
               Geographically
               prefigure
               his
               own
               possession
               or
               heritage
               .
            
          
           
             
               PROBLEM
               VI.
               How
               three
               staves
               ,
               knives
               ,
               or
               like
               bodies
               ,
               may
               be
               conceived
               to
               hang
               in
               the
               aire
               ,
               without
               being
               supported
               by
               any
               thing
               but
               by
               themselves
               .
            
             
               TAke
               the
               first
               staffe
               AB
               ,
               raise
               up
               in
               the
               aire
               the
               end
               B
               ,
               and
               upon
               him
               cros-wise
               place
               the
               staffe
               CB
               ,
               then
               lastly
               ,
               in
               Triangle
               wise
               place
               the
               third
               staffe
               EF
               ▪
               in
               such
               manner
               that
               it
               may
               be
               under
               AB
               ,
               and
               yet
               upon
               CD
               .
               I
               say
               that
               these
               staves
               so
               disposed
               cannot
               fall
               ,
               and
               
               the
               space
               CBE
               is
               made
               the
               stronger
               ,
               by
               how
               much
               the
               more
               it
               is
               pressed
               downe
               ,
               if
               the
               staves
               break
               not
               ,
               or
               sever
               themselves
               from
               the
               triangular
               forme
               :
               so
               that
               alwayes
               the
               Center
               of
               gravitie
               
               be
               in
               the
               Center
               of
               the
               Triangle
               :
               for
               AB
               is
               supported
               by
               EF
               ,
               and
               EF
               is
               held
               up
               by
               CD
               ,
               and
               CD
               is
               kept
               up
               from
               falling
               by
               AB
               ,
               therefore
               one
               of
               these
               staves
               cannot
               fall
               ,
               and
               so
               by
               consequence
               none
               .
            
          
           
             
               PROBLEM
               VII
               .
               How
               to
               dispose
               as
               many
               men
               ,
               or
               other
               things
               in
               such
               sort
               ,
               that
               rejecting
               ,
               or
               casting
               away
               the
               
                 6
                 ,
                 9
                 ,
                 10
              
               part
               ,
               unto
               a
               certain
               number
               ,
               there
               shall
               remaine
               these
               which
               you
               would
               have
               .
            
             
               ORdinarily
               the
               proposition
               is
               delivered
               in
               this
               wise
               :
               15
               Christians
               and
               15
               Turkes
               being
               at
               Sea
               in
               one
               Shippe
               ,
               an
               extreame
               tempest
               being
               risen
               ,
               the
               Pilot
               of
               the
               Shippe
               saith
               ,
               it
               is
               necessary
               to
               cast
               over
               board
               halfe
               of
               the
               number
               of
               Persons
               to
               disburthen
               the
               Shippe
               ,
               and
               
               to
               save
               the
               rest
               :
               now
               it
               was
               agreed
               to
               be
               done
               by
               lot
               ,
               and
               therefore
               they
               consent
               to
               put
               themselves
               in
               rank
               ,
               counting
               by
               nine
               and
               nine
               ,
               the
               ninth
               Person
               should
               alwayes
               be
               cast
               into
               the
               Sea
               ,
               untill
               there
               were
               halfe
               throwne
               over
               board
               ;
               Now
               the
               Pilote
               being
               a
               Christian
               indeavoured
               to
               save
               the
               Christians
               ,
               how
               ought
               he
               therefore
               to
               dispose
               the
               Christians
               ,
               that
               the
               lot
               might
               fall
               alwayes
               upon
               the
               Turkes
               ,
               and
               that
               none
               of
               the
               Christians
               be
               in
               the
               ninth
               place
               ?
            
             
               The
               resolution
               is
               ordinarily
               comprehended
               in
               this
               verse
               .
            
             
               Populeam
               virgam
               mater
               regina
               ferebat
               .
            
             
               For
               having
               respect
               unto
               the
               vowels
               ,
               making
               a
               one
               ,
               e
               two
               ,
               i
               three
               ,
               o
               foure
               ,
               and
               u
               five
               :
               o
               the
               first
               vowell
               in
               the
               first
               word
               sheweth
               that
               there
               must
               be
               placed
               4.
               
               Christians
               ;
               the
               next
               vowel
               u
               ,
               signifieth
               that
               next
               unto
               the
               4.
               
               Christians
               must
               be
               placed
               5
               Turkes
               ,
               and
               so
               to
               place
               both
               Christians
               and
               Turkes
               according
               to
               the
               quantity
               and
               value
               of
               the
               vowels
               in
               the
               words
               of
               the
               verse
               ,
               untill
               they
               be
               all
               placed
               :
               for
               then
               counting
               from
               the
               first
               Christian
               that
               was
               placed
               ,
               unto
               the
               ninth
               ,
               the
               lot
               will
               fall
               upon
               a
               Turk
               ,
               and
               so
               proceed
               .
               And
               here
               may
               be
               further
               noted
               that
               this
               Probleme
               is
               not
               to
               be
               limited
               ,
               seeing
               it
               extends
               to
               any
               number
               and
               order
               whatsoever
               ,
               and
               may
               many
               wayes
               be
               usefull
               for
               Captaines
               ,
               Magistrates
               ,
               or
               others
               which
               have
               divers
               persons
               to
               punish
               ,
               and
               would
               chastise
               chiefely
               the
               unruliest
               of
               them
               ,
               in
               taking
               the
               10
               ,
               20
               ,
               or
               100.
               person
               ,
               &c.
               as
               we
               reade
               was
               
               commonly
               practised
               amongst
               the
               ancient
               Romans
               :
               herefore
               to
               apply
               a
               generall
               rule
               in
               counting
               the
               third
               ,
               4
               ,
               9
               ,
               10
               ,
               &c.
               amongst
               30
               ,
               40
               ,
               50
               ,
               persons
               ,
               and
               more
               or
               lesse
               ;
               this
               is
               to
               be
               observed
               ,
               take
               as
               many
               units
               as
               there
               are
               persons
               ,
               and
               dispose
               them
               in
               order
               privately
               :
               as
               for
               example
               ,
               let
               24
               men
               be
               proposed
               to
               have
               committed
               some
               outrage
               ,
               6
               of
               them
               especially
               are
               found
               accessary
               :
               and
               let
               it
               be
               agreed
               that
               counting
               by
               8
               and
               8
               the
               eight
               man
               should
               be
               alwayes
               punished
               .
               Take
               therefore
               first
               24
               units
               ,
               or
               upon
               a
               piece
               of
               paper
               write
               down
               24
               cyphers
               ,
               and
               account
               from
               the
               beginning
               to
               the
               eighth
               ,
               which
               eighth
               mark
               ,
               and
               so
               continue
               counting
               alwayes
               marking
               the
               eighth
               ,
               untill
               you
               have
               markt
               6
               ,
               by
               which
               you
               may
               easily
               perceive
               how
               to
               place
               those
               6
               men
               that
               are
               to
               be
               punished
               ,
               and
               so
               of
               others
               .
            
             
               It
               is
               supposed
               that
               Josephus
               the
               Author
               of
               the
               
                 Jewish
                 History
              
               escaped
               the
               danger
               of
               death
               by
               help
               of
               this
               Problem
               ;
               for
               a
               worthy
               Author
               of
               beliefe
               reports
               in
               his
               eighth
               chapter
               of
               the
               third
               Book
               of
               the
               destruction
               of
               Jerusalem
               ,
               that
               the
               Town
               of
               Jotapata
               being
               taken
               by
               main
               force
               by
               
                 Vespatian
                 ,
                 Josephus
              
               being
               Governour
               of
               that
               Town
               ,
               accompanyed
               with
               a
               Troop
               of
               forty
               Souldiers
               ,
               hid
               themselves
               in
               a
               Cave
               ,
               in
               which
               they
               resolved
               rather
               to
               famish
               than
               to
               fall
               into
               the
               hands
               of
               Vespatian
               :
               and
               with
               a
               bloudy
               resolution
               in
               that
               great
               distresse
               would
               have
               butchered
               one
               another
               for
               sustenance
               ,
               had
               not
               Josephus
               perswaded
               them
               to
               die
               by
               lot
               and
               order
               ,
               upon
               which
               it
               should
               fall
               :
               Now
               
               seeing
               that
               Josephus
               did
               save
               himselfe
               by
               this
               Art
               ,
               it
               is
               thought
               that
               his
               industry
               was
               exercised
               by
               the
               helpe
               of
               this
               Problem
               ,
               so
               that
               of
               the
               40
               persons
               which
               he
               had
               ,
               the
               third
               was
               alwayes
               killed
               .
               Now
               by
               putting
               himselfe
               in
               the
               16
               or
               31
               place
               he
               was
               saved
               ,
               and
               one
               with
               him
               which
               he
               might
               kill
               ,
               or
               easily
               perswade
               to
               yeild
               unto
               the
               Romans
               .
            
          
           
             
               PROBLEM
               .
               VIII
               .
               Three
               things
               ,
               and
               three
               persons
               proposed
               ,
               to
               finde
               which
               of
               them
               hath
               either
               of
               these
               three
               things
               .
            
             
               LEt
               the
               three
               things
               be
               a
               Ring
               ,
               a
               piece
               of
               Gold
               ,
               and
               a
               piece
               of
               Silver
               ,
               or
               any
               other
               such
               like
               ,
               and
               let
               them
               be
               known
               privately
               to
               your self
               by
               these
               three
               Vowels
               
                 a
                 ,
                 e
                 ,
                 i
              
               ,
               or
               let
               there
               be
               three
               persons
               that
               have
               different
               names
               ,
               as
               
                 Ambrose
                 ,
                 Edmond
              
               ,
               and
               John
               ,
               which
               privately
               you
               may
               note
               or
               account
               to
               your selfe
               once
               known
               by
               the
               aforesaid
               Vowels
               ,
               which
               signifie
               for
               the
               first
               vowel
               1
               ,
               for
               the
               second
               vowell
               2
               ,
               for
               the
               third
               vowell
               3.
               
            
             
               Now
               if
               the
               said
               three
               persons
               should
               by
               the
               mutuall
               consent
               of
               each
               other
               privately
               change
               their
               names
               ,
               it
               is
               most
               facill
               by
               the
               course
               and
               excellencie
               of
               numbers
               ,
               distinctly
               to
               declare
               each
               ones
               name
               so
               interchanged
               ,
               or
               if
               three
               persons
               in
               private
               ,
               the
               one
               should
               take
               a
               Ring
               ,
               the
               
               other
               a
               piece
               of
               Gold
               ,
               and
               the
               third
               should
               take
               a
               piece
               of
               Silver
               ;
               it
               is
               easie
               to
               finde
               which
               hath
               the
               Gold
               ,
               the
               Silver
               ,
               or
               the
               Ring
               ,
               and
               it
               is
               thus
               done
               .
            
             
               Take
               30
               or
               40
               Counters
               (
               of
               which
               there
               is
               but
               24
               necessary
               )
               that
               so
               you
               may
               conceale
               the
               way
               the
               better
               ,
               and
               lay
               them
               down
               before
               the
               parties
               ,
               and
               as
               they
               sit
               or
               stand
               ,
               give
               to
               the
               first
               1.
               
               Counter
               ,
               which
               signifieth
               a
               ,
               the
               first
               vowell
               ;
               to
               the
               second
               2.
               
               Counters
               ,
               which
               represent
               e
               ,
               the
               second
               vowel
               ;
               and
               to
               the
               third
               3.
               
               Counters
               ,
               which
               stand
               for
               i
               ,
               the
               third
               vowell
               :
               then
               leaving
               the
               other
               Counters
               upon
               the
               Table
               ,
               retire
               apart
               ,
               and
               bid
               him
               which
               hath
               the
               Ring
               ,
               take
               as
               many
               Counters
               as
               you
               gave
               him
               ,
               and
               he
               that
               hath
               the
               Gold
               ,
               for
               every
               one
               that
               you
               gave
               him
               ,
               let
               him
               take
               2
               ,
               and
               he
               that
               hath
               the
               Silver
               for
               every
               one
               that
               you
               gave
               him
               ,
               let
               him
               take
               4.
               this
               being
               done
               ,
               consider
               to
               whom
               you
               gave
               one
               Counter
               ,
               to
               whom
               two
               ,
               and
               to
               whom
               three
               ;
               and
               mark
               what
               number
               of
               Counters
               you
               had
               at
               the
               first
               ,
               for
               there
               are
               necessarily
               but
               24.
               as
               was
               said
               before
               ,
               the
               surpluse
               you
               may
               privately
               reject
               .
               And
               then
               there
               will
               be
               left
               either
               1.2.3.5.6
               or
               7.
               and
               no
               other
               number
               can
               remaine
               ,
               which
               if
               there
               be
               ,
               then
               they
               have
               failed
               in
               taking
               according
               to
               the
               directions
               delivered
               :
               but
               if
               either
               of
               these
               numbers
               do
               remaine
               ,
               the
               resolution
               will
               be
               discovered
               by
               one
               of
               these
               6
               words
               following
               ,
               which
               ought
               to
               be
               had
               in
               memory
               ,
               viz.
               
               
                 
                   
                     Salve
                     ,
                  
                   
                     certa
                     ,
                  
                   
                     anima
                     ,
                  
                   
                     semita
                     ,
                  
                   
                     vita
                     ,
                  
                   
                     quies·
                  
                
                 
                   
                     1.
                     
                  
                   
                     2.
                     
                  
                   
                     3.
                     
                  
                   
                     5.
                     
                  
                   
                     6.
                     
                  
                   
                     7.
                     
                  
                
              
            
             
             
               As
               suppose
               5.
               did
               remaine
               ,
               the
               word
               belonging
               unto
               it
               is
               semita
               ,
               the
               vowels
               in
               the
               first
               two
               syllables
               are
               e
               and
               i
               ,
               vvhich
               shevveth
               according
               to
               the
               former
               directions
               ,
               that
               to
               vvhom
               you
               gave
               2
               Counters
               ,
               he
               hath
               the
               Ring
               (
               seeing
               it
               is
               the
               second
               vovvell
               represented
               by
               tvvo
               as
               before
               )
               and
               to
               vvhom
               you
               gave
               the
               3.
               
               Counters
               ,
               he
               hath
               the
               Gold
               ,
               for
               that
               i
               represents
               the
               third
               vovvel
               ,
               or
               3.
               in
               the
               former
               direction
               ,
               and
               to
               vvhom
               you
               gave
               one
               Counter
               ,
               he
               hath
               the
               Silver
               ,
               and
               so
               of
               the
               rest
               :
               the
               variety
               of
               changes
               ,
               in
               vvhich
               exercise
               ,
               is
               laid
               open
               in
               the
               Table
               follovving
               .
            
             
               
                 
                   
                     rest
                  
                   
                     men
                  
                   
                     hid
                  
                   
                     rest
                  
                   
                     men
                  
                   
                     hid
                  
                
                 
                   
                     1
                  
                   
                     1
                  
                   
                     a
                  
                   
                     5
                  
                   
                     1
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     e
                  
                   
                     2
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     i
                  
                   
                     3
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     1
                  
                   
                     e
                  
                   
                     6
                  
                   
                     1
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     a
                  
                   
                     2
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     i
                  
                   
                     3
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     1
                  
                   
                     a
                  
                   
                     7
                  
                   
                     1
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     i
                  
                   
                     2
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     e
                  
                   
                     3
                  
                   
                      
                  
                
              
            
             
             
               This
               feat
               may
               be
               done
               also
               without
               the
               former
               words
               by
               help
               of
               the
               Circle
               A.
               for
               having
               divided
               the
               Circle
               into
               6
               parts
               ,
               write
               1.
               within
               and
               1.
               vvithout
               ,
               2.
               vvithin
               and
               5.
               vvithout
               ,
               &c.
               the
               first
               1.2.3
               .
               vvhich
               are
               vvithin
               vvith
               the
               numbers
               over
               them
               ,
               belongs
               to
               the
               upper
               semicircle
               ;
               the
               other
               numbers
               both
               vvithin
               and
               vvithout
               ,
               to
               the
               under
               semicircle
               ;
               
               now
               if
               in
               the
               action
               there
               remaineth
               such
               a
               number
               which
               may
               be
               found
               in
               the
               upper
               semicircle
               without
               ,
               then
               that
               which
               is
               opposite
               within
               shews
               the
               first
               ,
               the
               next
               is
               the
               second
               ,
               &c.
               as
               if
               5
               remains
               ,
               it
               shews
               to
               whom
               he
               gave
               2
               ,
               he
               hath
               the
               Ring
               ;
               to
               whom
               you
               gave
               ●
               ,
               he
               hath
               the
               
                 Gold
                 ,
                 &c.
              
               
               But
               if
               the
               remainder
               be
               in
               the
               under
               semicircle
               ,
               that
               which
               is
               opposite
               to
               it
               is
               the
               first
               ;
               the
               next
               backwards
               towards
               the
               right
               hand
               is
               the
               second
               ;
               as
               if
               3
               remains
               ,
               to
               whom
               you
               gave
               1
               he
               hath
               the
               Ring
               ,
               he
               that
               had
               3
               he
               had
               the
               Gold
               ,
               &c.
               
            
          
           
             
               PROBLEM
               IX
               .
               How
               to
               part
               a
               Vessel
               which
               is
               full
               of
               wine
               conteining
               eight
               pints
               into
               two
               equall
               parts
               ,
               by
               two
               other
               vessels
               which
               conteine
               as
               much
               as
               the
               greater
               vessell
               ;
               as
               the
               one
               being
               5
               pints
               ,
               and
               the
               other
               3
               pints
               .
            
             
               LEt
               the
               three
               vessels
               be
               represented
               by
               ABC
               ,
               A
               being
               full
               ,
               the
               other
               two
               being
               empty
               ;
               first
               ,
               poure
               out
               A
               into
               B
               until
               it
               be
               full
               ,
               so
               there
               will
               be
               in
               B
               5
               pints
               ,
               and
               in
               A
               but
               3
               pints
               :
               then
               poure
               out
               of
               B
               into
               C
               untill
               it
               be
               full
               :
               so
               in
               C
               shall
               be
               3
               pints
               ,
               in
               B
               2
               pints
               ,
               and
               in
               A
               3
               pints
               ,
               then
               poure
               the
               wine
               which
               is
               in
               C
               into
               A
               ,
               so
               in
               A
               will
               be
               6
               pints
               ,
               in
               B
               2
               pints
               ,
               and
               in
               C
               nothing
               :
               then
               poure
               out
               the
               wine
               which
               is
               in
               B
               into
               the
               
               pot
               C
               ,
               so
               in
               C
               there
               is
               now
               2
               pints
               ,
               in
               B
               nothing
               ,
               and
               in
               A
               6
               pints
               ,
               .
               Lastly
               ,
               poure
               out
               of
               A
               into
               B
               untill
               it
               be
               full
               ,
               so
               there
               will
               be
               now
               in
               A
               only
               1
               pint
               in
               B
               5
               pints
               ,
               and
               in
               C
               2
               pints
               .
               But
               it
               is
               now
               evident
               ,
               that
               
               if
               from
               B
               you
               poure
               in
               unto
               the
               pot
               C
               untill
               it
               be
               full
               ,
               there
               wil
               remain
               in
               B
               4
               pints
               ,
               and
               if
               that
               which
               is
               in
               C
               ,
               viz.
               3
               pints
               be
               poured
               into
               the
               vessell
               A
               ,
               which
               before
               had
               1
               pint
               ,
               there
               shall
               be
               in
               the
               vessel
               A
               ,
               but
               halfe
               of
               its
               liquor
               that
               was
               in
               it
               at
               the
               first
               ,
               viz.
               4
               pints
               as
               was
               required
               .
               Otherwise
               poure
               out
               of
               A
               into
               C
               untill
               it
               be
               full
               ,
               which
               pour
               into
               B
               ,
               then
               poure
               out
               of
               A
               into
               C
               again
               untill
               it
               be
               full
               ,
               so
               there
               is
               now
               in
               A
               onely
               2
               pints
               ,
               in
               B
               3
               ,
               and
               in
               C
               3
               ,
               then
               pour
               from
               C
               into
               B
               untill
               it
               be
               full
               ,
               so
               in
               C
               there
               is
               now
               but
               1
               pint
               ,
               5
               in
               B
               ,
               and
               2
               in
               A
               :
               poure
               all
               that
               is
               in
               B
               into
               A
               ,
               then
               poure
               the
               wine
               which
               is
               in
               C
               into
               B
               ,
               so
               there
               is
               in
               C
               nothing
               ,
               in
               B
               onely
               1
               pint
               ,
               and
               in
               7
               A
               7
               pints
               :
               Lastly
               ,
               out
               of
               A
               fill
               the
               pot
               C
               ,
               so
               there
               will
               remain
               in
               A
               4
               pints
               ,
               or
               be
               but
               halfe
               full
               :
               then
               if
               the
               liquor
               in
               C
               be
               poured
               into
               B
               ,
               it
               will
               be
               the
               other
               half
               .
               In
               like
               manner
               might
               be
               taken
               the
               half
               of
               a
               vessell
               which
               conteins
               12
               pints
               ,
               by
               having
               but
               the
               measures
               5
               and
               7
               ,
               or
               5
               and
               8.
               
               Now
               such
               others
               might
               be
               proposed
               ,
               but
               we
               omit
               many
               ,
               in
               one
               and
               the
               same
               nature
               .
            
          
           
             
             
               PROBLEM
               .
               X.
               To
               make
               a
               stick
               stand
               upon
               the
               tip
               of
               ones
               finger
               ,
               without
               falling
               .
            
             
               FAsten
               the
               edges
               of
               tvvo
               knives
               or
               such
               like
               of
               equall
               poise
               ,
               at
               the
               end
               of
               the
               stick
               ,
               leaning
               out
               somevvhat
               from
               the
               stick
               ,
               so
               that
               they
               may
               counterpoise
               one
               another
               ;
               the
               stick
               being
               sharp
               at
               the
               end
               ,
               and
               held
               upon
               the
               top
               of
               the
               finger
               ,
               vvill
               there
               rest
               vvithout
               supporting
               :
               if
               it
               fall
               ,
               it
               must
               fall
               together
               ,
               and
               that
               perpendicular
               or
               plumb-wise
               ,
               
               or
               it
               must
               fall
               side-wise
               or
               before
               one
               another
               ;
               in
               the
               first
               manner
               it
               cannot
               :
               for
               the
               Centre
               of
               gravitie
               is
               supported
               by
               the
               top
               of
               the
               finger
               :
               and
               seeing
               that
               each
               part
               by
               the
               knives
               is
               counterpoised
               ,
               it
               cannot
               fall
               sidevvise
               ,
               therefore
               it
               can
               fall
               no
               vvise
               .
            
             
               In
               like
               manner
               may
               great
               pieces
               of
               Timber
               ,
               as
               Joists
               ,
               &c
               be
               supported
               ,
               if
               unto
               one
               of
               the
               ends
               be
               applied
               convenient
               proportionall
               counterpoises
               ,
               yea
               a
               Lance
               or
               Pike
               ,
               may
               stand
               perpendicular
               in
               the
               Aire
               upon
               the
               top
               of
               ones
               finger
               :
               or
               placed
               in
               the
               midst
               of
               a
               Court
               by
               help
               of
               his
               Centre
               of
               gravitie
               .
            
             
               
               
                 EXAMINATION
                 .
              
               
                 THis
                 Proposition
                 seems
                 doubtfull
                 ;
                 for
                 to
                 imagine
                 absolutely
                 ,
                 that
                 a
                 Pike
                 ,
                 or
                 such
                 like
                 ,
                 armed
                 with
                 two
                 Knives
                 ,
                 or
                 other
                 things
                 ,
                 shall
                 stand
                 upright
                 in
                 the
                 Aire
                 ,
                 and
                 so
                 remain
                 without
                 any
                 other
                 support
                 ,
                 seeing
                 that
                 all
                 the
                 parts
                 have
                 an
                 infinite
                 difference
                 of
                 propensity
                 to
                 fall
                 ;
                 and
                 it
                 is
                 without
                 question
                 that
                 a
                 staff
                 so
                 accommodated
                 upon
                 his
                 Centre
                 of
                 gravity
                 ,
                 but
                 that
                 it
                 may
                 incline
                 to
                 some
                 one
                 part
                 without
                 some
                 remedy
                 be
                 applied
                 ,
                 and
                 such
                 as
                 is
                 here
                 specified
                 in
                 the
                 Probleme
                 will
                 not
                 warrant
                 the
                 thing
                 ,
                 nor
                 keep
                 it
                 from
                 falling
                 ;
                 and
                 if
                 more
                 Knives
                 should
                 be
                 placed
                 about
                 it
                 ,
                 it
                 should
                 cause
                 it
                 to
                 fall
                 more
                 swiftly
                 ,
                 forasmuch
                 as
                 the
                 superiour
                 parts
                 (
                 by
                 reason
                 of
                 the
                 Centricall
                 motion
                 )
                 is
                 made
                 more
                 ponderous
                 ,
                 and
                 therefore
                 lesse
                 in
                 rest
                 .
              
               
                 To
                 place
                 therefore
                 this
                 prop
                 really
                 ,
                 let
                 the
                 two
                 Knives
                 ,
                 or
                 that
                 which
                 is
                 for
                 counterpoise
                 ,
                 be
                 longer
                 always
                 then
                 the
                 staffe
                 ,
                 and
                 so
                 it
                 will
                 hang
                 together
                 as
                 one
                 body
                 :
                 and
                 it
                 will
                 appear
                 admirable
                 if
                 you
                 place
                 the
                 Centre
                 of
                 gravity
                 ,
                 neer
                 the
                 side
                 of
                 the
                 top
                 of
                 the
                 finger
                 or
                 point
                 ;
                 for
                 it
                 will
                 then
                 hang
                 Horizontall
                 ,
                 and
                 seem
                 to
                 hang
                 onely
                 by
                 a
                 touch
                 ,
                 yet
                 more
                 strange
                 ,
                 if
                 you
                 turn
                 the
                 point
                 or
                 top
                 of
                 the
                 finger
                 upside
                 down
                 .
              
            
          
           
             
             
               PROBLEM
               XI
               .
               How
               a
               milstone
               or
               other
               Ponderosity
               ,
               may
               be
               supported
               by
               a
               small
               needle
               ,
               without
               breaking
               o●
               any
               wise
               bowing
               the
               same
               .
            
             
               LEt
               a
               needle
               be
               set
               perpendicular
               to
               the
               Horizon
               ,
               and
               the
               center
               of
               gravitie
               of
               the
               stone
               be
               placed
               on
               the
               top
               of
               the
               needle
               :
               it
               is
               evident
               that
               the
               stone
               cannot
               fall
               ,
               forasmuch
               as
               it
               hangs
               in
               aequilibra
               ,
               or
               is
               counterpoysed
               in
               all
               parts
               alike
               ;
               and
               moreover
               it
               cannot
               bow
               the
               needle
               more
               on
               the
               one
               side
               then
               on
               the
               other
               ,
               the
               needle
               will
               not
               therefore
               be
               either
               broken
               or
               bowed
               ;
               if
               otherwise
               then
               the
               parts
               of
               the
               needle
               must
               penetrate
               and
               sinke
               one
               with
               another
               :
               that
               which
               is
               absurd
               and
               impossible
               to
               nature
               ;
               therefore
               it
               shall
               be
               supported
               .
               The
               experiments
               
               which
               are
               made
               upon
               trencher
               plates
               ,
               or
               such
               like
               lesser
               thing
               doth
               make
               it
               most
               credible
               in
               greater
               bodies
               .
            
             
               But
               here
               especially
               is
               to
               be
               noted
               ,
               that
               the
               needle
               ought
               to
               be
               uniforme
               in
               matter
               and
               figure
               ,
               and
               that
               it
               be
               erected
               perpendicular
               to
               the
               Horizon
               ,
               and
               lastly
               ,
               that
               the
               Center
               of
               gravity
               be
               exactly
               found
               .
            
          
           
             
             
               PROBLEM
               XII
               .
               To
               make
               three
               Knives
               hang
               and
               move
               upon
               the
               point
               of
               a
               Needle
               .
            
             
               FIt
               the
               three
               Knives
               in
               form
               of
               a
               Ballance
               ,
               and
               holding
               a
               Needle
               in
               your
               hand
               ,
               and
               place
               the
               back
               of
               that
               ,
               Knife
               
               which
               lyes
               cross-wise
               to
               the
               other
               two
               ,
               upon
               the
               point
               of
               the
               Needle
               :
               as
               the
               figure
               here
               sheweth
               you
               ;
               for
               then
               in
               blowing
               softly
               upon
               them
               ,
               they
               will
               easily
               turne
               and
               move
               upon
               the
               point
               of
               the
               Needle
               with
               ●ou
               falling
               .
            
          
           
             
               PROBLEM
               XIII
               .
               To
               finde
               the
               weight
               of
               Smoak
               ,
               which
               is
               exhaled
               of
               any
               combustible
               body
               whatsoever
               .
            
             
               LEt
               it
               be
               supposed
               that
               a
               great
               heape
               of
               Fagots
               ,
               or
               a
               load
               of
               straw
               weighing
               500
               pound
               should
               be
               fired
               ,
               it
               is
               evident
               that
               this
               grosse
               substance
               will
               be
               all
               inverted
               into
               smoak
               and
               ashes
               :
               now
               it
               seems
               that
               the
               smoak
               weighs
               nothing
               ;
               seeing
               it
               is
               of
               a
               thin
               substance
               now
               dilated
               in
               the
               Aire
               ,
               notwithstanding
               if
               it
               were
               gathered
               and
               reduced
               into
               the
               thickest
               that
               it
               was
               at
               first
               ,
               it
               would
               be
               sensibly
               weighty
               :
               weigh
               therefore
               the
               ashes
               which
               admit
               50
               pound
               ,
               now
               seeing
               that
               
               the
               rest
               of
               the
               matter
               is
               not
               lost
               ,
               but
               is
               exhaled
               into
               smoake
               ,
               it
               must
               necessarily
               be
               ,
               that
               the
               rest
               of
               the
               weight
               (
               to
               wit
               )
               450
               pound
               ,
               must
               be
               the
               weight
               of
               the
               smoak
               required
               .
            
             
               
                 EXAMINATION
                 .
              
               
                 NOw
                 although
                 it
                 be
                 thus
                 delivered
                 ,
                 yet
                 here
                 may
                 be
                 noted
                 ,
                 that
                 a
                 ponderosity
                 in
                 his
                 own
                 medium
                 is
                 not
                 weighty
                 :
                 for
                 things
                 are
                 said
                 to
                 be
                 weighty
                 ,
                 when
                 they
                 are
                 out
                 of
                 their
                 place
                 ,
                 or
                 medium
                 ,
                 and
                 the
                 difference
                 of
                 such
                 gravity
                 ,
                 is
                 according
                 to
                 the
                 motion
                 :
                 the
                 smoak
                 therefore
                 certainly
                 is
                 light
                 being
                 in
                 its
                 true
                 medium
                 (
                 the
                 aire
                 ,
                 )
                 if
                 it
                 should
                 change
                 his
                 medium
                 ,
                 then
                 would
                 we
                 change
                 our
                 discourse
                 .
              
            
          
           
             
               PROBLEM
               XVI
               .
               Many
               things
               being
               disposed
               circular
               ,
               (
               or
               otherwise
               )
               to
               finde
               which
               of
               them
               ,
               any
               one
               thinks
               upon
               ▪
            
             
               SUppose
               that
               having
               ranked
               10
               things
               ,
               as
               ABCDEFGHIK
               ,
               Circular
               (
               as
               the
               figure
               sheweth
               )
               and
               that
               one
               had
               touched
               or
               thought
               upon
               G
               ,
               which
               is
               the
               7
               :
               ask
               the
               party
               at
               what
               
               letter
               he
               would
               begin
               to
               account
               (
               for
               account
               he
               must
               ,
               otherwise
               it
               cannot
               be
               done
               )
               which
               suppose
               ,
               at
               E
               which
               is
               the
               5
               place
               ,
               then
               add
               secretly
               to
               this
               5
               ,
               10
               (
               which
               is
               the
               number
               of
               the
               Circle
               )
               and
               it
               makes
               15
               ,
               bid
               him
               account
               15
               backward
               from
               E
               ,
               beginning
               his
               account
               with
               that
               number
               hee
               thought
               upon
               ,
               so
               at
               E
               he
               shal
               
               account
               to
               himself
               7
               ,
               at
               D
               account
               8
               ,
               at
               C
               account
               9
               ,
               &c.
               
               So
               the
               account
               of
               15
               wil
               exactly
               fall
               upon
               G
               ,
               the
               thing
               or
               number
               thought
               upon
               :
               and
               so
               of
               others
               :
               but
               to
               conceal
               it
               the
               more
               ,
               you
               may
               will
               the
               party
               from
               E
               to
               account
               25
               ,
               35
               ,
               &c.
               and
               it
               will
               be
               the
               same
               .
            
             
               There
               are
               some
               that
               use
               this
               play
               at
               Cards
               ,
               turned
               upside
               downe
               ,
               as
               the
               ten
               simple
               Cards
               ,
               with
               the
               King
               and
               Queen
               ,
               the
               King
               standing
               for
               12
               ,
               and
               the
               Queene
               for
               11
               ,
               and
               so
               knowing
               the
               situation
               of
               the
               Cards
               :
               and
               thinking
               a
               certain
               houre
               of
               the
               day
               :
               cause
               the
               party
               to
               account
               from
               what
               Card
               he
               pleaseth
               :
               with
               this
               Proviso
               ,
               that
               when
               you
               see
               where
               he
               intends
               to
               account
               ,
               set
               12
               to
               that
               number
               ,
               so
               in
               counting
               as
               before
               ,
               the
               end
               of
               the
               account
               shall
               fall
               upon
               the
               Card
               :
               which
               shall
               denote
               or
               shew
               the
               houre
               thought
               upon
               ,
               which
               being
               turned
               up
               will
               give
               grace
               to
               the
               action
               ,
               and
               wonder
               to
               those
               that
               are
               ignorant
               in
               the
               cause
               .
            
          
           
             
             
               PROBLEM
               XV.
               How
               to
               make
               a
               Door
               or
               Gate
               ,
               which
               shall
               open
               on
               both
               sides
               .
            
             
               ALL
               the
               skill
               and
               subtilty
               of
               this
               ,
               rests
               in
               the
               artificiall
               disposer
               of
               foure
               plates
               of
               Iron
               ,
               two
               at
               the
               higher
               end
               ,
               and
               two
               at
               the
               lower
               end
               of
               the
               Gate
               :
               so
               that
               one
               side
               may
               move
               upon
               the
               hooks
               or
               hinges
               of
               the
               Posts
               ,
               and
               by
               the
               other
               end
               may
               be
               made
               fast
               to
               the
               Gate
               ,
               and
               so
               moving
               upon
               these
               hinges
               ,
               the
               Gate
               will
               open
               upon
               one
               side
               with
               the
               aforesaid
               plates
               ,
               or
               hooks
               of
               Iron
               :
               and
               by
               help
               of
               the
               other
               two
               plates
               ,
               will
               open
               upon
               the
               other
               side
               .
            
          
           
             
               PROBLEM
               XVI
               .
               To
               shew
               how
               a
               Ponderosity
               ,
               or
               heavy
               thing
               ,
               may
               be
               supported
               upon
               the
               end
               of
               a
               staffe
               (
               or
               such
               like
               )
               upon
               a
               Table
               ,
               and
               nothing
               holding
               or
               touching
               it
               .
            
             
               TAke
               a
               pale
               which
               hath
               a
               handle
               ,
               and
               fill
               it
               full
               of
               water
               (
               or
               at
               pleasure
               :
               )
               then
               take
               a
               staffe
               or
               stick
               which
               may
               not
               rowle
               upon
               the
               Table
               as
               EC
               ,
               and
               place
               the
               handle
               of
               the
               Pale
               upon
               the
               staffe
               ;
               then
               place
               another
               staffe
               ,
               or
               stick
               ,
               under
               the
               staffe
               CE
               ,
               which
               may
               reach
               from
               the
               bottom
               of
               the
               Pale
               unto
               the
               former
               staffe
               CE
               ,
               perpendicular
               wise
               :
               which
               suppose
               FG
               ,
               then
               shall
               the
               Pale
               of
               water
               hang
               without
               
               falling
               ,
               for
               if
               it
               fall
               it
               
               must
               fall
               perpendicularly
               ,
               or
               plumbe
               wise
               :
               and
               that
               cannot
               be
               seeing
               the
               staffe
               CE
               supports
               it
               ,
               it
               being
               parallel
               to
               the
               Horizon
               and
               susteined
               by
               the
               Table
               ,
               and
               it
               is
               a
               thing
               admirable
               that
               if
               the
               staffe
               CE
               were
               alone
               from
               the
               table
               ,
               and
               that
               end
               of
               the
               staffe
               which
               is
               upon
               the
               Table
               were
               greater
               and
               heavier
               than
               the
               other
               :
               it
               would
               be
               constrained
               to
               hang
               in
               that
               nature
               .
            
             
               
                 EXAMINATION
                 .
              
               
                 NOw
                 without
                 some
                 experience
                 of
                 this
                 Probleme
                 ,
                 a
                 man
                 would
                 acknowledge
                 either
                 a
                 possibility
                 or
                 impossibity
                 ;
                 therefore
                 it
                 is
                 that
                 very
                 touchstone
                 of
                 knowledge
                 in
                 any
                 thing
                 ,
                 to
                 discourse
                 first
                 if
                 a
                 thing
                 be
                 possible
                 in
                 nature
                 ,
                 and
                 then
                 if
                 it
                 can
                 be
                 brought
                 to
                 experience
                 and
                 under
                 sence
                 without
                 seeing
                 it
                 done
                 .
                 At
                 the
                 first
                 ,
                 this
                 proposition
                 seems
                 to
                 be
                 absurd
                 ,
                 and
                 impossible
                 .
                 Notwithstanding
                 ,
                 being
                 supported
                 
                 with
                 two
                 sticks
                 ,
                 as
                 the
                 figure
                 declareth
                 ,
                 it
                 is
                 made
                 facile
                 :
                 for
                 the
                 Horizontall
                 line
                 to
                 the
                 edge
                 of
                 the
                 Table
                 ,
                 is
                 the
                 Centre
                 of
                 motion
                 ;
                 and
                 passeth
                 by
                 the
                 Centre
                 of
                 gravity
                 ,
                 which
                 necessarily
                 supporteth
                 it
                 .
              
            
          
           
             
               PROBLEM
               XVII
               .
               Of
               a
               deceitfull
               Bowle
               to
               play
               withall
               .
            
             
               MAke
               a
               hole
               in
               one
               side
               of
               the
               Bowle
               ,
               and
               cast
               molten
               Lead
               therein
               ,
               and
               then
               make
               up
               the
               hole
               close
               ,
               that
               the
               knavery
               or
               deceit
               be
               not
               perceived
               :
               you
               will
               have
               pleasure
               to
               see
               ,
               that
               notwithstanding
               the
               Bowle
               is
               cast
               directly
               to
               the
               play
               ,
               how
               it
               wil
               turn
               away
               side-wise
               :
               for
               that
               on
               that
               part
               of
               the
               Bowle
               which
               is
               heavier
               upon
               the
               one
               side
               then
               on
               the
               other
               ,
               it
               never
               will
               go
               truly
               right
               ,
               if
               artificially
               it
               be
               not
               corrected
               ;
               which
               will
               hazard
               the
               game
               to
               those
               which
               know
               it
               not
               :
               but
               if
               it
               be
               known
               that
               the
               leady
               side
               in
               rolling
               be
               always
               under
               or
               above
               ,
               it
               may
               go
               indifferently
               right
               ;
               if
               otherwise
               ,
               the
               weight
               will
               carry
               it
               always
               side-wise
               .
            
          
           
             
             
               PROBLEM
               .
               XVIII
               .
               To
               part
               an
               Apple
               into
               2.4
               .
               or
               8.
               like
               parts
               ,
               without
               breaking
               the
               Rinde
               .
            
             
               PAsse
               a
               needle
               and
               threed
               under
               the
               kinde
               of
               the
               Apple
               ,
               and
               then
               round
               it
               with
               divers
               turnings
               ,
               untill
               you
               come
               to
               the
               place
               where
               you
               began
               :
               then
               draw
               out
               the
               threed
               gently
               ,
               and
               part
               the
               Apple
               into
               as
               many
               parts
               as
               you
               think
               convenient
               :
               and
               so
               the
               parts
               may
               be
               taken
               out
               between
               the
               parting
               of
               the
               Rind
               ,
               and
               the
               rind
               remaining
               alwayes
               whole
               .
            
          
           
             
               PROBLEM
               XIX
               .
               To
               finde
               a
               number
               thought
               upon
               without
               asking
               of
               any
               question
               ,
               certaine
               operations
               being
               done
               .
            
             
               BId
               him
               adde
               to
               the
               number
               thought
               (
               as
               admit
               15
               )
               halfe
               of
               it
               ,
               if
               it
               may
               be
               ,
               if
               not
               the
               greatest
               halfe
               that
               exceeds
               the
               other
               but
               by
               an
               unite
               ,
               which
               is
               8
               ;
               and
               it
               makes
               23.
               
               Secondly
               ,
               unto
               this
               23.
               adde
               the
               halfe
               of
               it
               if
               it
               may
               be
               ,
               if
               not
               ,
               the
               greatest
               halfe
               ,
               viz.
               12.
               makes
               35.
               in
               the
               meane
               time
               ,
               note
               that
               if
               the
               number
               thought
               upon
               cannot
               be
               halfed
               at
               the
               first
               time
               ,
               as
               here
               it
               cannot
               ,
               then
               for
               it
               keep
               3
               in
               the
               memory
               ,
               if
               at
               the
               second
               time
               it
               will
               not
               be
               
               equally
               halfed
               ,
               reserve
               2
               in
               memory
               ,
               but
               if
               at
               both
               times
               it
               could
               not
               be
               equally
               halved
               ,
               then
               may
               you
               together
               reserve
               five
               in
               memory
               :
               this
               done
               ,
               cause
               him
               from
               the
               last
               summe
               ,
               viz.
               35.
               to
               subtract
               the
               double
               of
               the
               number
               thought
               ,
               viz.
               30.
               rest
               5.
               will
               him
               to
               take
               the
               halfe
               of
               that
               if
               he
               can
               ,
               if
               not
               ,
               reject
               1.
               and
               then
               take
               the
               halfe
               of
               the
               rest
               ,
               which
               keep
               in
               your
               memory
               :
               then
               will
               him
               to
               take
               the
               halfe
               againe
               if
               he
               can
               ,
               if
               not
               ,
               take
               one
               from
               it
               ,
               which
               reserve
               in
               your
               memory
               ,
               and
               so
               perpetually
               halveing
               untill
               1.
               remaine
               :
               for
               then
               mark
               how
               many
               halfes
               there
               were
               taken
               ,
               for
               the
               first
               halfe
               account
               2
               ,
               for
               the
               second
               4
               ,
               for
               the
               third
               8
               ,
               &c.
               and
               adde
               unto
               those
               numbers
               the
               one
               's
               which
               you
               reserved
               in
               memory
               ,
               so
               there
               being
               5
               remaining
               in
               this
               proposition
               ,
               there
               were
               2
               halfings
               :
               for
               which
               last
               !
               account
               4
               ,
               but
               because
               it
               could
               not
               exactly
               be
               halved
               without
               rejecting
               of
               1.
               
               I
               adde
               the
               1
               therefore
               to
               this
               4
               ,
               makes
               5
               ,
               which
               halfe
               or
               summe
               alwayes
               multiplied
               by
               4
               ,
               makes
               20.
               from
               which
               subtract
               the
               first
               3
               and
               2
               ,
               because
               the
               halfe
               could
               not
               be
               formerly
               added
               ,
               leaves
               15
               ,
               the
               number
               thought
               upon
               .
            
             
             
               
                 Other
                 Examples
              
               .
            
             
               
                 The
                 number
                 thought
                 upon
                 .
              
               
                 The
                 number
                 thought
              
               
                 12
              
               
                 The
                 halfe
                 of
                 it
              
               
                 6
              
               
                 The
                 summe
              
               
                 18
              
               
                 The
                 halfe
                 of
                 it
              
               
                 9
              
               
                 The
                 summe
                 of
                 it
              
               
                 27
              
               
                 The
                 double
                 of
                 the
                 number
                 ,
              
               
                 24
              
               
                 Which
                 taken
                 away
                 ,
                 rests
              
               
                 3
              
               
                 The
                 halfe
                 of
                 it
              
               
                 1
              
               
                 For
                 which
                 account
              
               
                 2
              
               
                 and
                 1
                 put
                 to
                 it
                 because
                 the
              
               
                 3
              
               
                 could
                 not
                 be
                 halfed
                 ,
                 makes
              
               
                 3
              
               
                 this
                 multiplied
                 by
                 4
                 makes
              
               
                 12
              
               
                 The
                 number
                 thought
              
               
                 79
              
               
                 The
                 greatest
                 halfe
              
               
                 40
                 3
              
               
                 The
                 summe
              
               
                 119
              
               
                 The
                 greatest
                 halfe
                 of
                 which
                 is
              
               
                 60
                 2
              
               
                 The
                 summe
                 of
                 it
                 is
              
               
                 179
              
               
                 The
                 double
                 of
                 79
                 is
              
               
                 158
              
               
                 Which
                 taken
                 from
                 it
                 ,
                 rests
              
               
                 21
              
               
                 The
                 lesser
                 half
                 10.
                 which
                 halve
                 :
              
               
                  
              
               
                 The
                 halfe
                 of
                 this
                 is
                 5
                 which
                 makes
              
               
                  
              
               
                 The
                 half
                 of
                 this
                 is
                 2
                 which
                 is
                 10
              
               
                  
              
               
                 The
                 half
                 of
                 this
                 is
                 1
                 ,
                 with
                 10
                 and
                 11
                 is
                 21.
                 
              
               
                  
              
               
                 this
                 21
                 which
                 is
                 the
                 double
                 of
                 the
                 last
                 halfe
                 with
                 the
                 remainder
                 being
                 multiplied
                 by
                 4.
                 makes
                 84
                 ,
                 from
                 which
                 take
                 the
                 aforesaid
                 3
                 and
                 2
                 ,
                 ●●st
                 79
                 ,
                 the
                 number
                 thought
                 upon
                 .
              
               
                  
              
            
          
           
             
               PROBLEM
               .
               XX.
               How
               to
               make
               an
               uniforme
               ,
               &
               an
               inflexible
               body
               ,
               to
               passe
               through
               two
               small
               holes
               of
               divers
               formes
               ,
               as
               one
               being
               circular
               ,
               and
               the
               other
               square
               ,
               Quadrangular
               ,
               and
               Triangular-wise
               ,
               yet
               so
               that
               the
               holes
               shall
               be
               exactly
               filled
               .
            
             
               THis
               Probleme
               is
               extracted
               from
               Geometricall
               observations
               ,
               and
               seemes
               at
               the
               first
               
               somewhat
               obscure
               ,
               yet
               that
               which
               may
               be
               extracted
               in
               this
               nature
               ,
               will
               appeare
               more
               difficult
               and
               admirable
               .
               Now
               in
               all
               Geometricall
               practises
               ,
               the
               lesser
               or
               easier
               Problemes
               do
               alwayes
               make
               way
               to
               facilitate
               the
               greater
               :
               and
               the
               aforesaid
               Probleme
               is
               thus
               resolved
               .
               Take
               a
               Cone
               or
               round
               Pyramide
               ,
               and
               make
               a
               Circular
               hole
               in
               some
               board
               ,
               or
               other
               hard
               material
               ,
               which
               may
               be
               equall
               to
               the
               bases
               of
               the
               Cone
               ,
               and
               also
               a
               Triangular
               hole
               ,
               one
               of
               whose
               sides
               may
               be
               equall
               to
               the
               Diameter
               of
               the
               circle
               ,
               and
               the
               other
               two
               sides
               equall
               to
               the
               length
               of
               the
               Cone
               :
               Now
               it
               is
               most
               
               evident
               ,
               that
               this
               Conicall
               or
               Pyramidall
               body
               ,
               will
               fill
               up
               the
               Circular
               hole
               ,
               and
               being
               placed
               side-wise
               will
               fill
               up
               the
               Triangular
               hole
               .
               Moreover
               ,
               if
               you
               cause
               a
               body
               to
               be
               turned
               ,
               which
               may
               be
               like
               to
               two
               Pyramides
               conjoyned
               ,
               then
               if
               a
               Circular
               hole
               be
               made
               ,
               whose
               Diameter
               is
               equal
               to
               the
               Diameter
               of
               the
               Cones
               conjoyned
               ,
               and
               a
               Quadrangular
               hole
               ,
               whose
               sloping
               sides
               be
               equall
               to
               the
               length
               of
               each
               side
               of
               the
               Pyramide
               ,
               and
               the
               breadth
               of
               the
               hol
               equal
               to
               the
               Diameter
               of
               the
               Circle
               ,
               this
               conjoyned
               Pyramide
               shall
               exactly
               fill
               both
               the
               Circular
               hole
               ,
               and
               also
               the
               Quadrangle
               hole
               .
            
          
           
             
             
               PROBLEM
               .
               XXI
               .
               How
               with
               one
               uniforme
               body
               or
               such
               like
               to
               fill
               three
               severall
               holes
               :
               of
               which
               the
               one
               is
               round
               ,
               the
               other
               a
               just
               square
               ,
               and
               the
               third
               an
               ovall
               forme
               ?
            
             
               THis
               Proposition
               seemes
               more
               subtill
               then
               the
               former
               ,
               yet
               it
               may
               be
               practised
               two
               wayes
               :
               for
               the
               first
               ,
               take
               a
               Cylindricall
               body
               as
               great
               or
               little
               as
               you
               please
               :
               Now
               it
               is
               evident
               that
               it
               will
               fill
               a
               Circular
               hole
               ,
               which
               is
               made
               equall
               to
               the
               basis
               of
               it
               ,
               if
               it
               be
               placed
               downe
               right
               ,
               and
               will
               also
               fill
               a
               long
               square
               ;
               whose
               sides
               are
               equall
               unto
               the
               Diameter
               and
               length
               of
               the
               Cylinder
               ,
               and
               
               acording
               to
               
                 Pergeus
                 ,
                 Archimedes
                 ,
                 &c.
              
               in
               their
               Cylindricall
               demonstrations
               ,
               a
               true
               Ovall
               is
               made
               when
               a
               Cylinder
               is
               cut
               slopewise
               ,
               therefore
               if
               the
               oval
               have
               breadth
               equall
               unto
               the
               Diameter
               of
               the
               Basis
               of
               the
               Cylinder
               ,
               &
               any
               length
               whatsoever
               :
               the
               Cylinder
               being
               put
               into
               his
               owne
               Ovall
               hole
               shall
               also
               exactly
               fill
               it
               .
            
             
               The
               second
               way
               is
               thus
               ,
               make
               a
               Circular
               hole
               in
               some
               board
               ,
               &
               also
               a
               square
               hole
               ,
               the
               side
               of
               which
               Square
               may
               be
               equall
               to
               the
               Diameter
               
               of
               the
               Circle
               :
               and
               lastly
               ,
               make
               a
               hole
               Oval-wise
               ,
               whose
               breadth
               may
               be
               equal
               unto
               the
               diagonall
               of
               the
               Square
               ;
               then
               let
               a
               Cylindricall
               body
               be
               made
               ,
               whose
               Basis
               may
               be
               equall
               unto
               the
               Circle
               ,
               and
               the
               length
               equall
               also
               to
               the
               same
               :
               Now
               being
               placed
               downe
               right
               shall
               fall
               in
               the
               Circle
               ,
               and
               flat-wise
               will
               fit
               the
               Square
               hole
               ,
               and
               being
               placed
               sloping-wise
               will
               fill
               the
               Ovall
               .
            
             
               
                 EXAMINATION
                 .
              
               
                 YOu
                 may
                 note
                 upon
                 the
                 last
                 two
                 Problemes
                 farther
                 ,
                 that
                 if
                 a
                 Cone
                 be
                 cut
                 Ecliptick-wise
                 ,
                 it
                 may
                 passe
                 through
                 an
                 Issoc●●●
                 Triangle
                 through
                 many
                 Scalen
                 Triangles
                 ,
                 and
                 through
                 an
                 Ellipsis
                 ;
                 and
                 if
                 there
                 be
                 a
                 Cone
                 cut
                 scalen-wise
                 ,
                 it
                 will
                 passe
                 through
                 all
                 the
                 former
                 ,
                 only
                 for
                 the
                 Ellipsis
                 place
                 a
                 Circle
                 :
                 and
                 further
                 ,
                 if
                 a
                 solid
                 colume
                 be
                 cut
                 Ecliptick-wise
                 it
                 may
                 fill
                 a
                 Circle
                 ,
                 a
                 Square
                 ,
                 divers
                 Parallelogrammes
                 ,
                 and
                 divers
                 Ellipses
                 ,
                 which
                 have
                 different
                 Diameters
                 .
              
            
          
           
             
             
               PROBLEM
               XXII
               .
               To
               finde
               a
               number
               thought
               upon
               ●fter
               another
               manner
               ,
               then
               what
               is
               formerly
               delivered
            
             
               BId
               him
               that
               he
               multiply
               the
               number
               thought
               upon
               ,
               by
               what
               number
               he
               pleaseth
               ,
               then
               bid
               him
               divide
               that
               product
               by
               any
               other
               number
               ,
               and
               then
               multiply
               that
               Quotient
               by
               some
               other
               number
               ;
               and
               that
               product
               againe
               divide
               by
               some
               other
               ,
               and
               so
               as
               often
               as
               he
               will
               :
               and
               here
               note
               ,
               that
               he
               declare
               or
               tell
               you
               by
               what
               number
               he
               did
               multiply
               &
               divide
               Now
               in
               the
               same
               time
               take
               a
               number
               at
               pleasure
               ,
               and
               secretly
               multiply
               and
               divide
               as
               often
               as
               he
               did
               :
               then
               bid
               him
               divide
               the
               last
               number
               by
               that
               which
               he
               thought
               upon
               .
               In
               like
               manner
               do
               yours
               privately
               ,
               then
               will
               the
               Quotient
               of
               your
               divisor
               be
               the
               same
               with
               his
               ,
               a
               thing
               which
               seemes
               admirable
               to
               those
               which
               are
               ignorant
               of
               the
               cause
               .
               Now
               to
               have
               the
               number
               thought
               upon
               without
               seeming
               to
               know
               the
               last
               Quotient
               ,
               bid
               him
               adde
               the
               number
               thought
               upon
               to
               it
               ,
               and
               aske
               him
               how
               much
               it
               makes
               :
               then
               subtract
               your
               Quotient
               from
               it
               ,
               there
               will
               remaine
               the
               number
               thought
               upon
               For
               example
               ,
               suppose
               the
               number
               thought
               upon
               were
               5
               ,
               multiply
               it
               by
               4
               makes
               20.
               this
               divided
               by
               2
               ,
               the
               Quotient
               makes
               10
               ,
               which
               multiplyed
               by
               6
               ,
               makes
               60
               ,
               and
               divided
               by
               4
               ,
               makes
               1●
               .
               in
               the
               same
               time
               admit
               you
               think
               upon
               4
               ,
               which
               multiplied
               by
               4
               ,
               makes
               16
               ,
               this
               divided
               by
               2
               ,
               makes
               8
               ,
               which
               
               multiplied
               by
               6
               makes
               48
               ,
               and
               divided
               by
               4
               makes
               1●
               ;
               then
               divide
               1●
               by
               the
               number
               thought
               ,
               which
               was
               5
               ,
               the
               Quotient
               is
               ●
               ;
               divide
               also
               12
               by
               the
               number
               you
               took
               ,
               viz.
               4
               ,
               the
               Quotient
               is
               also
               3.
               as
               was
               declared
               ;
               therefore
               if
               the
               Quo●ient
               ●
               be
               added
               unto
               the
               number
               thought
               ,
               viz.
               ●
               ,
               it
               makes
               8
               ,
               which
               being
               known
               ,
               the
               number
               thought
               upon
               is
               also
               knowne
               .
            
          
           
             
               PROBLEM
               XXIII
               .
               To
               finde
               out
               many
               numbers
               that
               sundry
               persons
               ,
               or
               one
               man
               hath
               thought
               upon
               .
            
             
               IF
               the
               multitude
               of
               numbers
               thought
               upon
               be
               odde
               ,
               as
               three
               numbers
               ,
               five
               numbers
               ,
               seven
               ,
               &c.
               as
               for
               example
               ,
               let
               5
               numbers
               thought
               upon
               be
               these
               ●
               2
               ,
               3
               ,
               4
               ,
               5
               ,
               6.
               bid
               him
               declare
               the
               sum
               of
               the
               first
               and
               second
               ,
               which
               will
               be
               5
               ,
               the
               second
               and
               third
               ,
               which
               makes
               7
               ,
               the
               third
               and
               fourth
               ,
               which
               makes
               9
               ,
               the
               fourth
               and
               fifth
               ,
               vvhich
               makes
               11
               ,
               and
               so
               alvvayes
               adding
               the
               tvvo
               next
               together
               ,
               aske
               him
               hovv
               much
               the
               first
               and
               last
               makes
               together
               ,
               vvhich
               is
               8.
               then
               take
               these
               summes
               ,
               and
               place
               them
               in
               order
               ,
               and
               adde
               all
               these
               together
               ,
               vvhich
               vvere
               in
               the
               odde
               places
               :
               that
               is
               the
               first
               ,
               third
               ,
               and
               fifth
               ,
               viz.
               5
               ,
               9
               ,
               ●
               ,
               makes
               22.
               
               In
               like
               manner
               adde
               all
               these
               numbets
               together
               ,
               vvhich
               are
               in
               the
               even
               places
               ,
               that
               is
               in
               the
               second
               and
               fourth
               places
               ,
               viz.
               7
               and
               1●
               makes
               18
               ,
               substract
               this
               from
               the
               former
               22
               ,
               then
               there
               vvill
               remaine
               the
               double
               of
               the
               
               first
               number
               thought
               upon
               ,
               viz.
               4.
               which
               known
               ,
               the
               rest
               is
               easily
               known
               :
               seeing
               you
               know
               the
               summe
               of
               the
               first
               and
               second
               ;
               but
               if
               the
               multitude
               of
               numbers
               be
               even
               as
               these
               six
               numbers
               ,
               viz.
               2
               ,
               ●
               ,
               4
               ,
               5
               ,
               6
               ,
               7
               ,
               cause
               the
               partie
               to
               declare
               the
               summe
               of
               each
               two
               ,
               by
               antecedent
               and
               consequent
               ,
               and
               also
               the
               summe
               of
               the
               second
               and
               last
               ,
               which
               will
               be
               5
               ,
               7
               ,
               9
               ,
               11
               ,
               13
               ,
               10
               ,
               then
               adde
               the
               odde
               places
               together
               ,
               except
               the
               first
               ,
               that
               is
               9
               ,
               and
               13
               ,
               makes
               22
               ,
               adde
               also
               the
               even
               places
               together
               ,
               that
               is
               7
               ,
               11
               ,
               10
               ,
               which
               makes
               28
               ,
               substract
               the
               one
               from
               the
               other
               ,
               there
               shall
               remaine
               the
               double
               of
               the
               second
               number
               thought
               upon
               ,
               which
               known
               all
               the
               rest
               are
               knowne
               .
            
          
           
             
               PROBLEM
               XXIV
               .
               How
               is
               it
               that
               a
               man
               in
               one
               and
               the
               same
               time
               ,
               may
               have
               his
               head
               upward
               ,
               and
               his
               feet
               upward
               ,
               being
               in
               one
               and
               the
               same
               place
               ?
            
             
               THe
               answer
               is
               very
               facill
               ,
               for
               to
               be
               so
               he
               must
               be
               supposed
               to
               be
               in
               the
               centre
               of
               the
               earth
               :
               for
               as
               the
               heaven
               is
               above
               on
               every
               side
               ,
               
                 Coelum
                 undique
                 sursum
              
               ,
               all
               that
               which
               looks
               to
               the
               heavens
               being
               distant
               from
               the
               centre
               is
               upward
               ;
               and
               it
               is
               in
               this
               sense
               that
               Ma●●olyeus
               in
               his
               Cosmographie
               ,
               &
               first
               dialogue
               ,
               reported
               of
               one
               that
               thought
               he
               was
               led
               by
               one
               of
               the
               Muses
               to
               hell
               ,
               where
               he
               saw
               Lucifer
               sitting
               
               in
               the
               middle
               of
               the
               World
               ,
               and
               in
               the
               Centre
               of
               the
               earth
               ,
               as
               in
               a
               Throne
               :
               having
               his
               head
               and
               feet
               upward
               .
            
          
           
             
               PROBLEM
               .
               XXV
               .
               Of
               a
               Ladder
               by
               which
               two
               men
               ascending
               at
               one
               time
               ;
               the
               more
               they
               ascend
               ,
               the
               more
               they
               shall
               be
               asunder
               ,
               notwithstanding
               one
               being
               as
               high
               as
               another
            
             
               THis
               is
               most
               evident
               ,
               that
               if
               there
               were
               a
               Ladder
               halfe
               on
               this
               side
               of
               the
               Centre
               of
               the
               earth
               ,
               and
               the
               other
               halfe
               on
               the
               other
               side
               :
               and
               that
               two
               at
               the
               Centre
               of
               the
               World
               at
               one
               instant
               being
               to
               ascend
               ,
               the
               one
               towards
               us
               ,
               and
               the
               other
               towards
               our
               Antipodes
               ,
               they
               should
               in
               ascending
               go
               farther
               and
               farther
               ,
               one
               from
               another
               ;
               notwithstanding
               both
               of
               them
               being
               of
               like
               height
               .
            
          
           
             
               PROBLEM
               .
               XXVI
               .
               How
               it
               is
               that
               a
               man
               having
               but
               a
               Rod
               or
               Pole
               of
               Land
               ,
               doth
               bragge
               that
               he
               may
               in
               a
               right
               line
               passe
               from
               place
               to
               place
               above
               3000
               miles
               .
            
             
               THe
               opening
               of
               this
               is
               easie
               ,
               forasmuch
               as
               he
               that
               possesseth
               a
               Rod
               of
               ground
               possesseth
               
               not
               only
               the
               exterior
               surface
               of
               the
               earth
               ,
               but
               is
               master
               also
               of
               that
               which
               extends
               even
               to
               the
               Centre
               of
               the
               earth
               ,
               and
               in
               this
               wise
               all
               heritages
               &
               possessions
               are
               as
               so
               many
               Pyramides
               ,
               whose
               summets
               or
               points
               meet
               in
               the
               centre
               of
               the
               earth
               ,
               and
               the
               basis
               of
               them
               are
               nothing
               else
               but
               each
               mans
               possession
               ,
               field
               ,
               or
               visible
               quantity
               ;
               and
               therefore
               if
               there
               were
               made
               or
               imagined
               so
               to
               be
               made
               ,
               a
               descent
               to
               go
               to
               the
               bottome
               of
               the
               heritage
               ,
               which
               would
               reach
               to
               the
               centre
               of
               the
               earth
               ;
               it
               would
               be
               above
               3000
               miles
               in
               a
               right
               line
               as
               before
               .
            
          
           
             
               PROBLEM
               .
               XXVII
               .
               How
               it
               is
               ,
               that
               a
               man
               standing
               upright
               ,
               and
               looking
               which
               way
               he
               will
               ,
               he
               looketh
               either
               true
               North
               or
               true
               South
               .
            
             
               THis
               happeneth
               that
               if
               the
               partie
               be
               under
               either
               of
               the
               Poles
               ,
               for
               if
               he
               be
               under
               the
               North-pole
               ,
               then
               looking
               any
               way
               he
               looketh
               South
               ,
               because
               all
               the
               Meridians
               concurre
               in
               the
               Poles
               of
               the
               world
               ,
               and
               if
               he
               be
               under
               the
               South-pole
               ,
               he
               looks
               directly
               North
               by
               the
               same
               reason
               .
            
          
           
             
             
               PROBLEM
               XXVIII
               .
               To
               tell
               any
               one
               what
               number
               remaines
               after
               certaine
               operations
               being
               ended
               ,
               without
               asking
               any
               question
               .
            
             
               BId
               him
               to
               think
               upon
               a
               number
               ,
               and
               will
               him
               to
               multiply
               it
               by
               what
               number
               you
               think
               convenient
               :
               and
               to
               the
               pro●●ct
               bid
               him
               adde
               what
               number
               you
               please
               ,
               or
               〈◊〉
               that
               secretly
               you
               consider
               ,
               that
               it
               ma●
               be
               divided
               by
               that
               which
               multiplied
               ,
               and
               〈…〉
               divide
               the
               sum
               by
               the
               number
               which
               he
               〈…〉
               by
               ,
               and
               substract
               from
               this
               Quotient
               the
               number
               thought
               upon
               :
               In
               the
               same
               time
               divide
               apart
               the
               number
               which
               was
               add●d
               by
               that
               which
               multiplied
               ,
               so
               then
               your
               Quotient
               shall
               be
               equall
               to
               his
               remainder
               ,
               wherefore
               without
               asking
               him
               any
               thing
               ,
               you
               shall
               tell
               him
               what
               did
               remaine
               ,
               which
               will
               seem
               strange
               to
               him
               that
               knoweth
               not
               the
               cause
               :
               for
               example
               ,
               suppose
               he
               thought
               7
               ,
               which
               multiplied
               by
               5
               makes
               35
               ,
               to
               which
               adde
               10
               ,
               makes
               45
               ,
               which
               divided
               by
               5
               ,
               yields
               9
               ,
               from
               which
               if
               you
               take
               away
               one
               the
               number
               thought
               ,
               (
               because
               the
               Multiplier
               divided
               by
               the
               Divisor
               gives
               the
               Quotient
               1
               ,
               )
               the
               rest
               will
               be
               two
               ,
               which
               will
               be
               also
               proved
               ,
               if
               10
               the
               number
               which
               was
               added
               ,
               were
               divided
               by
               5
               ,
               viz.
               2.
               
            
          
           
             
             
               PROBLEM
               XXIX
               .
               Of
               the
               play
               with
               two
               severall
               things
               .
            
             
               IT
               is
               a
               pleasure
               to
               see
               and
               consider
               how
               the
               science
               of
               numbers
               doth
               furnish
               us
               ,
               not
               only
               〈…〉
               recreate
               the
               spirits
               ,
               but
               also
               〈…〉
               knowledge
               of
               admirable
               things
               ,
               〈…〉
               measure
               be
               shewen
               in
               this
               〈…〉
               the
               meane
               time
               to
               produce
               alwayes
               some
               of
               them
               :
               suppose
               that
               a
               man
               hold
               divers
               things
               in
               his
               hand
               ,
               as
               Gold
               and
               ●ilver
               ▪
               and
               in
               one
               hand
               he
               held
               the
               Gold
               ,
               and
               in
               the
               other
               hand
               he
               held
               the
               Silver
               :
               to
               know
               subtilly
               ,
               and
               by
               way
               of
               divination
               ,
               or
               artificially
               in
               which
               hand
               the
               Gold
               or
               Silver
               is
               ;
               attribu●e
               t●
               the
               Gold
               ,
               or
               suppose
               it
               have
               a
               certaine
               price
               ,
               and
               so
               likewise
               attribute
               to
               the
               Silver
               another
               price
               ,
               conditionally
               that
               the
               one
               be
               odd
               ,
               and
               the
               other
               even
               :
               as
               for
               example
               ,
               bid
               h●m
               that
               the
               Gold
               be
               valued
               at
               4
               Crownes
               ,
               or
               Shillings
               ,
               and
               the
               Silver
               at
               ●
               Crownes
               ,
               or
               3
               Shillings
               ,
               or
               any
               other
               number
               ,
               so
               that
               one
               be
               odde
               ▪
               and
               the
               other
               even
               ,
               as
               before
               ;
               then
               bid
               him
               triple
               that
               which
               is
               in
               the
               right
               hand
               ,
               &
               double
               that
               which
               is
               in
               the
               left
               hand
               ,
               and
               bid
               him
               adde
               these
               two
               products
               together
               ,
               and
               aske
               him
               if
               it
               be
               even
               or
               odde
               ;
               if
               it
               be
               even
               ,
               then
               the
               Gold
               is
               in
               the
               right
               hand
               ;
               if
               odde
               ,
               the
               Gold
               is
               in
               the
               left
               hand
               .
            
          
           
             
             
               PROBLEM
               .
               XXX
               .
               Two
               numbers
               being
               proposed
               unto
               two
               severall
               parties
               ,
               to
               tell
               which
               of
               these
               numbers
               is
               taken
               by
               each
               of
               them
               .
            
             
               AS
               for
               example
               :
               admit
               you
               had
               proposed
               unto
               two
               men
               whose
               names
               were
               Peter
               and
               John
               ,
               two
               numbers
               ,
               or
               pieces
               of
               money
               ,
               the
               one
               even
               ,
               and
               the
               other
               odde
               ,
               as
               10.
               and
               9.
               and
               let
               the
               one
               of
               them
               take
               one
               of
               the
               numbers
               ,
               and
               the
               other
               partie
               take
               the
               other
               number
               ,
               which
               they
               place
               privately
               to
               themselves
               :
               how
               artificially
               ,
               according
               to
               the
               congruity
               ,
               and
               excellency
               of
               numbers
               ,
               to
               finde
               which
               of
               them
               did
               take
               10.
               and
               which
               9.
               without
               asking
               any
               qustion
               :
               and
               this
               seems
               most
               subtill
               ,
               yet
               delivered
               howsoever
               differing
               little
               from
               the
               former
               ,
               and
               is
               thus
               performed
               :
               Take
               privately
               to
               your selfe
               also
               two
               numbers
               ,
               the
               one
               even
               ,
               and
               the
               other
               odde
               ,
               as
               4.
               and
               3.
               then
               bid
               Peter
               that
               he
               double
               the
               number
               which
               he
               took
               ,
               and
               do
               you
               privately
               double
               also
               your
               greatest
               number
               ;
               then
               bid
               John
               to
               triple
               the
               number
               which
               he
               hath
               ,
               and
               do
               you
               the
               like
               upon
               your
               last
               number
               :
               adde
               your
               two
               products
               together
               ,
               &
               mark
               if
               it
               be
               even
               or
               odde
               ,
               then
               bid
               the
               two
               parties
               put
               their
               numbers
               together
               ,
               and
               bid
               them
               take
               the
               halfe
               of
               it
               ,
               which
               if
               they
               cannot
               do
               ,
               then
               immediately
               tell
               Peter
               he
               took
               10.
               and
               John
               9.
               because
               the
               aggregate
               of
               the
               double
               of
               4.
               and
               the
               triple
               of
               3.
               makes
               odde
               ,
               and
               such
               
               would
               be
               the
               aggregate
               or
               summe
               of
               the
               double
               of
               Peters
               number
               and
               Johns
               number
               ,
               if
               Peter
               had
               taken
               10.
               if
               otherwise
               ,
               then
               they
               might
               have
               taken
               halfe
               ,
               and
               so
               John
               should
               have
               taken
               10.
               and
               Peter
               9.
               as
               suppose
               Peter
               had
               taken
               10.
               the
               double
               is
               20.
               and
               the
               triple
               of
               9.
               the
               other
               ●umber
               is
               27.
               which
               put
               together
               makes
               47.
               odde
               :
               in
               like
               manner
               the
               double
               of
               your
               number
               conceived
               in
               minde
               ,
               viz.
               4.
               makes
               8.
               and
               the
               triple
               of
               the
               3.
               the
               other
               number
               ,
               makes
               9.
               which
               set
               together
               makes
               17.
               odde
               .
               Now
               you
               cannot
               take
               the
               halfe
               of
               17
               ,
               nor
               47.
               which
               argueth
               that
               Peter
               had
               the
               greater
               number
               ,
               for
               otherwise
               the
               double
               of
               9.
               is
               18.
               &
               the
               triple
               of
               10.
               is
               30.
               which
               set
               together
               makes
               48.
               the
               halfe
               of
               it
               may
               be
               taken
               :
               therefore
               in
               such
               case
               Peter
               the
               took
               lesse
               number
               :
               and
               John
               the
               greater
               ,
               and
               this
               being
               don
               cleanly
               carries
               much
               grace
               with
               it
               .
            
          
           
             
               PROBLEM
               .
               XXXI
               .
               How
               to
               describe
               a
               Circle
               that
               shall
               touch
               3
               :
               Points
               placed
               howsoever
               upon
               a
               plaine
               ,
               if
               they
               be
               not
               in
               a
               right
               line
               .
            
             
               LEt
               the
               three
               points
               be
               A.B.C.
               put
               one
               foot
               of
               the
               Compasse
               upon
               A.
               and
               describe
               an
               Arch
               of
               a
               Circle
               at
               pleasure
               :
               and
               placed
               at
               B.
               crosse
               that
               Arch
               in
               the
               two
               points
               E.
               and
               F.
               and
               placed
               in
               C.
               crosse
               the
               Arch
               in
               G.
               and
               H.
               then
               lay
               a
               ruler
               upon
               G.H.
               and
               draw
               a
               line
               ,
               and
               
               place
               a
               Ruler
               upon
               E.
               
               and
               F.
               cut
               the
               other
               line
               in
               K
               ▪
               so
               K
               is
               the
               Centre
               of
               the
               Circumference
               of
               a
               Circle
               ,
               which
               will
               passe
               by
               the
               said
               three
               points
               A.B.C.
               or
               it
               may
               be
               inverted
               ,
               having
               a
               Circle
               drawne
               ;
               to
               finde
               the
               Centre
               of
               that
               Circle
               ,
               make
               3.
               points
               in
               the
               circumference
               ,
               and
               then
               use
               the
               same
               way
               :
               so
               shall
               you
               have
               the
               Centre
               ,
               a
               thing
               most
               facill
               to
               every
               practitioner
               in
               the
               principles
               of
               Geometrie
               .
            
          
           
             
               PROBLEM
               .
               XXXII
               .
               How
               to
               change
               a
               Circle
               into
               a
               square
               forme
               ?
            
             
               M●ke
               a
               Circle
               upon
               past-board
               or
               other
               materiall
               ,
               as
               the
               Circle
               A.C.D.E.
               of
               which
               A.
               is
               the
               Centre
               ;
               then
               cut
               it
               into
               4
               quarters
               ,
               and
               dispose
               them
               so
               ,
               that
               A.
               at
               the
               centre
               of
               the
               Circle
               may
               alwayes
               be
               at
               the
               Angle
               of
               the
               square
               ,
               and
               so
               the
               foure
               quarters
               of
               the
               
               Circle
               being
               placed
               
               so
               ,
               it
               will
               make
               a
               perfect
               square
               ,
               whose
               side
               A.A.
               is
               equall
               to
               the
               Diameter
               B.D.
               Now
               here
               is
               to
               be
               noted
               that
               the
               square
               is
               greater
               then
               the
               Circle
               by
               the
               vacuity
               in
               the
               middle
               ,
               
                 viz.
                 M.
              
               
            
          
           
             
               PROBLEM
               .
               XXXIII
               .
               With
               one
               and
               the
               same
               comp●sses
               ,
               and
               at
               one
               and
               the
               same
               extent
               ,
               or
               opening
               ,
               how
               to
               describe
               many
               Circles
               concentricall
               ,
               that
               is
               ,
               greater
               or
               lesser
               one
               then
               another
               ?
            
             
               IT
               is
               not
               without
               cause
               that
               many
               admire
               how
               this
               Proposition
               is
               to
               be
               resolved
               ;
               yea
               in
               the
               judgement
               of
               some
               it
               is
               thought
               impossible
               :
               who
               consider
               not
               the
               industrie
               of
               an
               ingenious
               Geometrician
               ,
               who
               makes
               it
               possible
               ,
               and
               that
               most
               facill
               ,
               sundry
               wayes
               ;
               for
               in
               the
               first
               place
               if
               you
               make
               a
               Circle
               upon
               a
               fine
               plaine
               ,
               and
               upon
               the
               Centre
               of
               that
               Circle
               ,
               a
               small
               pegge
               of
               wood
               be
               placed
               ,
               to
               be
               raised
               up
               and
               put
               downe
               at
               pleasure
               by
               help
               of
               a
               small
               ho●e
               made
               in
               the
               Centre
               ,
               then
               with
               the
               same
               opening
               of
               the
               Compasses
               ,
               you
               may
               describe
               Circles
               Concentricall
               ,
               that
               is
               ,
               one
               greater
               or
               lesser
               than
               another
               ;
               for
               the
               higher
               the
               Center
               is
               lifted
               up
               ,
               the
               
               lesser
               the
               Circle
               will
               
               be
               .
               Secondly
               ,
               the
               compasse
               being
               at
               that
               extent
               upon
               a
               Gibus
               body
               ,
               a
               Circle
               may
               be
               described
               ,
               which
               will
               be
               lesse
               than
               the
               former
               ,
               upon
               a
               plaine
               ,
               and
               more
               artificially
               upon
               a
               Globe
               ,
               or
               round
               bowle
               :
               and
               this
               againe
               is
               most
               obvious
               upon
               a
               round
               Pyramide
               ,
               placing
               the
               Compasses
               upon
               the
               top
               of
               it
               ,
               which
               will
               be
               farre
               lesse
               than
               any
               of
               the
               former
               ;
               and
               this
               is
               demonstrated
               by
               the
               20.
               
               Prop.
               of
               the
               first
               of
               Euclids
               ,
               for
               the
               Diameter
               ●
               .
               D.
               is
               lesse
               than
               the
               line
               AD.A.E.
               taken
               together
               ,
               and
               the
               lines
               AD.AE.
               being
               equall
               to
               the
               Diameter
               BC.
               because
               of
               the
               same
               distance
               or
               extent
               of
               opening
               the
               compasses
               ,
               it
               followes
               that
               the
               Diameter
               E.D.
               and
               all
               his
               Circles
               together
               is
               much
               lesse
               than
               the
               Diameter
               ,
               and
               the
               Circle
               BC.
               which
               was
               to
               be
               performed
               .
            
          
           
             
             
               PROBLEM
               XXXIV
               .
               Any
               numbers
               under
               10.
               being
               thought
               upon
               ,
               to
               finde
               what
               numbers
               they
               were
               .
            
             
               LEt
               the
               first
               number
               be
               doubled
               ,
               and
               unto
               it
               adde
               5.
               and
               multiply
               that
               summe
               by
               5.
               and
               unto
               it
               adde
               10.
               and
               unto
               this
               product
               add
               the
               next
               number
               thought
               upon
               ;
               multiply
               this
               same
               againe
               by
               10.
               and
               adde
               unto
               it
               the
               next
               number
               ,
               and
               so
               proceed
               :
               now
               if
               he
               declare
               the
               last
               summe
               ;
               marke
               if
               he
               thought
               but
               upon
               one
               figure
               ,
               for
               then
               subtract
               only
               35.
               from
               it
               ,
               and
               the
               first
               figure
               in
               the
               place
               of
               tennes
               is
               the
               number
               thought
               upon
               :
               if
               he
               thought
               upon
               two
               figures
               ,
               then
               subtract
               also
               the
               said
               ●5
               .
               from
               his
               last
               summe
               ,
               and
               the
               two
               figures
               which
               remaine
               are
               the
               number
               thought
               upon
               :
               if
               he
               thought
               upo●
               three
               figures
               ,
               then
               subtract
               350.
               and
               then
               the
               first
               three
               figures
               are
               the
               numbers
               thought
               upon
               ,
               &c.
               so
               if
               one
               thought
               upon
               these
               numbers
               5.7.9.6
               .
               double
               the
               first
               ,
               makes
               1●
               .
               to
               which
               adde
               5.
               makes
               15.
               this
               multiplied
               by
               5.
               makes
               75.
               to
               which
               adde
               1●
               .
               makes
               85.
               to
               this
               adde
               the
               next
               number
               ,
               viz.
               7.
               makes
               92.
               this
               multiplied
               by
               10.
               makes
               920.
               to
               which
               adde
               the
               next
               number
               ,
               viz.
               9.
               makes
               929.
               which
               multiplied
               by
               10.
               makes
               9290.
               to
               which
               adde
               6.
               makes
               9296.
               from
               which
               subtract
               3500.
               resteth
               5796.
               the
               foure
               numbers
               thought
               upon
               .
               Now
               because
               the
               two
               last
               figures
               are
               like
               the
               two
               numbers
               thought
               
               upon
               :
               to
               conceale
               this
               ,
               bid
               him
               take
               the
               halfe
               of
               it
               ,
               or
               put
               first
               12.
               or
               any
               other
               number
               to
               it
               ,
               and
               then
               it
               will
               not
               be
               so
               open
               .
            
          
           
             
               PROBLEM
               .
               XXXV
               .
               Of
               the
               Play
               with
               the
               Ring
               .
            
             
               AMongst
               a
               company
               of
               9.
               or
               10.
               persons
               ,
               one
               of
               them
               having
               a
               Ring
               ,
               or
               such
               like
               :
               to
               finde
               out
               in
               which
               hand
               :
               upon
               which
               finger
               ,
               &
               joynt
               it
               is
               ;
               this
               will
               cause
               great
               astonishment
               to
               ignorant
               spirits
               ,
               which
               will
               make
               them
               beleeve
               that
               he
               that
               doth
               it
               works
               by
               Magick
               ,
               or
               Witchcraft
               :
               But
               in
               effect
               it
               is
               nothing
               else
               but
               a
               nimble
               act
               of
               Arithmetick
               ,
               founded
               upon
               the
               precedent
               Probleme
               :
               for
               first
               it
               is
               supposed
               that
               the
               persons
               stand
               or
               sit
               in
               order
               ,
               that
               one
               is
               first
               ,
               the
               next
               second
               ,
               &c.
               likewise
               there
               must
               be
               imagined
               that
               of
               these
               two
               hands
               the
               one
               is
               first
               ,
               and
               the
               other
               second
               :
               and
               also
               of
               the
               five
               fingers
               ,
               the
               one
               is
               first
               ,
               the
               next
               is
               second
               ,
               and
               lastly
               of
               the
               joynts
               ,
               the
               one
               is
               as
               1.
               the
               other
               is
               as
               2.
               the
               other
               as
               3.
               &c.
               from
               whence
               it
               appeares
               that
               in
               performing
               this
               Play
               there
               is
               nothing
               else
               to
               be
               done
               than
               to
               think
               4.
               numbers
               :
               for
               example
               ,
               if
               the
               fourth
               person
               had
               the
               Ring
               in
               his
               left
               hand
               ,
               and
               upon
               the
               fifth
               finger
               ,
               and
               third
               joynt
               ,
               and
               I
               would
               divine
               and
               finde
               it
               out
               :
               thus
               I
               would
               proceed
               ,
               as
               in
               the
               34
               Problem
               :
               in
               causing
               him
               to
               double
               the
               first
               number
               :
               that
               is
               ,
               the
               number
               of
               persons
               ,
               
               which
               was
               4.
               and
               it
               makes
               8.
               to
               which
               add
               5.
               makes
               13.
               this
               multiplied
               by
               5.
               makes
               65.
               put
               10.
               to
               it
               ,
               makes
               75.
               unto
               this
               put
               ●
               .
               for
               the
               number
               belonging
               to
               the
               left
               hand
               ,
               and
               so
               it
               makes
               77.
               which
               multiplied
               by
               10.
               makes
               770.
               to
               this
               adde
               the
               number
               of
               the
               fingers
               upon
               which
               the
               Ring
               is
               ,
               viz.
               5.
               makes
               775.
               this
               multiplied
               by
               10.
               makes
               7750.
               to
               which
               adde
               the
               number
               for
               the
               joynt
               upon
               which
               the
               Ring
               is
               ,
               viz
               the
               third
               joynt
               ,
               makes
               7●53
               .
               to
               which
               cause
               him
               to
               adde
               14.
               or
               some
               other
               number
               ,
               to
               conceale
               it
               the
               better
               :
               and
               it
               makes
               7767.
               which
               being
               declared
               unto
               you
               ,
               substract
               3514
               ▪
               and
               there
               will
               remaine
               4.2.5.3
               .
               which
               figures
               in
               order
               declares
               the
               whol
               mystery
               of
               that
               which
               is
               to
               be
               known
               :
               4.
               signifieth
               the
               fourth
               person
               ,
               2.
               the
               left
               hand
               ,
               5.
               the
               fifth
               finger
               ,
               and
               3.
               the
               third
               joynt
               of
               that
               finger
               .
            
          
           
             
               PROBLEM
               .
               XXXVI
               .
               The
               Play
               of
               34.
               or
               more
               Dice
               .
            
             
               THat
               which
               is
               said
               of
               the
               two
               precedent
               Problemes
               may
               be
               applied
               to
               this
               of
               Dice
               (
               and
               many
               other
               particular
               things
               )
               to
               finde
               what
               number
               appeareth
               upon
               each
               Dice
               being
               cast
               by
               some
               one
               ,
               for
               the
               points
               that
               are
               upon
               any
               side
               of
               a
               Dice
               are
               alwayes
               lesse
               than
               10
               and
               the
               points
               of
               each
               side
               of
               a
               Dice
               may
               be
               taken
               for
               a
               number
               thought
               upon
               :
               therefore
               the
               Rule
               will
               be
               as
               the
               former
               :
               As
               for
               example
               ,
               one
               having
               
               thrown
               three
               Dice
               ,
               and
               you
               would
               declare
               the
               numbers
               of
               each
               one
               ,
               or
               how
               much
               they
               make
               together
               ,
               bid
               him
               double
               the
               points
               of
               one
               of
               the
               Dice
               ,
               to
               which
               bid
               him
               adde
               5
               ,
               then
               multiply
               that
               by
               5.
               and
               to
               it
               adde
               10
               ,
               and
               to
               the
               summe
               bid
               him
               adde
               the
               number
               of
               the
               second
               Dice
               :
               and
               multiply
               that
               by
               10
               :
               lastly
               ,
               to
               this
               bid
               him
               adde
               the
               number
               of
               the
               last
               Dice
               ,
               and
               then
               let
               him
               declare
               the
               whole
               number
               :
               then
               if
               from
               it
               you
               subtract
               ●50
               .
               there
               will
               remaine
               the
               number
               of
               the
               three
               Dice
               throwne
               .
            
          
           
             
               PROBLEM
               .
               XXXVII
               .
               How
               to
               make
               water
               in
               a
               Glasse
               seeme
               to
               boyle
               and
               sparkle
               ?
            
             
               TAke
               a
               Glasse
               neere
               full
               of
               water
               or
               other
               liquor
               ;
               and
               setting
               one
               hand
               upon
               the
               foot
               of
               it
               ,
               to
               hold
               it
               fast
               :
               turne
               slightly
               one
               of
               the
               fingers
               of
               your
               other
               hand
               upon
               the
               brimme
               ,
               or
               edge
               of
               the
               Glasse
               ;
               having
               before
               privately
               wet
               your
               finger
               :
               and
               so
               passing
               softly
               on
               with
               your
               finger
               in
               pressing
               a
               little
               :
               for
               then
               first
               ,
               the
               Glasse
               will
               begin
               to
               make
               a
               noyse
               :
               secondly
               ,
               the
               parts
               of
               the
               Glasse
               will
               sensibly
               appeare
               to
               tremble
               ,
               with
               notable
               rarefaction
               and
               condensation
               :
               thirdly
               ,
               the
               water
               will
               shake
               ,
               seeme
               to
               boyle
               :
               fourthly
               ,
               it
               will
               cast
               it selfe
               out
               of
               the
               Glasse
               ,
               and
               leap
               out
               by
               small
               drops
               ,
               with
               great
               astonishment
               to
               the
               standers
               by
               ;
               if
               they
               be
               ignorant
               of
               the
               cause
               of
               it
               ,
               which
               
               is
               onely
               in
               the
               Rarefaction
               of
               the
               parts
               of
               the
               Glasse
               ,
               occasioned
               by
               the
               motion
               and
               pressure
               of
               the
               finger
               .
            
             
               
                 EXAMINATION
                 .
              
               
                 THe
                 cause
                 of
                 this
                 ,
                 is
                 not
                 in
                 the
                 rarefaction
                 of
                 the
                 parts
                 of
                 the
                 Glasse
                 ,
                 but
                 it
                 is
                 rather
                 in
                 the
                 quick
                 locall
                 motion
                 of
                 the
                 finger
                 ,
                 for
                 reason
                 sheweth
                 us
                 that
                 by
                 how
                 much
                 a
                 Body
                 draweth
                 nearer
                 to
                 a
                 quality
                 ,
                 the
                 lesse
                 is
                 it
                 subject
                 or
                 capable
                 of
                 another
                 which
                 is
                 contrary
                 unto
                 it
                 ?
                 now
                 condensation
                 ,
                 and
                 rarefaction
                 are
                 contrary
                 qualities
                 ,
                 and
                 in
                 this
                 Probleme
                 there
                 are
                 three
                 bodies
                 considered
                 ,
                 the
                 Glasse
                 ,
                 the
                 Water
                 ,
                 and
                 the
                 Aire
                 ,
                 now
                 it
                 is
                 evident
                 that
                 the
                 Glasse
                 being
                 the
                 most
                 solid
                 ,
                 and
                 impenitrable
                 Body
                 ,
                 is
                 lesse
                 subject
                 and
                 capable
                 of
                 rarefaction
                 than
                 the
                 water
                 ,
                 the
                 water
                 is
                 lesse
                 subject
                 than
                 the
                 Aire
                 ,
                 and
                 if
                 there
                 be
                 any
                 rarefaction
                 ,
                 it
                 is
                 rather
                 considerable
                 in
                 the
                 Aire
                 then
                 in
                 the
                 Water
                 ,
                 which
                 is
                 inscribed
                 by
                 the
                 Glasse
                 ,
                 and
                 above
                 the
                 Water
                 ,
                 and
                 rather
                 in
                 the
                 Water
                 then
                 in
                 the
                 Glasse
                 :
                 the
                 agitation
                 ,
                 or
                 the
                 trembling
                 of
                 the
                 parts
                 of
                 the
                 Glasse
                 to
                 the
                 sense
                 appeares
                 not
                 :
                 for
                 it
                 is
                 a
                 continued
                 body
                 ;
                 if
                 in
                 part
                 ,
                 why
                 then
                 not
                 in
                 the
                 whole
                 ?
                 and
                 that
                 the
                 Water
                 turnes
                 in
                 the
                 Glasse
                 ,
                 this
                 appeares
                 not
                 ,
                 but
                 only
                 the
                 
                 upper
                 contiguous
                 parts
                 of
                 the
                 Water
                 :
                 that
                 at
                 the
                 bottome
                 being
                 lesse
                 subiect
                 to
                 this
                 agitation
                 ,
                 and
                 it
                 is
                 most
                 certaine
                 that
                 by
                 how
                 much
                 quicker
                 the
                 Circular
                 motion
                 of
                 the
                 finger
                 upon
                 the
                 edge
                 of
                 the
                 Glasse
                 is
                 ,
                 by
                 so
                 much
                 the
                 more
                 shall
                 the
                 Aire
                 be
                 agitated
                 ,
                 and
                 so
                 the
                 water
                 shall
                 receive
                 some
                 apparant
                 affection
                 more
                 or
                 lesse
                 from
                 it
                 ,
                 according
                 to
                 that
                 motion
                 :
                 as
                 we
                 see
                 from
                 the
                 quicknesse
                 of
                 winde
                 upon
                 the
                 Sea
                 ,
                 or
                 c●lme
                 thereof
                 ,
                 that
                 there
                 is
                 a
                 greater
                 or
                 lesser
                 agitation
                 in
                 the
                 water
                 ;
                 and
                 for
                 further
                 examination
                 ,
                 we
                 leave
                 it
                 to
                 the
                 search
                 of
                 those
                 which
                 are
                 curious
                 .
              
            
          
           
             
               PROBLEM
               .
               XXXVIII
               .
               Of
               a
               fine
               vessell
               which
               holds
               wine
               or
               water
               ,
               being
               cast
               in●o
               it
               at
               a
               certaine
               height
               ,
               but
               being
               filled
               higher
               ,
               it
               will
               runne
               out
               of
               its
               owne
               accord
               .
            
             
               LEt
               there
               be
               a
               vessell
               A.B.C.D.
               in
               the
               middle
               of
               which
               place
               a
               Pipe
               ;
               whose
               ends
               both
               above
               at
               E
               ,
               and
               below
               at
               the
               bottom
               of
               the
               vessell
               as
               at
               ●
               ▪
               are
               open
               ;
               let
               the
               end
               ●
               be
               somewhat
               lower
               than
               the
               brimme
               of
               the
               Glasse
               :
               about
               this
               Pipe
               ,
               place
               another
               Pipe
               as
               
                 H.
                 L
              
               ,
               which
               mounts
               a
               little
               above
               E
               and
               let
               it
               most
               diligently
               be
               closed
               at
               H
               ,
               that
               no
               Aire
               enter
               in
               thereby
               ,
               and
               this
               Pipe
               at
               the
               bottome
               may
               have
               a
               small
               hole
               to
               give
               passage
               unto
               the
               water
               ;
               
               then
               poure
               in
               water
               or
               wine
               ,
               and
               as
               long
               as
               it
               mounts
               not
               above
               E
               ,
               it
               is
               safe
               ;
               but
               if
               you
               poure
               in
               the
               water
               so
               that
               it
               mount
               above
               it
               ,
               farewell
               all
               :
               for
               it
               will
               not
               cease
               untill
               it
               be
               all
               gone
               out
               ;
               the
               same
               may
               be
               
               done
               in
               disposing
               any
               crooked
               Pipe
               in
               a
               vessell
               in
               the
               manner
               of
               a
               Faucet
               or
               funnell
               ,
               as
               in
               the
               figure
               H
               ,
               for
               fill
               it
               under
               H
               ,
               at
               pleasure
               ,
               and
               all
               will
               go
               well
               ;
               but
               if
               you
               fill
               it
               unto
               H.
               you
               will
               see
               fine
               sport
               ,
               for
               then
               all
               the
               vessell
               will
               be
               empty
               incontinent
               ,
               and
               the
               subtiltie
               of
               this
               will
               seeme
               more
               admirable
               ,
               if
               you
               conceale
               the
               Pipe
               by
               a
               Bird
               ,
               Serpent
               ,
               or
               such
               like
               ,
               in
               the
               middle
               of
               the
               Glasse
               .
               Now
               the
               reason
               of
               this
               is
               not
               difficult
               to
               those
               which
               know
               the
               nature
               of
               a
               Cock
               or
               Faucet
               ;
               for
               it
               is
               a
               bowed
               Pipe
               ,
               one
               end
               of
               which
               is
               put
               into
               the
               water
               or
               liquor
               ,
               and
               sucking
               at
               the
               other
               end
               untill
               the
               Pipe
               be
               full
               ,
               then
               will
               it
               run
               of
               it selfe
               ,
               and
               it
               is
               a
               fine
               secret
               in
               nature
               to
               see
               ,
               that
               if
               the
               end
               of
               the
               Pipe
               which
               is
               out
               of
               the
               water
               ,
               be
               lower
               then
               the
               water
               ,
               it
               will
               run
               out
               without
               ceasing
               :
               but
               if
               the
               mouth
               of
               the
               Pipe
               be
               higher
               then
               the
               water
               or
               levell
               with
               it
               ,
               it
               will
               not
               runne
               ,
               although
               the
               Pipe
               which
               is
               without
               be
               many
               times
               bigger
               than
               that
               which
               is
               in
               the
               water
               :
               for
               it
               is
               the
               property
               of
               water
               to
               keep
               alwayes
               exactly
               levell
               ▪
            
             
               
               
                 EXAMINATION
                 .
              
               
                 HEre
                 is
                 to
                 be
                 noted
                 ,
                 that
                 if
                 the
                 face
                 of
                 the
                 water
                 without
                 be
                 in
                 one
                 and
                 the
                 same
                 plaine
                 ,
                 with
                 that
                 which
                 is
                 within
                 ,
                 though
                 the
                 outtermost
                 Pipe
                 be
                 ten
                 times
                 greater
                 than
                 that
                 which
                 is
                 within
                 ;
                 the
                 water
                 naturally
                 will
                 not
                 runne
                 ,
                 but
                 if
                 the
                 plaine
                 of
                 the
                 water
                 without
                 be
                 any
                 part
                 lower
                 then
                 that
                 which
                 is
                 within
                 ,
                 it
                 will
                 freely
                 runne
                 :
                 and
                 here
                 may
                 be
                 noted
                 further
                 ,
                 that
                 if
                 the
                 mouth
                 of
                 the
                 Pipe
                 which
                 is
                 full
                 of
                 water
                 ,
                 doth
                 but
                 only
                 touch
                 the
                 superficies
                 of
                 the
                 water
                 within
                 ,
                 although
                 the
                 other
                 end
                 of
                 the
                 pipe
                 without
                 be
                 much
                 lower
                 than
                 that
                 within
                 ,
                 the
                 water
                 it
                 will
                 not
                 run
                 at
                 all
                 :
                 which
                 contradicts
                 the
                 first
                 ground
                 ;
                 hence
                 we
                 gather
                 that
                 the
                 pressure
                 or
                 ponderosity
                 of
                 the
                 water
                 within
                 ,
                 is
                 the
                 cause
                 of
                 running
                 in
                 some
                 respect
                 .
              
            
          
           
             
               PROBLEM
               .
               XXXIX
               .
               Of
               a
               Glasse
               very
               pleasant
               .
            
             
               SOmetimes
               there
               are
               Glasses
               which
               are
               made
               of
               a
               double
               fashion
               ,
               as
               if
               one
               Glasse
               were
               within
               another
               ,
               so
               that
               they
               seem
               but
               one
               ,
               but
               there
               is
               a
               little
               space
               between
               them
               .
               No●
               poure
               Wine
               or
               other
               liquor
               between
               the
               two
               
               edges
               by
               help
               of
               a
               Tunnell
               ,
               into
               a
               little
               hole
               left
               to
               this
               end
               ,
               so
               vvill
               there
               appeare
               tvvo
               fine
               delusions
               or
               fallacies
               ;
               for
               though
               there
               be
               not
               a
               drop
               of
               Wine
               vvithin
               the
               hollovv
               of
               the
               Glasse
               ,
               it
               vvill
               seem
               to
               those
               vvhich
               behold
               it
               that
               it
               is
               an
               ordinary
               Glasse
               full
               of
               Wine
               ,
               and
               that
               especially
               to
               those
               vvhich
               are
               side-vvise
               of
               it
               ,
               and
               if
               any
               one
               move
               it
               ,
               it
               vvill
               much
               confirme
               it
               ,
               because
               of
               the
               motion
               of
               the
               Wine
               ;
               but
               that
               vvhich
               vvill
               give
               most
               delight
               ,
               is
               that
               ,
               if
               any
               one
               shall
               take
               the
               Glasse
               ,
               and
               putting
               it
               to
               his
               mouth
               shall
               think
               to
               drink
               the
               Wine
               ,
               instead
               of
               vvhich
               he
               shall
               sup
               the
               Aire
               ,
               and
               so
               vvill
               cause
               laughter
               to
               those
               that
               stand
               by
               ,
               vvho
               being
               deceived
               ,
               vvill
               hold
               the
               Glass
               to
               the
               light
               ,
               &
               thereby
               considering
               that
               the
               raies
               or
               beames
               of
               the
               light
               are
               not
               reflected
               to
               the
               eye
               ,
               as
               they
               vvould
               be
               if
               there
               vvere
               a
               liquid
               substance
               in
               the
               Glasse
               ,
               hence
               they
               have
               an
               assured
               proofe
               to
               conclude
               ,
               that
               the
               hollovv
               of
               the
               Glasse
               is
               totally
               empty
               .
            
          
           
             
               PROBLEM
               .
               XL.
               If
               any
               one
               should
               hold
               in
               each
               hand
               ,
               as
               many
               pieces
               of
               money
               as
               in
               the
               other
               ,
               how
               to
               finde
               how
               much
               there
               is
               ?
            
             
               BId
               him
               that
               holds
               the
               money
               that
               he
               put
               out
               of
               one
               hand
               into
               the
               other
               vvhat
               number
               you
               think
               convenient
               :
               (
               provided
               that
               it
               may
               be
               done
               ,
               )
               this
               done
               ,
               bid
               him
               that
               out
               of
               the
               hand
               that
               he
               put
               the
               other
               number
               into
               ,
               that
               he
               
               take
               out
               of
               it
               as
               many
               as
               remaine
               in
               the
               other
               hand
               ,
               and
               put
               it
               into
               that
               hand
               :
               for
               then
               be
               assured
               that
               in
               the
               hand
               which
               was
               put
               the
               first
               taking
               away
               :
               there
               will
               be
               found
               just
               the
               double
               of
               the
               number
               taken
               away
               at
               the
               first
               .
               Example
               ,
               admit
               there
               were
               in
               each
               hand
               12
               Shi●lings
               or
               Counters
               ,
               and
               that
               out
               of
               the
               right
               hand
               you
               bid
               him
               take
               7.
               and
               put
               it
               into
               the
               left
               :
               and
               then
               put
               into
               the
               right
               hand
               from
               the
               left
               as
               many
               as
               doth
               remaine
               in
               the
               right
               ,
               which
               is
               5.
               so
               there
               will
               be
               in
               the
               left
               hand
               ●4
               ,
               which
               is
               the
               double
               of
               the
               number
               taken
               out
               of
               the
               right
               hand
               ,
               to
               wit
               7.
               then
               by
               some
               of
               the
               rules
               before
               delivered
               ,
               it
               is
               easie
               to
               finde
               how
               much
               is
               in
               the
               right
               hand
               ,
               viz.
               10.
               
            
          
           
             
               PROBLEM
               .
               XLI
               .
               Many
               Dice
               being
               cast
               ,
               how
               artificially
               to
               discover
               the
               number
               of
               the
               points
               that
               may
               arise
               .
            
             
               SVppose
               any
               one
               had
               cast
               three
               Dice
               secretly
               ,
               bid
               him
               that
               he
               adde
               the
               points
               that
               were
               upmost
               together
               :
               then
               putting
               one
               of
               the
               Dice
               apart
               ,
               unto
               the
               former
               summe
               adde
               the
               points
               which
               are
               under
               the
               other
               two
               ,
               then
               bid
               him
               throw
               these
               two
               Dice
               ,
               and
               mark
               how
               many
               points
               a
               paire
               are
               upwards
               ,
               which
               adde
               unto
               the
               former
               summe
               :
               then
               put
               one
               of
               these
               Dice
               away
               not
               changing
               the
               side
               ,
               mark
               the
               points
               which
               are
               under
               the
               other
               Dice
               ,
               and
               adde
               it
               to
               
               the
               former
               summe
               :
               lastly
               ,
               throw
               that
               one
               Dice
               ,
               and
               whatsoever
               appeares
               upward
               adde
               it
               unto
               the
               former
               summe
               ;
               and
               let
               the
               Dice
               remaine
               thus
               :
               this
               done
               ,
               comming
               to
               the
               Table
               ,
               note
               what
               points
               do
               appeare
               upward
               upon
               the
               three
               Dice
               ,
               which
               adde
               privately
               together
               ,
               and
               unto
               it
               adde
               ●1
               or
               3
               times
               7
               :
               so
               this
               Addition
               or
               summe
               shall
               be
               equall
               to
               the
               summe
               which
               the
               party
               privately
               made
               of
               all
               the
               operations
               which
               he
               formerly
               made
               .
               As
               if
               he
               should
               throw
               three
               Dice
               ,
               and
               there
               should
               appeare
               upward
               5
               ,
               3
               ,
               2.
               the
               sum
               of
               them
               is
               10.
               and
               setting
               one
               of
               them
               apart
               ,
               (
               as
               5.
               )
               unto
               10
               ,
               adde
               the
               points
               which
               are
               under
               3
               and
               2
               ,
               which
               is
               4
               and
               5
               ,
               and
               it
               makes
               19.
               then
               casting
               these
               two
               Dice
               suppose
               there
               should
               appeare
               4
               and
               1
               ,
               this
               added
               unto
               19
               makes
               24.
               and
               setting
               one
               of
               these
               two
               Dice
               apart
               as
               the
               4.
               unto
               the
               former
               24
               ,
               I
               adde
               the
               number
               of
               points
               which
               is
               under
               the
               other
               Dice
               ,
               viz.
               under
               1
               ,
               that
               is
               6
               ,
               which
               makes
               30.
               
               Last
               of
               all
               I
               throw
               that
               one
               Dice
               ,
               and
               suppose
               there
               did
               appeare
               2
               ,
               which
               I
               adde
               to
               the
               former
               30
               ,
               and
               it
               makes
               32
               ,
               then
               leaving
               the
               3
               dice
               thus
               ,
               the
               points
               which
               are
               upward
               will
               be
               these
               ,
               5
               ,
               4
               ,
               2
               unto
               which
               adde
               secretly
               21
               ,
               (
               as
               before
               was
               said
               )
               so
               have
               you
               32
               ,
               the
               same
               number
               whi●h
               he
               had
               ;
               and
               in
               the
               same
               manner
               you
               may
               practise
               with
               4
               ,
               5
               ,
               6
               ,
               or
               many
               Dice
               or
               other
               bodies
               ,
               observing
               only
               that
               you
               must
               adde
               the
               points
               opposite
               of
               the
               Dice
               ;
               for
               upon
               which
               depends
               the
               whole
               demonstration
               or
               secret
               of
               the
               play
               ;
               for
               alwayes
               that
               which
               is
               above
               and
               
               underneath
               makes
               7.
               but
               if
               it
               make
               another
               number
               ,
               then
               must
               you
               adde
               as
               often
               that
               number
               .
            
          
           
             
               PROBLEM
               .
               XLII
               .
               Two
               mettals
               ,
               as
               Gold
               and
               Silver
               ,
               or
               of
               other
               kin●●
               weighing
               alike
               ,
               being
               privately
               placed
               into
               two
               like
               Boxes
               ,
               to
               finde
               which
               of
               them
               the
               Gold
               or
               Silver
               is
               in
               .
            
             
             
               But
               because
               that
               this
               experiment
               in
               water
               hath
               divers
               accidents
               ,
               and
               therefore
               subject
               to
               a
               caution
               ;
               and
               namely
               ,
               because
               the
               matter
               of
               the
               chest
               ,
               mettall
               or
               other
               things
               may
               hinder
               .
            
             
               Behold
               here
               a
               more
               subtill
               and
               certaine
               invention
               to
               finde
               and
               discover
               it
               out
               without
               weighing
               it
               in
               the
               water
               ▪
               Now
               experience
               and
               reason
               sheweth
               us
               that
               two
               like
               bodies
               or
               magnitudes
               of
               equall
               weight
               ,
               and
               of
               divers
               mettalls
               ,
               are
               not
               of
               equal
               quantity
               :
               and
               seeing
               that
               Gold
               is
               the
               heaviest
               of
               all
               mettalls
               ,
               it
               will
               occupie
               less
               roome
               or
               place
               ;
               from
               which
               will
               follow
               that
               the
               like
               weight
               of
               Lead
               in
               the
               same
               forme
               ,
               will
               occupie
               or
               take
               up
               more
               roome
               or
               place
               .
               Now
               let
               there
               be
               therefore
               presented
               two
               Globes
               or
               Chests
               of
               wood
               or
               other
               matter
               alike
               ,
               &
               equall
               one
               to
               the
               other
               ,
               in
               one
               of
               which
               in
               the
               middle
               there
               is
               another
               Globe
               or
               body
               of
               lead
               weighing
               12.
               l.
               (
               as
               C
               ,
               )
               and
               in
               the
               other
               a
               Globe
               or
               like
               body
               of
               Gold
               weighing
               12
               pound
               (
               as
               B.
               )
               Now
               
               it
               is
               supposed
               that
               the
               wooden
               Globes
               or
               Chests
               are
               of
               equall
               weight
               ,
               forme
               ,
               and
               magnitude
               :
               and
               to
               discover
               in
               which
               the
               Gold
               or
               Lead
               is
               in
               ,
               take
               a
               broad
               paire
               of
               Compasses
               ,
               and
               clip
               one
               of
               the
               Coffers
               or
               Globes
               somewhat
               from
               the
               middle
               ,
               as
               at
               D.
               then
               fix
               in
               the
               Chest
               or
               Globe
               a
               small
               piece
               of
               Iron
               between
               the
               feet
               of
               the
               Compasses
               ,
               as
               EK
               ,
               at
               the
               end
               of
               which
               hang
               a
               vveight
               G
               ,
               so
               that
               the
               other
               end
               may
               be
               counterpoysed
               ,
               and
               hang
               
                 in
                 aequilibrio
              
               :
               and
               do
               the
               like
               to
               the
               other
               Chest
               or
               Globe
               .
               Novv
               if
               that
               the
               other
               Chest
               or
               Globe
               being
               clipped
               in
               like
               distance
               from
               the
               end
               ,
               and
               hanging
               at
               the
               other
               end
               the
               same
               weight
               G.
               there
               be
               found
               no
               difference
               ;
               then
               clip
               them
               nearer
               tovvards
               the
               middle
               ,
               that
               so
               the
               points
               of
               the
               Compasse
               may
               be
               against
               some
               of
               the
               mettall
               vvhich
               is
               inclosed
               ;
               or
               just
               against
               the
               extremitie
               of
               the
               Gold
               as
               in
               D
               ,
               and
               suppose
               it
               hang
               thus
               in
               aequilibrio
               ;
               it
               is
               certaine
               that
               in
               the
               other
               Coffer
               is
               the
               Lead
               ;
               for
               the
               points
               of
               the
               Compasses
               being
               advanced
               as
               much
               as
               before
               ,
               as
               at
               F
               ,
               vvhich
               takes
               up
               a
               part
               of
               the
               Lead
               ,
               (
               because
               it
               occupies
               a
               greater
               place
               than
               the
               Gold
               )
               therefore
               that
               shall
               help
               the
               vveight
               G.
               to
               vveigh
               ,
               and
               so
               vvill
               not
               hang
               in
               aequilibrio
               ,
               except
               G
               be
               placed
               neare
               to
               F.
               hence
               vve
               may
               conclude
               ,
               that
               there
               is
               the
               Lead
               ;
               and
               in
               the
               other
               Chest
               or
               Globe
               ,
               there
               is
               the
               Gold.
               
            
             
               
               
                 EXAMINATION
                 .
              
               
                 IF
                 the
                 two
                 Boxes
                 being
                 of
                 equall
                 magnitude
                 weighed
                 in
                 the
                 aire
                 be
                 found
                 to
                 be
                 of
                 equall
                 weight
                 ,
                 they
                 shall
                 necessarily
                 take
                 up
                 like
                 place
                 in
                 the
                 water
                 ,
                 and
                 therefore
                 weigh
                 also
                 one
                 as
                 much
                 as
                 another
                 :
                 hence
                 there
                 is
                 no
                 possibilitie
                 to
                 finde
                 the
                 inequalitie
                 of
                 the
                 mettalls
                 which
                 are
                 inclosed
                 in
                 these
                 Boxes
                 in
                 the
                 water
                 :
                 the
                 intention
                 of
                 Archimedes
                 was
                 not
                 upon
                 contrary
                 mettalls
                 inclosed
                 in
                 〈…〉
                 Boxes
                 ,
                 but
                 consisted
                 of
                 comparing
                 metta●●●
                 ,
                 simple
                 in
                 the
                 water
                 one
                 with
                 another
                 :
                 therefore
                 the
                 inference
                 is
                 false
                 and
                 absurd
                 .
              
            
          
           
             
               PROBLEM
               .
               XLIII
               .
               Two
               Globes
               of
               diverse
               mettalls
               ,
               (
               as
               one
               Gold
               ,
               and
               the
               other
               Copper
               )
               yet
               of
               equall
               weight
               being
               put
               into
               a
               box
               ,
               as
               BG
               ,
               to
               finde
               in
               which
               end
               the
               Gold
               or
               Copper
               is
               .
            
             
               THis
               is
               discovered
               by
               the
               changing
               of
               the
               places
               of
               the
               tvvo
               Bovvles
               or
               Globes
               ,
               having
               the
               same
               counterpoyse
               H
               to
               be
               hung
               at
               the
               other
               side
               ,
               as
               in
               N.
               and
               if
               the
               Gold
               vvhich
               is
               the
               lesser
               Globe
               ,
               vvere
               before
               the
               nearest
               to
               the
               handle
               D●
               ,
               having
               novv
               changed
               his
               place
               vvill
               be
               farthest
               from
               the
               handle
               DE
               ,
               as
               in
               K.
               
               therefore
               the
               Centre
               of
               gravity
               of
               the
               two
               Globes
               taken
               together
               ,
               shall
               be
               farther
               separate
               from
               the
               middle
               of
               the
               
               handle
               (
               under
               which
               is
               the
               Centre
               of
               gravity
               of
               the
               Box
               )
               than
               it
               was
               before
               ,
               and
               seeing
               that
               the
               handle
               is
               alwayes
               in
               the
               middle
               of
               the
               Box
               ,
               the
               vveight
               N.
               must
               be
               augmented
               ▪
               to
               keep
               it
               in
               equil●●●●
               and
               by
               this
               way
               one
               may
               knovv
               ,
               that
               if
               at
               the
               second
               time
               ,
               the
               counterpoise
               be
               too
               light
               ,
               it
               is
               a
               signe
               that
               the
               Gold
               is
               farthest
               off
               the
               handle
               ,
               as
               at
               the
               first
               triall
               it
               vvas
               nearest
               .
            
          
           
             
               PROBLEM
               .
               XLIIII
               .
               How
               to
               represent
               diverse
               sorts
               of
               Rainebowes
               here
               below
               ?
            
             
               THe
               Rainbovve
               is
               a
               thing
               admirable
               in
               the
               vvorld
               ,
               vvhich
               ravisheth
               often
               the
               eyes
               and
               spirits
               of
               men
               in
               consideration
               of
               his
               rich
               intermingled
               colours
               vvhich
               are
               seen
               under
               the
               clouds
               ,
               seeming
               as
               the
               glistering
               of
               the
               Starres
               ,
               precious
               stones
               ,
               and
               ornaments
               of
               the
               most
               beauteous
               flovvers
               :
               some
               part
               of
               it
               as
               the
               resplendent
               stars
               ,
               or
               as
               a
               Rose
               ,
               or
               burning
               Cole
               of
               fire
               ▪
               in
               it
               one
               may
               see
               Dyes
               of
               sundry
               sorts
               ,
               
               the
               Violet
               ,
               the
               Blew
               ,
               the
               Orange
               ,
               the
               Saphir
               ,
               the
               Jacinct
               ,
               and
               the
               Emerald
               colours
               ,
               as
               a
               lively
               plant
               placed
               in
               a
               green
               soile
               :
               and
               as
               a
               most
               rich
               treasure
               of
               nature
               ,
               it
               is
               a
               high
               work
               of
               the
               Sun
               who
               casteth
               his
               raies
               or
               beames
               as
               a
               curious
               Painter
               drawes
               strokes
               with
               his
               pensill
               ,
               and
               placeth
               his
               colours
               in
               an
               exquisite
               situation
               ;
               and
               Solomon
               saith
               ,
               Eccles.
               43.
               it
               is
               a
               chiefe
               and
               principall
               work
               of
               God.
               Notwithstanding
               there
               is
               left
               to
               industrie
               how
               to
               represent
               it
               from
               above
               ,
               here
               below
               ,
               though
               not
               in
               perfection
               ,
               yet
               in
               part
               ,
               with
               the
               same
               intermixture
               of
               colours
               that
               is
               above
               .
            
             
               Have
               you
               not
               seen
               how
               by
               Oares
               of
               a
               Boate
               it
               doth
               exceeding
               quickly
               glide
               upon
               the
               water
               with
               a
               pleasant
               grace
               ?
               Aristotle
               sayes
               ,
               that
               it
               coloureth
               the
               water
               ,
               and
               makes
               a
               thousand
               atomes
               ,
               upon
               which
               the
               beames
               of
               the
               Sunne
               reflecting
               ,
               make
               a
               kinde
               of
               coloured
               Rainbowe
               :
               or
               may
               we
               not
               see
               in
               houses
               or
               Gardens
               of
               pleasure
               artificiall
               fountaines
               ,
               which
               poure
               forth
               their
               droppie
               streames
               of
               water
               ,
               that
               being
               between
               the
               Sunne
               and
               the
               fountaine
               ,
               there
               will
               be
               presented
               as
               a
               continuall
               Rainbowe
               ?
               But
               not
               to
               go
               farther
               ,
               I
               will
               shew
               you
               how
               you
               may
               do
               it
               at
               your
               doore
               ,
               by
               a
               fine
               and
               facill
               experiment
               .
            
             
               Take
               water
               in
               your
               mouth
               ,
               and
               turne
               your
               back
               to
               the
               Sunne
               ,
               and
               your
               face
               against
               some
               obscure
               place
               ,
               then
               blow
               out
               the
               water
               which
               is
               in
               your
               mouth
               ,
               that
               it
               may
               be
               sprinkled
               in
               small
               drops
               and
               vapours
               :
               you
               shall
               see
               those
               
               atomes
               vapours
               in
               the
               beames
               of
               the
               Sunne
               to
               turne
               into
               a
               faire
               Rainebowe
               ,
               but
               all
               the
               griefe
               is
               ,
               that
               it
               lasteth
               not
               ,
               but
               soone
               is
               vanished
               .
            
             
               But
               to
               have
               one
               more
               stable
               and
               permanent
               in
               his
               colours
               :
               Take
               a
               Glasse
               full
               of
               water
               ,
               and
               expose
               it
               to
               the
               Sunne
               ,
               so
               that
               the
               raies
               that
               passe
               through
               strike
               upon
               a
               shadowed
               place
               ,
               you
               will
               have
               pleasure
               to
               see
               the
               fine
               forme
               of
               a
               Rainebovve
               by
               this
               reflection
               .
               Or
               take
               a
               Trigonall
               Glasse
               or
               Crystall
               Glasse
               of
               diverse
               Angles
               ,
               and
               look
               through
               it
               ,
               or
               let
               the
               beames
               of
               the
               Sunne
               passe
               through
               it
               ;
               or
               vvith
               a
               candle
               let
               the
               appearances
               be
               received
               upon
               a
               shadovved
               place
               :
               you
               vvill
               have
               the
               same
               contentment
               .
            
          
           
             
               PROBLEM
               XLV
               .
               How
               that
               if
               all
               the
               Powder
               in
               the
               world
               were
               in
               closed
               within
               a
               bowle
               of
               paper
               or
               glasse
               ,
               and
               being
               fired
               on
               all
               parts
               ,
               it
               could
               not
               break
               that
               bowle
               ?
            
             
               IF
               the
               bowle
               and
               the
               powder
               be
               uniforme
               in
               all
               his
               parts
               ,
               then
               by
               that
               means
               the
               powder
               would
               presse
               and
               move
               equally
               on
               each
               side
               ,
               in
               which
               there
               is
               no
               possibility
               whereby
               it
               ought
               to
               begin
               by
               one
               side
               more
               than
               another
               .
               Now
               it
               is
               impossible
               that
               the
               bowle
               should
               be
               broken
               in
               all
               his
               parts
               :
               for
               they
               are
               infinite
               .
            
             
               Of
               like
               fineness
               or
               subtiltie
               may
               it
               be
               that
               a
               bowle
               of
               Iron
               falling
               from
               a
               high
               place
               upon
               a
               plaine
               pavement
               of
               thin
               Glasse
               ,
               it
               were
               impossible
               
               any
               wise
               to
               break
               it
               ;
               if
               the
               bowle
               were
               perfectly
               round
               ,
               and
               the
               Glasse
               flat
               and
               uniforme
               in
               all
               his
               parts
               ▪
               for
               the
               bowle
               would
               touch
               the
               Glasse
               but
               in
               one
               point
               ,
               which
               is
               in
               the
               middle
               of
               infinite
               parts
               which
               are
               about
               it
               :
               neither
               is
               there
               any
               cause
               why
               it
               ought
               more
               on
               one
               side
               than
               on
               another
               ,
               seeing
               that
               it
               may
               not
               be
               done
               with
               all
               his
               sides
               together
               ;
               it
               may
               be
               concluded
               as
               speaking
               naturally
               ,
               that
               such
               a
               bovvle
               falling
               upon
               such
               a
               glasse
               vvill
               not
               break
               it
               .
               But
               this
               matter
               is
               meere
               Metaphysicall
               ,
               and
               all
               the
               vvorkmen
               in
               the
               vvorld
               cannot
               ever
               vvith
               all
               their
               industrie
               make
               a
               bovvle
               perfectly
               round
               ,
               or
               a
               Glasse
               uniforme
               .
            
          
           
             
               PROBLEM
               .
               XLVI
               .
               To
               finde
               a
               number
               which
               being
               divided
               by
               2
               ,
               there
               will
               remaine
               1
               ,
               being
               divided
               by
               3
               ,
               there
               will
               remaine
               1
               ;
               and
               so
               likewise
               being
               divided
               by
               
                 4
                 ,
                 5
              
               ,
               or
               6
               ,
               there
               would
               still
               remaine
               1
               ;
               but
               being
               didivided
               by
               7
               ,
               there
               will
               remaine
               nothing
               .
            
             
               IN
               many
               Authors
               of
               Arithmetick
               this
               Probleme
               is
               thus
               proposed
               :
               A
               vvoman
               carrying
               Egges
               to
               Market
               in
               a
               basket
               ,
               met
               an
               unruly
               fellovv
               who
               broke
               them
               :
               who
               vvas
               by
               order
               made
               to
               pay
               for
               them
               :
               and
               she
               being
               demanded
               what
               number
               she
               had
               ,
               she
               could
               not
               tell
               :
               but
               she
               remembred
               
               that
               counting
               them
               by
               2
               &
               2
               ,
               there
               remained
               1
               ▪
               likewise
               by
               3
               and
               3
               by
               4
               and
               4
               ,
               by
               5
               and
               5
               ,
               by
               6
               and
               6
               ;
               there
               still
               remained
               1.
               but
               when
               she
               counted
               them
               by
               7
               and
               7
               ,
               there
               remained
               nothing
               :
               Now
               how
               may
               the
               number
               of
               Egges
               be
               discovered
               ?
            
             
               Finde
               a
               number
               which
               may
               exactly
               be
               measured
               by
               7
               ,
               and
               being
               measured
               by
               2
               ,
               3
               ,
               4
               ,
               5
               ,
               and
               6
               ;
               there
               vvill
               still
               remaine
               a
               unite
               ▪
               multiply
               these
               numbers
               together
               ,
               makes
               720
               ,
               to
               which
               adde
               1
               ;
               so
               have
               you
               the
               number
               ,
               viz.
               721.
               in
               like
               manner
               301
               vvill
               be
               measured
               by
               2
               ,
               3
               ,
               4
               ,
               5
               ,
               6
               ;
               so
               that
               1
               remaines
               :
               but
               being
               measured
               by
               7
               ,
               nothing
               vvill
               remaine
               ;
               to
               vvhich
               continually
               adde
               220
               ,
               and
               you
               have
               other
               numbers
               vvhich
               vvill
               do
               the
               same
               :
               hence
               it
               is
               doubtfull
               vvhat
               number
               she
               had
               ,
               therefore
               not
               to
               faile
               ,
               it
               must
               be
               knovvn
               vvhether
               they
               did
               exceed
               400
               ,
               800
               ,
               &c.
               in
               vvhich
               it
               may
               be
               conjectured
               that
               it
               could
               not
               exceed
               4
               or
               5
               hundred
               ,
               seeing
               a
               man
               or
               vvoman
               could
               not
               carry
               7
               or
               8
               hundred
               Egges
               ,
               therefore
               the
               number
               vvas
               the
               former
               ●01
               .
               vvhich
               she
               had
               in
               her
               Basket
               :
               vvhich
               being
               counted
               by
               2
               and
               2
               ,
               there
               vvill
               remaine
               1
               ,
               by
               3
               and
               3
               ,
               &c.
               but
               counted
               by
               7
               and
               7
               ,
               there
               vvill
               remaine
               nothing
               .
            
          
           
             
             
               PROBLEM
               .
               XLVII
               .
               One
               had
               a
               certaine
               number
               of
               crownes
               ,
               and
               counting
               them
               by
               2
               and
               2
               ,
               there
               rested
               1.
               counting
               them
               by
               3
               and
               3
               ,
               there
               rested
               2.
               counting
               them
               by
               4
               and
               4
               ,
               there
               rested
               3.
               counting
               them
               by
               5
               and
               5
               ,
               there
               rested
               4.
               counting
               them
               by
               6
               &
               6
               ,
               there
               rested
               5.
               but
               counting
               them
               by
               7
               and
               7
               ,
               there
               remained
               nothing
               :
               how
               many
               crownes
               might
               he
               have
               ?
            
             
               THis
               Question
               hath
               some
               affinitie
               to
               the
               precedent
               ,
               and
               the
               resolution
               is
               almost
               in
               the
               same
               manner
               :
               for
               here
               there
               must
               be
               found
               a
               number
               ,
               vvhich
               multiplied
               by
               7
               ,
               and
               then
               divided
               by
               2
               ,
               3
               ,
               4
               ,
               5
               ,
               6
               ;
               there
               may
               alvvayes
               remaine
               a
               number
               lesse
               by
               1
               than
               the
               Divisor
               :
               Novv
               the
               first
               number
               vvhich
               arrives
               in
               this
               nature
               is
               119
               ,
               unto
               vvhich
               if
               420
               be
               added
               ,
               makes
               539
               ,
               vvhich
               also
               vvill
               do
               the
               same
               :
               and
               so
               by
               adding
               420
               ,
               you
               may
               have
               other
               numbers
               to
               resolve
               this
               proposition
               .
            
          
           
             
               PROBLEM
               .
               XLVIII
               .
               How
               many
               sorts
               of
               weights
               in
               the
               least
               manner
               must
               there
               be
               to
               weigh
               all
               sorts
               of
               things
               between
               1
               pound
               and
               40
               pound
               ,
               and
               so
               unto
               121
               ,
               &
               364
               pound
               .
            
             
               TO
               vveigh
               things
               betvveen
               1
               and
               40
               ,
               take
               numbers
               in
               triple
               proportion
               ,
               so
               that
               their
               
               summe
               be
               equall
               ,
               or
               somewhat
               greater
               than
               40
               ,
               as
               are
               the
               numbers
               1
               3.9.27
               .
               I
               say
               that
               with
               ●
               such
               weights
               ,
               the
               first
               being
               of
               1
               pound
               ,
               the
               second
               being
               3
               pound
               ,
               the
               third
               being
               9
               pound
               ,
               and
               the
               fourth
               being
               27
               :
               any
               weight
               between
               1
               and
               40
               pound
               may
               be
               weighed
               .
               As
               admit
               to
               weigh
               21
               pound
               ,
               put
               unto
               the
               thing
               that
               is
               to
               be
               weighed
               the
               9
               pound
               weight
               ,
               then
               in
               the
               other
               ballance
               put
               27
               pound
               and
               3
               pound
               ,
               which
               doth
               counterpoise
               21
               pound
               and
               9
               pound
               ,
               and
               if
               20
               pound
               were
               to
               be
               weighed
               ,
               put
               to
               it
               in
               the
               ballance
               9
               and
               1
               ,
               and
               in
               the
               other
               ballance
               put
               27
               and
               3
               ,
               and
               so
               of
               others
            
             
               In
               the
               same
               manner
               take
               those
               5
               weights
               ,
               1
               ,
               3
               ,
               9
               ,
               27
               ▪
               81
               ,
               you
               may
               weigh
               with
               them
               between
               1
               pound
               ,
               and
               121
               pound
               :
               and
               taking
               those
               6
               weights
               ▪
               as
               1
               ,
               3
               ,
               9
               ,
               2●
               ,
               81
               ,
               243
               ,
               you
               may
               weigh
               even
               from
               1
               pound
               unto
               364
               pound
               :
               this
               depends
               upon
               the
               property
               of
               continued
               proportionals
               ,
               the
               latter
               of
               which
               containing
               twice
               all
               the
               former
               .
            
          
           
             
               PROBLEM
               .
               XLIX
               .
               Of
               a
               deceitfull
               ballance
               which
               being
               c●●●ty
               seemes
               i●
               be
               just
               ,
               because
               it
               hangs
               in
               aequilibrio
               :
               not●ithstanding
               putting
               12
               pound
               in
               one
               ballance
               ,
               and
               11
               in
               the
               other
               ,
               it
               will
               remaine
               in
               aequilibrio
               .
            
             
               ARistotle
               maketh
               mention
               of
               this
               ballance
               in
               his
               mechanick
               Questions
               ,
               and
               saith
               ,
               that
               
               the
               Merchants
               of
               purpose
               in
               his
               time
               used
               them
               to
               deceive
               the
               world
               :
               the
               subtiltie
               or
               craft
               of
               which
               is
               thus
               ,
               that
               one
               arme
               of
               the
               ballance
               is
               longer
               then
               another
               ,
               by
               the
               same
               proportion
               ,
               that
               one
               weight
               is
               heavier
               then
               another
               :
               As
               if
               the
               beame
               were
               23
               inches
               long
               ,
               and
               the
               handle
               placed
               so
               that
               12
               inches
               should
               be
               on
               one
               side
               of
               it
               ,
               and
               11
               inches
               on
               the
               other
               side
               :
               conditionally
               
               that
               the
               shorter
               end
               should
               be
               as
               heavy
               as
               the
               longer
               ,
               a
               thing
               easie
               to
               be
               done
               :
               then
               afterwards
               put
               into
               the
               ballance
               two
               unequal
               weights
               in
               such
               proportion
               as
               the
               parts
               of
               the
               beame
               have
               one
               unto
               another
               ,
               which
               is
               12
               to
               11
               ,
               but
               so
               that
               the
               greater
               be
               placed
               in
               the
               ballance
               which
               hangs
               upon
               the
               shorter
               part
               of
               the
               beame
               ,
               and
               the
               lesser
               weight
               in
               the
               other
               ballance
               :
               it
               is
               most
               certaine
               that
               the
               ballances
               will
               hang
               
                 in
                 aequilibrio
              
               ,
               which
               will
               seem
               most
               sincere
               and
               just
               ;
               though
               it
               be
               most
               deceitfull
               ,
               abominable
               ,
               and
               false
               .
            
             
               The
               reason
               of
               this
               is
               drawne
               from
               the
               experiments
               of
               Archimedes
               ,
               who
               shewes
               that
               two
               unequall
               weights
               will
               counterpoyse
               one
               another
               ,
               when
               there
               is
               like
               proportion
               betweene
               the
               parts
               of
               the
               beame
               (
               that
               the
               handle
               separates
               )
               
               and
               the
               vveights
               themselves
               :
               for
               in
               one
               and
               the
               same
               counterpoise
               ,
               by
               hovv
               much
               it
               is
               farther
               from
               the
               Centre
               of
               the
               handle
               ,
               by
               so
               much
               it
               seems
               heavier
               ,
               therefore
               if
               there
               be
               a
               diversitie
               of
               distance
               that
               the
               ballances
               hang
               from
               the
               handle
               ,
               there
               must
               necessarily
               be
               an
               ineqality
               of
               weight
               in
               these
               ballances
               to
               make
               them
               hang
               in
               aequilibrio
               ,
               and
               to
               discover
               if
               there
               be
               deceit
               ,
               change
               the
               weight
               into
               the
               other
               ballance
               ,
               for
               as
               soone
               as
               the
               greater
               vveight
               is
               placed
               in
               the
               ballance
               that
               hangs
               on
               the
               longer
               parts
               of
               the
               beame
               :
               it
               vvill
               vveigh
               dovvne
               the
               other
               instantly
               .
            
          
           
             
               PROBLEM
               .
               L.
               To
               heave
               or
               lift
               up
               a
               bottle
               with
               a
               straw
               .
            
             
               TAke
               a
               stravv
               that
               is
               not
               bruised
               ,
               bovv
               it
               that
               it
               make
               an
               Angle
               ,
               and
               put
               it
               into
               the
               bottle
               so
               that
               the
               greatest
               end
               be
               in
               the
               neck
               ,
               then
               the
               Reed
               being
               put
               in
               
               the
               bovved
               part
               vvil
               cast
               side-vvise
               ,
               and
               make
               an
               Angle
               as
               in
               the
               figure
               may
               be
               seen
               :
               then
               may
               you
               take
               the
               end
               vvhich
               is
               out
               of
               the
               bottle
               in
               your
               hand
               ,
               and
               heave
               up
               the
               bottle
               ,
               
               and
               it
               is
               so
               much
               surer
               ,
               by
               how
               much
               the
               Angle
               is
               acuter
               or
               sharper
               ;
               and
               the
               end
               which
               is
               bowed
               approacheth
               to
               the
               other
               perpendicular
               parts
               which
               come
               out
               of
               the
               bottle
               .
            
          
           
             
               PROBLEM
               .
               LI.
               How
               in
               the
               middle
               of
               a
               wood
               or
               desert
               ,
               without
               the
               sight
               of
               the
               Sunne
               ,
               Starres
               ,
               Shadow
               or
               Compasse
               ,
               to
               finde
               out
               the
               North
               or
               South
               ,
               or
               the
               foure
               Cardinall
               points
               of
               the
               world
               ,
               East
               ,
               West
               ,
               &
               c
               ?
            
             
               IT
               is
               the
               opinion
               of
               some
               ,
               that
               the
               windes
               are
               to
               be
               observed
               in
               this
               :
               if
               it
               be
               hot
               ,
               the
               South
               is
               found
               by
               the
               windes
               that
               blow
               that
               way
               ,
               but
               this
               observation
               is
               uncertaine
               and
               subject
               to
               much
               error
               :
               nature
               will
               help
               you
               in
               some
               measure
               to
               make
               it
               more
               manifest
               than
               any
               of
               the
               former
               ,
               from
               a
               tree
               thus
               :
               Cut
               a
               small
               tree
               off
               ,
               even
               to
               the
               ground
               ,
               and
               mark
               the
               many
               circles
               that
               are
               about
               the
               sap
               or
               pith
               of
               the
               tree
               ,
               which
               seem
               nearer
               together
               in
               some
               part
               than
               in
               other
               ,
               which
               is
               by
               reason
               of
               the
               Suns
               motion
               about
               the
               tree
               :
               for
               that
               the
               humiditie
               of
               the
               parts
               of
               the
               tree
               towards
               the
               South
               by
               the
               heat
               of
               the
               Sun
               is
               rarified
               ,
               and
               caused
               to
               extend
               :
               and
               the
               S●n
               not
               giving
               such
               heat
               towards
               the
               North-part
               of
               the
               tree
               ,
               the
               sap
               is
               lesser
               rarefied
               ,
               but
               condensed
               ;
               by
               which
               the
               circles
               are
               nearer
               together
               on
               the
               North-part
               ,
               than
               on
               the
               South-part
               :
               therefore
               if
               a
               line
               be
               drawne
               from
               the
               
               widest
               to
               the
               narrowest
               
               part
               of
               the
               circles
               ,
               it
               shall
               shew
               the
               North
               &
               South
               of
               the
               world
               .
               Another
               Experiment
               may
               be
               thus
               :
               Take
               a
               small
               needle
               ,
               such
               as
               women
               work
               with
               :
               place
               it
               gently
               downe
               flatwise
               upon
               still
               water
               ,
               and
               it
               will
               not
               sink
               ,
               (
               which
               is
               against
               the
               generall
               tenet
               that
               Iron
               will
               not
               swimme
               )
               which
               needle
               will
               by
               little
               and
               little
               turne
               to
               the
               North
               and
               South-points
               .
               But
               if
               the
               needle
               be
               great
               and
               will
               not
               swim
               ,
               thrust
               it
               through
               a
               small
               piece
               of
               Cork
               ,
               or
               some
               such
               like
               thing
               ,
               and
               then
               it
               will
               do
               the
               same
               :
               for
               such
               is
               the
               property
               of
               Iron
               when
               it
               is
               placed
               
                 in
                 aequilibrio
              
               ,
               it
               strives
               to
               finde
               out
               the
               Poles
               of
               the
               world
               or
               points
               of
               North
               and
               South
               in
               a
               manner
               as
               the
               magnes
               doth
               .
            
             
               
                 EXAMINATION
                 .
              
               
                 HEre
                 is
                 observable
                 ,
                 that
                 the
                 moisture
                 which
                 aideth
                 to
                 the
                 growth
                 of
                 the
                 tree
                 ,
                 is
                 dilated
                 and
                 rarefied
                 by
                 the
                 Meridionall
                 heat
                 ,
                 and
                 contracted
                 by
                 the
                 Septentrionall
                 cold
                 :
                 this
                 rarefaction
                 works
                 upon
                 the
                 part
                 of
                 the
                 humour
                 or
                 moisture
                 that
                 is
                 more
                 thinne
                 ,
                 which
                 doth
                 easily
                 dissipate
                 and
                 evaporate
                 :
                 which
                 
                 evaporation
                 carries
                 a
                 part
                 of
                 the
                 salt
                 with
                 it
                 ;
                 and
                 because
                 that
                 solidation
                 or
                 condensation
                 ,
                 so
                 that
                 there
                 is
                 left
                 but
                 a
                 part
                 of
                 the
                 nourishment
                 which
                 the
                 heat
                 bakes
                 up
                 and
                 consumes
                 :
                 so
                 contrarily
                 on
                 the
                 other
                 side
                 the
                 condensation
                 and
                 restrictive
                 quality
                 of
                 the
                 moisture
                 causeth
                 lesse
                 evaporation
                 and
                 perdition
                 :
                 and
                 so
                 consequently
                 there
                 remaines
                 more
                 nourishment
                 ,
                 which
                 makes
                 a
                 greater
                 increase
                 on
                 that
                 side
                 than
                 on
                 the
                 other
                 side
                 :
                 for
                 as
                 trees
                 have
                 their
                 growth
                 in
                 winter
                 ,
                 because
                 of
                 their
                 pores
                 and
                 these
                 of
                 the
                 earth
                 are
                 shut
                 up
                 :
                 so
                 in
                 the
                 spring
                 when
                 their
                 pores
                 are
                 open
                 ,
                 and
                 when
                 the
                 sappe
                 and
                 moisture
                 is
                 drawne
                 by
                 it
                 ,
                 there
                 is
                 not
                 such
                 cold
                 on
                 the
                 North-side
                 that
                 it
                 may
                 be
                 condensed
                 at
                 once
                 :
                 But
                 contrarily
                 to
                 the
                 side
                 which
                 is
                 South
                 ,
                 the
                 heat
                 may
                 be
                 such
                 ,
                 that
                 in
                 little
                 time
                 by
                 continuance
                 ,
                 this
                 moisture
                 is
                 dissipated
                 greatly
                 :
                 and
                 cold
                 is
                 nothing
                 but
                 that
                 which
                 hardneth
                 and
                 contracteth
                 the
                 moisture
                 of
                 the
                 tree
                 ,
                 and
                 so
                 converteth
                 it
                 into
                 wood
                 .
              
            
          
           
             
               PROBLEM
               .
               LII
               .
               Three
               persons
               having
               taken
               Counters
               ,
               Cards
               ,
               or
               other
               things
               ,
               to
               finde
               how
               much
               each
               one
               hath
               taken
               .
            
             
               CAuse
               the
               third
               party
               to
               take
               a
               number
               which
               ma●
               be
               divided
               by
               4
               ,
               and
               as
               often
               as
               he
               takes
               4
               ,
               let
               the
               second
               party
               take
               7
               ,
               and
               the
               
               first
               take
               13
               ,
               then
               cause
               them
               to
               put
               them
               all
               together
               ,
               and
               declare
               the
               summe
               of
               it
               ;
               which
               secretly
               divide
               by
               3
               ,
               and
               the
               Quotient
               is
               the
               double
               of
               the
               number
               which
               the
               third
               person
               did
               take
               .
               Or
               cause
               the
               third
               to
               give
               unto
               the
               second
               and
               first
               ,
               as
               many
               as
               each
               of
               them
               hath
               ;
               then
               let
               the
               second
               give
               unto
               the
               first
               and
               third
               ,
               as
               many
               as
               each
               of
               them
               hath
               ;
               lastly
               ,
               let
               the
               third
               give
               unto
               the
               second
               and
               first
               ,
               as
               many
               as
               each
               of
               them
               hath
               ;
               and
               then
               aske
               how
               much
               one
               of
               them
               hath
               ;
               (
               for
               they
               will
               have
               then
               all
               alike
               ,
               )
               so
               halfe
               of
               that
               number
               is
               the
               number
               that
               the
               third
               person
               had
               at
               the
               first
               :
               which
               knowne
               all
               is
               knowne
               .
            
          
           
             
               PROBLEM
               .
               LIII
               .
               How
               to
               make
               a
               consort
               of
               musick
               of
               many
               parts
               with
               one
               voyce
               ,
               or
               one
               instrument
               only
               ?
            
             
               THis
               Probleme
               is
               resolved
               ,
               so
               that
               a
               finger
               or
               player
               upon
               an
               instrument
               ,
               be
               neare
               an
               Echo
               which
               answereth
               his
               voice
               or
               instrument
               ;
               and
               if
               the
               Echo
               answereth
               but
               once
               at
               a
               time
               ,
               he
               may
               make
               a
               double
               ;
               if
               twice
               ,
               then
               a
               triple
               ,
               if
               three
               times
               ,
               then
               an
               harmonie
               of
               foure
               parts
               ,
               for
               it
               must
               be
               such
               a
               one
               that
               is
               able
               to
               exercise
               both
               tune
               and
               note
               as
               occasion
               requires
               .
               As
               when
               he
               begins
               ut
               ,
               before
               the
               Echo
               answer
               ,
               he
               may
               begin
               sol
               ,
               and
               pronounce
               it
               in
               the
               same
               tune
               that
               ●he
               Echo
               answereth
               ,
               by
               which
               meanes
               you
               ●ave
               a
               fifth
               ,
               agreeable
               consort
               of
               musick
               :
               then
               
               in
               the
               same
               time
               that
               the
               Echo
               followeth
               ,
               to
               sound
               the
               second
               note
               sol
               ,
               he
               may
               sound
               forth
               another
               sol
               higher
               or
               lower
               to
               make
               an
               eight
               ,
               the
               most
               perfect
               consort
               of
               musick
               ,
               and
               so
               of
               others
               ,
               if
               he
               will
               continue
               his
               voice
               with
               the
               Echo
               ,
               and
               sing
               alone
               with
               two
               parts
               .
               Now
               experience
               sheweth
               this
               to
               be
               true
               ,
               which
               often
               comes
               to
               passe
               in
               many
               Churches
               ,
               making
               one
               to
               beleeve
               that
               there
               are
               many
               more
               parts
               in
               the
               musick
               of
               a
               Quire
               ,
               then
               in
               effect
               truly
               there
               are
               because
               of
               the
               resounding
               and
               multiplying
               of
               the
               voic●
               ,
               and
               redoubling
               of
               the
               Quire.
               
            
          
           
             
               PROBLEM
               .
               LIIII
               .
               T●
               make
               or
               describe
               an
               Ovall
               form
               ,
               or
               that
               which
               neare
               resembles
               unto
               it
               ,
               at
               one
               turning
               with
               a
               paire
               of
               common
               Compasses
               .
            
             
               THere
               are
               many
               fine
               wayes
               in
               Geometricall
               practices
               ,
               to
               make
               an
               Ovall
               figure
               or
               one
               neare
               unto
               it
               ,
               by
               severall
               centres
               :
               any
               of
               which
               I
               will
               not
               touch
               upon
               ,
               but
               shew
               how
               it
               may
               be
               done
               promptly
               upon
               one
               centre
               only
               .
               In
               which
               I
               will
               say
               nothing
               of
               the
               Ovall
               forme
               ,
               which
               appeares
               ,
               when
               one
               describeth
               circles
               with
               the
               points
               of
               a
               common
               Compasses
               ,
               somewhat
               deep
               upon
               a
               skinne
               stretched
               forth
               hard
               :
               which
               contracting
               it selfe
               in
               some
               parts
               of
               the
               skinne
               maketh
               an
               Ovall
               forme
               .
               But
               it
               will
               more
               evidently
               appeare
               upon
               a
               Columne
               or
               Cylinder
               :
               if
               paper
               
               be
               placed
               upon
               it
               ,
               then
               with
               a
               paire
               of
               Compasses
               describe
               as
               it
               were
               a
               circle
               upon
               it
               ,
               which
               paper
               afterwards
               being
               extended
               ,
               will
               not
               be
               circular
               but
               ovall-wise
               :
               and
               a
               paire
               of
               Compasses
               may
               be
               so
               accommodated
               ,
               that
               it
               may
               be
               done
               also
               upon
               a
               plaine
               thus
               .
               As
               let
               the
               length
               of
               the
               Ovall
               be
               
                 H.
                 K
              
               ,
               fasten
               2
               pinnes
               or
               nailes
               neare
               the
               end
               of
               that
               line
               as
               
                 F.
                 G
              
               ,
               and
               take
               a
               threed
               which
               is
               double
               to
               the
               length
               of
               
               
                 G.
                 H
              
               ,
               or
               
                 F.
                 K
              
               ,
               then
               if
               you
               take
               a
               Compasse
               which
               may
               have
               one
               foot
               lower
               than
               another
               ,
               with
               a
               spring
               between
               his
               legges
               :
               and
               placing
               one
               foot
               of
               this
               Compasse
               in
               the
               Centre
               of
               the
               Ovall
               ,
               and
               guiding
               the
               threed
               by
               the
               other
               foot
               of
               the
               Compasses
               ,
               and
               so
               carrying
               it
               about
               :
               the
               spring
               will
               help
               to
               describe
               and
               draw
               the
               Ovall
               forme
               .
               But
               in
               stead
               of
               the
               Compasses
               it
               may
               be
               done
               with
               ones
               hand
               only
               ,
               as
               in
               the
               figure
               may
               appeare
               .
            
          
           
             
               PROBLEM
               .
               LV.
               Of
               a
               pu●se
               difficult
               to
               be
               opened
               .
            
             
               IT
               is
               made
               to
               shut
               and
               open
               with
               Rings
               :
               first
               at
               each
               side
               there
               is
               a
               strap
               or
               string
               ,
               as
               AB
               .
               
               and
               CD
               ,
               at
               the
               end
               of
               which
               are
               2
               rings
               ,
               B
               &
               D
               ,
               and
               the
               string
               CD
               passeth
               through
               the
               ring
               B
               ,
               so
               that
               it
               may
               not
               come
               out
               againe
               ;
               or
               be
               parted
               one
               from
               another
               :
               and
               so
               that
               the
               ring
               B
               ,
               may
               slide
               up
               and
               downe
               upon
               the
               string
               CD
               ,
               then
               over
               the
               purse
               ,
               there
               is
               a
               piece
               of
               Leather
               EFGH
               ,
               which
               covers
               the
               opening
               of
               the
               purse
               ,
               and
               there
               is
               another
               piece
               of
               Leather
               AE
               ,
               which
               passeth
               
               through
               many
               rings
               :
               which
               hath
               a
               slit
               towards
               the
               end
               I
               ,
               so
               great
               that
               the
               string
               BC
               may
               slide
               into
               it
               :
               Now
               all
               the
               cunning
               or
               craft
               is
               how
               to
               make
               fast
               or
               to
               open
               the
               purse
               ,
               which
               consists
               in
               making
               the
               string
               BC
               slide
               through
               the
               side
               at
               I
               ,
               therefore
               bring
               down
               B
               to
               I
               ,
               then
               make
               the
               end
               I
               passe
               through
               the
               ring
               B
               ,
               and
               also
               D
               with
               his
               string
               to
               passe
               through
               the
               slit
               I
               ,
               so
               shall
               the
               purse
               be
               fast
               ,
               and
               then
               may
               the
               strings
               be
               put
               as
               before
               ,
               and
               it
               will
               seem
               difficult
               to
               discover
               how
               it
               was
               done
               .
               Now
               to
               open
               the
               purse
               ,
               put
               through
               the
               end
               I
               through
               the
               ring
               B
               ,
               and
               then
               through
               the
               slit
               I
               ,
               by
               which
               you
               put
               through
               the
               string
               DC
               ,
               by
               this
               way
               the
               purse
               will
               be
               opened
               .
            
          
           
             
             
               PROBLEM
               .
               LVI
               .
               Whether
               it
               is
               more
               hard
               and
               admirable
               without
               Compasses
               to
               make
               a
               perfect
               circle
               ,
               or
               being
               made
               to
               finde
               out
               the
               Centre
               of
               it
               ?
            
             
               IT
               is
               said
               that
               upon
               a
               time
               past
               ,
               two
               Mathematicians
               met
               ,
               and
               they
               would
               make
               tryall
               of
               their
               industry
               :
               the
               one
               made
               instantly
               a
               Perfect
               circle
               without
               Compasses
               ,
               and
               the
               other
               immediately
               pointed
               out
               the
               Centre
               thereof
               with
               the
               point
               of
               a
               needle
               ;
               now
               which
               is
               the
               chiefest
               action
               ?
               it
               seems
               the
               first
               ,
               for
               to
               draw
               the
               most
               noblest
               figure
               upon
               a
               plaine
               Table
               without
               other
               help
               than
               the
               hand
               ,
               and
               the
               minde
               ,
               is
               full
               of
               admiration
               ;
               to
               finde
               the
               Centre
               is
               but
               to
               finde
               out
               only
               one
               point
               ,
               but
               to
               draw
               a
               round
               ,
               there
               must
               be
               almost
               infinite
               points
               ,
               equidistant
               from
               the
               Centre
               or
               middle
               ;
               that
               in
               conclusion
               it
               is
               both
               the
               Circle
               and
               the
               Centre
               together
               .
               But
               contrarily
               it
               may
               seem
               that
               to
               finde
               the
               Centre
               is
               more
               difficult
               ,
               for
               what
               attention
               ,
               vivacitie
               ,
               and
               subtiltie
               must
               there
               be
               in
               the
               spirit
               ,
               in
               the
               eye
               ,
               in
               the
               hand
               ,
               which
               will
               chuse
               the
               true
               point
               amongst
               a
               thousand
               other
               points
               ?
               He
               that
               makes
               a
               circle
               keeps
               alwayes
               the
               same
               distance
               ,
               and
               is
               guided
               by
               a
               halfe
               distance
               to
               finish
               the
               rest
               ;
               but
               he
               that
               must
               finde
               the
               Centre
               ,
               must
               in
               the
               same
               time
               take
               heed
               to
               the
               parts
               about
               it
               ,
               and
               choose
               one
               only
               point
               which
               is
               equall
               distant
               from
               an
               infinite
               of
               other
               
               points
               which
               are
               in
               the
               circumference
               ;
               which
               is
               very
               difficult
               .
               Aristotle
               confirmes
               this
               amongst
               his
               morals
               ,
               and
               seems
               to
               explaine
               the
               difficultie
               which
               is
               to
               be
               found
               in
               the
               middle
               of
               vertue
               ;
               for
               it
               may
               want
               a
               thousand
               wayes
               ,
               and
               be
               farre
               separated
               from
               the
               true
               Centre
               of
               the
               end
               of
               a
               right
               mediocritie
               of
               a
               vertuous
               action
               ;
               for
               to
               do
               well
               it
               must
               touch
               the
               middle
               point
               which
               is
               but
               one
               ,
               and
               there
               must
               be
               a
               true
               point
               which
               respects
               the
               end
               ,
               and
               that
               's
               but
               one
               only
               .
               Now
               to
               judge
               which
               is
               the
               most
               difficult
               ,
               as
               before
               is
               said
               ,
               either
               to
               draw
               the
               round
               or
               to
               finde
               the
               Centre
               ,
               the
               round
               seems
               to
               be
               harder
               than
               to
               finde
               the
               Centre
               ,
               because
               that
               in
               finding
               of
               it
               ,
               it
               is
               done
               at
               once
               ,
               and
               hath
               an
               equall
               distance
               from
               the
               whole
               ;
               But
               ,
               as
               before
               ,
               to
               draw
               a
               round
               there
               is
               a
               visible
               point
               imagined
               ,
               about
               which
               the
               circle
               is
               to
               be
               drawne
               .
               I
               esteeme
               that
               it
               is
               as
               difficult
               therefore
               ,
               if
               not
               more
               ,
               to
               make
               the
               circle
               without
               a
               Centre
               ,
               as
               to
               finde
               the
               middle
               or
               Centre
               of
               that
               circle
               .
            
          
           
             
               PROBLEM
               .
               LVII
               .
               Any
               one
               having
               taken
               3
               Cards
               ,
               to
               finde
               how
               many
               points
               they
               containe
            
             
               THis
               is
               to
               be
               exercised
               upon
               a
               full
               Pack
               of
               Cards
               of
               52
               ,
               then
               let
               one
               choose
               any
               three
               at
               pleasure
               secretly
               from
               your
               sight
               ,
               and
               bid
               him
               secretly
               account
               the
               points
               in
               each
               Card
               ,
               and
               will
               him
               to
               take
               as
               many
               Cards
               as
               will
               make
               up
               15
               to
               each
               of
               the
               points
               of
               his
               Cards
               ,
               
               then
               will
               him
               to
               give
               you
               the
               rest
               of
               the
               Cards
               ,
               for
               4
               of
               them
               being
               rejected
               ,
               the
               rest
               shew
               the
               number
               of
               points
               that
               his
               three
               Cards
               which
               he
               took
               at
               the
               first
               did
               conteine
               .
               As
               if
               the
               3
               Cards
               were
               7
               ,
               10
               ,
               and
               4
               ;
               now
               7
               wants
               of
               15
               ,
               8.
               take
               8
               Cards
               therefore
               for
               your
               first
               Card
               :
               the
               10
               wants
               of
               15
               ▪
               5
               ,
               take
               5
               cards
               for
               your
               second
               card
               :
               lastly
               4
               wants
               of
               15
               ,
               11
               ,
               take
               11
               Cards
               for
               your
               third
               Card
               ,
               &
               giving
               him
               the
               rest
               of
               the
               Cards
               ,
               there
               will
               be
               25
               ;
               from
               which
               take
               4
               ,
               there
               remaines
               21
               ,
               the
               number
               of
               the
               three
               Cards
               taken
               ,
               viz.
               7
               ,
               10
               ,
               and
               4.
               
            
             
               Whosoever
               would
               practise
               this
               play
               with
               4
               ,
               5
               ,
               6
               ,
               or
               more
               Cards
               ,
               and
               that
               the
               whole
               number
               of
               Cards
               be
               more
               or
               lesse
               than
               52
               ;
               and
               that
               the
               terme
               be
               15
               ,
               14
               ,
               12
               ,
               &c
               ,
               this
               generall
               rule
               ensuing
               may
               serve
               :
               multiply
               the
               terme
               by
               the
               number
               of
               Cards
               taken
               at
               first
               :
               to
               the
               product
               adde
               the
               number
               of
               Cards
               taken
               ,
               then
               subtract
               this
               summe
               from
               the
               whole
               number
               of
               Cards
               ;
               the
               remainder
               is
               the
               number
               which
               must
               be
               subtracted
               from
               the
               Cards
               ,
               which
               remaines
               to
               make
               up
               the
               game
               :
               if
               there
               remaine
               nothing
               after
               the
               Subtraction
               ,
               then
               the
               number
               of
               Cards
               remaining
               doth
               justly
               shew
               the
               number
               of
               points
               which
               were
               in
               the
               Cards
               chosen
               .
               If
               the
               Subtraction
               cannot
               be
               made
               ,
               then
               subtract
               the
               number
               of
               Cards
               from
               that
               number
               ,
               and
               the
               remainder
               added
               unto
               the
               Cards
               that
               did
               remaine
               ,
               the
               summe
               will
               be
               the
               number
               of
               points
               in
               the
               Cards
               taken
               ,
               as
               if
               the
               Cards
               were
               7
               ,
               10
               ,
               5
               ,
               8
               ,
               and
               the
               terme
               given
               were
               12
               ;
               
               so
               the
               first
               wants
               5
               ,
               the
               second
               wants
               2
               ,
               the
               third
               wants
               7
               ,
               and
               the
               fourth
               wants
               4
               Cards
               ,
               which
               taken
               ,
               the
               party
               gives
               you
               the
               rest
               of
               the
               Cards
               :
               then
               secretly
               multiply
               12
               by
               4
               ,
               makes
               48
               ;
               to
               which
               adde
               4
               ,
               the
               number
               of
               Cards
               taken
               makes
               52
               ,
               from
               which
               52
               should
               be
               taken
               ,
               rest
               nothing
               :
               therefore
               according
               to
               the
               direction
               of
               the
               remainder
               of
               the
               Cards
               which
               are
               30
               ,
               is
               equall
               to
               the
               points
               of
               the
               foure
               Cards
               taken
               ,
               viz.
               7
               ,
               10
               ,
               5
               ,
               8.
               
               Againe
               ,
               let
               these
               five
               Cards
               be
               supposed
               to
               be
               taken
               ,
               8
               ,
               6
               ,
               10
               ,
               3
               ,
               7
               ;
               their
               differences
               to
               15
               ,
               the
               termes
               are
               7
               ,
               9
               ,
               5
               ,
               12
               ,
               8
               ,
               which
               number
               of
               Cards
               taken
               ,
               there
               will
               remaine
               but
               6
               Cards
               :
               then
               privately
               multiply
               15
               by
               5
               ,
               makes
               75
               ,
               to
               which
               adde
               5
               makes
               80
               ,
               from
               this
               take
               52
               the
               number
               of
               Cards
               ,
               rest
               28
               ,
               to
               vvhich
               add
               the
               remainder
               of
               Cards
               ,
               make
               34.
               the
               summe
               with
               8
               ,
               6
               ,
               10
               ,
               3
               ,
               7.
               
            
          
           
             
               PROBLEM
               .
               LVII
               .
               Many
               Cards
               placed
               in
               diverse
               ranks
               ,
               to
               finde
               which
               of
               these
               Cards
               any
               one
               hath
               thought
               .
            
             
               TAke
               15
               Cards
               ,
               and
               place
               them
               in
               3
               heaps
               in
               rank-wise
               ,
               5
               in
               a
               heap
               :
               now
               suppose
               any
               one
               had
               thought
               one
               of
               these
               Cards
               in
               any
               one
               of
               the
               heaps
               ,
               it
               is
               easie
               to
               finde
               vvhich
               of
               the
               Cards
               it
               is
               ,
               and
               it
               is
               done
               thus
               ;
               ask
               him
               in
               vvhich
               of
               the
               heaps
               it
               is
               ,
               vvhich
               place
               in
               the
               middle
               of
               the
               other
               tvvo
               ;
               then
               throvv
               dovvne
               the
               Cards
               by
               1
               and
               1
               into
               three
               severall
               heaps
               in
               rank-vvise
               ,
               untill
               all
               be
               cast
               dovvne
               ,
               then
               aske
               him
               
               in
               which
               of
               the
               rankes
               his
               Card
               is
               ,
               which
               heap
               place
               in
               the
               middle
               of
               the
               other
               two
               heaps
               alwayes
               ,
               and
               this
               do
               foure
               times
               at
               least
               ,
               so
               in
               putting
               the
               Cards
               altogether
               ,
               look
               upon
               the
               Cards
               ,
               or
               let
               their
               back
               be
               towards
               you
               ,
               and
               throw
               out
               the
               eight
               Card
               ,
               for
               that
               was
               the
               Card
               thought
               upon
               without
               faile
               .
            
          
           
             
               PROBLEM
               .
               LVIII
               .
               Many
               Cards
               being
               offered
               to
               sundry
               persons
               ,
               to
               finde
               which
               of
               these
               Cards
               any
               one
               thinketh
               upon
               .
            
             
               ADmit
               there
               were
               4
               persons
               ,
               then
               take
               4
               Cards
               ,
               and
               shew
               them
               to
               the
               first
               ,
               bid
               him
               think
               one
               of
               them
               ,
               and
               put
               these
               4
               away
               ,
               then
               take
               4
               other
               Cards
               ,
               and
               shew
               them
               in
               like
               manner
               to
               the
               second
               person
               ,
               and
               bid
               him
               think
               any
               one
               of
               these
               Cards
               ,
               and
               so
               do
               to
               the
               third
               person
               ,
               and
               so
               the
               fourth
               ,
               &c.
               
               Then
               take
               the
               4
               Cards
               of
               the
               first
               person
               ,
               and
               dispose
               them
               in
               4
               rankes
               ,
               and
               upon
               them
               the
               4
               Cards
               of
               the
               second
               person
               ,
               upon
               them
               also
               these
               of
               the
               third
               person
               ,
               and
               lastly
               ,
               upon
               them
               these
               of
               the
               fourth
               person
               ,
               then
               shew
               unto
               eaeh
               of
               these
               parties
               each
               of
               these
               ranks
               ,
               and
               aske
               him
               if
               his
               Card
               be
               in
               it
               which
               he
               thought
               ,
               for
               infallibly
               that
               vvhich
               the
               first
               partie
               thought
               upon
               vvill
               be
               in
               the
               first
               rank
               ,
               and
               at
               the
               bottome
               ,
               the
               Card
               of
               the
               second
               person
               vvill
               be
               in
               the
               second
               ranke
               ,
               
               the
               Card
               of
               the
               third
               thought
               upon
               will
               be
               in
               the
               third
               rank
               ,
               and
               the
               fourth
               mans
               Card
               will
               be
               in
               the
               fourth
               rank
               ,
               and
               so
               of
               others
               ,
               if
               there
               be
               more
               persons
               use
               the
               same
               method
               .
               This
               may
               be
               practised
               by
               other
               things
               ,
               ranking
               them
               by
               certaine
               numbers
               :
               allotted
               to
               pieces
               of
               money
               ,
               or
               such
               like
               things
               .
            
          
           
             
               PROBLEM
               .
               LIX
               .
               How
               to
               make
               an
               instrument
               to
               help
               hearing
               ,
               as
               Galileus
               made
               to
               help
               the
               sight
               ?
            
             
               THink
               not
               that
               the
               Mathematickes
               (
               which
               hath
               furnished
               us
               with
               such
               admirable
               helps
               for
               seeing
               )
               is
               wanting
               for
               that
               of
               hearing
               ,
               it
               s
               well
               knowne
               that
               long
               trunks
               or
               pipes
               make
               one
               heare
               well
               farre
               off
               ,
               and
               experience
               shewes
               us
               that
               in
               certaine
               places
               of
               the
               Orcades
               in
               a
               hollow
               vault
               ,
               that
               a
               man
               speaking
               but
               softly
               at
               one
               corner
               thereof
               ,
               may
               be
               audibly
               understood
               at
               the
               other
               end
               :
               notwithstanding
               those
               which
               are
               between
               the
               parties
               cannot
               heare
               him
               speak
               at
               all
               :
               And
               it
               is
               a
               generall
               principle
               ,
               that
               pipes
               do
               greatly
               help
               to
               strengthen
               the
               activitie
               of
               naturall
               causes
               :
               we
               see
               that
               〈◊〉
               contracted
               in
               a
               pipe
               ,
               burnes
               4
               or
               5
               foot
               high
               ,
               which
               would
               scarce
               heat
               ,
               being
               in
               the
               open
               aire
               :
               the
               rupture
               or
               violence
               of
               water
               issuing
               out
               of
               a
               fountaine
               ,
               shewes
               us
               that
               vvater
               being
               contracted
               into
               a
               pipe
               ,
               causeth
               a
               violence
               in
               its
               passage
               .
               The
               Glasses
               of
               Galeileus
               makes
               us
               
               see
               how
               usefull
               pipes
               or
               trunkes
               are
               to
               make
               the
               light
               and
               species
               more
               visible
               ,
               and
               proportionable
               to
               our
               eye
               .
               It
               is
               said
               that
               a
               Prince
               of
               Italy
               hath
               a
               faire
               hall
               ,
               in
               which
               he
               can
               with
               facility
               heare
               distinctly
               the
               discourses
               of
               those
               which
               walk
               in
               the
               adjacent
               Gardens
               ,
               which
               is
               by
               certaine
               vessels
               and
               pipes
               that
               answer
               from
               the
               Garden
               to
               the
               Hall.
               Vitruvius
               makes
               mention
               also
               of
               such
               vessels
               and
               pipes
               ,
               to
               strengthen
               the
               voice
               and
               action
               of
               Comedians
               :
               and
               in
               these
               times
               amongst
               many
               noble
               personages
               ▪
               the
               new
               kinde
               of
               trunkes
               are
               used
               to
               help
               the
               hearing
               ,
               being
               made
               of
               silver
               ,
               copper
               ,
               or
               other
               resounding
               materiall
               ;
               in
               funnell-wise
               putting
               the
               widest
               end
               to
               him
               which
               speaketh
               ,
               to
               the
               end
               to
               contract
               the
               voice
               ,
               that
               so
               by
               the
               pipe
               applied
               to
               the
               eare
               it
               may
               be
               more
               uniform
               and
               lesse
               in
               danger
               to
               dissipate
               the
               voice
               ,
               and
               so
               consequently
               more
               fortified
               .
            
          
           
             
               PROBLEM
               .
               LX.
               Of
               a
               fine
               lamp
               which
               goes
               not
               out
               ,
               though
               one
               carry
               it
               in
               ones
               pocket
               :
               or
               being
               rolled
               upon
               the
               ground
               will
               still
               burne
               .
            
             
               IT
               must
               be
               observed
               that
               the
               vessell
               in
               which
               the
               oile
               is
               put
               into
               ,
               have
               two
               pinnes
               on
               the
               sides
               of
               it
               ,
               one
               against
               another
               ,
               being
               included
               within
               a
               circle
               :
               this
               circle
               ought
               to
               have
               two
               other
               pinnes
               ,
               to
               enter
               into
               another
               circle
               of
               
               brasse
               ,
               or
               other
               solid
               matter
               :
               lastly
               ,
               this
               second
               circle
               hath
               two
               pinnes
               ,
               which
               may
               hang
               within
               some
               box
               to
               containe
               the
               whole
               lamp
               ,
               in
               such
               manner
               ,
               that
               there
               be
               6
               pinnes
               in
               different
               position
               :
               Now
               by
               the
               aid
               of
               these
               pegges
               or
               pinnes
               ,
               the
               lamp
               that
               is
               in
               the
               middle
               will
               be
               alwayes
               well
               situated
               according
               to
               his
               Centre
               of
               gravity
               ,
               though
               it
               
               be
               turned
               any
               way
               :
               though
               if
               you
               endeavour
               to
               turne
               it
               upside
               downe
               ,
               it
               will
               lie
               levell
               ▪
               which
               is
               pleasant
               and
               admirable
               to
               behold
               to
               those
               which
               know
               not
               the
               cause
               :
               And
               it
               is
               facil
               from
               his
               to
               make
               a
               place
               to
               rest
               quiet
               in
               ,
               though
               there
               be
               great
               agitation
               in
               the
               outvvard
               parts
               .
            
          
           
             
               PROBLEM
               .
               LXI
               .
               Any
               one
               having
               thought
               a
               Card
               amongst
               many
               Cards
               ,
               how
               artificially
               to
               discover
               it
               out
               ?
            
             
               TAke
               any
               number
               of
               Cards
               as
               10
               ,
               12
               ,
               &c.
               and
               open
               some
               4
               or
               5
               to
               the
               parties
               sight
               ,
               and
               bid
               him
               think
               one
               of
               them
               ,
               but
               let
               him
               note
               vvhether
               it
               be
               the
               first
               ,
               second
               ,
               third
               ,
               &c.
               then
               vvith
               promptness
               learn
               vvhat
               number
               of
               Cards
               
               you
               had
               in
               your
               hands
               ,
               and
               take
               the
               other
               part
               of
               the
               Cards
               ,
               and
               place
               them
               on
               the
               top
               of
               these
               you
               hold
               in
               your
               hand
               ;
               and
               having
               done
               so
               ,
               aske
               him
               whether
               his
               Card
               were
               the
               first
               ,
               second
               ,
               &c.
               then
               before
               knowing
               the
               number
               of
               Cards
               that
               were
               at
               the
               bottome
               ,
               account
               backwards
               untill
               you
               come
               to
               it
               :
               so
               shall
               you
               easily
               take
               out
               the
               card
               that
               he
               thought
               upon
               .
            
          
           
             
               PROBLEM
               .
               LXII
               .
               Three
               Women
               AB.C.
               carried
               apples
               to
               a
               marke
               to
               sell
               ,
               A
               had
               20
               ,
               B
               
                 30
                 ▪
              
               and
               C
               40
               ,
               they
               sold
               as
               many
               for
               a
               penny
               ,
               the
               one
               as
               the
               other
               :
               and
               brought
               home
               one
               as
               much
               money
               as
               another
               ,
               how
               could
               this
               be
               ?
            
             
               THe
               answer
               to
               the
               Probleme
               is
               easie
               ▪
               as
               suppose
               at
               the
               beginning
               of
               the
               Market
               :
               A
               ▪
               sold
               
               her
               apples
               at
               a
               penny
               an
               apple
               :
               and
               sold
               but
               2.
               which
               was
               2
               pence
               ,
               and
               so
               she
               had
               18
               left
               :
               but
               B.
               sold
               17.
               which
               was
               17
               pence
               ,
               and
               so
               had
               13
               left
               :
               C.
               sold
               32.
               which
               was
               32
               pence
               ,
               and
               so
               had
               8
               apples
               left
               ▪
               then
               A
               said
               she
               would
               not
               sell
               her
               apples
               so
               
               cheap
               ,
               but
               would
               sell
               them
               for
               3
               pence
               the
               peece
               ,
               which
               she
               did
               :
               and
               so
               her
               apples
               came
               to
               54
               pence
               ,
               and
               B
               having
               left
               but
               13
               apples
               sold
               them
               at
               the
               same
               rate
               ,
               which
               came
               to
               39
               pence
               :
               and
               lastly
               ▪
               C.
               had
               but
               8
               apples
               ,
               which
               at
               the
               same
               rate
               came
               to
               24
               pence
               :
               these
               summes
               of
               money
               which
               each
               others
               before
               received
               come
               to
               56
               pence
               ,
               and
               so
               much
               each
               one
               received
               ;
               and
               so
               consequently
               brought
               home
               one
               as
               much
               as
               another
               .
            
          
           
             
               PROBLEM
               .
               LXIII
               .
               Of
               the
               properties
               of
               some
               numbers
               .
            
             
               FIrst
               ,
               any
               two
               numbers
               is
               just
               the
               summe
               of
               a
               number
               ,
               that
               have
               equall
               distance
               from
               the
               halfe
               of
               that
               number
               ▪
               the
               one
               augmenting
               ,
               and
               the
               other
               diminishing
               ,
               as
               7
               and
               7
               ,
               of
               8
               and
               ●
               ,
               of
               9
               and
               5
               ,
               of
               10
               and
               4
               ,
               of
               11
               and
               3
               ,
               of
               12
               and
               2
               ,
               of
               13
               and
               ●
               .
               as
               the
               one
               is
               more
               than
               the
               halfe
               ,
               the
               other
               is
               lesse
               .
            
             
               Secondly
               ,
               it
               is
               difficult
               to
               finde
               two
               numbers
               whose
               summe
               and
               product
               is
               alike
               ,
               (
               that
               is
               )
               if
               the
               numbers
               be
               multiplied
               one
               by
               another
               ,
               and
               added
               together
               ,
               will
               be
               equall
               ,
               which
               two
               numbers
               are
               2
               and
               2
               ,
               for
               to
               multiply
               2
               by
               2
               makes
               4
               ,
               and
               adding
               2
               unto
               2
               makes
               the
               same
               :
               this
               property
               is
               in
               no
               other
               two
               whole
               numbers
               ,
               but
               in
               broken
               numbers
               there
               are
               infinite
               ,
               whose
               summe
               and
               product
               will
               be
               equall
               one
               to
               another
               .
               As
               Clavius
               shewes
               upon
               the
               36
               Pro.
               of
               the
               9t
               h
               book
               of
               Euclide
               .
            
             
             
               Thirdly
               ,
               the
               numbers
               5
               and
               6
               are
               called
               circular
               numbers
               ,
               because
               the
               circle
               turnes
               to
               the
               point
               from
               whence
               it
               begins
               :
               so
               these
               numbers
               multiplied
               by
               themselves
               ,
               do
               end
               alwayes
               in
               5
               and
               6
               ,
               as
               5
               times
               5
               makes
               25
               ,
               that
               againe
               by
               5
               makes
               125
               ,
               so
               6
               times
               6
               makes
               36
               ,
               and
               that
               by
               6
               makes
               216
               ,
               &c.
               
            
             
               Fourthly
               ,
               the
               number
               6
               ,
               is
               the
               first
               which
               Arithmeticians
               call
               a
               perfect
               number
               ,
               that
               is
               ,
               whose
               parts
               are
               equall
               unto
               it
               ,
               so
               the
               6
               part
               of
               it
               is
               1
               ,
               the
               third
               part
               is
               2
               ,
               the
               halfe
               is
               3
               ,
               which
               are
               all
               his
               parts
               :
               now
               1
               ,
               2
               ,
               and
               3
               ,
               is
               equall
               to
               6.
               
               It
               is
               wonderfull
               to
               conceive
               that
               there
               is
               so
               few
               of
               them
               ,
               and
               how
               rare
               these
               numbers
               are
               ▪
               50
               of
               perfect
               men
               :
               for
               betwixt
               1
               &
               1000000000000
               numbers
               there
               is
               but
               ten
               ,
               that
               is
               ;
               6
               ,
               28
               ,
               486.
               8128.
               120816.
               2096128.
               33550336.
               536854528.
               8589869056
               ,
               &
               137438691328
               ▪
               with
               this
               admirable
               property
               ,
               that
               alternately
               they
               end
               all
               in
               6
               and
               8
               ,
               &
               the
               twentieth
               perfect
               number
               is
               151115727451553768931328.
               
            
             
               Fiftly
               ,
               the
               number
               9
               amongst
               other
               priviledges
               carries
               with
               it
               an
               excellent
               property
               :
               for
               take
               what
               number
               you
               will
               ,
               either
               in
               grosse
               or
               in
               part
               ,
               the
               nines
               of
               the
               whole
               or
               in
               its
               parts
               rejected
               ,
               and
               taken
               simply
               will
               be
               the
               same
               ,
               as
               ●7
               it
               makes
               3
               times
               9
               ,
               so
               vvhether
               the
               nines
               be
               rejected
               of
               27
               ,
               or
               of
               the
               summe
               of
               2
               and
               7
               ,
               it
               is
               all
               one
               ,
               so
               if
               the
               nines
               vvere
               taken
               avvay
               of
               240.
               it
               is
               all
               one
               ,
               if
               the
               nines
               vvere
               taken
               avvay
               of
               2
               ,
               4
               ,
               and
               0
               ;
               for
               there
               vvould
               remaine
               6
               in
               either
               ;
               and
               so
               of
               others
               .
            
             
             
               Sixtly
               ,
               11
               being
               multiplied
               by
               2
               ,
               4
               ,
               5
               ,
               6
               ,
               7
               ,
               8
               ,
               or
               9
               ,
               will
               end
               and
               begin
               with
               like
               numbers
               ;
               so
               11
               multiplied
               by
               5
               makes
               55
               ,
               if
               multiplied
               by
               8
               ,
               it
               makes
               88
               ,
               &c.
               
            
             
               Seventhly
               ,
               the
               numbers
               220
               and
               284
               being
               unequall
               ,
               notwithstanding
               the
               parts
               of
               the
               one
               number
               do
               alwayes
               equalize
               the
               other
               number
               :
               so
               the
               aliquot
               parts
               of
               220
               are
               110
               ,
               54
               ,
               44
               ,
               22
               ,
               20
               ,
               11
               ,
               10
               ,
               5
               ,
               4
               ,
               2
               ,
               1
               ,
               which
               together
               makes
               284.
               the
               aliquot
               parts
               of
               284
               ,
               are
               142
               ,
               71
               ,
               4
               ,
               2
               ,
               1.
               which
               together
               makes
               220
               ,
               a
               thing
               rare
               and
               admirable
               ,
               and
               difficult
               to
               finde
               in
               other
               numbers
               .
            
             
             
             
               I●
               one
               be
               taken
               from
               any
               square
               number
               which
               is
               odde
               ,
               the
               square
               o●
               halfe
               of
               it
               being
               added
               to
               the
               first
               square
               ,
               will
               make
               a
               square
               number
               .
            
             
               The
               square
               of
               halfe
               any
               even
               number
               +
               .
               1
               being
               added
               to
               that
               even
               number
               makes
               a
               square
               number
               ,
               and
               the
               even
               number
               taken
               from
               it
               leaves
               a
               square
               number
               .
            
             
               If
               odde
               numbers
               be
               continually
               added
               from
               the
               unitie
               successively
               ,
               there
               will
               be
               made
               all
               square
               numbers
               ,
               and
               if
               cubick
               numbers
               be
               added
               successively
               from
               the
               unitie
               ,
               there
               will
               be
               likewise
               made
               square
               numbers
               .
            
          
           
             
               PROBLEM
               .
               LXIV
               .
               Of
               an
               excellent
               lamp
               ,
               which
               serves
               or
               furnisheth
               it selfe
               with
               oile
               ,
               and
               burnes
               a
               long
               time
               .
            
             
               I
               Speak
               not
               here
               of
               a
               common
               lamp
               which
               Ca●danus
               writes
               upon
               in
               his
               book
               
                 de
                 subtilita●●
              
               ,
               for
               that
               's
               a
               little
               vessell
               in
               columne-wise
               ,
               
               which
               is
               full
               of
               Oile
               ,
               and
               because
               there
               is
               but
               one
               little
               hole
               at
               the
               bottome
               neare
               the
               weeke
               or
               match
               ;
               the
               oile
               runnes
               not
               ,
               for
               feare
               that
               there
               be
               emptinesse
               above
               :
               when
               the
               match
               is
               kindled
               it
               begins
               to
               heat
               the
               lamp
               ,
               and
               rarefying
               the
               oile
               it
               issueth
               by
               this
               occasion
               :
               and
               so
               sends
               his
               more
               airie
               parts
               above
               to
               avoid
               vacuitie
               .
            
             
             
             
               It
               is
               certaine
               that
               such
               a
               lampe
               the
               Atheniaus
               used
               ,
               which
               lasted
               a
               whole
               yeare
               without
               being
               touched
               :
               which
               was
               placed
               before
               the
               statue
               of
               Minerva
               ,
               for
               they
               might
               put
               a
               certaine
               quantitie
               of
               oile
               in
               the
               lamp
               CD
               ,
               and
               a
               match
               to
               burne
               without
               being
               consumed
               :
               such
               as
               the
               naturalists
               write
               of
               ,
               by
               which
               the
               lamp
               will
               furnish
               it selfe
               ,
               and
               so
               continue
               in
               burning
               :
               and
               here
               may
               be
               noted
               that
               the
               oile
               may
               be
               poured
               in
               ,
               at
               the
               top
               of
               th●
               vessell
               at
               a
               little
               hole
               ,
               and
               then
               made
               fast
               againe
               that
               the
               aire
               get
               not
               in
               .
            
          
           
             
               PROBLEM
               .
               LXV
               .
               Of
               the
               play
               at
               Keyles
               or
               nine
               Pinnes
               .
            
             
               YOu
               will
               scarce
               beleeve
               that
               with
               one
               bowle
               and
               at
               one
               blow
               playing
               freely
               ,
               one
               may
               strike
               downe
               all
               the
               Keyles
               at
               once
               :
               yet
               from
               Mathematicall
               principles
               it
               is
               easie
               to
               be
               demonstrated
               ,
               that
               if
               the
               hand
               of
               him
               that
               playes
               were
               so
               well
               assured
               by
               experience
               ,
               as
               reason
               induceth
               one
               thereto
               ;
               one
               might
               at
               one
               blow
               strike
               downe
               all
               the
               Keyles
               ,
               of
               at
               least
               7
               or
               8
               ,
               or
               such
               a
               number
               as
               one
               pleaseth
               .
            
             
               For
               they
               are
               but
               9
               in
               all
               disposed
               or
               placed
               in
               a
               perfect
               square
               ,
               having
               three
               every
               way
               .
               Let
               us
               suppose
               then
               that
               a
               good
               player
               beginning
               to
               play
               at
               1
               somewhat
               low
               ,
               should
               so
               strike
               it
               ,
               that
               it
               should
               strike
               down
               the
               Keyles
               2
               and
               5
               ,
               and
               these
               might
               in
               their
               violence
               strike
               
               
               downe
               the
               Keyles
               3
               ,
               6
               ,
               and
               9
               ,
               and
               the
               bowle
               being
               in
               motion
               may
               strike
               down
               the
               Keyle
               4
               ,
               and
               7
               ;
               which
               4
               Keyle
               may
               strike
               the
               Keyle
               8
               ,
               &
               so
               all
               the
               9
               Keyles
               may
               be
               striken
               down
               at
               once
               .
            
          
           
             
               PROBLEM
               .
               LXIV
               .
               Of
               Spectacles
               of
               pleasure
               .
            
             
               SImple
               Spectacles
               of
               blew
               ,
               yellow
               ,
               red
               or
               green
               colour
               ,
               are
               proper
               to
               recreate
               the
               sight
               ,
               and
               will
               present
               the
               objects
               died
               in
               like
               colour
               that
               the
               Glasses
               are
               ,
               only
               those
               of
               the
               greene
               do
               somewhat
               degenerate
               ;
               instead
               of
               shewing
               a
               lively
               colour
               it
               will
               represent
               a
               pale
               dead
               colour
               ,
               and
               it
               is
               because
               they
               are
               not
               dyed
               greene
               enough
               ,
               or
               receive
               not
               light
               enough
               for
               greene
               :
               and
               colour
               these
               images
               that
               passe
               through
               these
               Glasses
               unto
               the
               bottome
               of
               the
               eye
               .
            
             
               
                 EXAMINATION
                 .
              
               
                 IT
                 is
                 certaine
                 ,
                 that
                 not
                 onely
                 Glasses
                 dyed
                 green
                 ,
                 but
                 all
                 other
                 Glasses
                 coloured
                 ,
                 yield
                 the
                 app●arances
                 of
                 objects
                 strong
                 or
                 weak
                 in
                 colour
                 according
                 to
                 the
                 quantity
                 of
                 the
                 dye
                 ,
                 more
                 or
                 lesse
                 ,
                 as
                 one
                 being
                 very
                 yellow
                 ,
                 
                 another
                 a
                 pale
                 yellow
                 ;
                 now
                 all
                 colours
                 are
                 not
                 proper
                 to
                 Glasses
                 to
                 give
                 colour
                 ,
                 hence
                 the
                 defect
                 is
                 not
                 that
                 they
                 want
                 facultie
                 to
                 receive
                 light
                 ,
                 or
                 resist
                 the
                 penetration
                 of
                 the
                 beams
                 ;
                 for
                 in
                 the
                 same
                 Glasses
                 those
                 which
                 are
                 most
                 dyed
                 ,
                 give
                 alwayes
                 the
                 objects
                 more
                 high
                 coloured
                 and
                 obscure
                 ,
                 and
                 those
                 which
                 are
                 lesse
                 dyed
                 give
                 them
                 more
                 pale
                 and
                 cleare
                 :
                 and
                 this
                 is
                 daily
                 made
                 manifest
                 by
                 the
                 painting
                 of
                 Glasse
                 ,
                 which
                 hinders
                 more
                 the
                 penetration
                 of
                 the
                 light
                 than
                 dying
                 doth
                 ,
                 where
                 all
                 the
                 matter
                 by
                 fire
                 is
                 forced
                 into
                 the
                 Glasse
                 ,
                 leaving
                 it
                 in
                 all
                 parts
                 transparent
                 .
              
               
                 Spectacles
                 of
                 Crystall
                 cut
                 with
                 divers
                 Angles
                 diamond-wise
                 do
                 make
                 a
                 marvellous
                 multiplication
                 of
                 the
                 appearances
                 ,
                 for
                 looking
                 towards
                 a
                 house
                 it
                 becomes
                 as
                 a
                 Towne
                 ,
                 a
                 Towne
                 becomes
                 like
                 a
                 Citie
                 ,
                 an
                 armed
                 man
                 seems
                 as
                 a
                 whole
                 company
                 caused
                 solely
                 by
                 the
                 diversity
                 of
                 refractions
                 ,
                 for
                 as
                 many
                 plaines
                 as
                 there
                 are
                 on
                 the
                 outside
                 of
                 the
                 spectacle
                 ,
                 so
                 many
                 times
                 will
                 the
                 object
                 be
                 multiplied
                 in
                 the
                 appearance
                 ,
                 because
                 of
                 diverse
                 Images
                 cast
                 into
                 the
                 eye
                 .
                 These
                 are
                 pleasurable
                 spectacles
                 for
                 avaricious
                 persons
                 that
                 love
                 Gold
                 and
                 silver
                 ,
                 for
                 one
                 piece
                 will
                 seeme
                 many
                 ,
                 or
                 one
                 heap
                 of
                 money
                 will
                 seeme
                 as
                 a
                 treasury
                 :
                 but
                 all
                 the
                 mischiefe
                 is
                 ,
                 he
                 will
                 not
                 have
                 his
                 end
                 in
                 the
                 enjoying
                 of
                 it
                 ,
                 for
                 indeavouring
                 to
                 take
                 
                 it
                 ,
                 it
                 will
                 appeare
                 but
                 a
                 deceitfull
                 Image
                 ,
                 or
                 delusion
                 of
                 nothing
                 .
                 Here
                 may
                 you
                 note
                 that
                 if
                 the
                 finger
                 be
                 directed
                 by
                 one
                 and
                 the
                 same
                 ray
                 or
                 beam
                 ,
                 which
                 pointeth
                 to
                 one
                 and
                 the
                 same
                 object
                 ,
                 then
                 at
                 the
                 first
                 you
                 may
                 touch
                 that
                 visible
                 object
                 without
                 being
                 deceived
                 :
                 otherwise
                 you
                 may
                 faile
                 often
                 in
                 touching
                 that
                 which
                 you
                 see
                 .
                 Againe
                 ,
                 there
                 are
                 Spectacles
                 made
                 which
                 do
                 diminish
                 the
                 thing
                 seen
                 very
                 much
                 ,
                 and
                 bring
                 it
                 to
                 a
                 faire
                 perspective
                 forme
                 ,
                 especially
                 if
                 one
                 look
                 upon
                 a
                 faire
                 Garden
                 plat
                 ,
                 a
                 greater
                 walk
                 ,
                 a
                 stately
                 building
                 ,
                 or
                 great
                 Court
                 ,
                 the
                 industry
                 of
                 an
                 exquisite
                 Painter
                 cannot
                 come
                 neare
                 to
                 expresse
                 the
                 lively
                 forme
                 of
                 it
                 as
                 this
                 Glasse
                 will
                 represent
                 it
                 ;
                 you
                 will
                 have
                 pleasure
                 to
                 see
                 it
                 really
                 experimented
                 ,
                 and
                 the
                 cause
                 of
                 this
                 is
                 ,
                 that
                 the
                 Glasses
                 of
                 th●se
                 Spectacles
                 are
                 hollow
                 and
                 thinner
                 in
                 the
                 middle
                 ,
                 than
                 at
                 the
                 edges
                 by
                 which
                 the
                 visuall
                 Angle
                 is
                 made
                 lesser
                 :
                 you
                 may
                 observe
                 a
                 further
                 secret
                 in
                 these
                 Spectacles
                 ,
                 for
                 in
                 placing
                 them
                 upon
                 a
                 window
                 one
                 may
                 see
                 those
                 that
                 passe
                 to
                 and
                 fro
                 in
                 the
                 streets
                 ,
                 without
                 being
                 seen
                 of
                 any
                 ,
                 for
                 their
                 property
                 is
                 to
                 raise
                 up
                 the
                 objects
                 that
                 it
                 lookes
                 upon
                 .
              
               
                 Now
                 I
                 would
                 not
                 passe
                 this
                 Probleme
                 without
                 saying
                 something
                 of
                 Galileus
                 admirable
                 Glasse
                 ,
                 for
                 the
                 common
                 simple
                 perspective
                 Glasses
                 give
                 to
                 aged
                 men
                 but
                 the
                 eyes
                 or
                 sight
                 of
                 young
                 men
                 ,
                 but
                 this
                 of
                 Galileus
                 gives
                 a
                 man
                 an
                 Eagles
                 eye
                 ,
                 or
                 an
                 eye
                 that
                 pierceth
                 the
                 heavens
                 :
                 first
                 it
                 discovereth
                 the
                 spottie
                 and
                 shadowed
                 opacous
                 bodies
                 that
                 are
                 found
                 about
                 the
                 Sunne
                 ,
                 which
                 darknet
                 and
                 diminisheth
                 the
                 splendor
                 of
                 that
                 beautifull
                 and
                 shining
                 Luminary
                 :
                 secondly
                 ,
                 it
                 shewes
                 the
                 new
                 Planets
                 that
                 accompany
                 
                 Saturne
                 and
                 Jupiter
                 :
                 thirdly
                 ,
                 in
                 Venus
                 is
                 seen
                 the
                 new
                 ,
                 full
                 ,
                 and
                 quartill
                 increase
                 ;
                 as
                 in
                 the
                 Moon
                 by
                 her
                 separation
                 from
                 the
                 Sunne
                 :
                 fourthly
                 ,
                 the
                 artificiall
                 structure
                 of
                 this
                 instrument
                 helpeth
                 us
                 to
                 see
                 an
                 innumerable
                 number
                 of
                 stars
                 ,
                 which
                 otherwise
                 are
                 obscured
                 ,
                 by
                 reason
                 of
                 the
                 naturall
                 weaknesse
                 of
                 our
                 sight
                 ,
                 yea
                 the
                 starres
                 in
                 
                   via
                   lactea
                
                 are
                 seen
                 most
                 apparantly
                 ;
                 where
                 there
                 seem
                 no
                 starres
                 to
                 be
                 ,
                 this
                 Instrument
                 makes
                 apparantly
                 to
                 be
                 seen
                 ,
                 and
                 further
                 delivers
                 them
                 to
                 the
                 eye
                 in
                 their
                 true
                 and
                 lively
                 colour
                 ,
                 as
                 they
                 are
                 in
                 the
                 heavens
                 :
                 in
                 which
                 the
                 splendor
                 of
                 some
                 is
                 as
                 the
                 Sunne
                 in
                 his
                 most
                 glorious
                 beauty
                 .
                 This
                 Glasse
                 hath
                 also
                 a
                 most
                 excellent
                 use
                 in
                 observing
                 the
                 body
                 of
                 the
                 Moone
                 in
                 time
                 of
                 Eclipses
                 ,
                 for
                 it
                 augments
                 it
                 manifold
                 ,
                 and
                 most
                 manifestly
                 shewes
                 the
                 true
                 forme
                 of
                 the
                 cloudy
                 substance
                 in
                 the
                 Sunne
                 ;
                 and
                 by
                 it
                 is
                 seene
                 when
                 the
                 shadow
                 of
                 the
                 earth
                 begins
                 to
                 eclipse
                 the
                 Moon
                 ,
                 &
                 when
                 totally
                 she
                 is
                 over
                 shadowed
                 :
                 besides
                 the
                 celestiall
                 uses
                 which
                 are
                 made
                 of
                 this
                 Glasse
                 ,
                 it
                 hath
                 another
                 noble
                 property
                 ;
                 it
                 farre
                 exceedeth
                 the
                 ordinary
                 perspective
                 Glasses
                 ,
                 which
                 are
                 used
                 to
                 see
                 things
                 remote
                 upon
                 the
                 earth
                 ,
                 for
                 as
                 this
                 Glasse
                 reacheth
                 up
                 to
                 the
                 heavens
                 and
                 excelleth
                 them
                 there
                 in
                 his
                 performance
                 ,
                 so
                 on
                 the
                 earth
                 it
                 claimeth
                 
                 preheminency
                 ,
                 for
                 the
                 objects
                 which
                 are
                 farthest
                 remote
                 ,
                 and
                 most
                 obscure
                 ,
                 are
                 seen
                 plainer
                 than
                 those
                 which
                 are
                 neere
                 at
                 hand
                 ,
                 scorning
                 as
                 it
                 were
                 all
                 small
                 and
                 triviall
                 services
                 ,
                 as
                 leaving
                 them
                 to
                 an
                 inferiour
                 help
                 :
                 great
                 use
                 may
                 be
                 made
                 of
                 this
                 Glass
                 in
                 discovering
                 of
                 Ships
                 ,
                 Armies
                 ,
                 &c.
                 
                 Now
                 the
                 apparell
                 or
                 parts
                 of
                 this
                 instrument
                 or
                 Glasse
                 ,
                 is
                 very
                 meane
                 or
                 simple
                 ,
                 which
                 makes
                 it
                 the
                 more
                 admirable
                 (
                 seeing
                 it
                 performes
                 such
                 great
                 service
                 )
                 having
                 but
                 a
                 convex
                 Glasse
                 thickest
                 in
                 the
                 middle
                 ,
                 to
                 unite
                 and
                 amasse
                 the
                 rayes
                 ,
                 and
                 mak
                 the
                 object
                 the
                 greater
                 :
                 to
                 the
                 augmenting
                 the
                 visuall
                 Angle
                 ,
                 as
                 also
                 a
                 pipe
                 or
                 trunk
                 to
                 amasse
                 the
                 Species
                 ,
                 and
                 hinder
                 the
                 greatness
                 of
                 the
                 light
                 which
                 is
                 about
                 it
                 :
                 
                   (
                   to
                   see
                   well
                   ,
                   the
                   object
                   must
                   be
                   well
                   inlightened
                   ,
                   and
                   the
                   eye
                   in
                   obscurity
                   ;
                   )
                
                 then
                 there
                 is
                 adjoyned
                 unto
                 it
                 a
                 Glasse
                 of
                 a
                 short
                 sight
                 to
                 distinguish
                 the
                 rayes
                 ,
                 which
                 the
                 other
                 would
                 make
                 more
                 confused
                 if
                 alone
                 .
                 As
                 for
                 the
                 proportion
                 of
                 those
                 Glasses
                 to
                 the
                 Trunk
                 ,
                 though
                 there
                 be
                 certaine
                 rules
                 to
                 make
                 them
                 ,
                 yet
                 it
                 is
                 often
                 by
                 hazard
                 that
                 there
                 is
                 made
                 an
                 excellent
                 one
                 there
                 being
                 so
                 many
                 difficulties
                 in
                 the
                 action
                 ,
                 therefore
                 many
                 ought
                 to
                 be
                 tryed
                 ,
                 seeing
                 that
                 exact
                 proportion
                 ,
                 in
                 Geometricall
                 calculation
                 cannot
                 serve
                 for
                 diversity
                 of
                 sights
                 in
                 the
                 observation
                 .
              
            
          
           
             
             
               PROBLEM
               .
               LXVII
               .
               Of
               the
               Adamant
               or
               Magnes
               ,
               and
               the
               needles
               touched
               therewith
               .
            
             
               WHo
               would
               beleeve
               if
               he
               saw
               not
               with
               his
               eyes
               ,
               that
               a
               needle
               of
               steel
               being
               once
               touched
               with
               the
               magnes
               ,
               turnes
               not
               once
               ,
               not
               a
               yeare
               ▪
               but
               as
               long
               as
               the
               World
               lasteth
               ;
               his
               end
               towards
               the
               North
               and
               South
               ,
               yea
               though
               one
               remove
               it
               ,
               and
               turne
               it
               from
               his
               position
               ,
               it
               will
               come
               againe
               to
               his
               points
               of
               North
               and
               South
               .
               Who
               would
               have
               ever
               thought
               that
               a
               brute
               stone
               black
               and
               ill
               formed
               ,
               touching
               a
               ring
               of
               Iron
               ,
               should
               hang
               it
               in
               the
               aire
               ,
               and
               that
               ring
               support
               a
               second
               ,
               that
               to
               support
               a
               third
               ,
               and
               so
               unto
               10
               ,
               12
               ,
               or
               more
               ,
               according
               to
               the
               strength
               of
               the
               magnes
               ;
               making
               as
               it
               vvere
               a
               chaine
               without
               a
               line
               ,
               without
               souldering
               together
               ,
               or
               without
               any
               other
               thing
               to
               support
               them
               onely
               ;
               but
               a
               most
               occult
               and
               hidden
               vertue
               ,
               yet
               most
               evident
               in
               this
               effect
               ,
               which
               penetrateth
               insensibly
               from
               the
               first
               to
               the
               second
               ,
               from
               the
               second
               to
               the
               third
               ,
               &c.
               
            
             
             
               What
               is
               there
               in
               the
               world
               that
               is
               more
               capable
               to
               cast
               a
               deeper
               astonishment
               in
               our
               minds
               than
               a
               great
               massie
               substance
               of
               Iron
               to
               hang
               in
               the
               aire
               in
               the
               middest
               of
               a
               building
               without
               any
               thing
               in
               the
               world
               touching
               it
               ,
               only
               but
               the
               aire
               ?
               As
               some
               histories
               assure
               us
               ,
               that
               by
               the
               aid
               of
               a
               Magnes
               or
               Adamant
               ,
               placed
               at
               the
               roof
               of
               one
               of
               the
               Turkish
               Synagogues
               in
               Meca
               :
               the
               sepulchre
               of
               that
               infamous
               Mah●met
               rests
               suspended
               in
               the
               aire
               ;
               and
               Plinie
               in
               his
               naturall
               Historie
               writes
               that
               the
               Architect
               or
               Democrates
               did
               begin
               to
               vault
               the
               Temple
               of
               A●sin●e
               in
               Alexandria
               ,
               with
               store
               of
               magnes
               to
               produce
               the
               like
               deceit
               ,
               to
               hang
               the
               sepulchre
               of
               that
               Goddesse
               likewise
               in
               the
               aire
               .
            
             
               I
               should
               passe
               the
               bounds
               of
               my
               counterpoise
               ,
               if
               I
               should
               divulge
               all
               the
               secrets
               of
               this
               
               stone
               ,
               and
               should
               expose
               my selfe
               to
               the
               laughter
               of
               the
               world
               :
               if
               I
               should
               brag
               to
               shew
               others
               the
               cause
               how
               this
               appeareth
               ,
               than
               in
               its
               owne
               naturall
               sympathy
               ,
               for
               why
               is
               it
               that
               a
               magnes
               with
               one
               end
               will
               cast
               the
               Iron
               away
               ,
               &
               attract
               it
               with
               the
               other
               ?
               from
               whence
               commeth
               it
               that
               all
               the
               magnes
               is
               not
               proper
               to
               give
               a
               true
               touch
               to
               the
               needle
               ,
               but
               only
               in
               the
               two
               Poles
               of
               the
               stone
               :
               which
               is
               known
               by
               hanging
               the
               stone
               by
               a
               threed
               in
               the
               aire
               untill
               it
               be
               quiet
               ,
               or
               placed
               upon
               a
               peece
               of
               Cork
               in
               a
               dish
               of
               water
               ,
               or
               upon
               some
               thinne
               board
               ,
               for
               the
               Pole
               of
               the
               stone
               will
               then
               turne
               towards
               the
               Poles
               of
               the
               world
               ,
               and
               point
               out
               the
               North
               and
               South
               ,
               and
               so
               shew
               by
               which
               of
               these
               ends
               the
               needle
               is
               to
               be
               touched
               ?
            
             
               From
               whence
               comes
               it
               that
               there
               is
               a
               variation
               in
               the
               needle
               ,
               and
               pointeth
               not
               out
               truly
               the
               North
               and
               South
               of
               the
               world
               ,
               but
               only
               in
               some
               place
               of
               the
               earth
               ?
            
             
               How
               is
               it
               that
               the
               needle
               made
               with
               pegges
               and
               inclosed
               within
               two
               Glasses
               ,
               sheweth
               the
               height
               of
               the
               Pole
               ,
               being
               elevated
               as
               many
               degrees
               as
               the
               Pole
               is
               above
               the
               Horizon
               ?
            
             
               What
               's
               the
               cause
               that
               fire
               and
               Garlick
               takes
               away
               the
               propertie
               of
               the
               magnes
               ?
               There
               are
               many
               great
               hidden
               mysteries
               in
               this
               stone
               ,
               which
               have
               troubled
               the
               heads
               of
               the
               most
               learned
               in
               all
               ages
               ;
               and
               to
               this
               time
               the
               world
               remaines
               ignorant
               of
               declaring
               the
               rrue
               cause
               thereof
               .
            
             
               Some
               say
               ,
               that
               by
               help
               of
               the
               Magnes
               persons
               which
               are
               absent
               may
               know
               each
               others
               
               minde
               ,
               as
               if
               one
               being
               here
               at
               London
               ,
               and
               another
               at
               Prague
               in
               Germany
               :
               if
               each
               of
               them
               had
               a
               needle
               touched
               with
               one
               magnes
               ,
               then
               the
               vertue
               is
               such
               that
               in
               the
               same
               time
               that
               the
               needle
               which
               is
               at
               Prague
               shall
               move
               ,
               this
               that
               is
               at
               London
               shall
               also
               ;
               provided
               that
               the
               parties
               have
               like
               secret
               notes
               or
               alphabets
               ,
               and
               the
               observation
               be
               at
               a
               set
               houre
               of
               the
               day
               or
               night
               ;
               and
               when
               the
               one
               party
               will
               declare
               unto
               the
               other
               ,
               then
               let
               that
               party
               move
               the
               needle
               to
               these
               letters
               which
               will
               declare
               the
               matter
               to
               the
               other
               ,
               and
               the
               moving
               of
               the
               other
               parties
               needle
               shall
               open
               his
               intention
               .
            
             
               The
               invention
               is
               subtile
               ,
               but
               I
               doubt
               whether
               in
               the
               world
               there
               can
               be
               found
               so
               great
               a
               stone
               ▪
               or
               such
               a
               Magnes
               which
               carries
               with
               it
               such
               vertue
               :
               neither
               is
               it
               expedient
               ,
               for
               treasons
               would
               be
               then
               too
               frequent
               and
               open
               .
            
             
               
                 EXAMINATION
                 .
              
               
                 THe
                 experimentall
                 difference
                 of
                 rejection
                 ,
                 and
                 attraction
                 proceeds
                 not
                 from
                 the
                 different
                 nature
                 of
                 Stones
                 ,
                 but
                 from
                 the
                 quality
                 of
                 the
                 Iron
                 ;
                 and
                 the
                 vertue
                 of
                 the
                 stone
                 consisteth
                 only
                 ,
                 and
                 especially
                 in
                 his
                 poles
                 ,
                 which
                 being
                 hanged
                 in
                 the
                 Aire
                 ,
                 turnes
                 one
                 of
                 his
                 ends
                 alwayes
                 naturally
                 towards
                 the
                 South
                 ,
                 and
                 the
                 other
                 towards
                 the
                 North
                 :
                 but
                 if
                 a
                 rod
                 of
                 Iron
                 be
                 touched
                 with
                 one
                 of
                 the
                 ends
                 thereof
                 ,
                 it
                 hath
                 the
                 like
                 property
                 in
                 
                 turning
                 North
                 and
                 South
                 ,
                 as
                 the
                 magnes
                 hath
                 :
                 notwithstanding
                 the
                 end
                 of
                 the
                 Iron
                 Rod
                 touched
                 ,
                 hath
                 a
                 contrary
                 position
                 ,
                 to
                 that
                 end
                 of
                 the
                 stone
                 that
                 touched
                 it
                 ;
                 yet
                 the
                 same
                 end
                 will
                 attract
                 it
                 ,
                 and
                 the
                 other
                 end
                 reject
                 it
                 :
                 and
                 so
                 contrarily
                 this
                 may
                 easily
                 be
                 experimented
                 upon
                 two
                 needles
                 touched
                 with
                 one
                 or
                 different
                 stones
                 ,
                 though
                 they
                 have
                 one
                 and
                 the
                 same
                 position
                 ;
                 for
                 as
                 you
                 come
                 unto
                 them
                 apply
                 one
                 end
                 of
                 the
                 magnes
                 neare
                 unto
                 them
                 ,
                 the
                 North
                 of
                 the
                 one
                 will
                 abhorre
                 the
                 North
                 of
                 the
                 other
                 ,
                 but
                 the
                 North
                 of
                 the
                 one
                 will
                 alwayes
                 approach
                 to
                 the
                 South
                 of
                 the
                 other
                 :
                 and
                 the
                 same
                 affection
                 is
                 in
                 the
                 stones
                 themselves
                 .
                 For
                 the
                 finding
                 of
                 the
                 Poles
                 of
                 the
                 magnes
                 ,
                 it
                 may
                 be
                 done
                 by
                 holding
                 a
                 small
                 needle
                 between
                 your
                 fingers
                 softly
                 ,
                 and
                 so
                 moving
                 it
                 from
                 part
                 to
                 part
                 over
                 the
                 stone
                 untill
                 it
                 be
                 held
                 perpendicular
                 ,
                 for
                 that
                 shall
                 be
                 one
                 of
                 the
                 Poles
                 of
                 the
                 stone
                 which
                 you
                 may
                 marke
                 out
                 ;
                 in
                 like
                 manner
                 finde
                 out
                 the
                 other
                 Pole
                 :
                 Now
                 to
                 finde
                 out
                 which
                 of
                 those
                 Poles
                 is
                 North
                 or
                 South
                 ,
                 place
                 a
                 needle
                 being
                 touched
                 with
                 one
                 of
                 the
                 Poles
                 upon
                 a
                 smooth
                 convex
                 body
                 ,
                 (
                 as
                 the
                 naile
                 of
                 ones
                 finger
                 or
                 such
                 like
                 ,
                 )
                 and
                 marke
                 which
                 way
                 the
                 end
                 of
                 the
                 needle
                 that
                 was
                 touched
                 turneth
                 :
                 if
                 to
                 the
                 South
                 ,
                 then
                 the
                 point
                 that
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 touched
                 it
                 was
                 the
                 South-Pole
                 ,
                 &c.
                 and
                 it
                 is
                 most
                 certain
                 and
                 according
                 to
                 reason
                 and
                 experience
                 :
                 that
                 if
                 it
                 be
                 suspended
                 in
                 aequilibrio
                 in
                 the
                 aire
                 ,
                 or
                 supported
                 upon
                 the
                 water
                 ,
                 it
                 will
                 turne
                 contrary
                 to
                 the
                 needle
                 that
                 toucheth
                 it
                 ;
                 for
                 then
                 the
                 pole
                 that
                 was
                 marked
                 for
                 the
                 South
                 shall
                 turne
                 to
                 the
                 North
                 ,
                 &c.
                 
              
            
          
           
             
               PROBLEM
               .
               LXVIII
               .
               Of
               the
               properties
               of
               Aeolipiles
               or
               bowels
               to
               blow
               the
               fire
               .
            
             
               THese
               are
               concave
               vessels
               of
               Brass
               or
               Copper
               or
               other
               material
               ,
               which
               may
               indure
               the
               ,
               fire
               :
               having
               a
               small
               hole
               very
               narrow
               ,
               by
               which
               it
               is
               filled
               with
               water
               ,
               then
               placing
               it
               to
               the
               fire
               ,
               before
               it
               be
               hot
               there
               is
               no
               effect
               seen
               ;
               but
               assoone
               as
               the
               heat
               doth
               penetrate
               it
               ,
               the
               water
               begins
               to
               rarefie
               ,
               &
               issueth
               forth
               with
               a
               hidious
               and
               marvelous
               force
               ;
               it
               is
               pleasure
               to
               see
               how
               it
               blowes
               the
               fire
               with
               great
               noise
               .
            
             
             
               Novv
               touching
               the
               forme
               of
               these
               vessels
               ,
               they
               are
               not
               made
               of
               one
               like
               fashion
               :
               some
               makes
               them
               like
               a
               bovvle
               ,
               some
               like
               a
               head
               painted
               representing
               the
               vvinde
               ,
               some
               make
               them
               like
               a
               Peare
               :
               as
               though
               one
               vvould
               put
               it
               to
               rost
               at
               the
               fire
               ,
               vvhen
               one
               vvould
               have
               it
               to
               blovv
               ,
               for
               the
               taile
               of
               it
               is
               hollovv
               ,
               in
               forme
               of
               a
               funnell
               ,
               having
               at
               the
               top
               a
               very
               little
               hole
               no
               greater
               than
               the
               head
               of
               a
               pinne
               .
            
             
               Some
               do
               accustome
               to
               put
               vvithin
               the
               Aeolipile
               a
               crooked
               funnell
               of
               many
               foldings
               ,
               to
               the
               end
               that
               the
               vvinde
               that
               impetuously
               rolles
               ▪
               to
               and
               fro
               vvithin
               ,
               may
               imitate
               the
               noise
               of
               thunder
               .
               Others
               content
               themselves
               vvith
               a
               simple
               funnell
               placed
               right
               upvvard
               ,
               somevvhat
               vvider
               at
               the
               top
               than
               elsevvhere
               like
               a
               Cone
               ,
               vvhose
               basis
               is
               the
               mouth
               of
               the
               funnell
               :
               and
               there
               may
               be
               placed
               a
               bovvle
               of
               Iron
               or
               Brasse
               ,
               vvhich
               by
               the
               vapours
               that
               are
               cast
               out
               vvill
               cause
               it
               to
               leap
               up
               ,
               and
               dance
               over
               the
               mouth
               of
               the
               Aeolipile
               .
            
             
               Lastly
               ,
               some
               apply
               near
               to
               the
               hole
               smal
               Windmils
               ,
               or
               such
               like
               ,
               vvhich
               easily
               turne
               by
               reason
               of
               the
               vapours
               ;
               or
               by
               help
               of
               tvvo
               or
               more
               bovved
               funnels
               ,
               a
               bowle
               may
               be
               made
               to
               turne●
               these
               Aeolipiles
               are
               of
               excellent
               use
               for
               the
               melting
               of
               mettalls
               and
               such
               like
               .
            
             
             
               Now
               it
               is
               cunning
               and
               subtiltie
               to
               fill
               one
               of
               these
               Aeolipiles
               with
               water
               at
               so
               little
               a
               hole
               ,
               and
               therefore
               requires
               the
               knowledge
               of
               a
               Philosopher
               to
               finde
               it
               out
               :
               and
               the
               way
               is
               thus
               .
            
             
               Heat
               the
               Aeolipiles
               being
               empty
               ,
               and
               the
               aire
               which
               is
               within
               it
               will
               become
               extreamely
               rarefied
               ;
               then
               being
               thus
               hot
               throw
               it
               into
               water
               ,
               and
               the
               aire
               will
               begin
               to
               be
               condensed
               :
               by
               which
               meanes
               it
               will
               occupie
               lesse
               roome
               ,
               therefore
               the
               water
               will
               immediately
               enter
               in
               at
               the
               hole
               to
               avoide
               vacuitie
               :
               thus
               you
               have
               some
               practicall
               speculation
               upon
               the
               Aeolipile
               .
            
          
           
             
               PROBLEM
               .
               LXIX
               .
               Of
               the
               Thermometer
               :
               or
               an
               instrument
               to
               measure
               the
               degrees
               of
               heat
               and
               cold
               in
               the
               aire
               .
            
             
               THis
               Instrument
               is
               like
               a
               Cylindricall
               pipe
               of
               Glasse
               ,
               which
               hath
               a
               little
               ball
               or
               bowle
               at
               the
               toppe
               ▪
               the
               small
               end
               of
               which
               is
               placed
               into
               a
               vessell
               of
               water
               below
               ,
               as
               by
               the
               figure
               may
               be
               seene
               .
            
             
               Then
               put
               some
               coloured
               liquor
               into
               the
               Cylindricall
               glasse
               ,
               as
               blew
               ,
               red
               ,
               yellow
               ,
               green
               ,
               or
               such
               like
               :
               such
               as
               is
               not
               thick
               .
               This
               being
               done
               the
               use
               may
               be
               thus
               .
            
             
             
               Those
               that
               will
               determine
               this
               change
               by
               numbers
               and
               degrees
               ,
               may
               draw
               a
               line
               upon
               the
               Cylinder
               of
               the
               Thermometer
               ;
               and
               divide
               it
               into
               4
               degrees
               ,
               according
               to
               the
               ancient
               Philosophers
               ,
               or
               into
               4
               degrees
               according
               to
               the
               Physicians
               ,
               dividing
               each
               of
               these
               8
               into
               8
               others
               :
               to
               have
               in
               all
               64
               divisions
               ,
               &
               by
               this
               vvay
               they
               may
               not
               only
               distinguish
               upon
               vvhat
               degree
               the
               vvater
               ascendeth
               in
               the
               morning
               ,
               at
               midday
               ,
               &
               at
               any
               other
               houre
               :
               but
               also
               one
               may
               knovv
               hovv
               much
               one
               day
               is
               hotter
               or
               colder
               than
               another
               :
               by
               marking
               hovv
               many
               degrees
               the
               vvater
               ascendeth
               or
               descendeth
               ,
               one
               may
               compare
               the
               hottest
               and
               coldest
               dayes
               in
               a
               vvhole
               year
               together
               vvith
               these
               of
               another
               year
               :
               againe
               one
               may
               knovv
               hovv
               much
               hotter
               one
               roome
               is
               than
               another
               ,
               by
               vvhich
               also
               one
               might
               keep
               a
               chamber
               ,
               a
               furnace
               ,
               a
               stove
               ,
               &c.
               alvvayes
               in
               an
               equalitie
               of
               heat
               ,
               by
               making
               the
               vvater
               of
               the
               Thermometer
               rest
               alvvayes
               upon
               one
               &
               the
               same
               degree
               :
               in
               brief
               ,
               one
               may
               judge
               in
               some
               measure
               the
               burning
               of
               Fevers
               ,
               and
               neare
               unto
               what
               extension
               the
               aire
               can
               be
               rarefied
               by
               the
               greatest
               heat
               .
            
             
               Many
               make
               use
               of
               these
               glasses
               to
               judge
               of
               the
               vveather
               :
               for
               it
               is
               observed
               that
               if
               the
               vvater
               fall
               in
               3
               or
               4
               hours
               a
               degree
               or
               thereabout
               ,
               that
               raine
               insueth
               ;
               and
               the
               vvater
               vvill
               stand
               at
               that
               stay
               ,
               untill
               the
               vveather
               change
               :
               marke
               the
               water
               at
               your
               going
               to
               bed
               ,
               for
               if
               in
               the
               morning
               it
               hath
               descended
               raine
               followeth
               ,
               but
               if
               it
               be
               
               mounted
               higher
               ,
               it
               argueth
               faire
               weather
               :
               so
               in
               very
               cold
               weather
               ,
               if
               it
               fall
               suddenly
               ,
               it
               is
               snow
               or
               some
               sleekey
               weather
               that
               wiil
               insue
               ,
            
          
           
             
               PROBLEM
               .
               LXX
               .
               Of
               the
               proportion
               of
               humane
               bodies
               of
               statues
               ,
               of
               Colossus
               or
               huge
               images
               ,
               and
               of
               monstrous
               Giants
               .
            
             
               PYthagoras
               had
               reason
               to
               say
               that
               man
               is
               the
               measure
               of
               all
               things
               .
            
             
               First
               ,
               because
               he
               is
               the
               most
               perfect
               amongst
               all
               bodily
               creatures
               ,
               &
               according
               to
               the
               Maxime
               of
               Philosophers
               ,
               that
               which
               is
               most
               perfect
               and
               the
               first
               in
               rank
               ,
               measureth
               all
               the
               rest
               .
            
             
               Secondly
               ,
               because
               in
               effect
               the
               ordinary
               measure
               of
               a
               foot
               ,
               the
               inch
               ,
               the
               cubit
               ,
               the
               pace
               ,
               have
               taken
               their
               names
               and
               greatnesse
               from
               humane
               bodies
               .
            
             
               Thirdly
               ,
               because
               the
               symmetrie
               and
               concordancie
               of
               the
               parts
               is
               so
               admirable
               ,
               that
               all
               workes
               which
               are
               well
               proportionable
               ,
               as
               namely
               the
               building
               of
               Temples
               ,
               of
               Shippes
               ,
               of
               Pillars
               ,
               and
               such
               like
               pieces
               of
               Architecture
               ,
               are
               in
               some
               measure
               fashioned
               and
               composed
               after
               his
               proportion
               .
               And
               we
               know
               that
               the
               Arke
               of
               Noah
               built
               by
               the
               commandement
               of
               God
               ,
               was
               in
               length
               300
               Cubits
               ,
               in
               breadth
               50
               Cubits
               ,
               in
               height
               or
               depth
               30
               cubits
               ,
               so
               that
               the
               length
               containes
               the
               breadth
               6
               times
               ,
               and
               10
               times
               the
               depth
               :
               now
               a
               man
               being
               measured
               
               you
               will
               finde
               him
               to
               have
               the
               same
               proportion
               in
               length
               ,
               breadth
               ,
               and
               depth
               .
            
             
               Vilalpandus
               treating
               of
               the
               Temple
               of
               Solomon
               (
               that
               chieftaine
               of
               works
               )
               was
               modulated
               all
               of
               good
               Architecture
               ,
               and
               curiously
               to
               be
               observed
               in
               many
               pieces
               to
               keep
               the
               same
               proportion
               as
               the
               body
               to
               his
               parts
               :
               so
               that
               by
               the
               greatnesse
               of
               the
               work
               and
               proportionable
               symmetrie
               ,
               some
               dare
               assure
               themselves
               that
               by
               knowledge
               of
               one
               onely
               part
               of
               that
               building
               ,
               one
               might
               know
               all
               the
               measures
               of
               that
               goodly
               structure
               .
            
             
               Some
               Architects
               say
               that
               the
               foundation
               of
               houses
               ,
               and
               basis
               of
               columnes
               ,
               are
               as
               the
               foot
               ;
               the
               top
               ,
               and
               roofe
               as
               the
               head
               ;
               the
               rest
               as
               the
               body
               :
               those
               which
               have
               beene
               somewhat
               more
               curious
               ,
               have
               noted
               that
               as
               in
               humane
               bodies
               ,
               the
               parts
               are
               uniforme
               ,
               as
               the
               nose
               ,
               the
               mouth
               ,
               &c.
               these
               which
               are
               double
               are
               put
               on
               one
               side
               or
               other
               ,
               with
               a
               perfect
               equality
               in
               the
               same
               Architecture
               .
            
             
               In
               like
               manner
               ,
               some
               have
               been
               yet
               more
               curious
               than
               solid
               ;
               comparing
               all
               the
               ornaments
               of
               a
               Corinth
               to
               the
               parts
               of
               the
               face
               ,
               as
               the
               brow
               ,
               the
               eyes
               ,
               the
               nose
               ,
               the
               mouth
               ;
               the
               rounding
               of
               Pillars
               ,
               to
               the
               vvrithing
               of
               haire
               ,
               the
               channells
               of
               columnes
               ,
               to
               the
               fouldings
               of
               vvomens
               Robes
               ,
               &c.
               
            
             
               Novv
               building
               being
               a
               vvork
               of
               the
               best
               Artist
               ,
               there
               is
               much
               reason
               vvhy
               man
               ought
               to
               make
               his
               imitation
               from
               the
               chiefe
               vvork
               of
               nature
               ;
               vvhich
               is
               man.
               
            
             
               Hence
               it
               is
               that
               Vitru●ius
               in
               his
               third
               book
               ,
               
               and
               all
               the
               best
               Architectes
               ,
               treate
               of
               the
               proportion
               of
               man
               ;
               amongst
               others
               
                 Albert
                 Durens
              
               hath
               made
               a
               whole
               book
               of
               the
               measures
               of
               mans
               body
               ,
               from
               the
               foot
               to
               the
               head
               ,
               let
               them
               read
               it
               who
               wil
               ,
               they
               may
               have
               a
               prefect
               knowledge
               thereof
               :
               But
               I
               will
               content
               my selfe
               and
               it
               may
               satisfie
               some
               with
               that
               which
               followeth
               .
            
             
               First
               ,
               the
               length
               of
               a
               man
               well
               made
               ,
               which
               commonly
               is
               called
               height
               ,
               is
               equall
               to
               the
               distance
               from
               one
               end
               of
               his
               finger
               to
               the
               other
               :
               when
               the
               armes
               are
               extended
               as
               wide
               as
               they
               may
               be
               .
            
             
               Secondly
               ,
               if
               a
               man
               have
               his
               feet
               and
               hands
               extended
               or
               stretched
               in
               forme
               of
               S.
               Andrews
               Crosse
               ,
               placing
               one
               foot
               of
               a
               paire
               of
               Compasses
               upon
               his
               navill
               ,
               one
               may
               describe
               a
               circle
               which
               will
               passe
               by
               the
               ends
               of
               his
               hands
               and
               feet
               ,
               and
               drawing
               lines
               by
               the
               termes
               of
               the
               hands
               and
               feet
               ,
               you
               have
               a
               square
               within
               a
               circle
               .
            
             
               Thirdly
               ,
               the
               breadth
               of
               man
               ,
               or
               the
               space
               which
               is
               from
               one
               side
               to
               another
               ;
               the
               breast
               ,
               the
               head
               ,
               and
               the
               neck
               ,
               make
               the
               6
               part
               of
               all
               the
               body
               taken
               in
               length
               or
               height
               .
            
             
               Fourthly
               ,
               the
               length
               of
               the
               face
               is
               equall
               to
               the
               length
               of
               the
               hand
               ,
               taken
               from
               the
               small
               of
               the
               arme
               ,
               unto
               the
               extremity
               of
               the
               longest
               finger
               .
            
             
               Fiftly
               ,
               the
               thicknesse
               of
               the
               body
               taken
               from
               the
               belly
               to
               the
               back
               ;
               the
               one
               or
               the
               other
               is
               the
               tenth
               part
               of
               the
               whole
               body
               ,
               or
               as
               some
               will
               have
               it
               ,
               the
               ninth
               part
               ,
               little
               lesse
               .
            
             
               Sixtly
               ,
               the
               height
               of
               the
               brow
               ,
               the
               length
               of
               
               the
               nose
               ,
               the
               space
               between
               the
               nose
               and
               the
               chinne
               ,
               the
               length
               of
               the
               eares
               ,
               the
               greatnesse
               of
               the
               thumbe
               ,
               are
               perfectly
               equall
               one
               to
               the
               other
               .
            
             
               What
               would
               you
               say
               to
               make
               an
               admirable
               report
               of
               the
               other
               parts
               ,
               if
               I
               should
               reckon
               them
               in
               their
               least
               ?
               but
               in
               that
               I
               desire
               to
               be
               excused
               ,
               and
               will
               rather
               extract
               some
               conclusion
               upon
               ▪
               that
               which
               is
               delivered
               .
            
             
               In
               the
               first
               place
               ,
               knowing
               the
               proportion
               of
               a
               man
               ,
               it
               is
               easie
               to
               Painters
               ,
               Image-makers
               ,
               &c.
               perfectly
               to
               proportionate
               their
               work
               ;
               and
               by
               the
               same
               is
               made
               most
               evident
               ,
               that
               which
               is
               related
               of
               the
               images
               and
               statues
               of
               Greece
               ,
               that
               upon
               a
               day
               diverse
               workmen
               having
               enterprised
               to
               make
               the
               face
               of
               a
               man
               ,
               being
               severed
               one
               from
               another
               in
               sundry
               places
               ,
               all
               the
               parts
               being
               made
               and
               put
               together
               ,
               the
               face
               was
               found
               in
               a
               most
               lively
               and
               true
               proportion
               .
            
             
               Secondly
               ,
               it
               is
               a
               thing
               most
               cleare
               ,
               that
               by
               the
               help
               of
               proportion
               ,
               the
               body
               of
               Hercules
               was
               measured
               by
               the
               knowledge
               of
               his
               foot
               onely
               ,
               a
               Lion
               by
               his
               claw
               ,
               the
               Giant
               by
               his
               thumb
               ,
               and
               a
               man
               by
               any
               part
               of
               his
               body
               .
               For
               so
               it
               was
               that
               Pythagoras
               having
               measured
               the
               length
               of
               Hercules
               foot
               ,
               by
               the
               steps
               which
               were
               left
               upon
               the
               ground
               ,
               found
               out
               all
               his
               height
               :
               and
               so
               it
               was
               that
               Phidias
               having
               onely
               the
               claw
               of
               a
               Lion
               ,
               did
               figure
               and
               draw
               out
               all
               the
               beast
               according
               to
               his
               true
               type
               or
               forme
               ,
               so
               the
               exquisite
               Painter
               Timantes
               ,
               having
               painted
               a
               Pygmey
               or
               Dwarfe
               ,
               which
               he
               measured
               with
               a
               fadome
               made
               with
               the
               inch
               of
               a
               Giant
               ,
               it
               was
               sufficient
               
               to
               know
               the
               greatnesse
               of
               that
               Giant
               -
            
             
               To
               be
               short
               ,
               we
               may
               by
               like
               methode
               come
               easily
               to
               the
               knowledge
               of
               many
               fine
               antiquities
               touching
               Statues
               ,
               Colossus
               ,
               and
               monstrous
               Giants
               ,
               onely
               supposing
               one
               had
               found
               but
               one
               only
               part
               of
               them
               ,
               as
               the
               head
               ,
               the
               hand
               ,
               the
               foot
               or
               some
               bone
               mentioned
               in
               ancient
               Histories
               .
            
             
               
                 Of
                 Statues
                 ,
                 of
                 Colossus
                 ,
                 or
                 huge
                 images
                 .
              
               
                 VItruvius
                 relates
                 in
                 his
                 second
                 book
                 ,
                 that
                 the
                 
                   Architect
                   Dinocrates
                
                 was
                 desirous
                 to
                 put
                 out
                 to
                 the
                 world
                 some
                 notable
                 thing
                 ,
                 went
                 to
                 Alexander
                 the
                 great
                 ,
                 and
                 proposed
                 unto
                 him
                 a
                 high
                 and
                 speciall
                 piece
                 of
                 work
                 which
                 he
                 had
                 projected
                 :
                 as
                 to
                 figure
                 out
                 the
                 mount
                 Athos
                 in
                 forme
                 of
                 a
                 great
                 Statue
                 ,
                 which
                 should
                 hold
                 in
                 his
                 right
                 hand
                 a
                 Towne
                 capable
                 to
                 receive
                 ten
                 thousand
                 men
                 :
                 and
                 in
                 his
                 left
                 hand
                 a
                 vessell
                 to
                 receive
                 all
                 the
                 water
                 that
                 floweth
                 from
                 the
                 Mountaine
                 ,
                 which
                 with
                 an
                 ingine
                 should
                 cast
                 into
                 the
                 Sea.
                 This
                 is
                 a
                 pretty
                 project
                 ,
                 said
                 Alexander
                 ,
                 but
                 because
                 there
                 was
                 not
                 field-roome
                 thereabout
                 to
                 nourish
                 and
                 reteine
                 the
                 Citizens
                 of
                 that
                 place
                 ,
                 Alexander
                 was
                 wise
                 not
                 to
                 entertaine
                 the
                 designe
                 .
              
               
                 Now
                 let
                 it
                 be
                 required
                 of
                 what
                 greatnesse
                 this
                 Statue
                 might
                 have
                 been
                 ,
                 the
                 Towne
                 in
                 his
                 right
                 hand
                 ,
                 and
                 the
                 receiver
                 of
                 water
                 in
                 his
                 left
                 hand
                 if
                 it
                 had
                 been
                 made
                 .
              
               
                 For
                 the
                 Statue
                 ,
                 it
                 could
                 not
                 be
                 higher
                 than
                 the
                 Mountaine
                 it selfe
                 ,
                 and
                 the
                 Mountaine
                 was
                 about
                 a
                 mile
                 in
                 height
                 plumb
                 or
                 perpendicular
                 ;
                 
                 therefore
                 the
                 hand
                 of
                 this
                 Statue
                 ought
                 to
                 be
                 the
                 10th
                 part
                 of
                 his
                 height
                 ,
                 which
                 would
                 be
                 500
                 foot
                 ,
                 and
                 so
                 the
                 breadth
                 of
                 his
                 hand
                 would
                 be
                 250
                 foot
                 ,
                 the
                 length
                 now
                 multiplyed
                 by
                 the
                 breadth
                 ,
                 makes
                 an
                 hundred
                 twenty
                 five
                 thousand
                 square
                 feet
                 ,
                 for
                 the
                 quantitie
                 of
                 his
                 hand
                 to
                 make
                 the
                 towne
                 in
                 ,
                 to
                 lodge
                 the
                 said
                 10
                 thousand
                 men
                 ,
                 allowing
                 to
                 each
                 man
                 neere
                 about
                 12
                 foot
                 of
                 square
                 ground
                 :
                 now
                 judge
                 the
                 capacitie
                 of
                 the
                 other
                 parts
                 of
                 this
                 Collossus
                 by
                 that
                 which
                 is
                 already
                 delivered
                 .
              
               
                 Secondly
                 ,
                 Plinie
                 in
                 his
                 34
                 book
                 of
                 his
                 natural
                 History
                 ,
                 speakes
                 of
                 the
                 famous
                 Colossus
                 that
                 was
                 at
                 Rhodes
                 ,
                 between
                 whose
                 legges
                 a
                 Shippe
                 might
                 passe
                 with
                 his
                 sailes
                 open
                 or
                 displayed
                 ,
                 the
                 Statue
                 being
                 of
                 70
                 cubits
                 high
                 :
                 and
                 other
                 Histories
                 report
                 that
                 the
                 Sarasens
                 having
                 broken
                 it
                 ,
                 did
                 load
                 900
                 Camels
                 with
                 the
                 mettal
                 of
                 it
                 ,
                 now
                 what
                 might
                 be
                 the
                 greatnesse
                 and
                 weight
                 of
                 this
                 Statue
                 ?
              
               
                 For
                 answer
                 ,
                 it
                 is
                 usually
                 allowed
                 for
                 a
                 Camels
                 burthen
                 1200
                 pound
                 weight
                 ,
                 therefore
                 all
                 the
                 Collosus
                 did
                 weigh
                 1080000
                 pound
                 weight
                 ,
                 which
                 is
                 ten
                 hundred
                 and
                 fourescore
                 thousand
                 pound
                 vveight
                 .
              
               
                 Novv
                 according
                 to
                 the
                 former
                 rules
                 ,
                 the
                 head
                 being
                 the
                 tenth
                 part
                 of
                 the
                 body
                 ,
                 this
                 Statues
                 head
                 should
                 be
                 of
                 7
                 cubits
                 ,
                 that
                 is
                 to
                 say
                 ,
                 10
                 foot
                 and
                 a
                 halfe
                 ,
                 and
                 seeing
                 that
                 the
                 Nose
                 ,
                 the
                 brovv
                 ,
                 and
                 the
                 thumbe
                 ,
                 are
                 the
                 third
                 part
                 of
                 the
                 face
                 ,
                 his
                 Nose
                 vvas
                 3
                 foot
                 and
                 a
                 halfe
                 long
                 ,
                 and
                 so
                 much
                 also
                 vvas
                 his
                 thumbe
                 in
                 length
                 :
                 novv
                 the
                 thicknesse
                 being
                 alvvayes
                 the
                 third
                 part
                 of
                 
                 the
                 length
                 ,
                 it
                 should
                 seem
                 that
                 his
                 thumb
                 was
                 a
                 foot
                 thick
                 at
                 the
                 least
                 .
              
               
                 Thirdly
                 ,
                 the
                 said
                 Plinie
                 in
                 the
                 same
                 place
                 reports
                 that
                 Nero
                 did
                 cause
                 to
                 come
                 out
                 of
                 France
                 into
                 Italy
                 ,
                 a
                 brave
                 and
                 bold
                 Statue-maker
                 called
                 Zenodocus
                 ,
                 to
                 erect
                 him
                 a
                 Colossus
                 of
                 brasse
                 ,
                 which
                 was
                 made
                 of
                 120
                 foot
                 in
                 height
                 ,
                 which
                 Nero
                 caused
                 to
                 be
                 painted
                 in
                 the
                 same
                 height
                 .
                 Now
                 would
                 you
                 know
                 the
                 greatnesse
                 of
                 the
                 members
                 of
                 this
                 Colossus
                 ,
                 the
                 breadth
                 would
                 be
                 20
                 foot
                 ,
                 his
                 face
                 12
                 foote
                 ,
                 his
                 thumb
                 and
                 his
                 nose
                 4
                 foot
                 ,
                 according
                 to
                 the
                 proportion
                 before
                 delivered
                 .
              
               
                 Thus
                 I
                 have
                 a
                 faire
                 field
                 or
                 subject
                 to
                 extend
                 my selfe
                 upon
                 ,
                 but
                 it
                 is
                 upon
                 another
                 occasion
                 that
                 it
                 was
                 undertaken
                 ,
                 let
                 us
                 speak
                 therefore
                 a
                 word
                 touching
                 the
                 Giants
                 ,
                 and
                 then
                 passe
                 away
                 to
                 the
                 matter
                 .
              
            
             
               
                 Of
                 monstrous
                 Giants
                 .
              
               
                 YOu
                 will
                 hardly
                 beleeve
                 all
                 that
                 which
                 I
                 say
                 touching
                 this
                 ,
                 neither
                 will
                 I
                 beleeve
                 all
                 that
                 which
                 Authors
                 say
                 upon
                 this
                 subject
                 :
                 notwithstanding
                 you
                 nor
                 I
                 cannot
                 deny
                 but
                 that
                 long
                 ago
                 there
                 have
                 been
                 men
                 of
                 a
                 most
                 prodigious
                 greatnesse
                 ;
                 for
                 the
                 holy
                 vvritings
                 vvitnesse
                 this
                 themselves
                 in
                 
                   Deut
                   ,
                   Chap.
                
                 3.
                 that
                 there
                 vvas
                 a
                 certaine
                 Giant
                 called
                 Og
                 ,
                 of
                 the
                 Town
                 of
                 Rabath
                 ,
                 vvho
                 had
                 a
                 bed
                 of
                 Iron
                 ,
                 the
                 length
                 thereof
                 vvas
                 9
                 cubits
                 ,
                 and
                 in
                 breadth
                 4
                 cubits
                 .
              
               
                 So
                 in
                 the
                 first
                 of
                 
                   Kings
                   Chap.
                
                 17.
                 there
                 is
                 mention
                 made
                 of
                 Goliah
                 ,
                 vvhose
                 height
                 vvas
                 a
                 
                 palme
                 and
                 6
                 cubits
                 ,
                 that
                 is
                 more
                 then
                 9
                 foot
                 ,
                 he
                 was
                 armed
                 from
                 the
                 head
                 to
                 the
                 foot
                 ,
                 and
                 his
                 Curiat
                 onely
                 with
                 the
                 Iron
                 of
                 his
                 lance
                 ,
                 weighed
                 five
                 thousand
                 and
                 six
                 hundred
                 shekels
                 ,
                 which
                 in
                 our
                 common
                 weight
                 ,
                 is
                 more
                 than
                 233
                 pound
                 ,
                 of
                 12
                 ounces
                 to
                 the
                 pound
                 :
                 Now
                 it
                 is
                 certaine
                 ,
                 that
                 the
                 rest
                 of
                 his
                 armes
                 taking
                 his
                 Target
                 ,
                 Helmet
                 ,
                 Bracelets
                 ,
                 and
                 other
                 Armour
                 together
                 ,
                 did
                 weigh
                 at
                 the
                 least
                 5
                 hundred
                 pound
                 ,
                 a
                 thing
                 prodigious
                 ;
                 seeing
                 that
                 the
                 strongest
                 man
                 that
                 now
                 is
                 ,
                 can
                 hardly
                 beare
                 200
                 pound
                 ,
                 yet
                 this
                 Giant
                 carries
                 this
                 as
                 a
                 vesture
                 without
                 paine
                 .
              
               
                 Solinus
                 reporteth
                 in
                 his
                 5
                 Chap.
                 of
                 his
                 Historie
                 ,
                 that
                 during
                 the
                 Grecians
                 warre
                 after
                 a
                 great
                 overflowing
                 of
                 the
                 Rivers
                 ,
                 there
                 was
                 found
                 upon
                 the
                 sands
                 the
                 carcase
                 of
                 a
                 man
                 ,
                 whose
                 length
                 was
                 33
                 Cubits
                 ,
                 (
                 that
                 is
                 49
                 foot
                 and
                 a
                 halfe
                 )
                 therefore
                 according
                 to
                 the
                 proportion
                 delivered
                 ,
                 his
                 face
                 should
                 be
                 5
                 foot
                 in
                 length
                 ,
                 a
                 thing
                 prodigious
                 and
                 monstrous
                 .
              
               
                 Plinie
                 in
                 his
                 7.
                 book
                 and
                 16
                 Chap.
                 saith
                 ,
                 that
                 in
                 the
                 Isle
                 of
                 Crete
                 or
                 Candie
                 ,
                 a
                 mountaine
                 being
                 cloven
                 by
                 an
                 Earth-quake
                 ,
                 there
                 was
                 a
                 body
                 standing
                 upright
                 ,
                 which
                 had
                 46
                 Cubits
                 of
                 height
                 :
                 some
                 beleeve
                 that
                 it
                 was
                 the
                 body
                 of
                 Orion
                 or
                 Othus
                 ,
                 (
                 but
                 I
                 think
                 rather
                 it
                 was
                 some
                 Ghost
                 or
                 some
                 delusion
                 )
                 whose
                 hand
                 should
                 have
                 beene
                 7
                 foot
                 ,
                 and
                 his
                 nose
                 two
                 foot
                 and
                 a
                 half
                 long
                 .
                 But
                 that
                 which
                 Plutarch
                 in
                 the
                 l●fe
                 of
                 Sertorius
                 reports
                 of
                 ,
                 is
                 more
                 strange
                 ,
                 who
                 saith
                 ,
                 that
                 in
                 Timgy
                 a
                 Morative
                 Towne
                 ,
                 where
                 
                 it
                 is
                 thought
                 that
                 the
                 Giant
                 Antheus
                 was
                 buried
                 ,
                 Sertorius
                 could
                 not
                 beleeve
                 that
                 which
                 was
                 reported
                 of
                 his
                 prodigious
                 greatnesse
                 ,
                 caused
                 his
                 sepulchre
                 to
                 be
                 opened
                 ,
                 and
                 found
                 that
                 his
                 body
                 did
                 containe
                 60
                 Cubits
                 in
                 length
                 ,
                 then
                 by
                 proportion
                 he
                 should
                 be
                 10
                 Cubits
                 or
                 15
                 foot
                 in
                 breadth
                 ;
                 9
                 foot
                 for
                 the
                 length
                 of
                 his
                 face
                 ,
                 3
                 foot
                 for
                 his
                 thumb
                 ,
                 which
                 is
                 neare
                 the
                 capacitie
                 of
                 the
                 Colossus
                 at
                 Rhodes
                 .
              
               
                 But
                 behold
                 here
                 a
                 fine
                 fable
                 of
                 
                   Symphoris
                   Campesius
                
                 ,
                 in
                 his
                 book
                 intituled
                 
                   Hortus
                   Gallicus
                
                 ,
                 who
                 sayes
                 that
                 in
                 the
                 Kingdome
                 of
                 Sicilie
                 ,
                 at
                 the
                 foot
                 of
                 a
                 mountaine
                 neare
                 Trepane
                 ,
                 in
                 opening
                 the
                 foundation
                 of
                 a
                 house
                 ,
                 they
                 found
                 a
                 Cave
                 in
                 which
                 was
                 ●aid
                 a
                 Giant
                 ,
                 which
                 held
                 in
                 stead
                 of
                 a
                 staffe
                 a
                 great
                 post
                 like
                 the
                 mast
                 of
                 a
                 Ship
                 :
                 and
                 going
                 to
                 handle
                 it
                 ,
                 it
                 mouldered
                 all
                 into
                 ashes
                 ,
                 except
                 the
                 bones
                 which
                 remained
                 of
                 an
                 exceeding
                 great
                 measure
                 ,
                 that
                 in
                 his
                 head
                 there
                 might
                 be
                 easily
                 placed
                 5
                 quarters
                 of
                 corn
                 ,
                 and
                 by
                 proportion
                 it
                 should
                 seeme
                 that
                 his
                 length
                 was
                 200
                 cubits
                 ,
                 or
                 300
                 foot
                 :
                 if
                 he
                 had
                 said
                 that
                 he
                 had
                 been
                 300
                 cubits
                 in
                 length
                 ,
                 then
                 he
                 might
                 have
                 made
                 us
                 beleeve
                 that
                 Noahs
                 Ark
                 was
                 but
                 great
                 enough
                 for
                 his
                 sepulchre
                 .
              
               
                 Who
                 can
                 believe
                 that
                 any
                 man
                 ever
                 had
                 20
                 cubits
                 ,
                 or
                 30
                 foot
                 in
                 length
                 for
                 his
                 face
                 ,
                 and
                 a
                 nose
                 of
                 10
                 foot
                 long
                 ?
                 but
                 it
                 is
                 very
                 certaine
                 that
                 there
                 have
                 been
                 men
                 of
                 very
                 great
                 stature
                 ,
                 as
                 the
                 holy
                 Scriptures
                 before
                 witnesse
                 ,
                 and
                 many
                 Authours
                 worthy
                 of
                 beliefe
                 relate
                 :
                 
                   Josephus
                   Acosta
                
                 in
                 his
                 first
                 book
                 of
                 the
                 Indian
                 History
                 ,
                 Chap.
                 19.
                 a
                 late
                 writer
                 ,
                 reporteth
                 ,
                 that
                 
                 at
                 Peru
                 was
                 found
                 the
                 bones
                 of
                 a
                 Giant
                 ,
                 which
                 was
                 3
                 times
                 greater
                 than
                 these
                 of
                 ours
                 are
                 ,
                 that
                 is
                 18
                 foot
                 ,
                 for
                 it
                 is
                 usually
                 attributed
                 to
                 the
                 tallest
                 ordinary
                 man
                 in
                 these
                 our
                 times
                 but
                 6
                 foot
                 of
                 length
                 ;
                 and
                 Histories
                 are
                 full
                 of
                 the
                 description
                 of
                 other
                 Giants
                 of
                 9
                 ,
                 10
                 ,
                 and
                 12
                 foot
                 of
                 height
                 ,
                 and
                 it
                 hath
                 been
                 seen
                 in
                 our
                 times
                 some
                 which
                 have
                 had
                 such
                 heights
                 as
                 these
                 .
              
            
          
           
             
               PROBLEM
               .
               LXXI
               .
               Of
               the
               game
               at
               the
               Palme
               ,
               at
               Trap
               ,
               at
               Bowles
               ,
               Paile-maile
               ,
               and
               others
               .
            
             
               THe
               Mathematickes
               often
               findeth
               place
               in
               sundry
               Games
               to
               aid
               and
               assist
               the
               Gamesters
               ,
               though
               not
               unknowne
               unto
               them
               ,
               hence
               by
               Mathematicall
               principles
               ,
               the
               games
               at
               Tennis
               may
               be
               assisted
               ,
               for
               all
               the
               moving
               in
               it
               is
               by
               right
               lines
               and
               reflections
               .
               From
               whence
               comes
               it
               ,
               that
               from
               the
               appearances
               of
               flat
               or
               convex
               Glasses
               ,
               the
               production
               and
               reflection
               of
               the
               species
               are
               explained
               ;
               is
               it
               not
               by
               right
               lines
               ?
               in
               the
               same
               proportion
               one
               might
               sufficiently
               deliver
               the
               motion
               of
               a
               Ball
               or
               Bowle
               by
               Geometrical
               lines
               and
               angles
               .
            
             
             
               And
               the
               first
               maxime
               is
               thus
               :
               When
               a
               Bowle
               toucheth
               another
               Bowle
               ▪
               or
               when
               a
               trapstick
               striketh
               the
               Ball
               ,
               the
               moving
               of
               the
               Ball
               is
               made
               in
               a
               right
               line
               ,
               which
               is
               drawne
               from
               the
               Centre
               of
               the
               Bowle
               by
               the
               point
               of
               contingencie
               .
            
             
               Secondly
               ,
               in
               all
               kinde
               of
               such
               motion
               ;
               when
               a
               Ball
               or
               Bowle
               rebounds
               ,
               be
               it
               either
               against
               wood
               ,
               a
               wall
               ,
               upon
               a
               Drumme
               ,
               a
               pavement
               ,
               or
               upon
               a
               Racket
               ;
               the
               incident
               Angle
               is
               alwayes
               equall
               to
               the
               Angle
               of
               reflection
               .
            
             
               Now
               following
               these
               maximes
               ,
               it
               is
               easie
               to
               canclude
               ,
               first
               ,
               in
               what
               part
               of
               the
               wood
               or
               wall
               ,
               one
               may
               make
               the
               Bowle
               or
               Ball
               go
               to
               reflect
               or
               rebound
               ,
               to
               such
               a
               place
               as
               one
               would
               .
               Secondly
               ,
               how
               one
               may
               cast
               a
               Bowle
               upon
               another
               ,
               in
               such
               sort
               that
               the
               first
               or
               the
               second
               shall
               go
               and
               meet
               with
               the
               third
               ,
               keeping
               the
               reflection
               or
               Angle
               of
               incidence
               equal
               .
            
             
               Thirly
               ,
               how
               one
               may
               touch
               a
               Bowle
               to
               send
               it
               to
               what
               part
               one
               pleaseth
               :
               such
               and
               many
               other
               practices
               may
               be
               done
               .
               At
               the
               exercises
               at
               Keyls
               there
               must
               be
               taken
               heed
               that
               the
               motion
               slack
               or
               diminish
               by
               little
               and
               little
               ,
               and
               
               may
               be
               noted
               that
               the
               Maximes
               of
               reflections
               cannot
               be
               exactly
               observed
               by
               locall
               motion
               ,
               as
               in
               the
               beames
               of
               light
               and
               of
               other
               quallities
               ,
               whereof
               it
               is
               necessary
               to
               supply
               it
               by
               industry
               or
               by
               strength
               ,
               otherwise
               one
               may
               be
               frustrated
               in
               that
               respect
               .
            
          
           
             
               PROBLEM
               .
               LXXII
               .
               Of
               the
               Game
               of
               square
               formes
               .
            
             
               NVmbers
               have
               an
               admirable
               secrecie
               ,
               diversly
               applied
               ,
               as
               before
               in
               part
               is
               shewed
               ,
               and
               here
               I
               will
               say
               something
               by
               way
               of
               transmutation
               of
               numbers
               .
            
             
             
               It
               's
               answered
               thus
               ,
               in
               the
               first
               forme
               the
               men
               were
               as
               the
               figure
               A
               ,
               then
               each
               of
               these
               4
               Souldiers
               placed
               themselves
               at
               each
               Gate
               ,
               and
               removing
               one
               man
               from
               each
               Angle
               to
               each
               Gate
               ,
               then
               would
               they
               be
               also
               9
               in
               each
               side
               according
               to
               the
               figure
               B.
               Lastly
               ,
               these
               4
               Souldiers
               at
               the
               Gates
               take
               away
               each
               one
               his
               Cumrade
               ,
               and
               placing
               two
               of
               these
               men
               which
               are
               at
               each
               Gate
               to
               each
               Angle
               ,
               there
               will
               be
               still
               9
               for
               each
               side
               of
               the
               square
               ,
               according
               to
               the
               figure
               C.
               In
               like
               manner
               if
               there
               were
               12
               men
               ,
               how
               might
               they
               be
               placed
               about
               a
               square
               that
               the
               first
               side
               shall
               have
               3
               every
               way
               ,
               then
               disordered
               ,
               so
               that
               they
               might
               be
               4
               every
               way
               ;
               and
               lastly
               ,
               being
               transported
               might
               make
               5
               every
               way
               ?
               &
               this
               is
               according
               to
               the
               figures
               ,
               
                 F.
                 G.H
              
            
          
           
             
             
               PROBLEM
               .
               LXXIII
               .
               How
               to
               make
               the
               string
               of
               a
               Viole
               sensibly
               shake
               ,
               without
               any
               one
               touching
               it
               ?
            
             
               THis
               is
               a
               miracle
               in
               musick
               ,
               yet
               easie
               to
               be
               experimented
               .
               Take
               a
               Viole
               or
               other
               Instrument
               ,
               and
               choose
               two
               strings
               ,
               so
               that
               there
               be
               one
               between
               them
               ;
               make
               these
               two
               strings
               ,
               agree
               in
               one
               and
               the
               same
               tune
               :
               then
               move
               the
               Viole-bowe
               upon
               the
               greater
               string
               ,
               and
               you
               shall
               see
               a
               wonder
               :
               for
               in
               the
               same
               time
               that
               that
               shakes
               which
               you
               play
               upon
               ,
               the
               other
               will
               likewise
               sensibly
               shake
               without
               any
               one
               touching
               it
               ;
               and
               it
               is
               more
               admirable
               that
               the
               string
               which
               is
               between
               them
               will
               not
               shake
               at
               all
               :
               and
               if
               you
               put
               the
               first
               string
               to
               another
               tune
               or
               note
               ,
               and
               loosing
               the
               pin
               of
               the
               string
               ,
               or
               stopping
               it
               with
               your
               finger
               in
               any
               fret
               ,
               the
               other
               string
               will
               not
               shake
               :
               and
               the
               same
               will
               happen
               if
               you
               take
               two
               Violes
               ,
               and
               strike
               upon
               a
               string
               of
               the
               one
               ,
               the
               string
               of
               the
               other
               will
               sensibly
               shake
               .
            
             
               Now
               it
               may
               be
               demanded
               ,
               how
               comes
               this
               shaking
               ,
               is
               it
               in
               the
               occult
               sympathie
               ,
               or
               is
               it
               in
               the
               strings
               being
               wound
               up
               to
               like
               notes
               or
               tunes
               ,
               that
               so
               easily
               the
               other
               may
               receive
               the
               impression
               of
               the
               aire
               ,
               which
               is
               agitated
               or
               moved
               by
               the
               shaking
               or
               the
               trembling
               of
               the
               other
               ?
               &
               whence
               is
               it
               that
               the
               Viole-bowe
               moved
               upon
               the
               first
               string
               ,
               doth
               instantly
               in
               the
               same
               time
               move
               the
               third
               string
               ,
               and
               not
               the
               second
               ?
               if
               the
               cause
               be
               not
               either
               in
               the
               first
               or
               second
               ?
               I
               leave
               to
               others
               to
               descant
               on
               .
            
             
               
               
                 EXAMINATION
                 .
              
               
                 IN
                 this
                 Examination
                 we
                 have
                 something
                 else
                 to
                 imagine
                 ,
                 than
                 the
                 bare
                 sympathie
                 of
                 the
                 Cords
                 one
                 to
                 another
                 :
                 for
                 first
                 there
                 ought
                 to
                 be
                 considered
                 the
                 different
                 effect
                 that
                 it
                 produceth
                 by
                 extention
                 upon
                 one
                 and
                 the
                 same
                 Cord
                 in
                 capacitie
                 :
                 then
                 what
                 might
                 be
                 produced
                 upon
                 different
                 Cords
                 of
                 length
                 and
                 bigness
                 to
                 make
                 them
                 accord
                 in
                 a
                 unisone
                 or
                 octavo
                 ,
                 or
                 some
                 consort
                 intermediate
                 :
                 this
                 being
                 naturally
                 examined
                 ,
                 it
                 will
                 be
                 facill
                 to
                 lay
                 open
                 a
                 way
                 to
                 the
                 knowledge
                 of
                 the
                 true
                 and
                 immediate
                 cause
                 of
                 this
                 noble
                 and
                 admirable
                 Phaenomeny
                 .
                 Now
                 this
                 will
                 sensibly
                 appeare
                 when
                 the
                 Cords
                 are
                 of
                 equall
                 length
                 and
                 greatnesse
                 ,
                 and
                 set
                 to
                 an
                 unisone
                 ;
                 but
                 when
                 the
                 Cords
                 differ
                 from
                 their
                 equalitie
                 ,
                 it
                 will
                 be
                 lesse
                 sensible
                 :
                 hence
                 in
                 one
                 and
                 the
                 same
                 Instrument
                 ,
                 Cords
                 at
                 a
                 unisone
                 shall
                 excite
                 or
                 shake
                 more
                 than
                 that
                 which
                 is
                 at
                 an
                 octavo
                 ,
                 and
                 more
                 than
                 those
                 which
                 are
                 of
                 an
                 intermediate
                 proportionall
                 consort
                 :
                 as
                 for
                 the
                 other
                 consorts
                 they
                 are
                 not
                 exempted
                 ,
                 though
                 the
                 effect
                 be
                 not
                 so
                 sensible
                 ,
                 yet
                 more
                 in
                 one
                 than
                 in
                 another
                 :
                 and
                 the
                 experiment
                 will
                 seem
                 more
                 admirable
                 in
                 taking
                 2
                 Lutes
                 ,
                 Viols
                 ,
                 &c.
                 &
                 in
                 setting
                 them
                 to
                 one
                 tune
                 :
                 for
                 then
                 in
                 touching
                 the
                 Cord
                 of
                 the
                 one
                 ,
                 it
                 will
                 
                 give
                 a
                 sensible
                 motion
                 to
                 the
                 Cord
                 of
                 the
                 other
                 :
                 and
                 not
                 onely
                 so
                 but
                 also
                 a
                 harmony
                 .
              
            
          
           
             
               PROBLEM
               .
               LXXIIII
               .
               Of
               a
               vessell
               which
               containes
               three
               severall
               kindes
               of
               liquor
               ,
               all
               put
               in
               at
               one
               bung-hole
               ,
               and
               drawn
               out
               at
               one
               tap
               severally
               without
               mixture
               .
            
             
               THe
               vessell
               is
               thus
               made
               ,
               it
               must
               be
               divided
               into
               three
               Cells
               for
               to
               conteine
               the
               three
               liquors
               ,
               which
               admit
               to
               be
               Sack
               ,
               Claret
               ,
               and
               White-wine
               :
               Now
               in
               the
               bung-hole
               there
               is
               an
               Engine
               with
               three
               pipes
               ,
               each
               extending
               to
               his
               proper
               Cell
               ,
               into
               which
               there
               is
               put
               a
               broach
               or
               funnell
               pierced
               in
               three
               places
               ,
               in
               such
               sort
               ,
               that
               placing
               one
               of
               the
               holes
               right
               against
               the
               pipe
               which
               answereth
               unto
               him
               ,
               the
               other
               tvvo
               pipes
               are
               stopped
               ;
               then
               vvhen
               it
               is
               full
               ,
               turne
               the
               funnel
               ,
               and
               then
               the
               former
               hole
               vvill
               be
               stopped
               ,
               and
               another
               open
               ,
               to
               cast
               in
               other
               vvine
               vvithout
               mixing
               it
               vvith
               the
               other
               .
            
             
               Novv
               to
               dravv
               out
               also
               vvithout
               mixture
               ,
               at
               the
               bottome
               of
               the
               vessell
               there
               must
               be
               placed
               a
               pipe
               or
               broach
               ,
               vvhich
               may
               have
               three
               pipes
               ;
               and
               a
               cock
               piersed
               vvith
               three
               holes
               so
               artificially
               done
               ,
               that
               turning
               the
               cock
               ,
               the
               whole
               vvhich
               ansvvereth
               to
               such
               of
               the
               pipes
               that
               is
               placed
               at
               the
               bottom
               ,
               may
               issue
               forth
               such
               vvine
               as
               belongeth
               to
               that
               pipe
               ,
               &
               turning
               the
               Cock
               to
               another
               pipe
               ,
               the
               former
               hole
               vvil
               be
               stopped
               ;
               
               and
               so
               there
               will
               issue
               
               forth
               another
               kinde
               of
               wine
               without
               any
               mixtures
               ;
               but
               the
               Cocke
               may
               be
               so
               ordered
               that
               there
               may
               come
               out
               by
               it
               two
               wines
               together
               ,
               or
               all
               three
               kindes
               at
               once
               :
               but
               it
               seems
               best
               when
               that
               in
               one
               vessell
               and
               at
               one
               Cocke
               ,
               a
               man
               may
               draw
               severall
               kindes
               of
               wine
               ,
               and
               which
               he
               pleaseth
               to
               drink
               .
            
          
           
             
               PROBLEM
               .
               LXXV
               .
               Of
               burning-Glasses
               .
            
             
               IN
               this
               insuing
               discourse
               I
               will
               shew
               the
               invention
               of
               Prom●theus
               ,
               how
               to
               steale
               fire
               from
               Heaven
               ,
               and
               bring
               it
               down
               to
               the
               Earth
               ;
               this
               is
               done
               by
               a
               little
               round
               Glasse
               ,
               or
               made
               of
               steele
               ,
               by
               which
               one
               may
               light
               a
               Candle
               ,
               and
               make
               it
               flame
               ,
               kindle
               Fire-brands
               to
               wake
               them
               burne
               ,
               melt
               Lead
               ,
               ●inne
               ,
               Gold
               ,
               and
               Silver
               ,
               in
               a
               little
               time
               ▪
               with
               as
               great
               ease
               as
               though
               it
               had
               been
               put
               into
               a
               Cruzet
               over
               a
               great
               fire
               .
            
             
             
               But
               this
               is
               nothing
               to
               the
               burning
               of
               those
               Glasses
               which
               are
               hollow
               ,
               namely
               those
               which
               are
               of
               steele
               well
               polished
               ,
               according
               to
               a
               par●bolicall
               or
               ovall
               section
               .
               A
               sphericall
               Glasse
               ,
               or
               that
               which
               is
               according
               to
               the
               segment
               of
               a
               Sphere
               ,
               burnes
               very
               effectually
               about
               the
               fourth
               part
               of
               the
               Diameter
               ;
               notwithstanding
               the
               Parabolie
               and
               Ecliptick
               sections
               have
               a
               great
               effect
               :
               by
               which
               Glasses
               there
               are
               also
               diverse
               figures
               represented
               forth
               to
               the
               eye
               .
            
             
               The
               cause
               of
               this
               burning
               is
               the
               uniting
               of
               the
               beames
               of
               the
               Sunne
               ,
               which
               heat
               mightily
               in
               the
               point
               of
               concourse
               or
               inflammation
               ,
               
               which
               is
               either
               by
               transmissi●n
               or
               reflection
               ▪
               Now
               it
               is
               pleasant
               to
               behold
               when
               one
               breatheth
               in
               the
               point
               of
               concourse
               ,
               or
               throweth
               small
               dust
               there
               ,
               or
               sprinkles
               vapours
               of
               hot
               water
               in
               that
               place
               ;
               by
               which
               the
               Pyramidall
               point
               ,
               or
               point
               of
               inflammation
               is
               knowne
               .
               Now
               some
               Authors
               promise
               to
               make
               Glasses
               which
               shall
               burne
               a
               great
               distance
               off
               ,
               but
               yet
               not
               seen
               vulgarly
               produced
               ,
               of
               which
               if
               they
               were
               made
               ,
               the
               Parabolie
               makes
               the
               greatest
               eff●ct
               ,
               and
               is
               g●nerally
               held
               to
               be
               the
               invention
               of
               Archimedes
               or
               Pro●●us
               .
            
             
               Maginus
               in
               the
               5
               Chap.
               of
               his
               Treatise
               of
               sphericall
               Glasses
               ,
               shewes
               how
               one
               may
               serve
               himselfe
               with
               a
               concave
               Glasse
               ,
               to
               light
               fire
               in
               the
               shadow
               ,
               or
               neare
               such
               a
               place
               where
               the
               Sunne
               shines
               not
               ,
               which
               is
               by
               help
               of
               a
               flat
               Glasse
               ,
               by
               which
               may
               be
               made
               a
               percussion
               of
               the
               beames
               of
               the
               Sun
               into
               the
               concave
               Glasse
               ,
               adding
               unto
               it
               that
               it
               serves
               to
               good
               use
               to
               put
               fi●e
               to
               a
               Mine
               ,
               provided
               that
               the
               combustible
               matter
               be
               well
               applyed
               before
               the
               concave
               Glasse
               ;
               in
               which
               he
               saies
               true
               :
               but
               because
               all
               the
               effect
               of
               the
               practice
               depends
               upon
               the
               placing
               of
               the
               Glasse
               and
               the
               Powder
               which
               he
               speaks
               not
               of
               :
               I
               will
               deliver
               here
               a
               rule
               more
               generall
               .
            
             
               How
               one
               may
               place
               a
               Burning-glasse
               with
               his
               combust●ble
               matter
               in
               such
               sort
               ,
               that
               at
               a
               convenient
               houre
               of
               the
               day
               ,
               the
               Sun
               shining
               ,
               it
               shall
               take
               fire
               and
               burne
               :
               Now
               it
               is
               certaine
               
               that
               the
               point
               of
               inflammation
               or
               burning
               ,
               is
               changed
               as
               the
               Sun
               changeth
               place
               ,
               and
               no
               more
               nor
               lesse
               ,
               than
               the
               shadow
               turnes
               about
               the
               style
               of
               a
               Dyall
               ;
               therefore
               have
               regard
               to
               the
               Suns
               motion
               ,
               and
               ●is
               height
               and
               place
               :
               a
               Bowle
               of
               Crystall
               in
               the
               same
               place
               that
               the
               top
               of
               the
               style
               is
               ,
               and
               the
               Powder
               or
               other
               combustible
               matter
               under
               the
               Meridian
               ,
               or
               houre
               of
               12
               ,
               1
               ,
               2
               ,
               3
               ,
               &c.
               or
               any
               other
               houre
               ,
               and
               under
               the
               Suns
               arch
               for
               that
               day
               :
               now
               the
               Sunne
               comming
               to
               the
               houre
               of
               12
               ,
               to
               ●
               ,
               2
               ,
               ●
               ,
               &c.
               the
               Sunne
               casting
               his
               beames
               through
               the
               Crystall
               Bowle
               ,
               will
               fire
               the
               materiall
               or
               combustible
               thing
               ,
               which
               meets
               in
               the
               point
               of
               burning
               :
               the
               like
               may
               be
               observed
               of
               other
               Burning-glasses
               .
            
             
               
                 EXAMINATION
                 .
              
               
                 IT
                 is
                 certaine
                 in
                 the
                 first
                 part
                 of
                 this
                 Probleme
                 that
                 Conicall
                 ,
                 ●oncave
                 and
                 sphericall
                 Glasses
                 ,
                 of
                 what
                 matter
                 soever
                 ,
                 being
                 placed
                 to
                 receive
                 the
                 beames
                 of
                 the
                 Sun
                 will
                 excite
                 heat
                 ,
                 and
                 that
                 heat
                 is
                 so
                 much
                 the
                 greater
                 ,
                 by
                 how
                 much
                 it
                 is
                 neere
                 the
                 point
                 of
                 conc●rse
                 or
                 inflamatio●
                 .
                 But
                 that
                 Archimedes
                 or
                 Proclus
                 d●d
                 fire
                 or
                 burne
                 Shipps
                 with
                 such
                 Glasses
                 ,
                 the
                 ancient
                 Histories
                 are
                 silent
                 ,
                 yea
                 the
                 selves
                 say
                 nothing
                 :
                 besides
                 the
                 great
                 difficultie
                 that
                 doth
                 oppose
                 it
                 in
                 remotenesse
                 ,
                 and
                 the
                 matter
                 that
                 the
                 effect
                 is
                 to
                 work
                 upon
                 :
                 Now
                 
                 by
                 a
                 common
                 Glasse
                 we
                 fire
                 things
                 neare
                 at
                 hand
                 ,
                 from
                 which
                 it
                 seems
                 very
                 facil
                 to
                 such
                 which
                 are
                 lesse
                 read
                 ,
                 to
                 do
                 it
                 at
                 a
                 farre
                 greater
                 distance
                 ,
                 and
                 so
                 by
                 re●ation
                 some
                 deliver
                 to
                 the
                 World
                 by
                 supposition
                 that
                 which
                 never
                 was
                 done
                 in
                 action
                 :
                 this
                 we
                 say
                 the
                 rather
                 ,
                 not
                 to
                 take
                 away
                 the
                 most
                 excellent
                 and
                 admirable
                 effects
                 which
                 are
                 in
                 Burning-glasses
                 ,
                 but
                 to
                 shew
                 the
                 variety
                 of
                 Antiquity
                 ,
                 and
                 truth
                 of
                 History
                 :
                 and
                 as
                 touching
                 to
                 burne
                 at
                 a
                 great
                 distance
                 ,
                 as
                 is
                 said
                 of
                 some
                 ,
                 it
                 is
                 absolutely
                 impossible
                 ;
                 and
                 that
                 the
                 Parabolicall
                 and
                 Ovall
                 Glasses
                 were
                 of
                 Archimedes
                 and
                 ●roclus
                 invention
                 is
                 much
                 uncertaine
                 :
                 for
                 besides
                 the
                 construction
                 of
                 such
                 Glasses
                 ,
                 they
                 are
                 more
                 difficult
                 than
                 the
                 obtuse
                 concave
                 ones
                 are
                 ;
                 and
                 further
                 ,
                 they
                 cast
                 not
                 a
                 great
                 heat
                 but
                 neere
                 at
                 hand
                 ;
                 for
                 if
                 it
                 be
                 cast
                 farre
                 off
                 ,
                 the
                 effect
                 is
                 little
                 ,
                 and
                 the
                 heat
                 weake
                 ,
                 or
                 otherwise
                 such
                 Glasses
                 must
                 be
                 greatly
                 extended
                 to
                 contract
                 many
                 beames
                 to
                 amasse
                 a
                 sufficient
                 quantity
                 of
                 beames
                 in
                 Parabolicall
                 and
                 Conicall
                 Glasses
                 ,
                 the
                 point
                 of
                 inflammation
                 ought
                 to
                 concur
                 in
                 a
                 point
                 ,
                 which
                 is
                 very
                 difficult
                 to
                 be
                 done
                 in
                 a
                 due
                 proportion
                 .
                 Moreover
                 if
                 the
                 place
                 be
                 farre
                 remote
                 ,
                 as
                 is
                 supposed
                 before
                 ,
                 such
                 a
                 Glasse
                 cannot
                 be
                 used
                 but
                 at
                 a
                 great
                 inclination
                 of
                 
                 the
                 Sunne
                 ▪
                 by
                 which
                 the
                 eff●ct
                 of
                 ●urning
                 is
                 d●min●shed
                 ,
                 by
                 reason
                 of
                 the
                 weaknesse
                 of
                 the
                 Sunne-beames
                 .
              
               
                 And
                 here
                 may
                 be
                 noted
                 in
                 the
                 last
                 part
                 of
                 this
                 Probleme
                 ,
                 that
                 by
                 r●ason
                 of
                 obstacles
                 if
                 one
                 plaine
                 Glasse
                 be
                 not
                 sufficient
                 ,
                 a
                 second
                 Glasse
                 may
                 be
                 applyed
                 to
                 help
                 it
                 :
                 that
                 so
                 if
                 by
                 one
                 simple
                 reflection
                 it
                 cannot
                 be
                 done
                 ,
                 yet
                 by
                 a
                 double
                 reflection
                 the
                 Sun-beames
                 may
                 be
                 ●ast
                 into
                 the
                 said
                 Caverne
                 or
                 Mine
                 ,
                 and
                 though
                 the
                 reflected
                 beams
                 in
                 this
                 case
                 be
                 weak
                 ▪
                 yet
                 upon
                 a
                 〈◊〉
                 c●mbustible
                 matter
                 it
                 will
                 not
                 faile
                 to
                 do
                 the
                 effect
                 .
              
            
          
           
             
               PROBLEM
               .
               LXXVI
               .
               Containing
               m●ny
               ple●sant
               Questions
               by
               way
               of
               Arithmetick●
               .
            
             
               J
               Will
               not
               in●ert
               i●
               this
               Probleme
               that
               which
               is
               drawne
               from
               the
               ●reek
               Epigrams
               ,
               but
               proposing
               the
               Question
               immediately
               will
               give
               the
               an●wer
               also
               ,
               without
               ●●aying
               to
               shew
               the
               manner
               how
               they
               are
               answered
               ;
               in
               this
               J
               will
               〈◊〉
               be
               tied
               to
               the
               ●reek
               tearms
               ,
               w●●ch
               J
               account
               no●
               proper
               to
               this
               place
               ,
               nei●●er
               to
               my
               purpose
               :
               ●et
               t●o●e
               ●ead
               that
               will
               
                 Di●phanta
                 S●●●●biliu●
              
               upon
               Eu●li●●
               and
               others
               ,
               and
               they
               may
               be
               satisf●ed
            
             
               
                 Of
                 the
                 〈…〉
                 the
                 Mule.
                 
              
               
                 JT
                 〈◊〉
                 ●hat
                 ●he
                 Mule
                 and
                 the
                 Asse
                 upon
                 a
                 day
                 〈◊〉
                 a
                 voyage
                 each
                 of
                 them
                 carried
                 
                 a
                 Barrell
                 full
                 of
                 Wine
                 :
                 now
                 the
                 las●e
                 Asse
                 f●lt
                 her selfe
                 over-loaden
                 ,
                 complained
                 and
                 bowed
                 under
                 her
                 burthen
                 ;
                 which
                 th●
                 Mule
                 seeing
                 said
                 unto
                 her
                 being
                 angry
                 ,
                 (
                 for
                 it
                 was
                 in
                 the
                 time
                 when
                 beasts
                 spake
                 )
                 Thou
                 great
                 Asse
                 ,
                 wherefore
                 complainest
                 thou
                 ?
                 if
                 I
                 had
                 but
                 onely
                 one
                 measure
                 of
                 that
                 which
                 thou
                 carriest
                 ,
                 I
                 should
                 be
                 loaden
                 twice
                 as
                 much
                 as
                 thou
                 art
                 ,
                 and
                 if
                 J
                 should
                 give
                 a
                 measure
                 of
                 my
                 loading
                 to
                 thee
                 ,
                 yet
                 my
                 burthen
                 would
                 be
                 as
                 much
                 as
                 thine
                 .
              
               
                 Now
                 how
                 many
                 measures
                 did
                 each
                 of
                 them
                 carry
                 ?
                 Answer
                 ,
                 the
                 Mule
                 did
                 carry
                 7
                 measures
                 ,
                 and
                 the
                 Asse
                 5
                 measures
                 :
                 for
                 if
                 the
                 Mule
                 had
                 one
                 of
                 the
                 measures
                 of
                 the
                 Asses
                 loading
                 ,
                 then
                 the
                 Mule
                 would
                 have
                 8
                 measures
                 ,
                 which
                 is
                 double
                 to
                 4
                 ,
                 and
                 giving
                 one
                 to
                 the
                 Asse
                 ,
                 each
                 of
                 them
                 would
                 have
                 equall
                 burthens
                 :
                 to
                 wit
                 ,
                 6
                 measures
                 apiece
                 .
              
            
             
               
                 Of
                 the
                 number
                 of
                 Souldiers
                 that
                 fought
                 before
                 old
                 Troy.
                 
              
               
                 HOmer
                 being
                 asked
                 by
                 He●iodus
                 how
                 many
                 Grecian
                 Souldiers
                 came
                 against
                 Troy
                 ?
                 who
                 answered
                 him
                 thus
                 ;
                 The
                 Grecians
                 ,
                 said
                 Homer
                 ,
                 made
                 7
                 fires
                 ,
                 or
                 had
                 7
                 Kitchins
                 ,
                 and
                 before
                 every
                 fire
                 ,
                 or
                 in
                 every
                 Kitchin
                 there
                 were
                 50
                 broaches
                 turning
                 to
                 rost
                 a
                 great
                 quantitie
                 of
                 flesh
                 ,
                 and
                 each
                 broach
                 had
                 meat
                 enough
                 to
                 satisfie
                 900
                 men
                 :
                 now
                 judge
                 how
                 many
                 men
                 there
                 might
                 be
                 .
                 Answer
                 ,
                 315000.
                 that
                 is
                 ,
                 three
                 hundred
                 and
                 fifteen
                 thousand
                 men
                 ,
                 which
                 is
                 cleare
                 by
                 multiplying
                 7
                 by
                 50
                 ,
                 and
                 the
                 product
                 by
                 900
                 makes
                 the
                 said
                 315000.
                 
              
            
             
               
               
                 Of
                 the
                 number
                 of
                 Crownes
                 that
                 two
                 men
                 had
                 .
              
               
                 JOhn
                 and
                 Peter
                 had
                 certaine
                 number
                 of
                 crowns
                 :
                 John
                 said
                 to
                 Peter
                 ,
                 If
                 you
                 give
                 me
                 10
                 of
                 your
                 crownes
                 ,
                 I
                 shall
                 have
                 three
                 times
                 as
                 much
                 as
                 you
                 have
                 :
                 but
                 Peter
                 said
                 to
                 J●hn
                 ,
                 If
                 you
                 give
                 me
                 10
                 of
                 your
                 crownes
                 I
                 shall
                 have
                 5
                 times
                 as
                 much
                 as
                 you
                 have
                 :
                 how
                 much
                 had
                 each
                 of
                 them
                 ?
                 Answere
                 ,
                 John
                 had
                 15
                 crownes
                 and
                 5
                 sevenths
                 of
                 a
                 crowne
                 ,
                 and
                 Peter
                 had
                 18
                 crownes
                 ,
                 and
                 4
                 sevenths
                 of
                 a
                 crowne
                 .
                 For
                 if
                 you
                 adde
                 10
                 of
                 Peters
                 crownes
                 to
                 those
                 of
                 Johns
                 ,
                 then
                 should
                 John
                 have
                 25
                 crownes
                 and
                 5
                 sevenths
                 of
                 a
                 crowne
                 ,
                 which
                 is
                 triple
                 to
                 that
                 of
                 Peters
                 ,
                 viz.
                 8
                 ▪
                 and
                 4
                 sevenths
                 :
                 and
                 John
                 giving
                 10
                 to
                 
                   Peter
                   ,
                   Peter
                
                 should
                 have
                 then
                 28
                 crownes
                 ,
                 and
                 4
                 sevenths
                 of
                 a
                 crowne
                 ,
                 which
                 is
                 Quintupla
                 ,
                 or
                 5
                 times
                 as
                 much
                 as
                 John
                 had
                 left
                 ,
                 viz.
                 5
                 crownes
                 and
                 5
                 sevenths
                 .
              
               
                 In
                 like
                 manner
                 two
                 Gamesters
                 playing
                 together
                 ,
                 A
                 and
                 B
                 ▪
                 after
                 play
                 A
                 said
                 to
                 B
                 ,
                 Give
                 me
                 2
                 crownes
                 of
                 thy
                 money
                 ,
                 and
                 I
                 shall
                 have
                 twice
                 as
                 much
                 as
                 thou
                 hast
                 :
                 and
                 B
                 said
                 to
                 A
                 ,
                 Give
                 me
                 2
                 crownes
                 of
                 thy
                 money
                 ,
                 and
                 I
                 shall
                 have
                 4
                 times
                 as
                 much
                 as
                 thou
                 hast
                 :
                 now
                 how
                 much
                 had
                 each
                 ?
                 Answer
                 ,
                 A
                 had
                 3
                 and
                 5
                 seventhes
                 ,
                 and
                 B
                 had
                 4
                 and
                 6
                 seventhes
                 .
              
            
             
               
               
                 About
                 the
                 houre
                 of
                 the
                 day
                 .
              
               
                 SOme
                 one
                 asked
                 a
                 Mathemacian
                 what
                 a
                 clocke
                 it
                 was
                 ;
                 who
                 answered
                 that
                 the
                 rest
                 of
                 the
                 day
                 is
                 foure
                 thirds
                 of
                 that
                 which
                 is
                 past
                 :
                 now
                 judge
                 what
                 a
                 clock
                 it
                 is
                 .
                 Answer
                 ,
                 if
                 the
                 day
                 were
                 according
                 to
                 the
                 Jewes
                 and
                 ancient
                 Romanes
                 ,
                 which
                 ma●e
                 it
                 alwayes
                 to
                 be
                 12
                 houres
                 ,
                 it
                 was
                 then
                 the
                 ●
                 houre
                 ,
                 and
                 one
                 seventh
                 of
                 an
                 hou●e
                 ,
                 so
                 there
                 remained
                 of
                 the
                 whole
                 day
                 6
                 ,
                 that
                 is
                 ,
                 6
                 houres
                 ,
                 and
                 6
                 sevenths
                 of
                 an
                 hour
                 .
                 Now
                 if
                 you
                 take
                 the
                 1
                 /
                 ●
                 of
                 5
                 ●
                 /
                 7
                 it
                 is
                 ●2
                 /
                 7
                 or
                 ●
                 and
                 ●
                 7
                 ,
                 which
                 multipled
                 by
                 4
                 makes
                 6
                 and
                 6
                 /
                 7
                 ,
                 which
                 is
                 the
                 remainder
                 of
                 the
                 day
                 ,
                 as
                 before
                 :
                 but
                 if
                 the
                 day
                 had
                 been
                 24
                 houres
                 ,
                 then
                 the
                 houre
                 had
                 been
                 10
                 of
                 the
                 clock
                 ▪
                 and
                 two
                 seventhes
                 of
                 an
                 houre
                 ,
                 which
                 is
                 found
                 ▪
                 out
                 by
                 dividing
                 12
                 ,
                 or
                 24
                 by
                 ●
                 .
              
               
                 There
                 might
                 have
                 been
                 added
                 many
                 curious
                 propositions
                 in
                 this
                 kinde
                 ,
                 but
                 they
                 vvould
                 be
                 too
                 difficult
                 for
                 the
                 most
                 part
                 of
                 people
                 ▪
                 therefore
                 I
                 have
                 omi●ted
                 them
                 ▪
              
            
             
               
                 Of
                 Pythagoras
                 his
                 Schollers
                 .
              
               
                 PYthagoras
                 being
                 asked
                 what
                 number
                 of
                 Schollers
                 he
                 had
                 ,
                 ansvvered
                 ,
                 that
                 halfe
                 of
                 them
                 studied
                 Mathematickes
                 ,
                 the
                 fourth
                 part
                 Physick
                 ,
                 the
                 seventh
                 part
                 Rethorick
                 ,
                 and
                 besides
                 he
                 had
                 3
                 vvomen
                 :
                 novv
                 judge
                 you
                 saith
                 he
                 ,
                 hovv
                 many
                 Schollers
                 I
                 have
                 .
                 Ansvver
                 ,
                 he
                 had
                 in
                 all
                 28
                 ,
                 the
                 halfe
                 of
                 vvhich
                 is
                 14
                 ,
                 the
                 quarter
                 
                 of
                 which
                 is
                 7
                 ,
                 and
                 the
                 seventh
                 part
                 of
                 which
                 is
                 which
                 14
                 ,
                 7
                 ,
                 and
                 4
                 ,
                 makes
                 25
                 ,
                 and
                 the
                 other
                 3
                 to
                 make
                 up
                 the
                 28
                 ,
                 were
                 the
                 3
                 women
                 .
              
            
             
               
                 Of
                 the
                 number
                 of
                 Apples
                 given
                 amongst
                 the
                 Graces
                 and
                 the
                 Muses
                 .
              
               
                 THe
                 three
                 Graces
                 carrying
                 Apples
                 upon
                 a
                 day
                 ,
                 the
                 one
                 as
                 many
                 as
                 the
                 other
                 ,
                 met
                 with
                 the
                 9
                 Muses
                 ,
                 who
                 asked
                 of
                 them
                 some
                 of
                 their
                 Apples
                 ;
                 so
                 each
                 of
                 the
                 Graces
                 gave
                 to
                 each
                 of
                 the
                 Muses
                 alike
                 ,
                 and
                 the
                 distribution
                 being
                 made
                 ,
                 they
                 found
                 that
                 the
                 Graces
                 &
                 the
                 Muses
                 had
                 one
                 as
                 many
                 as
                 the
                 other
                 :
                 The
                 question
                 is
                 how
                 many
                 Apples
                 each
                 Grace
                 had
                 ,
                 and
                 how
                 many
                 they
                 gave
                 to
                 each
                 Muse
                 ?
                 ●o
                 ansvver
                 the
                 qeustion
                 ,
                 joyne
                 the
                 number
                 of
                 Graces
                 and
                 Muses
                 together
                 vvhich
                 makes
                 12
                 ,
                 and
                 so
                 many
                 Apples
                 had
                 each
                 Grace
                 :
                 Novv
                 may
                 you
                 take
                 the
                 double
                 ,
                 triple
                 ,
                 &c.
                 of
                 12
                 that
                 is
                 24
                 ,
                 36
                 ,
                 &c.
                 conditionally
                 ,
                 that
                 if
                 each
                 Grace
                 had
                 but
                 12
                 ,
                 then
                 may
                 there
                 be
                 allotted
                 to
                 each
                 Muse
                 but
                 one
                 onely
                 ;
                 if
                 24
                 ,
                 then
                 to
                 each
                 2
                 Apples
                 ,
                 if
                 ●6
                 ,
                 then
                 to
                 each
                 Muse
                 3
                 Apples
                 ,
                 and
                 so
                 the
                 distribution
                 being
                 made
                 ,
                 they
                 have
                 a
                 like
                 number
                 ,
                 that
                 is
                 one
                 as
                 many
                 as
                 the
                 other
                 .
              
            
             
               
                 Of
                 the
                 Testament
                 or
                 last
                 Will
                 of
                 a
                 dying
                 Father
                 .
              
               
                 A
                 Dying
                 Father
                 left
                 a
                 thousand
                 Crovvnes
                 amongst
                 his
                 tvvo
                 children
                 ;
                 the
                 one
                 being
                 legitimate
                 ,
                 and
                 the
                 other
                 a
                 Bastard
                 ,
                 conditionally
                 
                 that
                 the
                 fifth
                 part
                 which
                 his
                 legittimate
                 Sonne
                 should
                 have
                 ,
                 should
                 exceed
                 by
                 10
                 ,
                 the
                 fourth
                 part
                 of
                 that
                 which
                 the
                 Bastard
                 should
                 have
                 :
                 what
                 was
                 each
                 〈◊〉
                 part
                 ?
                 Answer
                 ,
                 the
                 legitimate
                 Sonne
                 had
                 577
                 crownes
                 and
                 7
                 /
                 ●
                 ,
                 and
                 the
                 Bastard
                 42●
                 crownes
                 and
                 2
                 /
                 9
                 now
                 the
                 fifth
                 part
                 of
                 577
                 and
                 7
                 ninthes
                 is
                 1●5
                 ,
                 and
                 5
                 /
                 9
                 ,
                 and
                 the
                 fourth
                 part
                 of
                 422
                 and
                 ●
                 is
                 105
                 and
                 ●
                 which
                 is
                 lesse
                 then
                 ●15
                 ●
                 by
                 10
                 ,
                 according
                 to
                 the
                 Will
                 of
                 the
                 Testator
                 .
              
            
             
               
                 Of
                 the
                 Cups
                 of
                 Croesus
                 .
              
               
                 CRoesus
                 gave
                 to
                 the
                 Temple
                 of
                 the
                 ●ods
                 six
                 Cups
                 of
                 Gold
                 ▪
                 which
                 weighed
                 together
                 ●00
                 Drammes
                 ,
                 but
                 each
                 cup
                 was
                 heavier
                 one
                 than
                 another
                 by
                 one
                 Dram
                 :
                 how
                 much
                 did
                 each
                 of
                 them
                 therefore
                 weigh
                 ?
                 Answer
                 ,
                 the
                 first
                 weighed
                 102
                 Drammes
                 and
                 a
                 halfe
                 ;
                 the
                 second
                 101
                 Drammes
                 and
                 a
                 halfe
                 ,
                 the
                 third
                 100
                 Drammes
                 and
                 ●
                 ,
                 the
                 fourth
                 99
                 a
                 &
                 halfe
                 ,
                 the
                 fifth
                 98
                 &
                 a
                 halfe
                 ;
                 and
                 the
                 sixt
                 Cup
                 weighed
                 97
                 Drammes
                 and
                 a
                 halfe
                 ▪
                 which
                 together
                 makes
                 600
                 Drams
                 as
                 before
                 .
              
            
             
               
                 Of
                 Cupids
                 Apples
                 .
              
               
                 CVpid
                 complained
                 to
                 his
                 mother
                 that
                 the
                 Muses
                 had
                 taken
                 away
                 his
                 Apples
                 ,
                 Clio
                 ,
                 said
                 he
                 ,
                 took
                 from
                 me
                 the
                 fifth
                 part
                 ,
                 Euterp
                 the
                 twelfth
                 part
                 ,
                 Thalia
                 the
                 eighth
                 part
                 ,
                 M●lp●meno
                 the
                 twentieth
                 part
                 ,
                 Erates
                 the
                 seventh
                 part
                 ▪
                 Terpomene
                 the
                 fourth
                 part
                 ,
                 Polyhymnia
                 took
                 away
                 30
                 ,
                 Vrania
                 220
                 ,
                 and
                 Calliope
                 300.
                 so
                 
                 there
                 vvere
                 left
                 me
                 but
                 5
                 Appls
                 ,
                 hovv
                 many
                 had
                 he
                 in
                 all
                 at
                 the
                 first
                 ?
                 I
                 ansvver
                 3●60
                 .
              
               
                 
                   There
                   are
                   an
                   infinite
                   of
                   such
                   like
                   questions
                   amongst
                   the
                   Greek
                   Epigrams
                   :
                   but
                   it
                   would
                   be
                   unpleasant
                   to
                   expresse
                   them
                   all
                   :
                   I
                   will
                   onely
                   adde
                   one
                   more
                   ,
                   and
                   shew
                   a
                   generall
                   rule
                   for
                   all
                   the
                   rest
                   .
                
              
            
             
               
                 Of
                 a
                 Mans
                 Age.
                 
              
               
                 A
                 Man
                 vvas
                 said
                 to
                 passe
                 the
                 sixth
                 part
                 of
                 his
                 life
                 in
                 childe-hood
                 ,
                 the
                 fourth
                 part
                 in
                 his
                 youth
                 ,
                 the
                 ●hird
                 part
                 in
                 Manhood
                 ,
                 and
                 18
                 yeares
                 besides
                 in
                 old
                 age
                 :
                 what
                 might
                 his
                 Age
                 be
                 ?
                 the
                 ansvver
                 is
                 ,
                 72
                 yeares
                 :
                 vvhich
                 and
                 all
                 others
                 is
                 thus
                 resolved
                 :
                 multiply
                 1
                 /
                 ●
                 ▪
                 ¼
                 and
                 ⅓
                 ▪
                 together
                 ,
                 that
                 is
                 ,
                 6
                 by
                 4
                 makes
                 24
                 ,
                 and
                 that
                 againe
                 by
                 3
                 makes
                 72
                 ,
                 then
                 take
                 the
                 third
                 part
                 of
                 72
                 ,
                 vvhich
                 is
                 24
                 ,
                 the
                 fourth
                 part
                 of
                 it
                 ,
                 vvhich
                 is
                 18
                 ,
                 and
                 the
                 sixth
                 part
                 of
                 it
                 vvhich
                 is
                 12
                 ,
                 these
                 added
                 together
                 make
                 54
                 ,
                 vvhich
                 taken
                 from
                 72
                 ,
                 rests
                 18
                 this
                 divided
                 by
                 18
                 (
                 spoken
                 in
                 the
                 Question
                 )
                 gives
                 1
                 ,
                 which
                 multiplied
                 by
                 the
                 summe
                 of
                 the
                 parts
                 ,
                 viz.
                 72
                 ,
                 makes
                 72
                 ,
                 the
                 Ansvver
                 as
                 before
                 .
              
            
             
               
                 Of
                 the
                 Lion
                 of
                 Bronze
                 placed
                 upon
                 a
                 Fountaine
                 with
                 this
                 Epigramme
                 .
              
               
                 OVt
                 of
                 my
                 right
                 eye
                 if
                 I
                 let
                 vvater
                 passe
                 ,
                 I
                 can
                 fill
                 the
                 Cisterne
                 in
                 2
                 dayes
                 :
                 if
                 I
                 let
                 it
                 passe
                 out
                 of
                 the
                 left
                 eye
                 ,
                 it
                 vvill
                 be
                 filled
                 in
                 3
                 dayes
                 :
                 if
                 it
                 passe
                 out
                 of
                 my
                 feet
                 ,
                 the
                 Cistern
                 vvill
                 be
                 4
                 dayes
                 a●filling
                 ;
                 but
                 if
                 I
                 let
                 the
                 vvater
                 passe
                 out
                 of
                 my
                 mouth
                 ,
                 I
                 can
                 fill
                 the
                 Cistern
                 then
                 in
                 6
                 
                 houres
                 :
                 in
                 vvhat
                 time
                 should
                 I
                 fill
                 it
                 ,
                 if
                 I
                 poure
                 forth
                 the
                 vvater
                 at
                 all
                 the
                 passages
                 at
                 once
                 ?
              
               
                 The
                 Greeks
                 (
                 the
                 greatest
                 talkers
                 in
                 the
                 vvorld
                 )
                 variously
                 apply
                 this
                 question
                 to
                 divers
                 statues
                 ,
                 and
                 pipes
                 of
                 Fountaines
                 :
                 and
                 the
                 solution
                 is
                 by
                 the
                 Rule
                 of
                 ●
                 ,
                 by
                 a
                 generall
                 Rule
                 ,
                 or
                 by
                 ●lgebra
                 .
                 They
                 have
                 also
                 in
                 their
                 Anthologie
                 many
                 other
                 questions
                 ,
                 but
                 because
                 they
                 are
                 more
                 proper
                 to
                 exercise
                 ,
                 than
                 to
                 recreate
                 the
                 spirit
                 ,
                 I
                 passe
                 them
                 over
                 (
                 as
                 before
                 )
                 with
                 silence
                 .
              
            
          
           
             
               PROBLEM
               .
               LXXVII
               .
               Divers
               excellent
               and
               admirable
               experiments
               upon
               Glasses
               .
            
             
               THere
               is
               nothing
               in
               the
               world
               so
               beautifull
               as
               light
               :
               and
               nothing
               more
               recreative
               to
               the
               sight
               ,
               than
               Glasses
               vvhich
               reflect
               :
               therefore
               I
               vvill
               novv
               produce
               some
               experiments
               upon
               them
               ,
               not
               that
               vvill
               dive
               into
               their
               depth
               (
               that
               vvere
               to
               lay
               open
               a
               mysterious
               thing
               )
               but
               that
               vvhich
               may
               delight
               and
               recreate
               the
               spirits
               :
               Let
               us
               suppose
               therefore
               these
               principles
               ,
               upon
               which
               is
               built
               the
               demonstration
               of
               the
               appar●nces
               which
               are
               made
               ●n
               all
               sort
               of
               Glasses
               .
            
             
               First
               ,
               that
               the
               rayes
               or
               beames
               ,
               vvhich
               reflect
               upon
               a
               Glasse
               ,
               make
               the
               Angle
               of
               incident
               equall
               to
               the
               Angle
               of
               Reflection
               ,
               by
               the
               first
               Theo.
               of
               the
               Catoptick
               of
               Euc.
               
            
             
               Secondly
               ,
               that
               in
               all
               plain
               Glasses
               ,
               the
               Images
               are
               seen
               in
               the
               perpendicular
               line
               to
               the
               Glasse
               ,
               
               as
               far
               within
               the
               glass
               as
               the
               object
               is
               without
               it
               .
            
             
               Thirdly
               ,
               in
               Concave
               ,
               or
               Convex
               Glasses
               ,
               the
               Images
               are
               seen
               in
               the
               right
               line
               which
               passeth
               from
               the
               object
               and
               through
               the
               Centre
               in
               the
               Glasse
               .
               Theo.
               17.
               and
               18.
               
            
             
               And
               here
               you
               are
               to
               understand
               ,
               that
               there
               is
               not
               meant
               only
               those
               which
               are
               simple
               Glasses
               or
               Glasses
               of
               steele
               ,
               but
               all
               other
               bodies
               ,
               which
               may
               represent
               the
               visible
               Image
               of
               things
               by
               reason
               of
               their
               reflection
               ,
               as
               Water
               ,
               Marble
               ,
               Mettal
               ,
               or
               such
               like
               .
               Now
               take
               a
               Glasse
               in
               your
               hand
               and
               make
               experiment
               upon
               that
               which
               followeth
               .
            
             
               
                 Experiment
                 upon
                 flat
                 and
                 plaine
                 Glasses
                 .
              
               
                 FIrst
                 ,
                 a
                 man
                 cannot
                 see
                 any
                 thing
                 in
                 these
                 Glasses
                 ,
                 if
                 he
                 be
                 not
                 directly
                 and
                 in
                 a
                 perpendicular
                 line
                 before
                 it
                 ,
                 neither
                 can
                 he
                 see
                 an
                 object
                 in
                 these
                 Glasses
                 ,
                 if
                 it
                 be
                 not
                 in
                 such
                 a
                 place
                 ,
                 that
                 makes
                 the
                 Angle
                 of
                 incidence
                 equall
                 to
                 the
                 Angle
                 of
                 reflexion
                 :
                 therefore
                 when
                 a
                 Glasse
                 stands
                 upright
                 ,
                 that
                 is
                 ,
                 perpendicular
                 to
                 the
                 Horizon
                 ,
                 you
                 cannot
                 see
                 that
                 which
                 is
                 above
                 ,
                 except
                 the
                 Glasse
                 be
                 placed
                 down
                 flat
                 :
                 and
                 to
                 see
                 that
                 on
                 the
                 right
                 hand
                 ,
                 you
                 must
                 be
                 on
                 the
                 left
                 hand
                 ,
                 &c.
                 
              
               
                 Secondly
                 ,
                 an
                 image
                 cannot
                 be
                 seen
                 in
                 a
                 Glass
                 if
                 it
                 be
                 not
                 raised
                 above
                 the
                 surface
                 of
                 it
                 ;
                 or
                 place
                 a
                 Glasse
                 upon
                 a
                 wall
                 ,
                 you
                 shall
                 see
                 nothing
                 which
                 is
                 upon
                 the
                 plaine
                 of
                 the
                 wall
                 ,
                 and
                 place
                 it
                 upon
                 a
                 Table
                 or
                 Horizontal
                 Plaine
                 ,
                 you
                 shall
                 see
                 nothing
                 of
                 that
                 which
                 is
                 upon
                 the
                 Table
                 .
              
               
               
                 Thirdly
                 ,
                 in
                 a
                 plaine
                 Glasse
                 all
                 that
                 is
                 seene
                 appeares
                 or
                 seemes
                 to
                 sink
                 behinde
                 the
                 Glasse
                 ,
                 as
                 much
                 as
                 the
                 image
                 is
                 before
                 the
                 Glasse
                 ,
                 as
                 before
                 is
                 said
                 .
              
               
                 Fourthly
                 ,
                 (
                 as
                 in
                 water
                 )
                 a
                 Glasse
                 lying
                 downe
                 flat
                 ,
                 or
                 Horizontall
                 ,
                 Towers
                 ,
                 Trees
                 ,
                 Men
                 ,
                 or
                 any
                 height
                 doth
                 appeare
                 ,
                 inversed
                 or
                 upside
                 downe
                 ;
                 and
                 a
                 Glasse
                 placed
                 upright
                 ,
                 the
                 right
                 hand
                 of
                 the
                 Jmage
                 seems
                 to
                 be
                 the
                 left
                 ,
                 and
                 the
                 left
                 seems
                 to
                 be
                 the
                 right
                 .
                 Fifthly
                 ,
                 will
                 you
                 see
                 in
                 a
                 Chamber
                 that
                 which
                 is
                 done
                 in
                 the
                 street
                 ,
                 without
                 being
                 seen
                 ▪
                 then
                 a
                 Glasse
                 must
                 be
                 disposed
                 ,
                 that
                 the
                 line
                 upon
                 which
                 the
                 Jmages
                 come
                 on
                 the
                 Glasse
                 ,
                 make
                 the
                 Angle
                 of
                 incidence
                 equall
                 to
                 that
                 Angle
                 of
                 reflexion
                 .
              
               
               
                 Seventhly
                 ,
                 present
                 a
                 Candle
                 upon
                 a
                 plaine
                 Glasse
                 ,
                 and
                 look
                 flaunting
                 upon
                 it
                 ,
                 so
                 that
                 the
                 Candle
                 and
                 the
                 Glasse
                 be
                 neere
                 in
                 a
                 right
                 line
                 ,
                 you
                 shall
                 see
                 3
                 ,
                 4
                 ,
                 5
                 ,
                 &c.
                 images
                 ,
                 from
                 one
                 and
                 the
                 same
                 Candle
                 .
              
               
                 Eightly
                 ,
                 take
                 tvvo
                 plaine
                 Glasses
                 ,
                 and
                 hold
                 them
                 one
                 against
                 the
                 other
                 ,
                 you
                 shall
                 alternately
                 see
                 them
                 oftentimes
                 one
                 vvithin
                 the
                 other
                 ,
                 yea
                 vvithin
                 themselves
                 ,
                 againe
                 and
                 againe
                 .
              
               
                 Ninthly
                 ,
                 if
                 you
                 hold
                 a
                 plaine
                 Glasse
                 behinde
                 your
                 head
                 ,
                 and
                 another
                 before
                 your
                 face
                 ,
                 you
                 may
                 see
                 the
                 h●nder
                 part
                 of
                 your
                 head
                 ,
                 in
                 that
                 Glasse
                 vvhich
                 you
                 hold
                 before
                 your
                 face
                 .
              
               
                 Tenthly
                 ,
                 you
                 may
                 have
                 a
                 fine
                 experiment
                 if
                 you
                 place
                 tvvo
                 Glasses
                 together
                 ,
                 that
                 they
                 make
                 an
                 acute
                 angle
                 ,
                 and
                 so
                 the
                 lesser
                 the
                 angle
                 is
                 ,
                 the
                 more
                 apparances
                 you
                 shall
                 see
                 ,
                 the
                 one
                 direct
                 ,
                 the
                 other
                 inversed
                 ,
                 the
                 one
                 approaching
                 ,
                 and
                 the
                 other
                 retiring
                 .
              
               
                 Eleventhly
                 ,
                 it
                 is
                 a
                 vvonder
                 &
                 astonishment
                 to
                 some
                 ,
                 to
                 see
                 within
                 a
                 Glasse
                 an
                 Image
                 vvithout
                 knovving
                 from
                 vvhence
                 it
                 came
                 ,
                 and
                 it
                 may
                 be
                 done
                 many
                 vvayes
                 :
                 as
                 place
                 a
                 Glass
                 higher
                 than
                 the
                 eye
                 of
                 the
                 beholder
                 ,
                 and
                 right
                 against
                 it
                 is
                 some
                 Image
                 ;
                 so
                 it
                 resteth
                 not
                 upon
                 the
                 beholder
                 ,
                 but
                 doth
                 cast
                 the
                 Image
                 upvvards
                 .
                 Then
                 place
                 another
                 object
                 ,
                 so
                 that
                 it
                 reflect
                 ,
                 or
                 cast
                 
                 the
                 Image
                 downeward
                 to
                 the
                 eye
                 of
                 the
                 spectator
                 ▪
                 without
                 perceiving
                 it
                 being
                 hid
                 behinde
                 something
                 ,
                 for
                 then
                 the
                 Glasse
                 will
                 represent
                 a
                 quite
                 contrary
                 thing
                 ,
                 either
                 that
                 which
                 is
                 before
                 the
                 Glasse
                 ,
                 or
                 that
                 which
                 is
                 about
                 it
                 ,
                 to
                 wit
                 ,
                 the
                 other
                 hidden
                 object
                 .
              
               
                 Twelfthly
                 ,
                 if
                 there
                 be
                 ingraved
                 behinde
                 the
                 backside
                 of
                 a
                 Glasse
                 ,
                 or
                 drawne
                 any
                 Image
                 upon
                 it
                 ,
                 it
                 will
                 appeare
                 before
                 as
                 an
                 Image
                 ,
                 without
                 any
                 appearance
                 :
                 o●
                 portraicture
                 to
                 be
                 perceived
                 .
              
               
                 
                   EXAMINATION
                   .
                
                 
                   THis
                   12
                   Article
                   
                     of
                     ingraving
                     an
                     Image
                     behinde
                     the
                     Glasse
                     ,
                     will
                     be
                     of
                     no
                     great
                     consequence
                     ▪
                     because
                     the
                     lineaments
                     will
                     seem
                     so
                     obscure
                     ,
                     but
                     if
                     there
                     were
                     painted
                     some
                     Image
                     ,
                     and
                     then
                     that
                     covered
                     according
                     to
                     the
                     usuall
                     covering
                     of
                     Glasses
                     behinde
                     ,
                     and
                     so
                     made
                     up
                     like
                     an
                     ordinary
                     looking-Glasse
                     having
                     an
                     Image
                     in
                     the
                     middle
                     ,
                     in
                     this
                     respect
                     it
                     would
                     be
                     sufficiently
                     pleasant
                     :
                     and
                     that
                     which
                     would
                     admire
                     the
                     ignorant
                     ,
                     and
                     able
                     to
                     exercise
                     the
                     most
                     subtillest
                     ,
                     and
                     that
                     principally
                     if
                     the
                     Glasse
                     be
                     in
                     an
                     obscure
                     place
                     ,
                     and
                     the
                     light
                     which
                     is
                     given
                     to
                     it
                     be
                     somewhat
                     farre
                     off
                     .
                  
                
                 
                   PLace
                   a
                   Glasse
                   neare
                   the
                   floor
                   of
                   a
                   Chamber
                   ,
                   &
                   make
                   a
                   hole
                   through
                   the
                   place
                   under
                   the
                   Glasse
                   ,
                   so
                   that
                   those
                   which
                   are
                   below
                   may
                   not
                   perceive
                   it
                   ,
                   and
                   dispose
                   a
                   bright
                   Image
                   under
                   
                   the
                   hole
                   so
                   that
                   it
                   may
                   cast
                   his
                   species
                   upon
                   the
                   Glasse
                   ,
                   and
                   it
                   will
                   cause
                   admiration
                   to
                   those
                   which
                   are
                   below
                   that
                   know
                   not
                   the
                   cause
                   ;
                   The
                   same
                   may
                   be
                   done
                   by
                   placing
                   the
                   Image
                   in
                   a
                   Chamber
                   adjoyning
                   ,
                   and
                   so
                   make
                   it
                   to
                   be
                   seen
                   upon
                   the
                   side
                   of
                   the
                   Wall.
                   
                
                 
                   14
                   In
                   these
                   Channel-Images
                   which
                   shew
                   one
                   side
                   a
                   deaths
                   head
                   ,
                   &
                   another
                   side
                   a
                   faire
                   face
                   :
                   and
                   right
                   before
                   some
                   other
                   thing
                   :
                   it
                   is
                   a
                   thing
                   evident
                   ,
                   that
                   setting
                   a
                   plaine
                   Glasse
                   sidewise
                   to
                   this
                   Image
                   you
                   shall
                   see
                   it
                   in
                   a
                   contrary
                   thing
                   ,
                   then
                   that
                   which
                   was
                   presented
                   before
                   sidewise
                   .
                
                 
                   15
                   Lastly
                   ,
                   it
                   is
                   a
                   fine
                   secret
                   to
                   present
                   unto
                   a
                   plaine
                   Glasse
                   writing
                   with
                   such
                   industry
                   ,
                   that
                   one
                   may
                   read
                   it
                   in
                   the
                   Glasse
                   ,
                   and
                   yet
                   out
                   of
                   the
                   Glasse
                   there
                   is
                   nothing
                   to
                   be
                   known
                   ,
                   which
                   will
                   thus
                   happen
                   ,
                   if
                   the
                   writing
                   be
                   writ
                   backward
                   :
                   but
                   that
                   which
                   is
                   more
                   strange
                   ,
                   to
                   shew
                   a
                   kinde
                   of
                   writing
                   to
                   a
                   plaine
                   Glasse
                   ,
                   it
                   shall
                   appear
                   another
                   kinde
                   of
                   writing
                   both
                   against
                   sense
                   and
                   forme
                   ,
                   as
                   if
                   there
                   were
                   presented
                   to
                   the
                   Glasse
                   WEL
                   it
                   would
                   shew
                   it
                   MET
                   ;
                   if
                   it
                   were
                   written
                   thus
                   MIV
                   ,
                   and
                   presented
                   to
                   the
                   Glasse
                   ,
                   it
                   would
                   appeare
                   thus
                   VIM
                   ;
                   for
                   in
                   the
                   first
                   ,
                   if
                   the
                   Glasse
                   ly
                   flat
                   ,
                   then
                   the
                   things
                   are
                   inversed
                   that
                   are
                   perpendicular
                   to
                   the
                   Glass
                   ,
                   if
                   the
                   Glass
                   and
                   the
                   object
                   be
                   upright
                   ,
                   then
                   that
                   on
                   the
                   right
                   hand
                   ,
                   is
                   turned
                   to
                   the
                   left
                   ,
                   as
                   in
                   the
                   latter
                   .
                
                 
                   And
                   here
                   I
                   cease
                   to
                   speak
                   further
                   of
                   these
                   plaine
                   Glasses
                   ,
                   either
                   of
                   the
                   Admirable
                   multiplications
                   ,
                   or
                   appearances
                   ,
                   which
                   is
                   made
                   in
                   a
                   great
                   number
                   of
                   them
                   ;
                   for
                   to
                   content
                   the
                   sight
                   
                   in
                   this
                   particular
                   ,
                   one
                   must
                   have
                   recourse
                   to
                   the
                   Cabinets
                   of
                   great
                   Personages
                   who
                   inrich
                   themselves
                   with
                   most
                   beautifull
                   ones
                   .
                
              
            
             
               
                 Experiments
                 upon
                 Gibbous
                 ,
                 or
                 convex
                 Sphericall
                 Glasses
                 .
              
               
                 IF
                 they
                 be
                 in
                 the
                 forme
                 of
                 a
                 Bowle
                 ,
                 or
                 part
                 of
                 a
                 great
                 Globe
                 of
                 Glasse
                 ,
                 there
                 is
                 singular
                 contentment
                 to
                 contemplate
                 on
                 them
                 .
              
               
                 First
                 ,
                 because
                 they
                 present
                 the
                 objects
                 lesse
                 and
                 more
                 gracious
                 ,
                 and
                 by
                 hovv
                 much
                 more
                 the
                 Images
                 are
                 separated
                 from
                 the
                 Glasse
                 ,
                 by
                 so
                 much
                 the
                 more
                 they
                 diminish
                 in
                 Magnitude
                 .
              
               
                 Secondly
                 ,
                 they
                 that
                 shew
                 the
                 Images
                 plaiting
                 ,
                 or
                 foulding
                 ,
                 which
                 is
                 very
                 pleasant
                 ,
                 especially
                 when
                 the
                 Glasse
                 is
                 placed
                 downe
                 ,
                 and
                 behold
                 in
                 it
                 some
                 Blanching
                 ,
                 feeling
                 ,
                 &c.
                 
                 The
                 upper
                 part
                 of
                 a
                 Gallerie
                 ,
                 the
                 porch
                 of
                 a
                 Hall
                 ,
                 &c.
                 for
                 they
                 will
                 be
                 represented
                 as
                 a
                 great
                 vessel
                 having
                 more
                 belly
                 in
                 the
                 middle
                 then
                 at
                 the
                 two
                 ends
                 ,
                 and
                 Posts
                 ,
                 and
                 Joists
                 of
                 Timber
                 will
                 seeme
                 as
                 Circles
                 .
              
               
                 Thirdly
                 ,
                 that
                 which
                 ravisheth
                 the
                 spirits
                 ,
                 by
                 the
                 eye
                 ,
                 and
                 which
                 shames
                 the
                 best
                 perspective
                 Painting
                 that
                 a
                 Painter
                 can
                 make
                 ,
                 is
                 the
                 beautifull
                 contraction
                 of
                 the
                 Images
                 ,
                 that
                 appeare
                 within
                 the
                 sphericity
                 of
                 these
                 small
                 Glasses
                 :
                 for
                 present
                 the
                 Glasse
                 to
                 the
                 lower
                 end
                 of
                 a
                 Gallarie
                 ,
                 or
                 at
                 the
                 Corner
                 of
                 a
                 great
                 Court
                 full
                 of
                 People
                 ,
                 or
                 towards
                 a
                 great
                 street
                 ,
                 Church
                 ,
                 fortification
                 ,
                 an
                 Army
                 of
                 men
                 ,
                 to
                 a
                 whole
                 Cittie
                 ;
                 all
                 the
                 faire
                 Architecture
                 ,
                 and
                 appearances
                 will
                 
                 be
                 seene
                 contracted
                 within
                 the
                 circuit
                 of
                 the
                 Glasse
                 with
                 such
                 varietie
                 of
                 Colours
                 ,
                 and
                 distinctions
                 in
                 the
                 lesser
                 parts
                 ,
                 that
                 I
                 know
                 not
                 in
                 the
                 world
                 what
                 is
                 more
                 agreeable
                 to
                 the
                 sight
                 ,
                 and
                 pleasant
                 to
                 behold
                 ,
                 in
                 which
                 you
                 will
                 not
                 have
                 an
                 exact
                 proportion
                 ,
                 but
                 it
                 will
                 be
                 variable
                 ,
                 according
                 to
                 the
                 distance
                 of
                 the
                 Object
                 from
                 the
                 Glasse
                 .
              
            
             
               
                 Exptriments
                 upon
                 hollow
                 ,
                 or
                 Concave
                 sphericall
                 Glasses
                 .
              
               
                 I
                 Have
                 heretofore
                 spoken
                 how
                 they
                 may
                 burne
                 ,
                 being
                 made
                 of
                 Glasse
                 ,
                 or
                 Metall
                 ,
                 it
                 remaines
                 now
                 that
                 I
                 deliver
                 some
                 pleasant
                 uses
                 of
                 them
                 ,
                 which
                 they
                 represent
                 unto
                 our
                 sight
                 ,
                 and
                 so
                 much
                 the
                 more
                 notable
                 it
                 will
                 be
                 ,
                 by
                 how
                 much
                 the
                 greater
                 the
                 Glasse
                 is
                 ,
                 and
                 the
                 Globe
                 from
                 whence
                 it
                 is
                 extracted
                 for
                 it
                 must
                 in
                 proportion
                 as
                 a
                 segment
                 of
                 some
                 be
                 made
                 circle
                 or
                 orbe
                 .
              
               
                 
                   EXAMINATION
                   .
                
                 
                   
                     IN
                     this
                     we
                     may
                     observe
                     that
                     a
                     section
                     of
                  
                   2.3
                   .
                   or
                   4.
                   
                   
                     Inches
                     in
                     diameter
                     ,
                     may
                     be
                     segments
                     of
                     spheres
                     of
                  
                   2.3
                   .
                   or
                   4.
                   
                     foot
                     ●
                     nay
                     of
                     so
                     many
                     fadome
                     ,
                     for
                     it
                     is
                     certaine
                     that
                     amongst
                     those
                     which
                     comprehend
                     a
                     great
                     portion
                     of
                     a
                     lesser
                     sphere
                     ,
                     and
                     those
                     which
                     comprehend
                     a
                     little
                     segment
                     of
                     a
                     great
                     spheere
                     ,
                     whether
                     they
                     be
                     equall
                     or
                     not
                     in
                     section
                     ,
                     there
                     will
                     happen
                     an
                     evident
                     difference
                     in
                     one
                     and
                     the
                     same
                     experiment
                     ,
                     
                     in
                     the
                     number
                     ,
                     situation
                     ,
                     quantitie
                     ,
                     and
                     figure
                     of
                     the
                     Images
                     of
                     one
                     or
                     many
                     different
                     objects
                     ,
                     and
                     in
                     burning
                     there
                     is
                     a
                     great
                     difference
                     .
                  
                
                 
                   MAginus
                   ,
                   in
                   a
                   little
                   Tractate
                   that
                   he
                   had
                   upon
                   these
                   Glasses
                   ,
                   witnesseth
                   of
                   himselfe
                   that
                   he
                   hath
                   caused
                   many
                   to
                   be
                   polished
                   for
                   sundry
                   great
                   Lords
                   of
                   Italy
                   ,
                   and
                   Germanie
                   ,
                   which
                   were
                   segments
                   of
                   Globes
                   of
                   2.3
                   .
                   and
                   4.
                   foot
                   diameter
                   ;
                   and
                   I
                   wish
                   you
                   had
                   some
                   such
                   like
                   to
                   see
                   the
                   experiments
                   of
                   that
                   which
                   followeth
                   ;
                   it
                   is
                   not
                   difficult
                   to
                   have
                   such
                   made
                   ,
                   or
                   bought
                   here
                   in
                   Town
                   ,
                   the
                   contentment
                   herein
                   would
                   beare
                   with
                   the
                   cost
                   .
                
              
               
                 
                   EXAMINATION
                   .
                
                 
                   TOuching
                   Maginus
                   
                     he
                     hath
                     nothing
                     ayded
                     us
                     to
                     the
                     knowledge
                     of
                     the
                     truth
                     by
                     his
                     extract
                     out
                     of
                  
                   Vitellius
                   ,
                   
                     but
                     left
                     it
                     :
                     expecting
                     it
                     from
                     others
                     ,
                     rather
                     than
                     to
                     be
                     plunged
                     in
                     the
                     search
                     of
                     it
                     himselfe
                     ,
                     affecting
                     rather
                     the
                     forging
                     of
                     the
                     matter
                     ,
                     and
                     composition
                     of
                     the
                     Glasses
                     ,
                     than
                     Geometrically
                     to
                     establish
                     their
                     effects
                     .
                  
                
                 
                   FIrst
                   therefore
                   in
                   concave
                   Glasses
                   ,
                   the
                   Images
                   are
                   seene
                   sometimes
                   upon
                   the
                   surface
                   of
                   the
                   Glasses
                   ,
                   sometimes
                   as
                   though
                   they
                   were
                   within
                   it
                   and
                   behinde
                   it
                   ,
                   deeply
                   sunk
                   into
                   it
                   ,
                   sometimes
                   they
                   are
                   seene
                   before
                   ,
                   and
                   without
                   the
                   Glasse
                   ,
                   sometimes
                   between
                   the
                   object
                   and
                   the
                   
                   Glasse
                   ;
                   sometimes
                   in
                   the
                   place
                   of
                   the
                   Eye
                   ,
                   sometimes
                   farther
                   from
                   the
                   Glasse
                   then
                   the
                   object
                   is
                   :
                   which
                   comes
                   to
                   passe
                   by
                   reason
                   of
                   the
                   divers
                   concourse
                   of
                   the
                   beames
                   ,
                   and
                   change
                   of
                   the
                   place
                   of
                   the
                   Images
                   in
                   the
                   line
                   of
                   reflection
                   .
                
              
               
                 
                   EXAMINATION
                   .
                
                 
                   THe
                   relation
                   of
                   these
                   appearances
                   passe
                   current
                   amongst
                   most
                   men
                   ,
                   but
                   because
                   the
                   curious
                   may
                   not
                   receive
                   prejudice
                   in
                   their
                   experiments
                   ,
                   something
                   ought
                   to
                   be
                   said
                   thereof
                   to
                   give
                   it
                   a
                   more
                   lively
                   touch
                   :
                   in
                   the
                   true
                   causes
                   of
                   these
                   appearances
                   ,
                   in
                   the
                   first
                   place
                   it
                   is
                   impossible
                   that
                   the
                   Image
                   can
                   be
                   upon
                   the
                   surface
                   of
                   the
                   Glasse
                   ,
                   and
                   it
                   is
                   a
                   principall
                   point
                   to
                   declare
                   truly
                   in
                   which
                   place
                   the
                   Image
                   is
                   seen
                   in
                   the
                   Glasse
                   those
                   that
                   are
                   more
                   learned
                   in
                   Opticall
                   knowledge
                   affirme
                   the
                   contrary
                   ,
                   and
                   nature
                   it selfe
                   gives
                   it
                   a
                   certaine
                   place
                   according
                   to
                   its
                   position
                   being
                   alwayes
                   seen
                   in
                   the
                   line
                   of
                   reflection
                   which
                   
                     Alhazen
                     ,
                     Vitellius
                  
                   ,
                   and
                   others
                   full
                   of
                   grea●
                   knowledge
                   ,
                   have
                   confirmed
                   by
                   their
                   writings
                   :
                   but
                   in
                   their
                   particular
                   they
                   were
                   too
                   much
                   occupied
                   by
                   the
                   authority
                   of
                   the
                   Ancients
                   who
                   were
                   not
                   s●fficiently
                   ci●cumspect
                   in
                   experience
                   upon
                   which
                   the
                   principles
                   of
                   this
                   sub●ect
                   ought
                   to
                   be
                   built
                   ,
                   an●
                   searched
                   not
                   fully
                   into
                   the
                   true
                   cause
                   of
                   these
                   appearances
                   ,
                   seeing
                   they
                   leave
                   unto
                   posterities
                   many
                   〈◊〉
                   in
                   their
                   writings
                   ,
                   ●nd
                   those
                   that
                   followed
                   
                   them
                   for
                   the
                   most
                   part
                   fell
                   into
                   the
                   like
                   errors
                   .
                
                 
                   As
                   for
                   the
                   Jmages
                   to
                   bid●
                   in
                   the
                   eye
                   ▪
                   it
                   cannot
                   be
                   but
                   is
                   imp●rtinent
                   and
                   absurd
                   ;
                   but
                   it
                   followeth
                   that
                   ,
                   by
                   how
                   much
                   neerer
                   the
                   ob●ect
                   appro●cheth
                   to
                   the
                   Glasse
                   ,
                   by
                   so
                   much
                   the
                   more
                   the
                   appearances
                   seem
                   to
                   come
                   to
                   the
                   eye
                   :
                   and
                   if
                   the
                   eye
                   be
                   without
                   the
                   point
                   of
                   concourse
                   ,
                   and
                   the
                   object
                   also
                   ;
                   as
                   long
                   as
                   the
                   object
                   approacheth
                   thereto
                   ,
                   the
                   representation
                   of
                   the
                   Image
                   cometh
                   neere
                   the
                   eye
                   ,
                   but
                   passing
                   the
                   point
                   of
                   concourse
                   it
                   goes
                   back
                   againe
                   :
                   these
                   appearances
                   thus
                   approaching
                   do
                   not
                   a
                   little
                   astonish
                   those
                   which
                   are
                   ignorant
                   of
                   the
                   cause
                   :
                   they
                   are
                   inversed
                   ,
                   if
                   the
                   eye
                   be
                   without
                   the
                   point
                   of
                   concourse
                   untill
                   the
                   object
                   be
                   within
                   ,
                   but
                   contrarily
                   if
                   the
                   eye
                   be
                   between
                   the
                   point
                   of
                   concourse
                   and
                   the
                   Glasse
                   ,
                   then
                   the
                   Jmages
                   are
                   direct
                   :
                   and
                   if
                   the
                   eye
                   or
                   the
                   object
                   be
                   in
                   the
                   point
                   of
                   concourse
                   ,
                   the
                   Glasse
                   will
                   be
                   enlightened
                   and
                   the
                   Jmages
                   confused
                   ,
                   and
                   if
                   there
                   were
                   but
                   a
                   spark
                   of
                   fire
                   in
                   the
                   said
                   point
                   of
                   concourse
                   ,
                   all
                   the
                   Glasse
                   would
                   seeme
                   a
                   burning
                   fire-brand
                   ,
                   and
                   we
                   dare
                   say
                   it
                   would
                   occurre
                   without
                   chance
                   ,
                   and
                   in
                   the
                   night
                   be
                   the
                   most
                   certaine
                   and
                   subtilest
                   light
                   that
                   can
                   be
                   ,
                   if
                   a
                   candle
                   were
                   placed
                   there
                   .
                   And
                   whosoever
                   shall
                   enter
                   into
                   the
                   search
                   of
                   the
                   truth
                   of
                   new
                   experiments
                   in
                   this
                   subject
                   without
                   doubt
                   he
                   will
                   confirme
                   what
                   we
                   here
                   speak
                   of
                   :
                   &
                   will
                   finde
                   new
                   lights
                   with
                   a
                   conveniable
                   position
                   to
                   the
                   Glasse
                   ,
                   he
                   will
                   have
                   reflection
                   of
                   quantities
                   ,
                   of
                   truth
                   ,
                   and
                   fine
                   secrets
                   in
                   nature
                   ,
                   yet
                   not
                   known
                   ,
                   which
                   he
                   may
                   easily
                   comprehend
                   
                   if
                   he
                   have
                   but
                   an
                   indifferent
                   sight
                   ,
                   and
                   may
                   assure
                   himselfe
                   that
                   the
                   Images
                   cannot
                   exceed
                   the
                   fight
                   ,
                   nor
                   trouble
                   it
                   ,
                   a
                   thing
                   too
                   much
                   absurd
                   to
                   nature
                   .
                
                 
                   And
                   it
                   is
                   an
                   absolute
                   verity
                   in
                   this
                   science
                   ,
                   that
                   the
                   eye
                   being
                   once
                   placed
                   in
                   the
                   line
                   of
                   reflection
                   of
                   any
                   object
                   ,
                   and
                   moved
                   in
                   the
                   same
                   line
                   :
                   the
                   obect
                   is
                   seene
                   in
                   one
                   and
                   the
                   same
                   place
                   immutable
                   ;
                   or
                   if
                   the
                   Image
                   and
                   the
                   eye
                   move
                   in
                   their
                   owne
                   lines
                   ,
                   the
                   representation
                   in
                   the
                   Glasse
                   seemes
                   to
                   invest
                   it selfe
                   continually
                   with
                   a
                   different
                   figure
                   .
                
                 
                   
                     NOw
                     the
                     Image
                     comming
                     thus
                     to
                     the
                     eye
                     ,
                     those
                     which
                     know
                     not
                     the
                     secret
                     ,
                     draw
                     their
                     sword
                     when
                     they
                     see
                     an
                     Image
                     thus
                     to
                     issue
                     out
                     of
                     the
                     Glasse
                     ,
                     or
                     a
                     Pistoll
                     which
                     some
                     one
                     holds
                     behinde
                     :
                     and
                     some
                     Glasses
                     will
                     shew
                     a
                     sword
                     wholly
                     drawne
                     out
                     ,
                     sepa●ated
                     from
                     the
                     Glasse
                     ,
                     as
                     though
                     it
                     were
                     in
                     the
                     aire
                     :
                     and
                     it
                     is
                     daily
                     exercised
                     ,
                     that
                     a
                     man
                     may
                     touch
                     the
                     Image
                     of
                     his
                     hand
                     or
                     his
                     face
                     out
                     of
                     the
                     Glasse
                     ,
                     which
                     comes
                     out
                     the
                     farther
                     ,
                     by
                     how
                     much
                     the
                     Glasse
                     is
                     great
                     and
                     the
                     Centre
                     remote
                     .
                  
                
              
               
                 
                   EXAMINATION
                   .
                
                 
                   NOw
                   that
                   a
                   Pistoll
                   being
                   presented
                   to
                   a
                   Glasse
                   behinde
                   a
                   man
                   ,
                   should
                   come
                   out
                   of
                   the
                   Glasse
                   ,
                   and
                   make
                   him
                   afraid
                   that
                   stands
                   before
                   ,
                   seeming
                   to
                   shoot
                   at
                   him
                   ,
                   this
                   cannot
                   be
                   :
                   for
                   no
                   object
                   whatsoever
                   
                   presented
                   to
                   a
                   concave
                   Glasse
                   ,
                   if
                   it
                   be
                   not
                   neerer
                   to
                   the
                   G●asse
                   then
                   the
                   eye
                   is
                   it
                   comes
                   not
                   out
                   to
                   the
                   sight
                   of
                   the
                   party
                   ;
                   therefore
                   he
                   needs
                   not
                   feare
                   that
                   which
                   is
                   said
                   to
                   be
                   behinde
                   his
                   back
                   ,
                   and
                   comes
                   out
                   of
                   the
                   Glasse
                   ;
                   for
                   if
                   it
                   doth
                   come
                   out
                   ,
                   it
                   must
                   then
                   necessarily
                   be
                   before
                   his
                   face
                   ,
                   so
                   in
                   a
                   concave
                   Glasse
                   whose
                   Centre
                   is
                   farre
                   remote
                   of
                   a
                   sword
                   ,
                   stick
                   ,
                   or
                   such
                   like
                   be
                   presented
                   to
                   the
                   Glasse
                   ,
                   it
                   shall
                   totally
                   be
                   seen
                   to
                   come
                   forth
                   of
                   the
                   Glasse
                   and
                   all
                   the
                   hand
                   that
                   holds
                   it
                   .
                   And
                   here
                   generally
                   note
                   that
                   if
                   an
                   Image
                   be
                   seen
                   to
                   issue
                   out
                   of
                   the
                   Glasse
                   to
                   come
                   towards
                   the
                   face
                   of
                   any
                   one
                   that
                   stands
                   by
                   ,
                   the
                   object
                   shall
                   be
                   likewise
                   seen
                   to
                   thrust
                   towards
                   that
                   face
                   in
                   the
                   Glass
                   and
                   may
                   easily
                   be
                   knowne
                   to
                   all
                   the
                   standers
                   by
                   :
                   so
                   many
                   persons
                   standing
                   before
                   a
                   Glasse
                   ,
                   if
                   one
                   of
                   the
                   company
                   take
                   a
                   sword
                   ,
                   and
                   would
                   make
                   it
                   issue
                   forth
                   towards
                   any
                   o●her
                   that
                   stands
                   there
                   :
                   let
                   him
                   chuse
                   his
                   Image
                   in
                   the
                   Gl●sse
                   and
                   carry
                   the
                   sword
                   right
                   towards
                   it
                   and
                   the
                   effect
                   will
                   follow
                   .
                   In
                   like
                   manner
                   ones
                   hand
                   being
                   presented
                   to
                   the
                   Glosse
                   as
                   it
                   is
                   thrust
                   towards
                   the
                   Centre
                   ,
                   s●
                   the
                   representation
                   of
                   it
                   comes
                   towards
                   it
                   ,
                   and
                   so
                   the
                   hands
                   will
                   seeme
                   to
                   be
                   united
                   ,
                   or
                   to
                   touch
                   one
                   another
                   .
                
                 
                   
                     FRom
                     which
                     may
                     be
                     concluded
                     ,
                     if
                     such
                     a
                     Glasse
                     be
                     placed
                     at
                     the
                     seeling
                     or
                     planching
                     of
                     a
                     Hall
                     ,
                     so
                     that
                     the
                     face
                     be
                  
                   Horizontall
                   
                     and
                     look
                     downward
                     ;
                     one
                     may
                     see
                     under
                     it
                     as
                     it
                     were
                     a
                     man
                     hanging
                     by
                     the
                     feet
                     ,
                     and
                     if
                     there
                     were
                     many
                     placed
                     so
                     ,
                     one
                     could
                     not
                     enter
                     into
                     that
                     place
                     without
                     great
                     feare
                     or
                     scaring
                     :
                     for
                     
                     one
                     should
                     see
                     many
                     men
                     in
                     the
                  
                   aire
                   
                     as
                     if
                     they
                     were
                     hanging
                     by
                     the
                     feet
                     .
                  
                
              
               
                 
                   EXAMINATION
                   .
                
                 
                   
                     TOuching
                     a
                  
                   Glasse
                   
                     tyed
                     at
                     a
                     seeling
                     or
                     planching
                     ,
                     that
                     one
                     may
                     see
                     a
                     man
                     hang
                     by
                     the
                     feet
                     in
                     the
                  
                   aire
                   ,
                   
                     and
                     so
                     many
                  
                   Glasses
                   ,
                   
                     many
                     men
                     may
                     be
                     seen
                     :
                     without
                     caution
                     this
                     is
                     very
                     absurd
                     for
                     if
                     the
                  
                   Glasse
                   or
                   Glasses
                   
                     be
                     not
                     so
                     great
                     that
                     the
                     Centre
                     of
                     the
                     sphere
                     upon
                     which
                     it
                     was
                     made
                     ,
                     extend
                     not
                     neere
                     to
                     the
                     head
                     of
                     him
                     that
                     is
                     under
                     it
                     ,
                     it
                     will
                     not
                     pleasantly
                     appeare
                     ,
                     and
                     though
                     the
                  
                   Glasse
                   
                     should
                     be
                     of
                     that
                     capacity
                     that
                     the
                  
                   Centre
                   
                     did
                     extend
                     so
                     farre
                     ,
                     yet
                     will
                     not
                     the
                  
                   Images
                   
                     be
                     seene
                     to
                     them
                     which
                     are
                     from
                     the
                  
                   Glasse
                   
                     but
                     on●y
                     to
                     those
                     which
                     are
                     under
                     it
                     ,
                     or
                     neere
                     unto
                     it
                     :
                     and
                     to
                     them
                     it
                     will
                     not
                     ably
                     appeare
                     ,
                     and
                     it
                     would
                     be
                     most
                     admirable
                     to
                     have
                     a
                  
                   Gallerie
                   
                     vaulted
                     over
                     with
                     such
                  
                   Glasses
                   
                     which
                     would
                     wonderfully
                     astonish
                     any
                     one
                     that
                     enters
                     into
                     it
                     :
                     for
                     a●l
                     the
                     things
                     in
                     the
                     Gallery
                     would
                     be
                     seen
                     to
                     hang
                     in
                     the
                  
                   aire
                   ,
                   
                     and
                     you
                     could
                     not
                     walk
                     without
                     incountering
                     airie
                     apparitions
                     .
                  
                
                 
                   SEcondly
                   ,
                   in
                   flat
                   or
                   plaine
                   Glasses
                   the
                   Image
                   is
                   seen
                   equall
                   to
                   his
                   object
                   ,
                   and
                   to
                   represent
                   a
                   whole
                   man
                   ,
                   there
                   ought
                   to
                   be
                   a
                   Glasse
                   as
                   great
                   as
                   the
                   Image
                   is
                   :
                   In
                   convex
                   Glasses
                   the
                   Images
                   are
                   seen
                   alwayes
                   lesse
                   ,
                   in
                   concave
                   Glasses
                   
                   they
                   may
                   be
                   seen
                   greater
                   or
                   lesser
                   ,
                   but
                   not
                   truly
                   proportionable
                   ,
                   by
                   reason
                   the
                   diverse
                   reflexions
                   which
                   contracts
                   or
                   inlargeth
                   the
                   Species
                   :
                   when
                   the
                   eye
                   is
                   between
                   the
                   Centre
                   and
                   the
                   surface
                   of
                   the
                   Glasse
                   ;
                   the
                   Image
                   appeares
                   sometimes
                   very
                   great
                   and
                   deformed
                   ,
                   and
                   those
                   which
                   have
                   but
                   the
                   appearance
                   of
                   the
                   beginning
                   of
                   a
                   beard
                   on
                   their
                   chinne
                   ,
                   may
                   cheare
                   up
                   themselves
                   to
                   see
                   they
                   have
                   a
                   great
                   beard
                   ;
                   those
                   that
                   seeme
                   to
                   be
                   faire
                   will
                   thrust
                   away
                   the
                   Glasse
                   with
                   despight
                   ,
                   because
                   it
                   will
                   transforme
                   their
                   beauty
                   :
                   those
                   that
                   put
                   their
                   hand
                   to
                   the
                   Glasse
                   vvill
                   seeme
                   to
                   have
                   the
                   hand
                   of
                   a
                   Giant
                   ,
                   and
                   if
                   one
                   puts
                   his
                   finger
                   to
                   the
                   Glasse
                   it
                   vvill
                   be
                   seen
                   as
                   a
                   great
                   Pyramide
                   of
                   flesh
                   ,
                   inversed
                   against
                   his
                   finger
                   .
                
                 
                   Thirdly
                   ,
                   it
                   is
                   a
                   thing
                   admirable
                   that
                   the
                   eye
                   being
                   approached
                   to
                   the
                   point
                   of
                   concourse
                   of
                   the
                   Glasse
                   ,
                   there
                   vvill
                   be
                   seen
                   nothing
                   but
                   an
                   intermixture
                   or
                   confusion
                   :
                   but
                   retiring
                   back
                   a
                   little
                   from
                   that
                   point
                   ,
                   (
                   because
                   the
                   rayes
                   do
                   there
                   meet
                   ▪
                   )
                   he
                   shall
                   see
                   his
                   Image
                   inversed
                   ,
                   having
                   his
                   head
                   belovv
                   and
                   his
                   feet
                   above
                   .
                
                 
                   Fourthly
                   ,
                   the
                   divers
                   appearances
                   caused
                   by
                   the
                   motion
                   of
                   objects
                   ,
                   either
                   retiring
                   or
                   approaching
                   :
                   whether
                   they
                   turne
                   to
                   the
                   right
                   hand
                   or
                   to
                   the
                   left
                   hand
                   ,
                   whether
                   the
                   Glasse
                   be
                   hung
                   against
                   a
                   wall
                   ,
                   or
                   whether
                   it
                   be
                   placed
                   upon
                   a
                   Pavement
                   ,
                   as
                   also
                   what
                   may
                   be
                   represented
                   by
                   the
                   mutuall
                   aspect
                   of
                   concave
                   Glasses
                   with
                   plaine
                   and
                   convex
                   Glasses
                   but
                   I
                   will
                   with
                   silence
                   passe
                   them
                   over
                   ,
                   only
                   say
                   something
                   of
                   two
                   rare
                   experiments
                   more
                   as
                   followeth
                   .
                
                 
                 
                   The
                   first
                   is
                   to
                   represent
                   by
                   help
                   of
                   the
                   Sun
                   ,
                   such
                   letters
                   as
                   one
                   would
                   upon
                   the
                   front
                   of
                   a
                   house
                   :
                   so
                   that
                   one
                   may
                   read
                   them
                   :
                   Maginus
                   doth
                   deliver
                   the
                   way
                   thus
                   .
                   Write
                   the
                   Letters
                   ,
                   saith
                   he
                   ,
                   sufficiently
                   bigge
                   ,
                   but
                   inversed
                   upon
                   the
                   surface
                   of
                   the
                   Glasse
                   ,
                   with
                   some
                   kinde
                   of
                   colour
                   ,
                   or
                   these
                   letters
                   may
                   be
                   written
                   with
                   wax
                   ,
                   (
                   the
                   easier
                   to
                   be
                   taken
                   out
                   againe
                   :
                   )
                   for
                   then
                   placing
                   the
                   Glasse
                   to
                   the
                   Sunne
                   ,
                   the
                   letters
                   which
                   are
                   written
                   there
                   will
                   be
                   reverberated
                   or
                   reflected
                   upon
                   the
                   Wall
                   :
                   hence
                   it
                   was
                   perhaps
                   that
                   Pythagoras
                   did
                   promise
                   with
                   this
                   invention
                   to
                   write
                   upon
                   the
                   Moone
                   .
                
                 
                   In
                   the
                   second
                   place
                   ,
                   how
                   a
                   man
                   may
                   sundry
                   wayes
                   help
                   himselfe
                   with
                   such
                   a
                   Glasse
                   ,
                   with
                   a
                   lighted
                   Torch
                   or
                   Candle
                   ,
                   placed
                   in
                   the
                   point
                   of
                   concourse
                   or
                   inflammation
                   ,
                   which
                   is
                   neare
                   the
                   fourth
                   part
                   of
                   the
                   Diameter
                   :
                   for
                   by
                   this
                   meanes
                   the
                   light
                   of
                   the
                   Candle
                   will
                   be
                   reverberated
                   into
                   the
                   Glasse
                   ,
                   and
                   vvill
                   be
                   cast
                   back
                   againe
                   very
                   farre
                   by
                   parrallel
                   lines
                   ,
                   making
                   so
                   great
                   a
                   light
                   that
                   one
                   may
                   clearly
                   see
                   that
                   vvhich
                   is
                   done
                   farre
                   off
                   ,
                   yea
                   in
                   the
                   camp
                   of
                   an
                   Enemie
                   :
                   and
                   those
                   which
                   shall
                   see
                   the
                   Glasse
                   a
                   farre
                   off
                   ,
                   will
                   think
                   they
                   see
                   a
                   Silver
                   Basin
                   inlightened
                   ,
                   or
                   a
                   fire
                   more
                   resplendent
                   then
                   the
                   Torch
                   .
                   It
                   is
                   this
                   way
                   that
                   there
                   are
                   made
                   certaine
                   Lanthorns
                   which
                   dazell
                   the
                   eyes
                   of
                   those
                   which
                   come
                   against
                   them
                   ;
                   yet
                   it
                   serves
                   singular
                   well
                   to
                   enlighten
                   those
                   which
                   carry
                   them
                   ,
                   accommodating
                   a
                   Candle
                   with
                   a
                   little
                   hollow
                   Glasse
                   ,
                   so
                   that
                   it
                   may
                   successively
                   be
                   applyed
                   to
                   the
                   point
                   of
                   inflammation
                   .
                
                 
                 
                   In
                   like
                   manner
                   by
                   this
                   reflected
                   light
                   ,
                   one
                   may
                   reade
                   farre
                   off
                   ,
                   provided
                   that
                   the
                   letters
                   be
                   indifferent
                   great
                   ,
                   as
                   an
                   Epitaph
                   placed
                   high
                   ,
                   or
                   in
                   a
                   place
                   obscure
                   ;
                   or
                   the
                   letter
                   of
                   a
                   friend
                   which
                   dares
                   not
                   approach
                   without
                   perill
                   or
                   suspicion
                   .
                
              
               
                 
                   EXAMINATION
                   .
                
                 
                   THis
                   will
                   be
                   scarce
                   sensible
                   upon
                   a
                   wall
                   remote
                   from
                   the
                   Glasse
                   ,
                   and
                   but
                   indifferently
                   seen
                   upon
                   a
                   wall
                   which
                   is
                   neare
                   the
                   Glasse
                   ,
                   and
                   withall
                   it
                   must
                   be
                   in
                   obscuritie
                   or
                   shadowed
                   ,
                   or
                   else
                   it
                   will
                   not
                   be
                   seen
                   .
                   To
                   cast
                   light
                   in
                   the
                   night
                   to
                   a
                   place
                   remote
                   ,
                   with
                   a
                   Candle
                   placed
                   in
                   the
                   point
                   of
                   concourse
                   or
                   inflammation
                   ,
                   is
                   one
                   of
                   the
                   most
                   notablest
                   properties
                   which
                   can
                   be
                   shewne
                   in
                   a
                   concave
                   Glasse
                   :
                   for
                   if
                   in
                   the
                   point
                   of
                   inflammation
                   of
                   a
                   parabolicall
                   section
                   ,
                   a
                   Candle
                   be
                   placed
                   ,
                   the
                   light
                   will
                   be
                   reflected
                   by
                   parallel
                   lines
                   ,
                   as
                   a
                   columne
                   or
                   Cylinder
                   ;
                   but
                   in
                   the
                   sphericall
                   section
                   it
                   is
                   defective
                   in
                   part
                   ,
                   the
                   beames
                   being
                   not
                   united
                   in
                   one
                   point
                   ,
                   but
                   somewhat
                   scattering
                   :
                   notwithstanding
                   it
                   casteth
                   a
                   very
                   great
                   beautifull
                   light
                   .
                
                 
                   
                     Lastly
                     ,
                     those
                     which
                     feare
                     to
                     hurt
                     their
                     sight
                     by
                     the
                     approach
                     of
                     Lampes
                     or
                     Candles
                     ,
                     may
                     by
                     this
                     artifice
                     place
                     at
                     some
                     corher
                     of
                     a
                     Chamber
                     ,
                     a
                     Lamp
                     with
                     a
                     hollow
                     Glasse
                     behinde
                     
                     it
                     ,
                     which
                     will
                     commodiously
                     reflect
                     the
                     light
                     upon
                     a
                  
                   Table
                   ,
                   
                     or
                     to
                     a
                     place
                     assigned
                     :
                     so
                     that
                     the
                  
                   Glasse
                   
                     be
                     somewhat
                     raised
                     to
                     make
                     the
                     light
                     to
                     streeke
                     upon
                     the
                     Table
                     with
                     sharp
                     Angles
                     ,
                     as
                     the
                     Sunne
                     doth
                     when
                     it
                     is
                     but
                     a
                     little
                     elevated
                     above
                     the
                  
                   Horizon
                   ,
                   
                     for
                     this
                     light
                     shall
                     exceed
                     the
                     light
                     of
                     many
                     Candles
                     placed
                     in
                     the
                     Roome
                     ,
                     and
                     be
                     more
                     pleasant
                     to
                     the
                     sight
                     of
                     him
                     that
                     useth
                     it
                     .
                  
                
              
            
             
               
                 Of
                 other
                 Glasses
                 of
                 pleasure
                 .
              
               
                 FIrst
                 ,
                 the
                 Columnary
                 and
                 
                   Pyramidall
                   Glasses
                
                 that
                 are
                 contained
                 under
                 right
                 lines
                 ,
                 do
                 represent
                 the
                 Images
                 as
                 plaine
                 Glasses
                 do
                 ;
                 and
                 if
                 they
                 be
                 bowing
                 ,
                 then
                 they
                 represent
                 the
                 Image
                 ,
                 as
                 the
                 concave
                 and
                 convex
                 Glasses
                 do
                 .
              
               
                 Secondly
                 ,
                 those
                 Glasses
                 which
                 are
                 plaine
                 ,
                 but
                 have
                 ascents
                 of
                 Angels
                 in
                 the
                 middle
                 ,
                 will
                 shew
                 one
                 to
                 have
                 foure
                 Eyes
                 ,
                 two
                 Mouthes
                 ,
                 two
                 Noses
                 ,
                 &c.
                 
              
               
                 
                   EXAMINATION
                   .
                
                 
                   TH●se
                   experiments
                   will
                   be
                   found
                   different
                   according
                   to
                   the
                   diverse
                   meeting
                   of
                   the
                   Glasses
                   ,
                   which
                   commonly
                   are
                   made
                   scuing-wise
                   at
                   the
                   end
                   ,
                   〈◊〉
                   which
                   there
                   will
                   be
                   two
                   divers
                   superficies
                   in
                   the
                   Glasse
                   ,
                   making
                   the
                   exteriour
                   Angle
                   somewhat
                   raised
                   ,
                   at
                   the
                   interiour
                   onely
                   one
                   superficies
                   ,
                   which
                   
                   may
                   be
                   covered
                   according
                   to
                   ordinary
                   Glasses
                   to
                   c●use
                   a
                   reflexion
                   ,
                   and
                   so
                   it
                   will
                   be
                   but
                   one
                   Glasse
                   ,
                   which
                   by
                   refraction
                   according
                   to
                   the
                   different
                   thicknesse
                   of
                   the
                   Glasse
                   ,
                   and
                   different
                   Angles
                   of
                   the
                   scuing
                   forme
                   ,
                   do
                   differently
                   present
                   the
                   Images
                   to
                   the
                   eye
                   ,
                   as
                   foure
                   eyes
                   ,
                   two
                   mouthes
                   ,
                   two
                   noses
                   ;
                   sometimes
                   three
                   eyes
                   one
                   mouth
                   ,
                   and
                   one
                   nose
                   ,
                   the
                   one
                   large
                   and
                   the
                   other
                   long
                   ,
                   sometimes
                   two
                   eyes
                   onely
                   :
                   with
                   the
                   mouth
                   and
                   the
                   nose
                   deformed
                   ,
                   which
                   the
                   Glasse
                   (
                   impenetrable
                   )
                   will
                   not
                   shew
                   .
                   And
                   if
                   there
                   be
                   an
                   interiour
                   solid
                   Angle
                   ,
                   according
                   to
                   the
                   difference
                   of
                   it
                   (
                   as
                   if
                   it
                   be
                   more
                   sharp
                   )
                   there
                   will
                   be
                   represented
                   two
                   distinct
                   double
                   Images
                   ,
                   that
                   is
                   ,
                   two
                   entire
                   visages
                   and
                   as
                   the
                   Angle
                   is
                   open
                   ,
                   by
                   so
                   much
                   the
                   more
                   the
                   double
                   Images
                   will
                   reunite
                   and
                   enter
                   one
                   within
                   another
                   ,
                   which
                   will
                   present
                   sometimes
                   a
                   whole
                   visage
                   extended
                   at
                   large
                   ,
                   to
                   have
                   foure
                   eyes
                   ,
                   two
                   noses
                   ,
                   and
                   two
                   mouthes
                   :
                   and
                   by
                   moving
                   the
                   Glasse
                   the
                   Angle
                   will
                   vanish
                   ,
                   and
                   so
                   the
                   two
                   superficies
                   will
                   be
                   turned
                   into
                   one
                   ,
                   and
                   the
                   duplicity
                   of
                   Images
                   will
                   also
                   vanish
                   and
                   appeare
                   but
                   one
                   onely
                   :
                   and
                   this
                   is
                   easily
                   experimented
                   with
                   two
                   little
                   Glasses
                   of
                   steel
                   ,
                   or
                   such
                   like
                   so
                   united
                   ,
                   that
                   they
                   make
                   divers
                   Angles
                   and
                   inclinations
                   .
                
                 
                   THirdly
                   ,
                   
                     there
                     are
                  
                   Glasses
                   
                     which
                     make
                     men
                     seeme
                  
                   pale
                   ,
                   red
                   ,
                   
                     and
                     coloured
                     in
                     diverse
                     manners
                     ,
                     which
                     is
                     caused
                     by
                     the
                     dye
                     of
                     the
                  
                   Glasse
                   ,
                   
                     or
                     the
                     diverse
                     refraction
                     of
                     the
                  
                   Species
                   :
                   
                     and
                     those
                     which
                     are
                     made
                     of
                  
                   Silver
                   ,
                   Latine
                   ,
                   Steele
                   ,
                   &c.
                   
                     do
                     give
                     the
                  
                   Images
                   
                     a
                     diverse
                     colour
                     also
                     .
                     
                     In
                     which
                     one
                     may
                     see
                     that
                     the
                     appearances
                     by
                     some
                     are
                     made
                     fairer
                     ,
                     younger
                     or
                     older
                     than
                     they
                     are
                     ;
                     and
                     contrarily
                     others
                     will
                     make
                     them
                     foule
                     and
                     deformed
                     :
                     and
                     give
                     them
                     a
                     contrary
                     visage
                     :
                     for
                     if
                     a
                     Glasse
                     be
                     cut
                     as
                     it
                     may
                     be
                     ,
                     or
                     if
                     many
                     pieces
                     of
                     Glasse
                     be
                     placed
                     together
                     to
                     make
                     a
                     conveniable
                     reflexion
                     :
                     there
                     might
                     be
                     made
                     of
                     a
                     Mole
                     (
                     as
                     it
                     were
                     )
                     a
                     mountaine
                     ,
                     of
                     one
                     Haire
                     a
                     Tree
                     ,
                     a
                     Fly
                     to
                     be
                     as
                     an
                     Elephant
                     ,
                     but
                     I
                     should
                     be
                     too
                     long
                     if
                     I
                     should
                     say
                     all
                     that
                     which
                     might
                     be
                     said
                     upon
                     the
                     property
                     of
                     Glasses
                     .
                     I
                     will
                     therefore
                     conclude
                     this
                     discourse
                     of
                     the
                     properties
                     of
                     these
                     Glasses
                     with
                     these
                     foure
                     recreative
                     Problemes
                     following
                     .
                  
                
              
            
          
           
             
               PROBLEM
               .
               LXXVIII
               .
               1
               How
               to
               shew
               to
               one
               that
               is
               suspitious
               ,
               what
               is
               done
               in
               another
               Chamber
               or
               Roome
               :
               notwithstanding
               the
               interposition
               of
               the
               wall
               .
            
             
               FOr
               the
               performance
               of
               this
               ,
               there
               must
               be
               placed
               three
               Glasses
               in
               the
               two
               Chambers
               ,
               of
               which
               one
               of
               them
               shall
               be
               tyed
               to
               the
               planching
               or
               seeling
               ,
               that
               it
               may
               be
               common
               to
               communicate
               the
               Species
               to
               each
               Glasse
               by
               reflexion
               ,
               there
               being
               left
               some
               hole
               at
               the
               top
               of
               the
               Wall
               against
               the
               Glasse
               to
               this
               end
               :
               the
               two
               other
               Glasses
               must
               be
               placed
               against
               the
               two
               Walls
               at
               right
               Angles
               ,
               as
               the
               figure
               here
               sheweth
               at
               B.
               and
               C.
               
            
             
             
               Then
               the
               sight
               at
               E
               by
               the
               line
               of
               incidence
               FE
               ,
               shall
               fall
               upon
               the
               Glasse
               BA
               ,
               and
               reflect
               upon
               the
               superficies
               of
               the
               Glasse
               BC
               ,
               in
               the
               point
               G
               ;
               so
               that
               if
               the
               
               eye
               be
               at
               G
               ,
               it
               should
               see
               E
               ,
               and
               E
               would
               reflect
               upon
               the
               third
               Glass
               in
               the
               point
               H
               ,
               and
               the
               eye
               that
               is
               at
               L
               ,
               will
               see
               the
               Image
               that
               is
               at
               E.
               in
               the
               point
               of
               the
               Cath●r●
               :
               which
               Image
               shall
               come
               to
               the
               eye
               of
               the
               suspicious
               ,
               viz.
               at
               L.
               by
               help
               of
               the
               third
               Glasse
               ,
               upon
               which
               is
               made
               the
               second
               reflexion
               ,
               and
               so
               brings
               unto
               the
               eye
               the
               object
               ,
               though
               a
               wall
               be
               between
               it
               .
            
             
               
                 Corolarie
                 .
                 1.
                 
              
               
                 BY
                 this
                 invention
                 of
                 reflections
                 the
                 besiegers
                 of
                 a
                 Towne
                 may
                 be
                 seene
                 upon
                 the
                 Rampart
                 :
                 notwithstanding
                 the
                 Parapet
                 ,
                 which
                 the
                 besieged
                 may
                 do
                 by
                 placing
                 a
                 Glasse
                 in
                 the
                 hollow
                 of
                 the
                 Ditch
                 ,
                 and
                 placing
                 another
                 upon
                 the
                 toppe
                 of
                 the
                 wall
                 ,
                 so
                 that
                 the
                 line
                 of
                 incidence
                 comming
                 to
                 the
                 bottom
                 of
                 the
                 Ditch
                 ,
                 make
                 an
                 Angle
                 equall
                 to
                 the
                 Angle
                 of
                 reflexion
                 ,
                 then
                 by
                 this
                 situation
                 and
                 reflexion
                 ,
                 the
                 Image
                 of
                 the
                 besiege●
                 〈◊〉
                 will
                 be
                 seen
                 to
                 him
                 is
                 upon
                 the
                 Rampart
              
            
             
               
               
                 Corolarie
                 2.
                 
              
               
                 BY
                 which
                 also
                 may
                 be
                 inferred
                 ,
                 that
                 the
                 same
                 reflexions
                 may
                 be
                 seen
                 in
                 a
                 Regular
                 Polygon
                 ,
                 and
                 placing
                 as
                 many
                 Glasses
                 as
                 there
                 are
                 sides
                 ,
                 counting
                 two
                 for
                 one
                 ;
                 for
                 then
                 the
                 object
                 being
                 set
                 to
                 one
                 of
                 the
                 Glasses
                 ,
                 and
                 the
                 eye
                 in
                 the
                 other
                 ,
                 the
                 Jmage
                 will
                 be
                 seen
                 easily
                 .
              
            
             
               
                 Corolarie
                 3.
                 
              
               
                 FArther
                 ,
                 notwithstanding
                 the
                 interposition
                 of
                 many
                 Walls
                 ,
                 Chambers
                 ,
                 or
                 Cabinets
                 ,
                 one
                 may
                 see
                 that
                 which
                 passeth
                 through
                 the
                 most
                 remotest
                 of
                 them
                 ,
                 by
                 placing
                 of
                 many
                 Glasses
                 as
                 there
                 are
                 openings
                 in
                 the
                 walls
                 ,
                 making
                 them
                 to
                 receive
                 the
                 incident
                 angles
                 equall
                 :
                 that
                 is
                 ,
                 placing
                 them
                 in
                 such
                 sort
                 by
                 some
                 Geometricall
                 assistant
                 ,
                 that
                 the
                 incident
                 points
                 may
                 meet
                 in
                 the
                 middle
                 of
                 the
                 Glasses
                 :
                 but
                 here
                 all
                 the
                 defect
                 will
                 be
                 ,
                 that
                 the
                 Jmages
                 passing
                 by
                 so
                 many
                 reflexions
                 ,
                 will
                 be
                 very
                 weak
                 and
                 scarce
                 observable
                 .
              
            
          
           
             
               PROBLEM
               .
               LXXIX
               .
               How
               with
               a
               Musket
               to
               strike
               a
               mark
               ,
               not
               looking
               towards
               it
               ,
               as
               exact
               as
               one
               aiming
               at
               it
               .
            
             
               AS
               let
               the
               eye
               be
               at
               O
               ▪
               and
               the
               mark
               C
               ,
               place
               a
               plaine
               Glasse
               perpendicular
               as
               AB
               .
               so
               the
               marke
               C
               shall
               be
               seen
               in
               
                 Catheti
                 CA
                 ,
                 viz.
              
               
               in
               D
               ,
               and
               the
               line
               of
               
               reflexion
               is
               D
               ,
               now
               let
               the
               Musket
               FE
               ,
               upon
               a
               rest
               ▪
               be
               moved
               to
               and
               fro
               untill
               it
               be
               seen
               in
               the
               line
               OD
               ,
               which
               admit
               to
               be
               HG
               ,
               so
               giving
               fire
               to
               the
               Musket
               ,
               it
               shall
               undoubtedly
               strike
               the
               mark
               .
            
             
               
                 Corolaries
                 .
                 From
                 which
                 may
                 be
                 gathered
                 ,
                 that
                 one
                 may
                 exactly
                 shoot
                 out
                 of
                 a
                 Musket
                 to
                 a
                 place
                 which
                 is
                 not
                 seen
                 ,
                 being
                 hindered
                 by
                 some
                 obstacle
                 ,
                 or
                 other
                 interposition
                 .
              
               
                 AS
                 let
                 the
                 eye
                 be
                 at
                 M
                 ,
                 the
                 mark
                 C
                 ,
                 and
                 the
                 wall
                 which
                 keeps
                 it
                 from
                 being
                 seene
                 ,
                 admit
                 to
                 be
                 QR
                 ,
                 then
                 
                 set
                 up
                 a
                 plaine
                 Glass
                 as
                 AB
                 ,
                 and
                 let
                 the
                 Musket
                 by
                 GH
                 ,
                 placed
                 upon
                 his
                 rest
                 PO.
                 Now
                 because
                 the
                 marke
                 C
                 is
                 seen
                 at
                 D
                 ,
                 move
                 the
                 Musket
                 to
                 and
                 fro
                 ,
                 untill
                 it
                 doth
                 agree
                 with
                 the
                 line
                 of
                 reflection
                 MB
                 ,
                 
                 which
                 suppose
                 at
                 LI
                 ,
                 so
                 shall
                 it
                 be
                 truly
                 placed
                 ,
                 and
                 giving
                 fire
                 to
                 the
                 Musket
                 ,
                 it
                 shall
                 not
                 faile
                 to
                 strike
                 the
                 said
                 mark
                 at
                 C.
                 
              
            
          
           
             
               PROBLEM
               .
               LXXX
               .
               How
               to
               make
               an
               Image
               to
               be
               seen
               hanging
               in
               the
               aire
               ,
               having
               his
               head
               downeward
               .
            
             
               TAke
               two
               Glasses
               ,
               and
               place
               them
               at
               right
               Angles
               one
               unto
               the
               other
               ,
               as
               admit
               AB
               ,
               and
               CB
               ,
               of
               which
               admit
               
                 CB
                 ,
                 Ho●izontall
              
               ,
               and
               let
               the
               eye
               be
               at
               H
               ,
               and
               the
               object
               or
               image
               to
               
               be
               DE
               ;
               so
               D
               will
               be
               reflected
               at
               F
               ,
               so
               to
               N
               ,
               so
               to
               HE
               :
               then
               at
               G
               ,
               so
               to
               ●
               and
               then
               to
               H
               ,
               and
               by
               a
               double
               reflection
               ED
               will
               seeme
               in
               QR
               ,
               the
               highest
               point
               D
               in
               R
               ,
               and
               the
               point
               L
               in
               Q
               inversed
               as
               was
               said
               ,
               taking
               D
               for
               the
               head
               ,
               and
               E
               for
               the
               feet
               ;
               so
               it
               will
               be
               a
               man
               inversed
               ,
               which
               will
               seem
               to
               be
               flying
               in
               the
               aire
               ,
               if
               the
               Jmage
               had
               wings
               unto
               it
               ,
               and
               had
               secretly
               〈◊〉
               motion
               :
               and
               if
               the
               Glasse
               were
               bigge
               enough
               to
               receive
               many
               reflexions
               ,
               it
               would
               deceive
               the
               sight
               the
               more
               by
               admiring
               the
               changing
               of
               colours
               that
               would
               be
               seen
               by
               that
               motion
               .
            
          
           
             
             
               PROBLEM
               .
               LXXXI
               .
               How
               to
               make
               a
               company
               of
               representative
               Souldiers
               seeme
               to
               be
               a
               Regiment
               ,
               or
               how
               few
               in
               number
               may
               be
               multiplyed
               to
               seem
               to
               be
               many
               in
               number
               .
            
             
               TO
               make
               the
               experiment
               upon
               men
               ,
               there
               must
               be
               prepared
               two
               great
               Glasses
               ;
               but
               in
               stead
               of
               it
               we
               will
               suppose
               two
               lesser
               ,
               as
               GH
               .
               and
               FI
               ,
               one
               placed
               right
               against
               another
               perpendicular
               to
               the
               Horizon
               ,
               upon
               a
               plaine
               levell
               Table
               :
               betvveene
               
               vvhich
               Glasses
               let
               there
               be
               ranged
               in
               Battalia-vvise
               upon
               the
               same
               Table
               a
               number
               of
               small
               men
               according
               to
               the
               square
               
                 G
                 ,
                 H
                 ,
                 I
                 ,
                 F
                 ,
              
               or
               in
               any
               other
               forme
               or
               posture
               :
               hen
               may
               you
               evidently
               see
               hovv
               the
               said
               battel
               vvill
               be
               multiplyed
               and
               seem
               farre
               bigger
               in
               the
               appearance
               than
               it
               is
               in
               effect
               .
            
             
               
                 Corolarie
                 .
              
               
                 BY
                 this
                 invention
                 you
                 may
                 make
                 a
                 little
                 Cabinet
                 of
                 foure
                 foot
                 long
                 ,
                 and
                 tvvo
                 foot
                 large
                 ,
                 (
                 more
                 or
                 lesse
                 )
                 vvhich
                 being
                 filled
                 vvith
                 
                 Rockes
                 or
                 such
                 like
                 things
                 ,
                 or
                 there
                 being
                 put
                 into
                 it
                 Silver
                 ,
                 Gold
                 ,
                 Stones
                 of
                 luster
                 ,
                 Jewels
                 ,
                 &c.
                 and
                 the
                 walls
                 of
                 the
                 said
                 Cabinet
                 being
                 all
                 covered
                 ,
                 or
                 hung
                 with
                 plaine
                 glasse
                 ;
                 these
                 visibles
                 will
                 appeare
                 manifoldly
                 increased
                 ,
                 by
                 reason
                 of
                 the
                 multiplicitie
                 of
                 reflexions
                 ,
                 and
                 at
                 the
                 opening
                 of
                 the
                 said
                 Cabinet
                 ,
                 having
                 set
                 something
                 which
                 might
                 hide
                 them
                 from
                 being
                 seen
                 ,
                 those
                 that
                 look
                 into
                 it
                 will
                 be
                 astonished
                 to
                 see
                 so
                 few
                 in
                 number
                 which
                 before
                 seemed
                 to
                 be
                 so
                 many
                 .
              
            
          
           
             
               PROBLEM
               .
               LXXXII
               .
               Of
               fine
               and
               pleasant
               Dyal●
               .
            
             
               COuld
               you
               choose
               a
               more
               ridiculous
               one
               than
               the
               natural
               Dyall
               written
               amongst
               the
               Greek
               Epigrams
               ,
               upon
               which
               some
               sound
               Poet
               made
               verses
               ;
               shewing
               that
               a
               man
               carrieth
               about
               him
               alwayes
               a
               Dyall
               in
               his
               face
               by
               meanes
               of
               the
               Nose
               and
               Teeth
               ?
               and
               is
               not
               this
               a
               jolly
               Dyall
               ?
               for
               he
               need
               not
               but
               open
               the
               mouth
               ,
               the
               lines
               shall
               be
               all
               the
               teeth
               ,
               and
               the
               nose
               shall
               serve
               for
               the
               style
               .
            
             
               
                 Of
                 a
                 Dyall
                 of
                 hearbes
                 .
              
               
                 CAn
                 you
                 have
                 a
                 finer
                 thing
                 in
                 a
                 Garden
                 ,
                 or
                 in
                 the
                 middle
                 of
                 a
                 Compartemeet
                 ,
                 than
                 to
                 see
                 the
                 lines
                 and
                 the
                 number
                 of
                 houres
                 represented
                 with
                 little
                 bushie
                 hearbes
                 ,
                 as
                 of
                 Hysope
                 
                 or
                 such
                 which
                 is
                 proper
                 to
                 be
                 cut
                 in
                 the
                 borders
                 ;
                 and
                 at
                 the
                 top
                 of
                 the
                 style
                 to
                 have
                 a
                 Fanne
                 to
                 shew
                 which
                 way
                 the
                 winde
                 b●oweth
                 ?
                 this
                 is
                 very
                 pleasant
                 and
                 useful
                 .
              
            
             
               
                 Of
                 the
                 Dyall
                 upon
                 the
                 fingers
                 and
                 the
                 hand
                 .
              
               
                 IS
                 it
                 nor
                 a
                 commoditie
                 very
                 agreeable
                 ,
                 when
                 one
                 is
                 in
                 the
                 fie●d
                 or
                 in
                 some
                 vil●age
                 vvithout
                 any
                 other
                 Dyall
                 ,
                 to
                 see
                 onely
                 by
                 the
                 hand
                 what
                 of
                 the
                 clock
                 it
                 is
                 ?
                 vvhich
                 gives
                 it
                 very
                 neare
                 ;
                 and
                 may
                 be
                 practised
                 by
                 the
                 left
                 hand
                 ,
                 in
                 this
                 manner
                 .
              
               
                 Take
                 a
                 stravv
                 or
                 like
                 thing
                 of
                 the
                 length
                 of
                 the
                 Index
                 or
                 the
                 second
                 finger
                 ,
                 hold
                 this
                 straw
                 very
                 right
                 betvveen
                 the
                 thumb
                 and
                 the
                 fore-finger
                 ,
                 then
                 stretch
                 forth
                 the
                 hand
                 ▪
                 and
                 turne
                 your
                 back
                 ,
                 and
                 the
                 palm
                 of
                 your
                 hand
                 tovvards
                 the
                 Sunne
                 ;
                 so
                 that
                 the
                 shadovv
                 of
                 the
                 muscle
                 vvhich
                 is
                 under
                 the
                 Thumb
                 ,
                 touch
                 the
                 line
                 of
                 life
                 ,
                 vvhich
                 is
                 betvveen
                 the
                 middle
                 of
                 the
                 tvvo
                 other
                 great
                 lines
                 ,
                 vvhich
                 is
                 seen
                 in
                 the
                 palme
                 of
                 the
                 hand
                 ,
                 this
                 done
                 ,
                 the
                 end
                 of
                 the
                 shadovv
                 vvill
                 shevv
                 vvhat
                 of
                 the
                 clock
                 it
                 is
                 :
                 for
                 at
                 the
                 end
                 of
                 the
                 first
                 finger
                 it
                 is
                 7
                 in
                 the
                 morning
                 ,
                 or
                 5
                 in
                 the
                 evening
                 ,
                 at
                 the
                 end
                 of
                 the
                 Ring-finger
                 it
                 is
                 8
                 in
                 the
                 morning
                 ,
                 or
                 4
                 in
                 the
                 evening
                 ,
                 at
                 the
                 end
                 of
                 the
                 little
                 finger
                 or
                 first
                 joynt
                 ,
                 it
                 is
                 9
                 in
                 the
                 morning
                 ,
                 or
                 3
                 in
                 the
                 after-noone
                 ,
                 10
                 &
                 2
                 at
                 the
                 second
                 joynt
                 ,
                 11
                 and
                 1
                 at
                 the
                 third
                 joynt
                 ,
                 and
                 midday
                 in
                 the
                 line
                 follovving
                 ,
                 vvhich
                 comes
                 from
                 the
                 end
                 of
                 the
                 Index
                 .
              
            
             
               
               
                 Of
                 a
                 Dyall
                 which
                 was
                 about
                 an
                 Obeliske
                 at
                 Rome
                 .
              
               
                 WAs
                 not
                 this
                 a
                 pretty
                 fetch
                 upon
                 a
                 pavement
                 ,
                 to
                 choose
                 an
                 Obeliske
                 for
                 a
                 Dyall
                 ,
                 having
                 106
                 foot
                 in
                 height
                 ,
                 without
                 removing
                 the
                 Basis
                 of
                 it
                 ?
                 Plinie
                 assures
                 us
                 in
                 his
                 26
                 book
                 and
                 8
                 Chap.
                 that
                 the
                 Emperour
                 Augustus
                 having
                 accom●odated
                 in
                 the
                 field
                 of
                 Mars
                 an
                 Obeliske
                 of
                 this
                 height
                 ,
                 he
                 made
                 about
                 it
                 a
                 pavement
                 ,
                 
                 and
                 by
                 the
                 industry
                 of
                 Man●lius
                 the
                 Mathematician
                 ,
                 there
                 were
                 enchaced
                 markes
                 of
                 Copper
                 upon
                 the
                 Pavement
                 ,
                 and
                 placed
                 also
                 an
                 Apple
                 of
                 Gold
                 upon
                 the
                 toppe
                 of
                 the
                 said
                 Obeliske
                 ,
                 to
                 know
                 the
                 houre
                 and
                 the
                 course
                 of
                 the
                 Sunne
                 ,
                 with
                 the
                 increase
                 and
                 decrease
                 of
                 dayes
                 by
                 the
                 same
                 shadow
                 :
                 and
                 in
                 the
                 same
                 manner
                 do
                 some
                 by
                 the
                 shadow
                 of
                 their
                 head
                 or
                 other
                 style
                 ,
                 make
                 the
                 like
                 experiments
                 in
                 Astronomie
                 .
              
            
             
               
                 Of
                 Dyals
                 with
                 Glasses
                 .
              
               
                 PT●lomie
                 w●ites
                 ,
                 as
                 Cardanus
                 reports
                 ,
                 that
                 long
                 ago
                 there
                 were
                 Glasses
                 which
                 served
                 for
                 Dyals
                 ,
                 and
                 presented
                 the
                 face
                 of
                 the
                 beholder
                 
                 as
                 many
                 times
                 as
                 the
                 houre
                 ought
                 to
                 be
                 ,
                 twice
                 if
                 it
                 were
                 2
                 of
                 the
                 clock
                 ,
                 9
                 if
                 it
                 were
                 9
                 ,
                 &c.
                 
                 But
                 this
                 was
                 thought
                 to
                 be
                 done
                 by
                 the
                 help
                 of
                 water
                 ,
                 and
                 not
                 by
                 Glasses
                 ,
                 which
                 did
                 leake
                 by
                 little
                 and
                 little
                 out
                 of
                 the
                 vessell
                 ,
                 discovering
                 anon
                 one
                 Glasse
                 ,
                 then
                 anon
                 two
                 Glasses
                 ,
                 then
                 3
                 ,
                 4
                 ,
                 5
                 Glasses
                 ,
                 &c.
                 to
                 shew
                 so
                 many
                 faces
                 as
                 there
                 were
                 houres
                 ,
                 which
                 was
                 onely
                 by
                 leaking
                 of
                 water
                 .
              
            
             
               
                 Of
                 a
                 Dyall
                 which
                 hath
                 a
                 Glasse
                 in
                 the
                 place
                 of
                 the
                 Style
                 .
              
               
                 WHat
                 will
                 you
                 say
                 of
                 the
                 invention
                 of
                 Mathematicians
                 ,
                 which
                 finde
                 out
                 daily
                 so
                 many
                 fine
                 and
                 curious
                 novelties
                 ?
                 they
                 have
                 now
                 a
                 way
                 to
                 make
                 Dyals
                 upon
                 the
                 wainscot
                 or
                 seeling
                 of
                 a
                 Chamber
                 ,
                 and
                 there
                 where
                 the
                 Sunne
                 can
                 never
                 shine
                 ,
                 or
                 the
                 beames
                 of
                 the
                 Sunne
                 cannot
                 directly
                 strike
                 :
                 and
                 this
                 is
                 done
                 in
                 placing
                 of
                 a
                 little
                 Glasse
                 in
                 the
                 place
                 of
                 the
                 style
                 which
                 reflecteth
                 the
                 light
                 ,
                 with
                 the
                 same
                 condition
                 that
                 the
                 shadow
                 of
                 the
                 style
                 sheweth
                 the
                 houre
                 :
                 and
                 it
                 is
                 easie
                 to
                 make
                 experiment
                 upon
                 a
                 common
                 Dyall
                 ,
                 changing
                 only
                 the
                 disposition
                 of
                 the
                 Dyall
                 ,
                 and
                 tying
                 to
                 the
                 end
                 of
                 the
                 style
                 a
                 piece
                 of
                 plaine
                 Glasse
                 .
                 The
                 Almaines
                 use
                 it
                 much
                 ,
                 who
                 by
                 this
                 way
                 have
                 no
                 greater
                 trouble
                 ,
                 but
                 to
                 put
                 their
                 Noses
                 out
                 of
                 their
                 beds
                 and
                 see
                 what
                 a
                 clock
                 it
                 is
                 ,
                 which
                 is
                 reflected
                 by
                 a
                 little
                 hole
                 in
                 the
                 Window
                 upon
                 the
                 wall
                 or
                 seeling
                 of
                 the
                 Chamber
                 .
              
               
                 
                 
                   EXAMINATION
                   .
                
                 
                   IN
                   this
                   there
                   are
                   two
                   experiments
                   considerable
                   ,
                   the
                   first
                   is
                   with
                   a
                   very
                   little
                   Glasse
                   placed
                   so
                   that
                   it
                   may
                   be
                   open
                   to
                   the
                   beames
                   of
                   the
                   Sunne
                   ,
                   the
                   other
                   hath
                   respect
                   to
                   a
                   spacious
                   or
                   great
                   Glasse
                   placed
                   to
                   a
                   very
                   little
                   hole
                   so
                   that
                   the
                   Sun
                   may
                   shine
                   on
                   it
                   ,
                   for
                   then
                   the
                   shadow
                   which
                   is
                   cast
                   upon
                   the
                   Dyall
                   is
                   converted
                   into
                   beames
                   of
                   the
                   Sunne
                   ,
                   and
                   will
                   reflect
                   and
                   becast
                   upon
                   a
                   plain
                   opposite
                   :
                   and
                   in
                   the
                   other
                   it
                   is
                   a
                   hole
                   in
                   the
                   window
                   or
                   such
                   like
                   ,
                   by
                   which
                   may
                   passe
                   the
                   beames
                   of
                   the
                   Sun
                   ,
                   which
                   represent
                   the
                   extreamity
                   of
                   the
                   style
                   ,
                   &
                   the
                   Glasse
                   representeth
                   the
                   plaine
                   of
                   the
                   Dyall
                   ,
                   upon
                   which
                   the
                   beames
                   being
                   in
                   manner
                   of
                   shadowes
                   reflect
                   cast
                   upon
                   a
                   plaine
                   opposite
                   :
                   and
                   it
                   is
                   needfull
                   that
                   in
                   this
                   second
                   way
                   the
                   Glasse
                   may
                   be
                   spacious
                   ,
                   as
                   before
                   ,
                   to
                   receive
                   the
                   delineaments
                   of
                   the
                   Dyall
                   .
                
                 
                   Otherwise
                   you
                   may
                   draw
                   the
                   lineaments
                   of
                   a
                   Dyall
                   upon
                   any
                   plaine
                   looking-glasse
                   which
                   reflecteth
                   the
                   Sunne-beames
                   ,
                   for
                   the
                   applying
                   a
                   style
                   or
                   a
                   pearle
                   at
                   the
                   extreamitie
                   of
                   it
                   :
                   and
                   placed
                   to
                   the
                   Sunne
                   ,
                   the
                   reflexion
                   will
                   be
                   answerable
                   to
                   the
                   delineaments
                   on
                   the
                   Glasse
                   :
                   but
                   here
                   note
                   ,
                   that
                   the
                   Glasse
                   ought
                   to
                   be
                   great
                   ,
                   and
                   so
                   the
                   delineaments
                   thereon
                   .
                
                 
                 
                   But
                   that
                   which
                   is
                   most
                   noble
                   ,
                   is
                   to
                   draw
                   houre-lines
                   upon
                   the
                   outside
                   of
                   the
                   Glasse
                   of
                   a
                   window
                   ,
                   and
                   placing
                   a
                   style
                   thereto
                   upon
                   the
                   outside
                   ,
                   the
                   shadow
                   of
                   the
                   style
                   will
                   be
                   seen
                   within
                   ,
                   and
                   so
                   you
                   have
                   the
                   hour
                   ,
                   more
                   certaine
                   without
                   any
                   difficulty
                   .
                
              
            
             
               
                 Of
                 Dyals
                 with
                 water
                 .
              
               
                 SVch
                 kinde
                 of
                 Dyals
                 were
                 made
                 in
                 ancient
                 times
                 ,
                 and
                 also
                 these
                 of
                 sand
                 :
                 before
                 they
                 had
                 skill
                 to
                 make
                 Sun-dyals
                 or
                 Dyals
                 with
                 wheeles
                 ;
                 for
                 they
                 used
                 to
                 fill
                 a
                 vessell
                 with
                 water
                 ,
                 and
                 having
                 experience
                 by
                 tryall
                 thar
                 it
                 would
                 runne
                 out
                 all
                 in
                 a
                 day
                 ,
                 they
                 did
                 marke
                 within
                 the
                 vessell
                 the
                 houres
                 noted
                 by
                 the
                 running
                 of
                 the
                 water
                 ;
                 and
                 some
                 did
                 set
                 a
                 piece
                 of
                 light
                 board
                 in
                 the
                 vessell
                 to
                 swimme
                 upon
                 the
                 top
                 of
                 the
                 water
                 ,
                 carrying
                 a
                 little
                 statue
                 ,
                 which
                 with
                 a
                 small
                 stick
                 did
                 point
                 out
                 the
                 houre
                 upon
                 a
                 columne
                 or
                 wall
                 ,
                 figured
                 with
                 houre-notes
                 ,
                 as
                 the
                 vessell
                 was
                 figured
                 within
                 .
              
               
               
                 Novv
                 it
                 seemes
                 a
                 safer
                 vvay
                 that
                 the
                 vvater
                 passe
                 out
                 by
                 drop
                 and
                 drop
                 ,
                 and
                 drop
                 into
                 a
                 Cylindricall
                 Glasse
                 by
                 help
                 of
                 a
                 Pipe
                 :
                 for
                 having
                 marked
                 the
                 exterior
                 part
                 of
                 the
                 Cylinder
                 in
                 the
                 houre
                 notes
                 ,
                 the
                 vvater
                 it selfe
                 vvhich
                 falls
                 vvithin
                 it
                 ,
                 vvill
                 shevv
                 vvhat
                 of
                 the
                 clock
                 it
                 is
                 ,
                 farre
                 better
                 than
                 the
                 running
                 of
                 sand
                 ,
                 for
                 by
                 this
                 may
                 you
                 have
                 the
                 parts
                 of
                 the
                 houres
                 most
                 accurate
                 ,
                 vvhich
                 commonly
                 by
                 sand
                 is
                 not
                 had
                 :
                 and
                 to
                 vvhich
                 may
                 be
                 added
                 the
                 houres
                 of
                 other
                 Countreys
                 vvith
                 greater
                 ease
                 .
                 And
                 here
                 note
                 ,
                 that
                 as
                 soone
                 as
                 the
                 vvater
                 is
                 out
                 ▪
                 of
                 one
                 of
                 the
                 Glasses
                 ,
                 you
                 may
                 turne
                 it
                 over
                 into
                 the
                 same
                 againe
                 out
                 of
                 the
                 other
                 ,
                 and
                 so
                 let
                 it
                 runne
                 anevv
                 .
              
            
          
           
             
             
               PROBLEM
               .
               LXXXIII
               .
               Of
               Cannons
               or
               great
               Artillery
               .
               Souldiers
               ,
               and
               others
               would
               willingly
               see
               〈◊〉
               Problems
               ,
               which
               containe
               :
               three
               or
               foure
               subtile
               questions
               :
            
             
               
                 The
                 first
                 is
                 ,
                 how
                 to
                 charge
                 a
                 Cannon
                 without
                 powder
                 ?
              
               
                 THis
                 may
                 be
                 done
                 vvith
                 aire
                 and
                 vvater
                 ,
                 only
                 having
                 throvvn
                 cold
                 vvater
                 into
                 the
                 Cannon
                 ,
                 vvhich
                 might
                 be
                 squirted
                 forceably
                 in
                 by
                 the
                 closure
                 of
                 the
                 mouth
                 of
                 the
                 Piece
                 ,
                 that
                 so
                 by
                 this
                 pressure
                 the
                 aire
                 might
                 more
                 condense
                 ;
                 then
                 having
                 a
                 round
                 piece
                 of
                 vvood
                 very
                 just
                 ,
                 and
                 oiled
                 vvell
                 for
                 the
                 better
                 to
                 slide
                 ,
                 and
                 thrust
                 the
                 Bullet
                 vvhen
                 it
                 shall
                 be
                 time
                 :
                 This
                 piece
                 of
                 vvood
                 may
                 be
                 held
                 fast
                 vvith
                 some
                 Pole
                 ,
                 for
                 feare
                 it
                 be
                 not
                 thrust
                 out
                 before
                 his
                 time
                 :
                 then
                 let
                 fire
                 be
                 made
                 about
                 the
                 Trunion
                 or
                 hinder
                 part
                 of
                 the
                 Piece
                 to
                 heat
                 the
                 aire
                 and
                 vvater
                 ,
                 and
                 then
                 vvhen
                 one
                 vvould
                 shoot
                 it
                 ,
                 let
                 the
                 pole
                 be
                 quickly
                 loosened
                 ,
                 for
                 then
                 the
                 aire
                 searching
                 a
                 greater
                 place
                 ,
                 and
                 having
                 vvay
                 novv
                 offered
                 ,
                 vvill
                 thrust
                 out
                 the
                 vvood
                 and
                 the
                 bullet
                 very
                 quick
                 :
                 the
                 experiment
                 vvhich
                 vve
                 have
                 in
                 long
                 trunkes
                 shooting
                 out
                 pellats
                 vvith
                 aire
                 only
                 ,
                 shevveth
                 the
                 verity
                 of
                 this
                 Probleme
                 .
              
            
             
               
               
                 2
                 In
                 the
                 second
                 question
                 it
                 may
                 be
                 demanded
                 ,
                 how
                 much
                 time
                 doth
                 the
                 Bull●●
                 of
                 a
                 Cannon
                 spend
                 in
                 the
                 aire
                 before
                 i●
                 falls
                 to
                 the
                 ground
                 ?
              
               
                 THe
                 resolution
                 of
                 this
                 Question
                 depends
                 upon
                 the
                 goodnesse
                 of
                 the
                 Piece
                 &
                 charge
                 thereof
                 ,
                 seeing
                 in
                 each
                 there
                 is
                 great
                 difference
                 .
                 It
                 is
                 reported
                 ,
                 that
                 
                   Tich●
                   Bra●e
                
                 ,
                 and
                 the
                 Landsgrave
                 did
                 make
                 an
                 experiment
                 upon
                 a
                 Cannon
                 in
                 Germany
                 ,
                 which
                 being
                 charged
                 and
                 
                 shot
                 off
                 ;
                 the
                 Bullet
                 spent
                 two
                 minutes
                 of
                 time
                 in
                 the
                 aire
                 before
                 it
                 fell
                 :
                 and
                 the
                 distance
                 was
                 a
                 Germane
                 mile
                 ,
                 which
                 distance
                 proportionated
                 to
                 an
                 hours
                 time
                 ,
                 makes
                 120
                 Italian
                 miles
                 .
              
            
             
               
                 3.
                 
                 In
                 the
                 third
                 question
                 it
                 may
                 be
                 asked
                 ,
                 how
                 it
                 comes
                 to
                 passe
                 ,
                 that
                 a
                 Cannon
                 shooting
                 upwards
                 ,
                 the
                 Bullet
                 flies
                 with
                 more
                 violence
                 than
                 being
                 shot
                 point-blanke
                 ,
                 or
                 shooting
                 downeward
                 ?
              
               
                 IF
                 we
                 regard
                 the
                 effect
                 of
                 a
                 Cannon
                 when
                 it
                 is
                 to
                 batter
                 a
                 wall
                 ,
                 the
                 Question
                 is
                 false
                 ,
                 seeing
                 it
                 is
                 most
                 evident
                 that
                 the
                 blowes
                 which
                 fall
                 Perpendicular
                 upon
                 a
                 wall
                 ,
                 are
                 more
                 violent
                 than
                 those
                 which
                 strike
                 byas-wise
                 or
                 glaunsingly
                 .
              
               
               
                 But
                 considering
                 the
                 strength
                 of
                 the
                 blow
                 only
                 ,
                 the
                 Question
                 is
                 most
                 true
                 ,
                 and
                 often
                 experimented
                 to
                 be
                 found
                 true
                 :
                 a
                 Piece
                 mounted
                 at
                 the
                 best
                 of
                 the
                 Randon
                 ,
                 which
                 is
                 neare
                 halfe
                 of
                 the
                 right
                 ,
                 conveyes
                 her
                 Bullet
                 with
                 a
                 farre
                 greater
                 violence
                 then
                 that
                 which
                 is
                 shot
                 at
                 point
                 blanke
                 ,
                 or
                 mounted
                 parallel
                 to
                 the
                 Horizon
                 .
                 The
                 common
                 reason
                 is
                 ,
                 that
                 shooting
                 high
                 ,
                 the
                 fire
                 carries
                 the
                 bowle
                 a
                 longer
                 time
                 in
                 the
                 aire
                 ,
                 and
                 the
                 aire
                 moves
                 more
                 ●acill
                 upwards
                 ,
                 than
                 dovvnevvards
                 ,
                 because
                 that
                 the
                 airy
                 circles
                 that
                 the
                 motion
                 of
                 the
                 bullet
                 makes
                 ,
                 are
                 soonest
                 broken
                 .
                 Hovvsoever
                 this
                 be
                 the
                 generall
                 tenet
                 ,
                 it
                 is
                 curious
                 to
                 finde
                 out
                 the
                 inequality
                 of
                 moving
                 of
                 the
                 aire
                 ;
                 vvhether
                 the
                 Bullet
                 fly
                 upvvard
                 ,
                 dovvnevvard
                 ,
                 or
                 right
                 forvvard
                 ,
                 to
                 produce
                 a
                 sensible
                 dfference
                 of
                 motion
                 ;
                 &
                 some
                 think
                 that
                 the
                 Cannon
                 being
                 mounted
                 ,
                 the
                 Bullet
                 pressing
                 the
                 povvder
                 maketh
                 a
                 greater
                 resistance
                 ,
                 and
                 so
                 causeth
                 all
                 the
                 Povvder
                 to
                 be
                 inflamed
                 before
                 the
                 Bullet
                 is
                 throvvne
                 out
                 ,
                 vvhich
                 makes
                 it
                 to
                 be
                 more
                 violent
                 than
                 othervvise
                 it
                 vvould
                 be
                 .
                 When
                 the
                 Cannon
                 is
                 othervvise
                 disposed
                 ,
                 the
                 contrary
                 arives
                 ,
                 the
                 fire
                 leaves
                 the
                 Bullet
                 ,
                 and
                 the
                 Bullet
                 rolling
                 from
                 the
                 Povvder
                 resists
                 lesse
                 :
                 and
                 it
                 is
                 usually
                 seene
                 ,
                 that
                 shooting
                 out
                 of
                 a
                 Musket
                 charged
                 onely
                 vvith
                 Povvder
                 ,
                 to
                 shoot
                 to
                 a
                 marke
                 of
                 Paper
                 placed
                 Point
                 blanke
                 ,
                 that
                 there
                 are
                 seene
                 many
                 small
                 holes
                 in
                 the
                 paper
                 ,
                 vvhich
                 cannot
                 be
                 other
                 than
                 the
                 graines
                 of
                 Powder
                 which
                 did
                 not
                 take
                 fire
                 :
                 but
                 this
                 latter
                 accident
                 may
                 happen
                 
                 from
                 the
                 over-charging
                 of
                 the
                 Piece
                 ,
                 or
                 the
                 length
                 of
                 it
                 ,
                 or
                 windy
                 ,
                 or
                 dampenesse
                 of
                 the
                 Powder
                 .
              
               
                 From
                 which
                 some
                 may
                 think
                 ,
                 that
                 a
                 Cannon
                 pointed
                 right
                 to
                 the
                 Zenith
                 ,
                 should
                 shoot
                 with
                 greater
                 violence
                 ,
                 then
                 in
                 any
                 other
                 mount
                 or
                 forme
                 whatsoever
                 :
                 and
                 by
                 some
                 it
                 hath
                 beene
                 imagined
                 ,
                 that
                 a
                 Bullet
                 shot
                 in
                 this
                 fashion
                 hath
                 been
                 consumed
                 ,
                 melted
                 ,
                 and
                 lost
                 in
                 the
                 Aire
                 ,
                 by
                 reason
                 of
                 the
                 violence
                 of
                 the
                 blow
                 ,
                 and
                 the
                 activity
                 of
                 the
                 sire
                 ,
                 and
                 that
                 sundry
                 experiments
                 have
                 been
                 made
                 in
                 this
                 nature
                 ,
                 and
                 the
                 Bullet
                 never
                 found
                 .
                 But
                 it
                 is
                 hard
                 to
                 believe
                 this
                 assertion
                 :
                 it
                 may
                 rather
                 be
                 supposed
                 that
                 the
                 Bullet
                 falling
                 farre
                 from
                 the
                 Piece
                 cannot
                 be
                 discerned
                 where
                 it
                 falls
                 :
                 and
                 so
                 comes
                 to
                 be
                 lost
                 .
              
            
             
               
                 4.
                 
                 In
                 the
                 fourth
                 place
                 it
                 may
                 be
                 asked
                 ,
                 whether
                 the
                 discharge
                 of
                 a
                 Cannon
                 b●
                 so
                 much
                 the
                 greater
                 ,
                 by
                 how
                 much
                 it
                 is
                 longer
                 ?
              
               
                 IT
                 seemeth
                 at
                 the
                 first
                 to
                 be
                 most
                 true
                 ,
                 that
                 the
                 longer
                 the
                 Piece
                 is
                 ,
                 the
                 more
                 violent
                 it
                 shoots
                 :
                 and
                 to
                 speak
                 generally
                 ,
                 that
                 which
                 is
                 direction
                 by
                 a
                 Trunke
                 ,
                 Pipe
                 ,
                 or
                 other
                 concavitie
                 ,
                 is
                 conveyed
                 so
                 much
                 the
                 more
                 violent
                 ,
                 or
                 better
                 ,
                 by
                 how
                 much
                 it
                 is
                 longer
                 ,
                 either
                 in
                 respect
                 of
                 the
                 Sight
                 ,
                 Hearing
                 ,
                 Water
                 ,
                 Fire
                 ,
                 &c.
                 &
                 the
                 reason
                 seems
                 to
                 hold
                 in
                 Cannons
                 ,
                 because
                 in
                 those
                 that
                 are
                 long
                 ,
                 the
                 fire
                 is
                 retained
                 a
                 longer
                 time
                 in
                 the
                 concavitie
                 of
                 the
                 Piece
                 ,
                 and
                 so
                 
                 throwes
                 out
                 the
                 Bullet
                 with
                 more
                 violence
                 ;
                 and
                 experience
                 lets
                 us
                 see
                 that
                 taking
                 Cannons
                 of
                 the
                 same
                 boare
                 ,
                 but
                 of
                 diversitie
                 of
                 length
                 from
                 8
                 foot
                 to
                 12
                 ,
                 that
                 the
                 Cannon
                 of
                 9
                 foot
                 long
                 hath
                 more
                 force
                 than
                 that
                 of
                 8
                 foot
                 long
                 ,
                 and
                 10
                 more
                 than
                 that
                 of
                 9
                 ,
                 and
                 so
                 unto
                 12
                 foote
                 of
                 length
                 .
                 Now
                 the
                 usuall
                 Cannon
                 carries
                 600
                 Paces
                 ,
                 some
                 more
                 ,
                 some
                 lesse
                 ,
                 yea
                 some
                 but
                 200
                 Paces
                 from
                 the
                 Piece
                 ,
                 and
                 may
                 shoot
                 into
                 soft
                 earth
                 15
                 or
                 17
                 foot
                 ,
                 into
                 sand
                 or
                 earth
                 which
                 is
                 loose
                 ,
                 22
                 or
                 24
                 foot
                 ,
                 and
                 in
                 firme
                 ground
                 ,
                 about
                 10
                 or
                 12
                 foot
                 ,
                 &c.
                 
              
               
                 It
                 hath
                 been
                 seen
                 lately
                 in
                 Germany
                 ,
                 where
                 there
                 were
                 made
                 Pieces
                 from
                 8
                 foot
                 long
                 to
                 17
                 foot
                 of
                 like
                 boare
                 ,
                 that
                 shooting
                 out
                 of
                 any
                 piece
                 which
                 was
                 longer
                 than
                 12
                 foot
                 ;
                 the
                 force
                 was
                 diminished
                 ,
                 and
                 the
                 more
                 in
                 length
                 the
                 Piece
                 increaseth
                 ,
                 the
                 lesse
                 his
                 force
                 was
                 :
                 therefore
                 the
                 length
                 ought
                 to
                 be
                 in
                 a
                 meane
                 measure
                 ,
                 and
                 it
                 is
                 often
                 seene
                 ,
                 the
                 greater
                 the
                 Cannon
                 is
                 ,
                 by
                 so
                 much
                 the
                 service
                 is
                 greater
                 :
                 but
                 to
                 have
                 it
                 too
                 long
                 or
                 too
                 short
                 ,
                 is
                 not
                 convenient
                 ,
                 but
                 a
                 meane
                 proportion
                 of
                 length
                 to
                 be
                 taken
                 ,
                 otherwise
                 the
                 flame
                 of
                 the
                 fire
                 will
                 be
                 over-pressed
                 with
                 Aire
                 :
                 whic
                 hinders
                 the
                 motion
                 in
                 respect
                 of
                 substance
                 ,
                 and
                 distance
                 of
                 getting
                 out
                 .
              
               
            
          
           
             
             
               PROBLEM
               .
               LXXXIIII
               .
               Of
               predigious
               progression
               and
               multiplication
               ,
               of
               Creatures
               ,
               Plants
               ,
               Fruits
               ,
               Numbers
               ,
               Gold
               ,
               Silver
               ,
               &c.
               when
               they
               are
               alwayes
               augmented
               by
               certaine
               proportion
               .
            
             
               HEre
               we
               shall
               shew
               things
               no
               lesse
               admirable
               ,
               as
               recreative
               ,
               and
               yet
               so
               certaine
               and
               easie
               to
               be
               demonstrated
               ,
               that
               there
               needs
               not
               but
               Multiplication
               only
               ,
               to
               try
               each
               particular
               :
               and
               first
               ,
            
             
               
                 Of
                 graines
                 of
                 Mustard-seed
                 .
              
               
                 FIrst
                 ,
                 therefore
                 it
                 is
                 certaine
                 that
                 the
                 increase
                 of
                 one
                 graine
                 of
                 Mustard-seed
                 for
                 20
                 yeares
                 space
                 ,
                 cannot
                 be
                 contained
                 within
                 the
                 visible
                 world
                 ,
                 nay
                 if
                 it
                 were
                 a
                 hundred
                 times
                 greater
                 than
                 it
                 is
                 :
                 and
                 holding
                 nothing
                 besides
                 from
                 the
                 Centre
                 of
                 the
                 earth
                 even
                 unto
                 the
                 firmament
                 ,
                 but
                 only
                 small
                 grains
                 of
                 Mustard-seed
                 :
                 Now
                 because
                 this
                 seems
                 but
                 words
                 ,
                 it
                 must
                 be
                 proved
                 by
                 Art
                 ,
                 as
                 may
                 be
                 done
                 in
                 this
                 wise
                 ,
                 as
                 suppose
                 one
                 Mustard-seed
                 sowne
                 to
                 bring
                 forth
                 a
                 tree
                 or
                 branch
                 ,
                 in
                 each
                 extendure
                 of
                 which
                 might
                 be
                 a
                 thousand
                 graines
                 :
                 but
                 we
                 will
                 suppose
                 onely
                 a
                 thousand
                 in
                 the
                 whole
                 tree
                 ,
                 and
                 let
                 us
                 proceed
                 to
                 ●0
                 yeares
                 ,
                 every
                 seed
                 to
                 bring
                 forth
                 yearely
                 a
                 thousand
                 graines
                 ,
                 now
                 multiplying
                 alwayes
                 by
                 a
                 thousand
                 ,
                 in
                 lesse
                 then
                 17
                 years
                 
                 you
                 shall
                 have
                 to
                 many
                 graines
                 which
                 will
                 surpasse
                 the
                 sands
                 ,
                 which
                 are
                 able
                 to
                 fill
                 the
                 whole
                 firmament
                 :
                 for
                 following
                 the
                 supposition
                 of
                 Archimedes
                 ,
                 and
                 the
                 most
                 probable
                 opinion
                 of
                 the
                 greatness
                 of
                 the
                 firmament
                 which
                 
                   ●i●ho
                   Brahe
                
                 hath
                 left
                 us
                 ;
                 the
                 number
                 of
                 graines
                 of
                 sand
                 will
                 be
                 sufficiently
                 expressed
                 with
                 49
                 Ciphers
                 ,
                 but
                 the
                 number
                 of
                 graines
                 of
                 Mustard-seed
                 at
                 the
                 end
                 of
                 17
                 yeares
                 will
                 have
                 52
                 Ciphers
                 :
                 and
                 moreover
                 ,
                 graines
                 of
                 Mustard-seed
                 ,
                 are
                 farre
                 greater
                 than
                 these
                 of
                 the
                 sands
                 :
                 it
                 is
                 therefore
                 evident
                 that
                 at
                 the
                 seventeenth
                 yeare
                 ,
                 all
                 the
                 graines
                 of
                 Mustard-seed
                 which
                 shall
                 successively
                 spring
                 from
                 one
                 graine
                 onely
                 ,
                 cannot
                 be
                 contained
                 within
                 the
                 limits
                 of
                 the
                 whole
                 firmament
                 ;
                 what
                 should
                 it
                 be
                 then
                 ,
                 if
                 it
                 should
                 be
                 multiplied
                 againe
                 by
                 a
                 thousand
                 for
                 the
                 ●8
                 yeare
                 :
                 and
                 that
                 againe
                 by
                 a
                 thousand
                 for
                 every
                 yeares
                 increase
                 untill
                 you
                 come
                 to
                 the
                 20
                 yeare
                 ,
                 it
                 's
                 a
                 thing
                 as
                 cleare
                 as
                 the
                 day
                 ,
                 that
                 such
                 a
                 heap
                 of
                 Mustard-seed
                 would
                 be
                 a
                 hundred
                 thousand
                 times
                 greater
                 than
                 the
                 Earth
                 :
                 and
                 bring
                 onely
                 but
                 the
                 increase
                 of
                 one
                 graine
                 in
                 20
                 yeares
                 .
              
            
             
               
                 Of
                 Pigges
                 .
              
               
                 SEcondly
                 ,
                 is
                 it
                 not
                 a
                 strange
                 proposition
                 ,
                 to
                 say
                 that
                 the
                 great
                 Turke
                 with
                 all
                 his
                 Revenues
                 ,
                 is
                 not
                 able
                 to
                 maintaine
                 for
                 one
                 yeares
                 time
                 ,
                 all
                 the
                 Pigges
                 that
                 a
                 Sow
                 may
                 pigge
                 with
                 all
                 her
                 race
                 ,
                 that
                 is
                 ,
                 the
                 increase
                 with
                 the
                 increase
                 unto
                 12
                 years
                 :
                 this
                 seemes
                 impossible
                 ,
                 yet
                 it
                 is
                 most
                 true
                 ,
                 for
                 let
                 us
                 suppose
                 and
                 put
                 ,
                 the
                 case
                 ,
                 
                 that
                 a
                 Sow
                 bring
                 forth
                 but
                 6
                 ,
                 two
                 Males
                 ,
                 and
                 4
                 Females
                 ,
                 and
                 that
                 each
                 Female
                 shall
                 bring
                 forth
                 as
                 many
                 every
                 yeare
                 ,
                 during
                 the
                 space
                 of
                 12
                 yeares
                 ,
                 at
                 the
                 end
                 of
                 the
                 time
                 there
                 will
                 be
                 found
                 above
                 3●
                 millions
                 of
                 Pigges
                 :
                 now
                 allowing
                 a
                 crowne
                 for
                 the
                 maintenance
                 of
                 each
                 Pigge
                 for
                 a
                 yeare
                 ,
                 (
                 which
                 is
                 as
                 little
                 as
                 may
                 be
                 ,
                 being
                 but
                 neare
                 a
                 halfe
                 of
                 a
                 farthing
                 allowance
                 for
                 each
                 day
                 ;
                 )
                 there
                 must
                 be
                 at
                 the
                 least
                 so
                 many
                 crownes
                 to
                 maintaine
                 them
                 ,
                 one
                 a
                 year
                 ,
                 viz.
                 33
                 millions
                 ,
                 which
                 exceeds
                 the
                 Turkes
                 revenue
                 by
                 much
                 .
              
            
             
               
                 Of
                 graines
                 of
                 Corne.
                 
              
               
                 THirdly
                 ,
                 it
                 will
                 make
                 one
                 astonished
                 to
                 think
                 that
                 a
                 graine
                 of
                 Corne
                 ,
                 with
                 his
                 increase
                 successively
                 for
                 the
                 space
                 of
                 12
                 yeares
                 will
                 produce
                 in
                 grains
                 24414062●000000000000
                 ,
                 which
                 is
                 able
                 to
                 load
                 almost
                 al
                 the
                 creatures
                 in
                 the
                 World.
                 
              
               
                 To
                 open
                 which
                 ,
                 let
                 it
                 be
                 supposed
                 that
                 the
                 first
                 yeare
                 one
                 graine
                 being
                 sowed
                 brings
                 forth
                 50
                 ,
                 (
                 but
                 sometimes
                 there
                 is
                 seen
                 70
                 ,
                 sometimes
                 100
                 fold
                 )
                 which
                 graines
                 sowen
                 the
                 next
                 yeare
                 ,
                 every
                 one
                 to
                 produce
                 50
                 ,
                 and
                 so
                 consequently
                 the
                 whole
                 and
                 increase
                 to
                 be
                 sowen
                 every
                 yeare
                 ,
                 until
                 12
                 yeares
                 be
                 expired
                 ,
                 there
                 will
                 be
                 of
                 increase
                 the
                 aforesaid
                 prodigious
                 summe
                 of
                 graines
                 ,
                 viz.
                 244140625000000000000
                 ,
                 which
                 will
                 make
                 a
                 cubical
                 heap
                 of
                 6258522
                 graines
                 every
                 way
                 ,
                 which
                 is
                 more
                 than
                 a
                 cubicall
                 body
                 of
                 31
                 miles
                 every
                 way
                 :
                 for
                 allowing
                 40
                 graines
                 
                 in
                 length
                 to
                 each
                 foot
                 ,
                 the
                 Cube
                 would
                 be
                 156463
                 foot
                 every
                 way
                 :
                 from
                 which
                 it
                 is
                 evident
                 that
                 if
                 there
                 were
                 two
                 hundred
                 thousand
                 Cities
                 as
                 great
                 as
                 London
                 ,
                 allowing
                 to
                 each
                 3
                 miles
                 square
                 every
                 way
                 ,
                 and
                 100
                 foot
                 in
                 height
                 ,
                 there
                 would
                 not
                 be
                 sufficient
                 roome
                 to
                 containe
                 the
                 aforesaid
                 quantitie
                 of
                 Corne
                 :
                 and
                 suppose
                 a
                 bushel
                 of
                 Corne
                 were
                 equal
                 unto
                 two
                 Cubicke
                 feet
                 ,
                 which
                 might
                 containe
                 twenty
                 hundred
                 thousand
                 graines
                 then
                 would
                 there
                 be
                 122070462500000.
                 bushells
                 ,
                 and
                 allowing
                 30
                 bushels
                 to
                 a
                 Tunne
                 ,
                 it
                 would
                 be
                 able
                 to
                 load
                 81380●0833
                 vessels
                 ,
                 which
                 is
                 more
                 than
                 eight
                 thousand
                 one
                 hundred
                 and
                 thirty
                 eight
                 millions
                 ,
                 ship
                 loadings
                 of
                 ●00
                 Tunne
                 to
                 each
                 ship
                 a
                 :
                 quantity
                 so
                 great
                 that
                 the
                 Sea
                 is
                 scarce
                 able
                 to
                 beare
                 ,
                 or
                 the
                 universal
                 world
                 able
                 to
                 finde
                 vessels
                 to
                 carry
                 it
                 .
                 And
                 if
                 this
                 Corne
                 should
                 be
                 valued
                 at
                 halfe
                 a
                 crown
                 the
                 bushel
                 ,
                 it
                 would
                 amount
                 unto
                 15258807812500
                 pounds
                 sterling
                 ,
                 which
                 I
                 think
                 exceeds
                 all
                 the
                 Treasures
                 of
                 all
                 the
                 Princes
                 ,
                 and
                 of
                 other
                 particular
                 men
                 in
                 the
                 whole
                 world
                 :
                 and
                 is
                 not
                 this
                 good
                 husbandry
                 to
                 sowe
                 one
                 grain
                 of
                 Corne
                 ;
                 and
                 to
                 continue
                 it
                 in
                 sowing
                 ,
                 the
                 increase
                 only
                 for
                 12
                 yeares
                 to
                 have
                 so
                 great
                 a
                 profit
                 ?
              
            
             
               
                 Of
                 the
                 increase
                 of
                 Sheep
                 .
              
               
                 FOurthly
                 ,
                 those
                 that
                 have
                 great
                 flocks
                 of
                 Sheep
                 may
                 be
                 quickly
                 rich
                 ,
                 if
                 they
                 would
                 preserve
                 their
                 Sheep
                 without
                 killing
                 or
                 selling
                 of
                 them
                 :
                 so
                 that
                 every
                 Sheep
                 produce
                 one
                 each
                 
                 yeare
                 ,
                 for
                 at
                 the
                 end
                 of
                 16
                 yeares
                 ,
                 100
                 Sheepe
                 will
                 multiply
                 and
                 increase
                 unto
                 6553600
                 ,
                 which
                 is
                 above
                 6
                 millions
                 ,
                 5
                 hundred
                 53
                 thousand
                 Sheep
                 :
                 now
                 supposing
                 them
                 worth
                 but
                 a
                 crown
                 a
                 piece
                 ,
                 it
                 would
                 amount
                 unto
                 1638400
                 pounds
                 sterling
                 ,
                 vvhich
                 is
                 above
                 1
                 million
                 6
                 hundred
                 38
                 thousand
                 pounds
                 ,
                 a
                 faire
                 increase
                 of
                 one
                 Sheep
                 :
                 and
                 a
                 large
                 portion
                 for
                 a
                 Childe
                 if
                 it
                 should
                 be
                 allotted
                 .
              
            
             
               
                 Of
                 the
                 increase
                 of
                 Cod-fish
                 ,
                 Carpes
                 ,
                 &c.
                 
              
               
                 FIfthly
                 ,
                 if
                 there
                 be
                 any
                 creatures
                 in
                 the
                 vvorld
                 that
                 do
                 abound
                 vvith
                 increase
                 or
                 fertilitie
                 ,
                 it
                 may
                 be
                 rightly
                 attributed
                 to
                 fish
                 ;
                 for
                 they
                 in
                 their
                 kindes
                 produce
                 such
                 a
                 great
                 multitude
                 of
                 Eggs
                 ,
                 and
                 brings
                 forth
                 so
                 many
                 little
                 ones
                 ,
                 that
                 if
                 a
                 great
                 part
                 vvere
                 not
                 destroyed
                 continually
                 ,
                 vvithin
                 a
                 ●ittle
                 vvhile
                 they
                 vvould
                 fill
                 all
                 the
                 Sea
                 ,
                 Ponds
                 ,
                 and
                 Rivers
                 in
                 the
                 vvorld
                 ;
                 and
                 it
                 is
                 easie
                 to
                 shevv
                 hovv
                 it
                 vvould
                 come
                 so
                 to
                 passe
                 ,
                 onely
                 by
                 supposing
                 them
                 to
                 increase
                 without
                 taking
                 or
                 destroying
                 them
                 for
                 the
                 space
                 of
                 10
                 or
                 12
                 yeares
                 :
                 having
                 regard
                 to
                 the
                 soliditie
                 of
                 the
                 waters
                 which
                 are
                 allotted
                 for
                 to
                 lodge
                 and
                 containe
                 these
                 creatures
                 ,
                 as
                 their
                 bounds
                 and
                 place
                 of
                 rest
                 to
                 live
                 in
                 .
              
            
             
               
                 Of
                 the
                 increase
                 and
                 multiplication
                 of
                 men
                 .
              
               
                 SIxthly
                 ,
                 there
                 are
                 some
                 that
                 cannot
                 conceive
                 how
                 it
                 can
                 be
                 that
                 from
                 eight
                 persons
                 (
                 which
                 
                 were
                 saved
                 after
                 the
                 deluge
                 or
                 Noahs
                 flood
                 )
                 should
                 spring
                 such
                 a
                 world
                 of
                 people
                 to
                 begin
                 a
                 Monarchie
                 under
                 Nimrod
                 ,
                 being
                 but
                 200
                 yeares
                 after
                 the
                 flood
                 ,
                 and
                 that
                 amongst
                 them
                 should
                 be
                 raised
                 an
                 army
                 of
                 two
                 hundred
                 thousand
                 fighting
                 men
                 :
                 But
                 it
                 is
                 easi●y
                 proved
                 if
                 vve
                 take
                 but
                 one
                 of
                 the
                 Children
                 of
                 Noah
                 ,
                 and
                 suppose
                 that
                 a
                 nevv
                 generation
                 of
                 people
                 begun
                 at
                 every
                 30
                 yeares
                 ,
                 and
                 that
                 it
                 be
                 continued
                 to
                 the
                 seventh
                 generation
                 vvhich
                 is
                 200
                 yeares
                 ;
                 for
                 then
                 of
                 one
                 only
                 family
                 there
                 vvould
                 be
                 produced
                 one
                 hundred
                 and
                 eleven
                 thousand
                 soules
                 ,
                 three
                 hundred
                 and
                 five
                 to
                 begin
                 the
                 vvorld
                 :
                 though
                 in
                 that
                 time
                 men
                 lived
                 longer
                 ,
                 and
                 vvere
                 more
                 capable
                 of
                 multiplication
                 and
                 increase
                 :
                 vvhich
                 number
                 springing
                 onely
                 from
                 a
                 simp●e
                 production
                 of
                 one
                 yearly
                 ,
                 vvould
                 be
                 farre
                 greater
                 ,
                 if
                 one
                 man
                 should
                 have
                 many
                 vvives
                 ,
                 vvhich
                 in
                 ancient
                 times
                 they
                 had
                 :
                 from
                 vvhich
                 it
                 is
                 also
                 that
                 the
                 Children
                 of
                 Israel
                 ,
                 vvho
                 came
                 into
                 Egypt
                 but
                 onely
                 70
                 soules
                 ,
                 yet
                 after
                 210
                 yeares
                 captivity
                 ,
                 they
                 came
                 forth
                 vvith
                 their
                 hostes
                 ,
                 that
                 there
                 vvere
                 told
                 six
                 hundred
                 thousand
                 fighting
                 men
                 ,
                 besides
                 old
                 people
                 ,
                 women
                 and
                 children
                 ;
                 and
                 he
                 that
                 shall
                 separate
                 but
                 one
                 of
                 the
                 families
                 of
                 Joseph
                 ,
                 it
                 would
                 be
                 sufficient
                 to
                 make
                 up
                 that
                 number
                 :
                 how
                 much
                 more
                 should
                 it
                 be
                 then
                 if
                 we
                 should
                 adjoyne
                 many
                 families
                 together
                 ?
              
            
             
               
                 Of
                 the
                 increase
                 of
                 numbers
                 .
              
               
                 SEventhly
                 ,
                 what
                 summe
                 of
                 money
                 shall
                 the
                 City
                 of
                 London
                 be
                 worth
                 ,
                 if
                 it
                 should
                 be
                 sold
                 ,
                 and
                 the
                 money
                 be
                 paid
                 in
                 a
                 yeare
                 after
                 this
                 
                 manner
                 :
                 the
                 first
                 week
                 to
                 pay
                 a
                 pinne
                 ,
                 the
                 second
                 week
                 2
                 pinnes
                 ,
                 the
                 third
                 week
                 4
                 pinnes
                 ,
                 the
                 fourth
                 week
                 8
                 pinnes
                 ,
                 the
                 fifth
                 week
                 16
                 pinnes
                 .
                 and
                 so
                 doubling
                 untill
                 the
                 52
                 weeks
                 ,
                 or
                 the
                 yeare
                 be
                 expired
                 .
              
               
                 Here
                 one
                 would
                 think
                 that
                 the
                 value
                 of
                 the
                 pinnes
                 would
                 amount
                 but
                 to
                 a
                 small
                 matter
                 ,
                 in
                 comparison
                 of
                 the
                 Treasures
                 ,
                 or
                 riches
                 of
                 the
                 whole
                 City
                 :
                 yet
                 it
                 is
                 most
                 probable
                 that
                 the
                 number
                 of
                 pinnes
                 would
                 amount
                 unto
                 the
                 sum
                 of
                 4519599628681215
                 ,
                 and
                 if
                 we
                 should
                 allow
                 unto
                 a
                 quarter
                 a
                 hundred
                 thousand
                 pinnes
                 ,
                 the
                 whole
                 would
                 contain
                 ninetie
                 eight
                 millions
                 ,
                 foure
                 hundred
                 thousand
                 Tunne
                 :
                 which
                 is
                 able
                 to
                 load
                 45930
                 Shippes
                 of
                 a
                 thousand
                 Tunne
                 apiece
                 :
                 and
                 if
                 we
                 should
                 allow
                 a
                 thousand
                 pins
                 for
                 a
                 penny
                 ,
                 the
                 summe
                 of
                 money
                 would
                 amount
                 unto
                 above
                 eighteen
                 thousand
                 ,
                 eight
                 hundred
                 and
                 thirty
                 millions
                 of
                 pounds
                 sterling
                 ,
                 an
                 high
                 price
                 to
                 sell
                 a
                 Citie
                 at
                 ,
                 yet
                 certain
                 ,
                 according
                 to
                 that
                 first
                 proposed
                 .
                 So
                 if
                 40
                 Townes
                 were
                 sold
                 upon
                 condition
                 to
                 give
                 for
                 the
                 first
                 a
                 penny
                 ,
                 for
                 the
                 second
                 2
                 pence
                 ,
                 for
                 the
                 third
                 4
                 pence
                 ,
                 &c.
                 by
                 doubling
                 all
                 the
                 rest
                 unto
                 the
                 last
                 ,
                 it
                 would
                 amount
                 unto
                 this
                 number
                 of
                 pence
                 ,
                 109951●62●●76
                 ,
                 which
                 in
                 pounds
                 is
                 4581298444
                 ,
                 that
                 is
                 foure
                 thousand
                 five
                 hundred
                 and
                 fourescore
                 millions
                 of
                 pounds
                 and
                 more
                 .
              
            
             
               
               
                 Of
                 a
                 man
                 that
                 gathered
                 up
                 Apples
                 ,
                 Stones
                 ,
                 or
                 such
                 like
                 upon
                 a
                 condition
                 .
              
               
                 EIghtly
                 ,
                 admit
                 there
                 were
                 an
                 hundred
                 Apples
                 ,
                 Stones
                 ,
                 or
                 such
                 like
                 things
                 that
                 were
                 plac'd
                 in
                 a
                 straight
                 line
                 or
                 right
                 forme
                 ,
                 a
                 Pace
                 one
                 from
                 another
                 ,
                 and
                 a
                 basket
                 being
                 placed
                 a
                 Pace
                 from
                 the
                 first
                 :
                 how
                 many
                 paces
                 would
                 there
                 be
                 made
                 to
                 put
                 all
                 these
                 Stones
                 into
                 the
                 basket
                 ,
                 by
                 fetching
                 one
                 by
                 one
                 ?
                 this
                 would
                 require
                 near
                 halfe
                 a
                 day
                 to
                 do
                 it
                 ,
                 for
                 there
                 would
                 be
                 made
                 ten
                 thousand
                 and
                 ninety
                 two
                 paces
                 before
                 he
                 should
                 gather
                 them
                 all
                 up
                 .
              
            
             
               
                 Of
                 Changes
                 in
                 Bells
                 ,
                 in
                 musicall
                 Instruments
                 ,
                 transmutation
                 of
                 places
                 ,
                 in
                 numbers
                 ,
                 letters
                 ,
                 men
                 or
                 such
                 like
                 .
              
               
                 NInethly
                 ,
                 is
                 it
                 not
                 an
                 admirable
                 thing
                 to
                 consider
                 how
                 the
                 skill
                 of
                 numbers
                 doth
                 easily
                 furnish
                 us
                 with
                 the
                 knowledge
                 of
                 mysterious
                 and
                 hidden
                 things
                 ?
                 which
                 simply
                 looked
                 into
                 by
                 others
                 that
                 are
                 not
                 versed
                 in
                 Arithmetick
                 ,
                 do
                 present
                 unto
                 them
                 a
                 world
                 of
                 confusion
                 and
                 difficultie
                 .
              
               
                 As
                 in
                 the
                 first
                 place
                 ,
                 it
                 is
                 often
                 debated
                 amongst
                 our
                 common
                 Ringers
                 ,
                 what
                 number
                 of
                 Changes
                 there
                 might
                 be
                 made
                 in
                 5
                 ,
                 6
                 ,
                 7
                 ,
                 8
                 ,
                 or
                 more
                 Bells
                 :
                 who
                 spend
                 much
                 time
                 to
                 answer
                 their
                 owne
                 doubts
                 ,
                 entring
                 often
                 into
                 a
                 Labyrinth
                 in
                 the
                 search
                 thereof
                 :
                 or
                 if
                 there
                 were
                 10
                 voyces
                 ,
                 how
                 many
                 severall
                 notes
                 might
                 there
                 
                 be
                 ?
                 These
                 are
                 propositions
                 of
                 such
                 facility
                 ,
                 that
                 a
                 childe
                 which
                 can
                 but
                 multiply
                 one
                 number
                 by
                 another
                 ,
                 may
                 easily
                 resolve
                 it
                 ,
                 which
                 is
                 but
                 only
                 to
                 multiply
                 every
                 number
                 from
                 the
                 unite
                 successively
                 in
                 each
                 others
                 product
                 ,
                 unto
                 the
                 terme
                 assigned
                 :
                 so
                 the
                 6
                 number
                 that
                 is
                 against
                 6
                 in
                 the
                 Table
                 ,
                 is
                 720
                 ,
                 and
                 so
                 many
                 (
                 hanges
                 may
                 be
                 made
                 upon
                 6
                 Bells
                 ,
                 upon
                 5
                 there
                 are
                 120
                 ,
                 &c.
                 
              
               
                 In
                 like
                 manner
                 against
                 10
                 in
                 the
                 Table
                 is
                 3618800
                 ,
                 that
                 is
                 ,
                 three
                 millions
                 ,
                 six
                 hundred
                 twenty
                 eight
                 thousand
                 ,
                 eight
                 hundred
                 :
                 which
                 shews
                 that
                 10
                 voices
                 may
                 have
                 so
                 many
                 consorts
                 ,
                 each
                 man
                 keeping
                 his
                 owne
                 note
                 ,
                 but
                 only
                 altering
                 his
                 place
                 ;
                 and
                 so
                 of
                 stringed
                 Instruments
                 ,
                 and
                 the
                 Gamat
                 may
                 be
                 varied
                 according
                 to
                 which
                 ,
                 answerable
                 to
                 the
                 number
                 against
                 X
                 ,
                 viz.
                 1124001075070399680000
                 notes
                 ,
                 from
                 which
                 may
                 be
                 drawne
                 this
                 ,
                 or
                 the
                 like
                 proposition
                 .
                 Suppose
                 that
                 7
                 Schollers
                 were
                 taken
                 out
                 of
                 a
                 free
                 Schoole
                 to
                 be
                 sent
                 to
                 an
                 Vniversitie
                 ,
                 there
                 to
                 be
                 entertained
                 in
                 some
                 Colledge
                 at
                 commons
                 for
                 a
                 certaine
                 summe
                 of
                 money
                 ,
                 so
                 that
                 each
                 of
                 them
                 have
                 two
                 meales
                 daily
                 ,
                 and
                 no
                 longer
                 to
                 continue
                 there
                 ,
                 then
                 that
                 sitting
                 all
                 together
                 upon
                 one
                 bench
                 or
                 forme
                 at
                 every
                 meale
                 ,
                 there
                 might
                 be
                 a
                 divers
                 transmutation
                 of
                 place
                 ,
                 of
                 account
                 in
                 some
                 one
                 of
                 them
                 ,
                 in
                 comparison
                 of
                 another
                 ,
                 and
                 never
                 the
                 whole
                 company
                 to
                 be
                 twice
                 alike
                 in
                 situation
                 :
                 how
                 long
                 may
                 the
                 Steward
                 entertaine
                 them
                 ?
                 (
                 who
                 being
                 not
                 skilled
                 in
                 this
                 fetch
                 may
                 answere
                 unadvisedly
                 .
                 )
                 It
                 is
                 most
                 certaine
                 that
                 there
                 will
                 be
                 
                 five
                 thousand
                 and
                 forty
                 several
                 
                   
                     
                       1
                    
                     
                       a
                    
                     
                       1
                    
                  
                   
                     
                       2
                    
                     
                       b
                    
                     
                       2
                    
                  
                   
                     
                       6
                    
                     
                       c
                    
                     
                       3
                    
                  
                   
                     
                       24
                    
                     
                       d
                    
                     
                       4
                    
                  
                   
                     
                       120
                    
                     
                       e
                    
                     
                       5
                    
                  
                   
                     
                       7●0
                    
                     
                       f
                    
                     
                       6
                    
                  
                   
                     
                       5040
                    
                     
                       g
                    
                     
                       7
                    
                  
                   
                     
                       403●0
                    
                     
                       h
                    
                     
                       8
                    
                  
                   
                     
                       362880
                    
                     
                       i
                    
                     
                       9
                    
                  
                   
                     
                       3628800
                    
                     
                       k
                    
                     
                       10
                    
                  
                   
                     
                       39916800
                    
                     
                       l
                    
                     
                       11
                    
                  
                   
                     
                       479001600
                    
                     
                       m
                    
                     
                       12
                    
                  
                   
                     
                       6227020800
                    
                     
                       n
                    
                     
                       13
                    
                  
                   
                     
                       87178291200
                    
                     
                       o
                    
                     
                       14
                    
                  
                   
                     
                       1307674368000
                    
                     
                       p
                    
                     
                       15
                    
                  
                   
                     
                       20922789888000
                    
                     
                       q
                    
                     
                       16
                    
                  
                   
                     
                       355687537996000
                    
                     
                       r
                    
                     
                       17
                    
                  
                   
                     
                       6402375683928000
                    
                     
                       s
                    
                     
                       18
                    
                  
                   
                     
                       121645137994632000
                    
                     
                       t
                    
                     
                       19
                    
                  
                   
                     
                       2432902759892640000
                    
                     
                       u
                    
                     
                       20
                    
                  
                   
                     
                       51090957957745440000
                    
                     
                       w
                    
                     
                       21
                    
                  
                   
                     
                       1124001075070399680000
                    
                     
                       x
                    
                     
                       22
                    
                  
                   
                     
                       25852024726619192640000
                    
                     
                       y
                    
                     
                       23
                    
                  
                   
                     
                       6●0448593438860623360000
                    
                     
                       z
                    
                     
                       24
                    
                  
                
                 positions
                 or
                 changings
                 in
                 the
                 seatings
                 ,
                 which
                 maks
                 14
                 years
                 time
                 wanting
                 10
                 weeks
                 and
                 3
                 dayes
                 .
                 Hence
                 from
                 this
                 mutability
                 of
                 transmutation
                 ,
                 it
                 is
                 no
                 marvell
                 tha●
                 by
                 24
                 letters
                 there
                 ariseth
                 and
                 is
                 made
                 such
                 variety
                 of
                 languages
                 in
                 the
                 world
                 ,
                 &
                 such
                 infinite
                 number
                 of
                 words
                 in
                 each
                 language
                 ;
                 seeing
                 the
                 diversity
                 of
                 syllables
                 produceth
                 that
                 effect
                 ,
                 and
                 also
                 by
                 the
                 interchanging
                 &
                 placing
                 of
                 letters
                 amongst
                 the
                 vowels
                 ,
                 &
                 amongst
                 themselves
                 maketh
                 these
                 syllables
                 :
                 vvhich
                 Alphabet
                 of
                 24
                 letters
                 may
                 be
                 varied
                 so
                 many
                 times
                 ,
                 viz.
                 620448593438860623360000
                 vvhich
                 is
                 six
                 hundred
                 tvventy
                 thousand
                 ,
                 foure
                 hundred
                 forty
                 eight
                 millions
                 of
                 millions
                 of
                 millions
                 five
                 hundred
                 ninety
                 three
                 thousand
                 ,
                 foure
                 hundred
                 thirty
                 eight
                 milions
                 of
                 milions
                 ,
                 &
                 more
                 .
              
               
                 Novv
                 allovving
                 that
                 a
                 man
                 may
                 reade
                 or
                 speak
                 one
                 hundred
                 thousand
                 vvords
                 in
                 an
                 houre
                 vvhich
                 is
                 tvvice
                 more
                 vvords
                 than
                 there
                 are
                 conteined
                 
                 in
                 the
                 Psalmes
                 of
                 David
                 ,
                 (
                 a
                 taske
                 too
                 great
                 for
                 any
                 man
                 to
                 do
                 in
                 so
                 short
                 a
                 time
                 )
                 and
                 if
                 there
                 were
                 foure
                 thousand
                 six
                 hundred
                 and
                 fifty
                 thousand
                 millions
                 of
                 men
                 ,
                 they
                 could
                 not
                 speak
                 these
                 words
                 (
                 according
                 to
                 the
                 hourely
                 proportion
                 aforesaid
                 )
                 in
                 threescore
                 and
                 ten
                 thousand
                 yeares
                 ;
                 which
                 variation
                 &
                 transmutation
                 of
                 letters
                 ,
                 if
                 they
                 should
                 be
                 written
                 in
                 bookes
                 ,
                 allowing
                 to
                 each
                 leaf
                 28000
                 words
                 ,
                 (
                 which
                 is
                 as
                 many
                 as
                 possibly
                 could
                 be
                 inserted
                 ,
                 )
                 and
                 to
                 each
                 book
                 a
                 reame
                 or
                 20
                 quire
                 of
                 the
                 largest
                 and
                 thinnest
                 printing
                 paper
                 ,
                 so
                 that
                 each
                 book
                 being
                 about
                 15
                 inches
                 long
                 ,
                 12
                 broad
                 ,
                 and
                 6
                 thick
                 :
                 the
                 books
                 that
                 would
                 be
                 made
                 of
                 the
                 transmutation
                 of
                 the
                 24
                 letters
                 aforesaid
                 ,
                 would
                 be
                 at
                 least
                 38778037089928788
                 :
                 and
                 if
                 a
                 Library
                 of
                 a
                 mile
                 square
                 every
                 way
                 ,
                 of
                 50
                 foot
                 high
                 ,
                 were
                 made
                 to
                 containe
                 250
                 Galleries
                 of
                 20
                 foot
                 broad
                 apiece
                 ,
                 it
                 would
                 containe
                 foure
                 hundred
                 mill●ons
                 of
                 the
                 said
                 books
                 :
                 so
                 there
                 must
                 be
                 to
                 containe
                 the
                 rest
                 no
                 lesse
                 than
                 9●945092
                 such
                 Libraries
                 ;
                 and
                 if
                 the
                 books
                 were
                 extended
                 over
                 the
                 surface
                 of
                 the
                 Globe
                 of
                 the
                 Earth
                 ,
                 it
                 would
                 be
                 a
                 decuple
                 covering
                 unto
                 it
                 :
                 a
                 thing
                 seeming
                 most
                 incredible
                 that
                 24
                 letters
                 in
                 their
                 transmutation
                 should
                 produce
                 such
                 a
                 prodigious
                 number
                 ,
                 yet
                 most
                 certaine
                 and
                 infallible
                 in
                 computation
                 .
              
            
             
               
                 Of
                 a
                 Servant
                 hired
                 upon
                 certaine
                 conditions
                 .
              
               
                 A
                 Servant
                 said
                 unto
                 his
                 Master
                 ,
                 that
                 he
                 would
                 dvvell
                 vvith
                 him
                 all
                 his
                 life-time
                 ,
                 if
                 
                 he
                 would
                 but
                 onely
                 lend
                 him
                 land
                 to
                 sowe
                 one
                 graine
                 of
                 Corne
                 with
                 all
                 his
                 increase
                 for
                 8
                 years
                 time
                 ;
                 how
                 think
                 you
                 of
                 this
                 bargaine
                 ?
                 for
                 if
                 he
                 had
                 but
                 a
                 quarter
                 of
                 an
                 inch
                 of
                 ground
                 for
                 each
                 graine
                 ,
                 and
                 each
                 graine
                 to
                 bring
                 forth
                 yearely
                 of
                 increase
                 40
                 graines
                 ,
                 the
                 whole
                 sum
                 would
                 amount
                 unto
                 ,
                 at
                 the
                 terme
                 aforesaid
                 ,
                 6553600000000
                 graines
                 :
                 and
                 seeing
                 that
                 three
                 thousand
                 and
                 six
                 hundred
                 millions
                 of
                 inches
                 do
                 but
                 make
                 one
                 mile
                 square
                 in
                 the
                 superficies
                 ,
                 it
                 shall
                 be
                 able
                 to
                 receive
                 foureteene
                 thousand
                 and
                 foure
                 hundred
                 millions
                 of
                 graines
                 ,
                 which
                 is
                 14400000000.
                 thus
                 dividing
                 the
                 aforesaid
                 6553600000000
                 ,
                 the
                 Quotient
                 will
                 be
                 455
                 ,
                 and
                 so
                 many
                 square
                 miles
                 of
                 land
                 must
                 there
                 be
                 to
                 sowe
                 the
                 increase
                 of
                 one
                 graine
                 of
                 Corne
                 for
                 8
                 yeares
                 ,
                 which
                 makes
                 at
                 the
                 least
                 foure
                 hundred
                 and
                 twenty
                 thousand
                 Acres
                 of
                 land
                 ,
                 which
                 rated
                 but
                 at
                 five
                 shillings
                 the
                 Acre
                 
                   per
                   Annum
                
                 ,
                 amounts
                 unto
                 one
                 hundred
                 thousand
                 pound
                 ;
                 which
                 is
                 twelve
                 thousand
                 and
                 five
                 hundred
                 pound
                 a
                 yeare
                 ,
                 to
                 be
                 continued
                 for
                 8
                 yeares
                 ;
                 a
                 pretty
                 pay
                 for
                 a
                 Masters
                 Servant
                 8
                 yeares
                 service
                 .
              
            
          
           
             
             
               PROBLEM
               .
               LXXXV
               .
               Of
               Fountaines
               ,
               Hydriatiques
               ,
               Machinecke
               ,
               and
               other
               experiments
               upon
               water
               ,
               or
               other
               liquor
               .
            
             
               
                 1.
                 
                 First
                 how
                 to
                 make
                 water
                 at
                 the
                 foot
                 of
                 a
                 mountaine
                 to
                 ascend
                 to
                 the
                 top
                 of
                 it
                 ,
                 and
                 so
                 to
                 descend
                 on
                 the
                 other
                 side
                 ?
              
               
                 TO
                 do
                 this
                 there
                 must
                 be
                 a
                 Pipe
                 of
                 lead
                 ,
                 which
                 may
                 come
                 from
                 the
                 fountaine
                 A
                 ,
                 to
                 the
                 top
                 of
                 the
                 Mountaine
                 B
                 ;
                 and
                 so
                 to
                 descend
                 on
                 the
                 other
                 side
                 a
                 little
                 lower
                 then
                 the
                 Fountaine
                 ,
                 as
                 at
                 C.
                 then
                 make
                 a
                 hole
                 in
                 the
                 Pipe
                 at
                 
                 the
                 top
                 of
                 the
                 Mountaine
                 ,
                 as
                 at
                 B
                 ,
                 and
                 stop
                 the
                 end
                 of
                 the
                 Pipe
                 at
                 A
                 and
                 C
                 ;
                 and
                 fill
                 this
                 Pipe
                 at
                 B
                 with
                 water
                 :
                 &
                 close
                 it
                 very
                 carefully
                 againe
                 at
                 B
                 ,
                 that
                 no
                 aire
                 get
                 in
                 :
                 then
                 unstop
                 the
                 end
                 at
                 A
                 ,
                 &
                 at
                 C
                 ;
                 then
                 will
                 the
                 water
                 perpetually
                 runne
                 up
                 the
                 hill
                 ,
                 and
                 descend
                 on
                 the
                 other
                 side
                 ,
                 which
                 is
                 an
                 invention
                 of
                 great
                 consequence
                 to
                 furnish
                 Villages
                 that
                 want
                 water
                 .
              
            
             
               
               
                 2.
                 
                 Secondly
                 ,
                 how
                 to
                 know
                 what
                 wine
                 or
                 other
                 liquor
                 there
                 is
                 in
                 a
                 vessell
                 without
                 opening
                 the
                 bung-hole
                 ,
                 and
                 without
                 making
                 any
                 other
                 hole
                 ,
                 than
                 that
                 by
                 which
                 it
                 runnes
                 out
                 at
                 the
                 top
                 ?
              
               
                 IN
                 this
                 problem
                 there
                 is
                 nothing
                 but
                 to
                 take
                 a
                 bowed
                 pipe
                 of
                 Glasse
                 ,
                 and
                 put
                 it
                 into
                 the
                 faucets
                 hole
                 ,
                 and
                 stopping
                 it
                 close
                 about
                 :
                 for
                 then
                 you
                 shall
                 see
                 the
                 wine
                 or
                 liquor
                 to
                 ascend
                 in
                 this
                 Pipe
                 ,
                 untill
                 it
                 be
                 just
                 even
                 with
                 the
                 liquor
                 in
                 the
                 vessel
                 ;
                 by
                 which
                 a
                 man
                 may
                 fill
                 the
                 vessel
                 ,
                 or
                 put
                 more
                 into
                 it
                 :
                 and
                 so
                 if
                 need
                 were
                 ,
                 one
                 may
                 empty
                 one
                 vessel
                 into
                 another
                 without
                 opening
                 the
                 bung-hole
                 .
              
            
             
               
                 3.
                 
                 Thirdly
                 ,
                 how
                 is
                 it
                 that
                 it
                 is
                 said
                 that
                 a
                 vessell
                 holds
                 more
                 water
                 being
                 placed
                 at
                 the
                 foot
                 of
                 a
                 Mountaine
                 ,
                 than
                 standing
                 upon
                 the
                 top
                 of
                 it
                 ?
              
               
                 THis
                 is
                 a
                 thing
                 most
                 certaine
                 ,
                 because
                 that
                 water
                 and
                 all
                 other
                 liquor
                 disposeth
                 it selfe
                 sphericaliy
                 about
                 the
                 Centre
                 of
                 the
                 earth
                 ;
                 and
                 by
                 how
                 much
                 the
                 vessel
                 is
                 nearer
                 the
                 Centre
                 ,
                 by
                 so
                 much
                 the
                 more
                 the
                 surface
                 of
                 the
                 water
                 makes
                 a
                 lesser
                 sphere
                 ,
                 and
                 therefore
                 every
                 part
                 more
                 gibbous
                 or
                 swelling
                 ,
                 than
                 the
                 like
                 part
                 in
                 a
                 greater
                 sphere
                 :
                 and
                 therefore
                 when
                 the
                 same
                 vessell
                 is
                 farther
                 from
                 the
                 Centre
                 of
                 the
                 earth
                 ,
                 the
                 surface
                 of
                 the
                 water
                 makes
                 a
                 greater
                 sphere
                 ,
                 and
                 therefore
                 lesse
                 gibbous
                 ,
                 or
                 swelling
                 over
                 the
                 
                 vessell
                 :
                 from
                 whence
                 it
                 is
                 evident
                 that
                 a
                 vessell
                 near
                 the
                 Centre
                 of
                 the
                 Earth
                 holds
                 more
                 water
                 than
                 that
                 which
                 is
                 farther
                 remote
                 from
                 it
                 ;
                 and
                 so
                 consequently
                 a
                 vessel
                 placed
                 at
                 the
                 bottome
                 of
                 the
                 Mountaine
                 holds
                 more
                 water
                 ,
                 than
                 being
                 placed
                 on
                 the
                 top
                 of
                 the
                 Mountaine
                 .
                 First
                 ,
                 therefore
                 one
                 may
                 conclude
                 ,
                 that
                 one
                 and
                 the
                 
                 same
                 vessel
                 will
                 alwayes
                 hold
                 more
                 :
                 by
                 how
                 much
                 it
                 is
                 nearer
                 the
                 Centre
                 of
                 the
                 earth
                 .
                 Secondly
                 ,
                 if
                 a
                 vessell
                 be
                 very
                 neare
                 the
                 Centre
                 of
                 the
                 earth
                 ,
                 there
                 will
                 be
                 more
                 water
                 above
                 the
                 brims
                 of
                 it
                 ,
                 than
                 there
                 is
                 within
                 the
                 vessel
                 .
                 Thirdly
                 ,
                 a
                 vessel
                 full
                 of
                 water
                 comming
                 to
                 the
                 Centre
                 wil
                 spherically
                 increase
                 ,
                 and
                 by
                 little
                 and
                 little
                 leave
                 the
                 vessel
                 ;
                 and
                 passing
                 the
                 Centre
                 ,
                 the
                 vessel
                 will
                 be
                 all
                 emptied
                 .
                 Fourthly
                 ,
                 one
                 cannot
                 carry
                 a
                 Paile
                 of
                 water
                 from
                 a
                 low
                 place
                 to
                 a
                 higher
                 ,
                 but
                 it
                 will
                 more
                 and
                 more
                 run
                 out
                 and
                 over
                 ,
                 because
                 that
                 in
                 ascending
                 it
                 lies
                 more
                 levell
                 ,
                 but
                 descending
                 it
                 swels
                 and
                 becomes
                 more
                 gibbous
                 .
              
            
             
               
                 4.
                 
                 Fourthly
                 ,
                 to
                 conduct
                 water
                 from
                 the
                 top
                 of
                 one
                 Mountaine
                 ,
                 to
                 the
                 top
                 of
                 another
                 .
              
               
                 AS
                 admit
                 on
                 the
                 top
                 of
                 a
                 Mountaine
                 there
                 is
                 a
                 spring
                 ,
                 and
                 at
                 the
                 toppe
                 of
                 the
                 other
                 
                 Mountaine
                 there
                 are
                 Inhabitants
                 which
                 want
                 water
                 :
                 now
                 to
                 make
                 a
                 bridge
                 from
                 one
                 Mountaine
                 to
                 another
                 ,
                 were
                 difficult
                 and
                 too
                 great
                 a
                 charge
                 ;
                 by
                 way
                 of
                 Pipes
                 it
                 is
                 easie
                 and
                 of
                 no
                 great
                 price
                 :
                 for
                 if
                 at
                 the
                 spring
                 on
                 the
                 top
                 of
                 the
                 Mountaine
                 be
                 placed
                 a
                 Pipe
                 ,
                 to
                 descend
                 into
                 the
                 valley
                 ,
                 and
                 ascend
                 to
                 the
                 other
                 Mountlaine
                 ,
                 the
                 water
                 will
                 runne
                 naturally
                 ,
                 and
                 continually
                 ,
                 provided
                 that
                 the
                 spring
                 be
                 somewhat
                 higher
                 than
                 the
                 passage
                 of
                 the
                 water
                 at
                 the
                 Inhabitants
                 .
              
            
             
               
                 5.
                 
                 Fifthly
                 ,
                 of
                 a
                 fine
                 Fountaine
                 which
                 spouts
                 water
                 very
                 high
                 ,
                 and
                 with
                 great
                 violence
                 by
                 turning
                 of
                 a
                 Cock.
                 
              
               
                 LEt
                 there
                 be
                 a
                 vessell
                 as
                 AB
                 ,
                 made
                 close
                 in
                 all
                 his
                 parts
                 ,
                 in
                 the
                 middle
                 of
                 which
                 let
                 CD
                 be
                 a
                 Pipe
                 open
                 at
                 D
                 neare
                 the
                 bottome
                 ,
                 and
                 then
                 with
                 a
                 Squirt
                 squirt
                 in
                 the
                 water
                 at
                 C
                 ,
                 stopped
                 above
                 by
                 the
                 cock
                 or
                 faucet
                 C
                 ,
                 vvith
                 as
                 great
                 violence
                 as
                 possible
                 you
                 can
                 ;
                 and
                 turne
                 the
                 cock
                 immediatly
                 .
                 
                 Novv
                 there
                 being
                 an
                 indifferent
                 quantity
                 of
                 vvater
                 and
                 aire
                 in
                 the
                 vessel
                 ,
                 the
                 vvater
                 keeps
                 it selfe
                 in
                 the
                 bottome
                 ,
                 and
                 the
                 aire
                 vvhich
                 vvas
                 greatly
                 pressed
                 ,
                 seeks
                 for
                 more
                 place
                 ,
                 that
                 
                 turning
                 the
                 Cock
                 the
                 water
                 issueth
                 forth
                 at
                 the
                 Pipe
                 ,
                 and
                 flyes
                 very
                 high
                 ,
                 and
                 that
                 especially
                 if
                 the
                 vessell
                 be
                 a
                 little
                 heated
                 :
                 some
                 make
                 use
                 of
                 this
                 for
                 an
                 Ewer
                 to
                 wash
                 hands
                 withall
                 ,
                 and
                 therefore
                 putting
                 a
                 moveable
                 Pipe
                 above
                 C
                 ,
                 such
                 as
                 the
                 figure
                 sheweth
                 :
                 which
                 the
                 water
                 will
                 cause
                 to
                 turne
                 very
                 quick
                 ,
                 pleasurable
                 to
                 behold
                 .
              
            
             
               
                 6.
                 
                 Sixtly
                 ,
                 of
                 Archimedes
                 screw
                 ,
                 which
                 makes
                 water
                 ascend
                 by
                 descending
                 .
              
               
                 THis
                 is
                 nothing
                 else
                 but
                 a
                 Cylinder
                 ,
                 about
                 the
                 which
                 is
                 a
                 Pipe
                 in
                 form
                 of
                 a
                 screw
                 ,
                 and
                 when
                 one
                 turnes
                 it
                 ,
                 the
                 water
                 descends
                 alwayes
                 in
                 respect
                 of
                 the
                 Pipe
                 :
                 for
                 it
                 passeth
                 from
                 one
                 part
                 which
                 is
                 higher
                 to
                 that
                 which
                 is
                 lower
                 ,
                 and
                 at
                 the
                 end
                 of
                 the
                 Engine
                 the
                 water
                 is
                 found
                 higher
                 than
                 it
                 was
                 at
                 the
                 spring
                 .
                 This
                 great
                 Enginer
                 admirable
                 in
                 all
                 Mathematicall
                 Arts
                 invented
                 this
                 Instrument
                 to
                 wash
                 King
                 Hieroies
                 
                 great
                 vessells
                 ,
                 as
                 some
                 Authors
                 saye
                 ,
                 also
                 to
                 water
                 the
                 fields
                 of
                 Egypt
                 ,
                 as
                 Diodorus
                 witnesseth
                 :
                 and
                 Cardanus
                 reporteth
                 that
                 a
                 Citizen
                 of
                 Milan
                 having
                 made
                 the
                 like
                 Engine
                 ,
                 thinking
                 himselfe
                 to
                 be
                 the
                 first
                 inventer
                 ,
                 conceived
                 such
                 exceeding
                 joy
                 ,
                 that
                 he
                 be
                 came
                 mad
                 ,
                 foll
                 .
                 2.
                 
              
               
                 Againe
                 a
                 thing
                 may
                 ascend
                 by
                 descending
                 ,
                 
                 if
                 a
                 spiral
                 line
                 be
                 made
                 having
                 many
                 circulations
                 or
                 revolutions
                 ;
                 the
                 last
                 being
                 alwayes
                 lesser
                 than
                 the
                 first
                 ,
                 yet
                 higher
                 than
                 the
                 Plaine
                 supposed
                 it
                 is
                 most
                 certaine
                 that
                 then
                 putting
                 a
                 ball
                 into
                 it
                 ,
                 and
                 turning
                 the
                 spirall
                 line
                 so
                 ,
                 that
                 the
                 first
                 circulation
                 may
                 be
                 perpendicular
                 ,
                 or
                 touch
                 alwayes
                 the
                 supposed
                 Plain
                 :
                 the
                 ball
                 shall
                 in
                 descending
                 continually
                 ascend
                 ,
                 untill
                 at
                 last
                 it
                 come
                 to
                 the
                 highest
                 part
                 of
                 the
                 spirall
                 line
                 ,
                 &
                 so
                 fall
                 out
                 .
                 And
                 here
                 especially
                 may
                 be
                 noted
                 ,
                 that
                 a
                 moving
                 body
                 as
                 water
                 ,
                 or
                 a
                 Bullet
                 ,
                 or
                 such
                 like
                 ,
                 will
                 never
                 ascend
                 if
                 the
                 Helicall
                 revolution
                 of
                 the
                 screw
                 be
                 not
                 inclining
                 to
                 the
                 Horizon
                 :
                 so
                 that
                 according
                 to
                 this
                 inclination
                 the
                 ball
                 or
                 liquor
                 ,
                 may
                 descend
                 alwayes
                 by
                 a
                 continuall
                 motion
                 and
                 revolution
                 .
                 And
                 this
                 experiment
                 may
                 be
                 more
                 usefull
                 ,
                 naturally
                 made
                 with
                 a
                 thred
                 of
                 ●ron
                 ,
                 or
                 Latine
                 turned
                 or
                 bowed
                 Helically
                 about
                 a
                 Cylinder
                 ,
                 with
                 some
                 distinction
                 of
                 distances
                 between
                 the
                 Heli●es
                 ,
                 for
                 then
                 having
                 drawn
                 out
                 the
                 Cylinder
                 ,
                 or
                 having
                 hung
                 or
                 tyed
                 some
                 weight
                 at
                 it
                 in
                 such
                 sort
                 ,
                 that
                 the
                 water
                 may
                 easily
                 drop
                 if
                 one
                 lift
                 up
                 the
                 said
                 thred
                 :
                 these
                 Helices
                 or
                 revolutions
                 ,
                 notwithstanding
                 will
                 remaine
                 inclining
                 to
                 the
                 Horizon
                 ,
                 and
                 then
                 turning
                 it
                 about
                 forward
                 ,
                 the
                 said
                 weight
                 will
                 ascend
                 ,
                 but
                 backward
                 it
                 will
                 descend
                 .
                 Now
                 if
                 the
                 revolutions
                 be
                 alike
                 ,
                 and
                 of
                 equallity
                 amongst
                 themselves
                 ,
                 and
                 the
                 whirling
                 or
                 turning
                 motion
                 be
                 quicke
                 ,
                 the
                 sight
                 vvill
                 be
                 so
                 deceived
                 ,
                 that
                 producing
                 the
                 action
                 it
                 vvill
                 seeme
                 to
                 the
                 ignorant
                 no
                 lesse
                 than
                 a
                 Miracle
                 .
              
            
             
               
               
                 7.
                 
                 Seventhly
                 ,
                 of
                 another
                 fine
                 Fountaine
                 of
                 pleasure
                 .
              
               
                 THis
                 is
                 an
                 Engine
                 that
                 hath
                 two
                 wheeles
                 with
                 Cogges
                 ,
                 or
                 teeth
                 as
                 AB
                 ,
                 which
                 are
                 placed
                 within
                 an
                 Ovall
                 CD
                 ,
                 in
                 such
                 sort
                 ,
                 that
                 the
                 teeth
                 of
                 the
                 one
                 ,
                 may
                 enter
                 into
                 the
                 notches
                 of
                 the
                 other
                 ;
                 but
                 so
                 just
                 that
                 neither
                 aire
                 nor
                 water
                 may
                 enter
                 into
                 the
                 Ovall
                 coffer
                 ,
                 either
                 by
                 the
                 middle
                 or
                 by
                 the
                 sides
                 ,
                 for
                 the
                 wheele
                 must
                 joyne
                 so
                 neare
                 to
                 the
                 sides
                 of
                 the
                 coffer
                 ,
                 that
                 there
                 be
                 no
                 vacuitie
                 :
                 to
                 this
                 there
                 is
                 an
                 axeltree
                 
                 with
                 a
                 handle
                 to
                 each
                 wheele
                 ,
                 so
                 that
                 they
                 may
                 be
                 turned
                 ,
                 and
                 A
                 being
                 turned
                 ,
                 that
                 turneth
                 the
                 other
                 wheele
                 that
                 is
                 opposite
                 :
                 by
                 which
                 motion
                 the
                 aire
                 that
                 is
                 in
                 E
                 ,
                 &
                 the
                 water
                 that
                 is
                 carried
                 by
                 the
                 hollow
                 of
                 the
                 wheeles
                 of
                 each
                 side
                 ,
                 by
                 continuall
                 motion
                 ,
                 is
                 constrained
                 to
                 mount
                 and
                 flie
                 out
                 by
                 the
                 funnell
                 F
                 :
                 now
                 to
                 make
                 the
                 water
                 runne
                 what
                 way
                 one
                 would
                 have
                 it
                 ,
                 there
                 may
                 be
                 applied
                 upon
                 the
                 top
                 of
                 the
                 Pipe
                 F
                 ,
                 two
                 other
                 moveable
                 Pipes
                 inserted
                 one
                 within
                 another
                 ;
                 as
                 the
                 figure
                 sheweth
                 .
                 But
                 here
                 note
                 ,
                 that
                 there
                 may
                 acrue
                 some
                 inconveniency
                 in
                 this
                 Machine
                 seeing
                 that
                 by
                 quick
                 turning
                 the
                 Cogges
                 
                 or
                 teeth
                 of
                 the
                 wheeles
                 running
                 one
                 against
                 another
                 ,
                 may
                 neare
                 break
                 them
                 ,
                 and
                 so
                 give
                 way
                 to
                 the
                 aire
                 to
                 enter
                 in
                 ,
                 which
                 being
                 violently
                 inclosed
                 vvill
                 escape
                 to
                 occupie
                 the
                 place
                 of
                 the
                 vvater
                 ,
                 vvhose
                 vveight
                 makes
                 it
                 so
                 quick
                 :
                 hovvsoever
                 ,
                 if
                 this
                 Machine
                 be
                 curiously
                 made
                 as
                 an
                 able
                 vvorkeman
                 may
                 easily
                 do
                 ,
                 it
                 is
                 a
                 most
                 sovereigne
                 Engine
                 ,
                 to
                 cast
                 vvater
                 high
                 and
                 farre
                 off
                 for
                 to
                 quench
                 fires
                 .
                 And
                 to
                 have
                 it
                 to
                 raine
                 to
                 a
                 place
                 assigned
                 ,
                 accommodate
                 a
                 socket
                 having
                 a
                 Pipe
                 at
                 the
                 middle
                 ,
                 vvhich
                 may
                 point
                 tovvards
                 the
                 place
                 being
                 set
                 at
                 the
                 top
                 thereof
                 ,
                 and
                 so
                 having
                 great
                 discretion
                 in
                 turning
                 the
                 Axis
                 of
                 the
                 vvheele
                 ,
                 it
                 may
                 vvork
                 exceeding
                 vvell
                 ,
                 and
                 continue
                 long
                 .
              
            
             
               
                 8.
                 
                 Eightly
                 ,
                 of
                 a
                 fine
                 watering
                 pot
                 for
                 gardens
                 .
              
               
                 THis
                 may
                 be
                 made
                 in
                 forme
                 of
                 a
                 Bottle
                 according
                 to
                 the
                 last
                 figure
                 or
                 such
                 like
                 ,
                 having
                 at
                 the
                 bottome
                 many
                 small
                 holes
                 ,
                 and
                 at
                 the
                 neck
                 of
                 it
                 another
                 hole
                 somevvhat
                 greater
                 than
                 those
                 at
                 the
                 bottome
                 ,
                 vvhich
                 hole
                 at
                 the
                 top
                 you
                 must
                 unstop
                 vvhen
                 you
                 vvould
                 fill
                 this
                 vvatering
                 pot
                 ,
                 for
                 then
                 it
                 is
                 nothing
                 but
                 putting
                 the
                 lovver
                 end
                 into
                 a
                 paile
                 of
                 vvater
                 ,
                 for
                 so
                 it
                 vvill
                 fill
                 it selfe
                 by
                 degrees
                 :
                 and
                 being
                 full
                 ,
                 put
                 your
                 thumb
                 on
                 the
                 hole
                 at
                 the
                 neck
                 to
                 stop
                 it
                 ,
                 for
                 then
                 may
                 you
                 carry
                 it
                 from
                 place
                 to
                 place
                 ,
                 and
                 it
                 vvill
                 not
                 sensibly
                 runne
                 out
                 ,
                 som●thing
                 it
                 vvill
                 ,
                 and
                 all
                 in
                 time
                 (
                 if
                 it
                 vvere
                 never
                 so
                 close
                 stopped
                 )
                 contrary
                 to
                 the
                 ancient
                 tenet
                 in
                 Philosophy
                 ,
                 that
                 aire
                 will
                 not
                 penetrate
                 .
              
            
             
               
               
                 9.
                 
                 Ninthly
                 ,
                 how
                 easily
                 to
                 take
                 wine
                 out
                 of
                 a
                 vessell
                 at
                 the
                 bu●g-hole
                 ,
                 without
                 piercing
                 of
                 a
                 hole
                 in
                 the
                 vessell
                 ?
              
               
                 IN
                 this
                 there
                 is
                 no
                 need
                 but
                 to
                 have
                 a
                 Cane
                 or
                 Pipe
                 of
                 Glasse
                 or
                 such
                 like
                 ,
                 one
                 of
                 the
                 ends
                 of
                 which
                 may
                 be
                 closed
                 up
                 almost
                 ,
                 leaving
                 some
                 small
                 hole
                 at
                 the
                 end
                 ;
                 for
                 then
                 if
                 that
                 end
                 be
                 set
                 into
                 the
                 vessell
                 at
                 the
                 bung-hole
                 ,
                 the
                 whole
                 
                 Cane
                 or
                 Pipe
                 will
                 be
                 filled
                 by
                 little
                 and
                 little
                 ;
                 and
                 once
                 being
                 full
                 ,
                 stop
                 the
                 other
                 end
                 which
                 is
                 without
                 and
                 then
                 pull
                 out
                 the
                 Cane
                 or
                 Pipe
                 ,
                 so
                 will
                 it
                 be
                 ful
                 of
                 wine
                 ,
                 then
                 opening
                 a
                 little
                 the
                 top
                 above
                 ,
                 you
                 may
                 fill
                 a
                 Glasse
                 or
                 other
                 Pot
                 with
                 it
                 ,
                 for
                 as
                 the
                 Wine
                 issueth
                 out
                 ,
                 the
                 aire
                 commeth
                 into
                 the
                 Cane
                 or
                 Pipe
                 to
                 supply
                 vacuity
                 .
              
            
             
               
                 10.
                 
                 Tenthly
                 ,
                 how
                 to
                 measure
                 irregular
                 bodies
                 by
                 help
                 of
                 water
                 ?
              
               
                 SOme
                 throw
                 in
                 the
                 body
                 or
                 magnitude
                 into
                 a
                 vessell
                 ,
                 and
                 keep
                 that
                 which
                 floweth
                 out
                 over
                 ,
                 saying
                 it
                 is
                 alwayes
                 equal
                 to
                 the
                 thing
                 cast
                 into
                 the
                 water
                 :
                 let
                 i●
                 is
                 more
                 nea●er
                 this
                 way
                 to
                 poure
                 into
                 a
                 vessell
                 such
                 a
                 quantity
                 of
                 water
                 ,
                 
                 which
                 may
                 be
                 thought
                 sufficient
                 to
                 cover
                 the
                 body
                 or
                 magnitude
                 ,
                 and
                 make
                 a
                 marke
                 how
                 high
                 the
                 water
                 is
                 in
                 the
                 vessell
                 ,
                 then
                 poure
                 out
                 all
                 this
                 water
                 into
                 another
                 vessell
                 ,
                 and
                 let
                 the
                 body
                 or
                 magnitude
                 be
                 placed
                 into
                 the
                 first
                 vessel
                 ;
                 then
                 poure
                 in
                 water
                 from
                 the
                 second
                 vessell
                 ,
                 until
                 it
                 ascend
                 unto
                 the
                 former
                 marke
                 made
                 in
                 the
                 first
                 vessell
                 ,
                 so
                 the
                 vvater
                 vvhich
                 remaines
                 in
                 the
                 second
                 vessel
                 is
                 equall
                 to
                 the
                 body
                 or
                 magnitude
                 put
                 into
                 the
                 water
                 :
                 but
                 here
                 note
                 that
                 this
                 is
                 not
                 exact
                 or
                 free
                 from
                 error
                 ,
                 yet
                 nearer
                 the
                 truth
                 than
                 any
                 Geometrician
                 can
                 otherwise
                 possibly
                 measure
                 ,
                 and
                 these
                 bodies
                 that
                 are
                 not
                 so
                 full
                 of
                 pores
                 are
                 more
                 truly
                 measured
                 this
                 way
                 ,
                 than
                 others
                 are
                 .
              
            
             
               
                 11.
                 
                 To
                 finde
                 the
                 weight
                 of
                 water
                 .
              
               
                 SEeing
                 that
                 574
                 /
                 1000
                 part
                 of
                 an
                 ounce
                 weight
                 ,
                 makes
                 a
                 cubicall
                 inch
                 of
                 water
                 :
                 and
                 every
                 pound
                 weight
                 Haverdepoize
                 makes
                 27
                 cubicall
                 inches
                 ,
                 and
                 1
                 9
                 /
                 ●
                 ;
                 fere
                 ,
                 and
                 that
                 ●
                 Gallons
                 and
                 a
                 halfe
                 wine
                 measure
                 makes
                 a
                 foot
                 cubicall
                 ,
                 it
                 is
                 easie
                 by
                 inversion
                 ,
                 that
                 knowing
                 the
                 quantity
                 of
                 a
                 vessel
                 in
                 Gallons
                 ,
                 to
                 finde
                 his
                 content
                 in
                 cubicall
                 feet
                 or
                 weight
                 :
                 and
                 that
                 late
                 famous
                 Geometrician
                 Master
                 Brigs
                 found
                 a
                 cubical
                 foot
                 of
                 vvater
                 to
                 vveigh
                 neare
                 62
                 pound
                 vveight
                 Haverdepoize
                 But
                 the
                 late
                 learned
                 
                   Simon
                   Stevin
                
                 found
                 a
                 cubicall
                 foot
                 of
                 vvater
                 to
                 vveigh
                 65
                 pound
                 ,
                 vvhich
                 difference
                 may
                 arise
                 from
                 the
                 inequalitie
                 of
                 vvater
                 ;
                 for
                 some
                 vvaters
                 are
                 more
                 ponderous
                 than
                 others
                 ,
                 and
                 some
                 difference
                 
                 may
                 be
                 from
                 the
                 weight
                 of
                 a
                 pound
                 ,
                 and
                 the
                 measure
                 of
                 a
                 foot
                 :
                 thus
                 the
                 weight
                 and
                 quantitie
                 of
                 a
                 solid
                 foot
                 settled
                 ,
                 it
                 is
                 easie
                 for
                 Arithmeticians
                 to
                 give
                 the
                 contents
                 of
                 vessells
                 or
                 bodies
                 which
                 containe
                 liquids
                 .
              
            
             
               
                 12.
                 
                 To
                 finde
                 the
                 charge
                 that
                 a
                 vessell
                 may
                 carry
                 as
                 Shippes
                 ,
                 Boates
                 ,
                 or
                 such
                 like
                 .
              
               
                 THis
                 is
                 generally
                 conceived
                 ,
                 that
                 a
                 vessell
                 may
                 carry
                 as
                 much
                 weight
                 as
                 that
                 water
                 weigheth
                 ,
                 which
                 is
                 equall
                 unto
                 the
                 vessell
                 in
                 bignesse
                 ,
                 in
                 abating
                 onely
                 the
                 weight
                 of
                 the
                 vessell
                 :
                 we
                 see
                 that
                 a
                 barrel
                 of
                 wine
                 or
                 water
                 cast
                 into
                 the
                 water
                 ,
                 will
                 not
                 sink
                 to
                 the
                 bottome
                 ,
                 but
                 swim
                 easily
                 ,
                 and
                 if
                 a
                 ship
                 had
                 not
                 Iron
                 and
                 other
                 ponderosities
                 in
                 it
                 ,
                 it
                 might
                 swim
                 full
                 of
                 water
                 without
                 sinking
                 :
                 in
                 the
                 same
                 manner
                 if
                 the
                 vessell
                 were
                 loaden
                 with
                 lead
                 ,
                 so
                 much
                 should
                 the
                 watter
                 weigh
                 :
                 hence
                 it
                 is
                 that
                 Marriners
                 call
                 Shippes
                 of
                 50
                 thousand
                 Tunnes
                 ,
                 because
                 they
                 may
                 containe
                 one
                 or
                 two
                 thousand
                 Tunne
                 ,
                 and
                 so
                 consequently
                 carry
                 as
                 much
                 .
              
            
             
               
                 13.
                 
                 How
                 comes
                 it
                 that
                 a
                 Shippe
                 having
                 safely
                 sayled
                 in
                 the
                 vast
                 Ocean
                 ,
                 and
                 being
                 come
                 into
                 the
                 Port
                 or
                 harbour
                 ,
                 without
                 any
                 tempest
                 will
                 sink
                 down
                 right
                 ?
              
               
                 THe
                 cause
                 of
                 this
                 is
                 that
                 a
                 vessel
                 may
                 carry
                 more
                 upon
                 some
                 kinde
                 of
                 water
                 than
                 upon
                 other
                 ;
                 now
                 the
                 water
                 of
                 the
                 Sea
                 is
                 thicker
                 and
                 heavier
                 than
                 that
                 of
                 Rivers
                 ,
                 Wels
                 ,
                 or
                 Fountains
                 ;
                 
                 therefore
                 the
                 loading
                 of
                 a
                 vessell
                 which
                 is
                 accounted
                 sufficient
                 in
                 the
                 Sea
                 ,
                 becomes
                 too
                 great
                 in
                 the
                 hurbour
                 or
                 sweet
                 water
                 .
                 Now
                 some
                 think
                 that
                 it
                 is
                 the
                 depth
                 of
                 the
                 water
                 that
                 makes
                 vessells
                 more
                 easie
                 to
                 swimme
                 ,
                 but
                 it
                 is
                 an
                 abuse
                 ;
                 for
                 if
                 the
                 loading
                 of
                 a
                 Ship
                 be
                 no
                 heavier
                 than
                 the
                 water
                 that
                 would
                 occupie
                 that
                 place
                 ,
                 the
                 Ship
                 should
                 as
                 easily
                 swim
                 upon
                 that
                 water
                 ,
                 as
                 if
                 it
                 did
                 swim
                 upon
                 a
                 thousand
                 fathom
                 deep
                 of
                 water
                 ,
                 and
                 if
                 the
                 vvater
                 be
                 no
                 thicker
                 than
                 a
                 leafe
                 of
                 paper
                 ,
                 and
                 weigheth
                 but
                 an
                 ounce
                 under
                 a
                 heavy
                 body
                 ,
                 it
                 vvill
                 support
                 it
                 ,
                 as
                 vvell
                 as
                 if
                 the
                 vvater
                 under
                 it
                 vveighed
                 ten
                 thousand
                 pound
                 vveight
                 :
                 hence
                 it
                 is
                 if
                 there
                 be
                 a
                 vessell
                 capable
                 of
                 a
                 little
                 more
                 than
                 a
                 thousand
                 pound
                 vveight
                 of
                 vvater
                 ,
                 you
                 may
                 put
                 into
                 this
                 vessell
                 a
                 piece
                 of
                 vvood
                 ,
                 vvhich
                 shall
                 vveigh
                 a
                 thousand
                 pound
                 vveight
                 ;
                 (
                 but
                 lighter
                 in
                 his
                 kinde
                 than
                 the
                 like
                 of
                 magnitude
                 of
                 vvater
                 :
                 )
                 for
                 then
                 pouring
                 in
                 but
                 a
                 quart
                 of
                 vvater
                 or
                 a
                 very
                 little
                 quantitie
                 of
                 vvater
                 ,
                 the
                 vvood
                 vvill
                 svvim
                 on
                 the
                 top
                 of
                 it
                 ,
                 (
                 provided
                 that
                 the
                 vvood
                 touch
                 not
                 the
                 sides
                 of
                 the
                 vessell
                 :
                 )
                 vvhich
                 is
                 a
                 fine
                 experiment
                 ,
                 and
                 seems
                 admirable
                 in
                 the
                 performance
                 .
              
            
             
               
                 14.
                 
                 How
                 a
                 grosse
                 body
                 of
                 mettle
                 may
                 swimme
                 upon
                 the
                 water
                 ?
              
               
                 THis
                 is
                 done
                 by
                 extending
                 the
                 mettle
                 into
                 a
                 thin
                 Plate
                 ,
                 to
                 make
                 it
                 hollovv
                 in
                 forme
                 of
                 a
                 vessel
                 ;
                 so
                 that
                 the
                 greatnesse
                 of
                 the
                 vessell
                 which
                 the
                 aire
                 vvith
                 it
                 containeth
                 ,
                 be
                 equal
                 to
                 
                 the
                 magnitude
                 of
                 the
                 vvater
                 ,
                 vvhich
                 vveighes
                 as
                 much
                 as
                 it
                 ,
                 for
                 all
                 bodies
                 may
                 svvim
                 vvithout
                 sinking
                 ,
                 if
                 they
                 occupie
                 the
                 place
                 of
                 vvater
                 equal
                 in
                 vveight
                 unto
                 them
                 ,
                 as
                 if
                 it
                 vveighed
                 12
                 pound
                 it
                 must
                 have
                 the
                 place
                 of
                 12
                 pound
                 of
                 vvater
                 :
                 hence
                 it
                 is
                 that
                 vve
                 see
                 floating
                 upon
                 the
                 vvater
                 great
                 vessells
                 of
                 Copper
                 or
                 Brasse
                 ,
                 vvhen
                 they
                 are
                 hollovv
                 in
                 forme
                 of
                 a
                 Caldron
                 .
                 And
                 how
                 can
                 it
                 be
                 otherwise
                 conceived
                 of
                 Islands
                 in
                 the
                 Sea
                 that
                 swim
                 and
                 float
                 ?
                 is
                 it
                 not
                 that
                 they
                 are
                 hollow
                 and
                 some
                 part
                 like
                 unto
                 a
                 Boat
                 ,
                 or
                 that
                 their
                 earth
                 is
                 very
                 light
                 and
                 spongeous
                 ,
                 or
                 having
                 many
                 concavities
                 in
                 the
                 body
                 of
                 it
                 ,
                 or
                 much
                 wood
                 within
                 it
                 ?
              
               
                 And
                 it
                 would
                 be
                 a
                 pretty
                 proposition
                 to
                 shew
                 how
                 much
                 every
                 kinde
                 of
                 metall
                 should
                 be
                 inlarged
                 ,
                 to
                 make
                 it
                 swim
                 upon
                 the
                 water
                 :
                 which
                 doth
                 depend
                 upon
                 the
                 proportion
                 that
                 is
                 between
                 the
                 vveight
                 of
                 the
                 vvater
                 and
                 each
                 metall
                 .
                 Novv
                 the
                 proportion
                 that
                 is
                 betvveene
                 metalls
                 and
                 water
                 of
                 equall
                 magnitude
                 ,
                 according
                 to
                 some
                 Authors
                 ,
                 is
                 as
                 followeth
                 .
              
               
                 A
                 magnitude
                 of
                 10
                 pound
                 weight
                 of
                 water
                 will
                 require
                 for
                 the
                 like
                 magnitude
                 of
                 
                   
                     Gold.
                     
                  
                   
                     187
                     ½
                  
                   
                     Lead
                     .
                  
                   
                     116
                     ½
                  
                   
                     Silver
                     .
                  
                   
                     104
                  
                   
                     Copper
                     .
                  
                   
                     91
                  
                   
                     Iron
                     .
                  
                   
                     81
                  
                   
                     Tinne
                     .
                  
                   
                     75
                  
                
              
               
                 From
                 which
                 is
                 inferred
                 ,
                 that
                 to
                 make
                 a
                 piece
                 of
                 Copper
                 of
                 ●0
                 pound
                 weight
                 to
                 swimme
                 ,
                 it
                 must
                 be
                 so
                 made
                 hollow
                 ,
                 that
                 it
                 may
                 hold
                 9
                 times
                 that
                 weight
                 of
                 water
                 and
                 somewhat
                 more
                 ,
                 that
                 is
                 to
                 say
                 ,
                 91
                 pound
                 :
                 seeing
                 that
                 Copper
                 
                 and
                 water
                 of
                 like
                 magnitudes
                 in
                 their
                 ponderosities
                 ,
                 are
                 as
                 before
                 ,
                 as
                 ●0
                 to
                 91.
                 
              
            
             
               
                 15.
                 
                 How
                 to
                 weigh
                 the
                 lightnesse
                 of
                 the
                 aire
                 ?
              
               
                 PLace
                 a
                 Ballance
                 of
                 wood
                 turned
                 upside
                 downe
                 into
                 the
                 water
                 ,
                 that
                 so
                 it
                 may
                 swim
                 ,
                 then
                 let
                 water
                 be
                 inclosed
                 within
                 some
                 body
                 ,
                 as
                 within
                 a
                 Bladder
                 or
                 such
                 like
                 ,
                 and
                 suppose
                 that
                 such
                 a
                 quantitie
                 of
                 aire
                 should
                 weigh
                 one
                 pound
                 ,
                 place
                 it
                 under
                 one
                 of
                 the
                 Ballances
                 ,
                 and
                 place
                 under
                 the
                 other
                 as
                 much
                 weight
                 of
                 lightnesse
                 as
                 may
                 counter-ballance
                 and
                 keep
                 the
                 other
                 Ballance
                 that
                 it
                 rise
                 not
                 out
                 of
                 the
                 water
                 :
                 by
                 which
                 you
                 shall
                 see
                 how
                 much
                 the
                 lightnesse
                 is
                 .
              
               
                 But
                 without
                 any
                 Ballance
                 do
                 this
                 ;
                 take
                 a
                 Cubicall
                 hollow
                 vessell
                 ,
                 or
                 that
                 which
                 is
                 Cylindricall
                 ,
                 which
                 may
                 swimme
                 on
                 the
                 water
                 ,
                 and
                 as
                 it
                 sinketh
                 by
                 placing
                 of
                 weights
                 upon
                 it
                 ,
                 marke
                 hovv
                 much
                 ,
                 for
                 then
                 if
                 you
                 vvould
                 examine
                 the
                 vveight
                 of
                 any
                 body
                 ,
                 you
                 have
                 nothing
                 to
                 do
                 but
                 to
                 put
                 it
                 into
                 this
                 vessell
                 ,
                 and
                 marke
                 hovv
                 deep
                 it
                 sinkes
                 ,
                 for
                 so
                 many
                 pound
                 it
                 vveighes
                 as
                 the
                 vveights
                 put
                 in
                 do
                 make
                 it
                 so
                 to
                 sinke
                 .
              
               
            
             
               
               
                 16.
                 
                 Being
                 given
                 a
                 body
                 ,
                 to
                 marke
                 it
                 about
                 ,
                 and
                 shew
                 how
                 much
                 of
                 it
                 will
                 sink
                 in
                 the
                 water
                 ,
                 or
                 swim
                 above
                 the
                 water
                 .
              
               
                 THis
                 is
                 done
                 by
                 knovving
                 the
                 vveight
                 of
                 the
                 body
                 vvhich
                 is
                 given
                 ,
                 and
                 the
                 quantity
                 of
                 vvater
                 ,
                 vvhich
                 vveighes
                 as
                 much
                 as
                 that
                 body
                 ;
                 for
                 then
                 certainly
                 it
                 vvill
                 sink
                 so
                 deep
                 ,
                 untill
                 it
                 occupieth
                 the
                 place
                 of
                 that
                 quantitie
                 of
                 vvater
                 .
              
            
             
               
                 17.
                 
                 To
                 finde
                 how
                 much
                 severall
                 mettle
                 or
                 other
                 bodies
                 doe
                 weigh
                 lesse
                 in
                 the
                 water
                 than
                 in
                 the
                 aire
                 :
              
               
                 TAke
                 a
                 Ballance
                 ,
                 &
                 vveigh
                 (
                 as
                 for
                 example
                 )
                 9
                 pound
                 of
                 Gold
                 ,
                 Silver
                 ,
                 Lead
                 ,
                 or
                 Stone
                 in
                 the
                 aire
                 ,
                 so
                 it
                 hang
                 in
                 aequilibrio
                 ;
                 then
                 comming
                 to
                 the
                 vvater
                 ,
                 take
                 the
                 same
                 quantity
                 of
                 Gold
                 Silver
                 ,
                 Lead
                 ,
                 or
                 Stone
                 ,
                 and
                 let
                 it
                 softly
                 dovvne
                 into
                 it
                 ,
                 and
                 you
                 shall
                 see
                 that
                 you
                 shall
                 need
                 a
                 lesse
                 counterpoise
                 in
                 the
                 other
                 Ballance
                 to
                 counter-ballance
                 it
                 :
                 vvherefore
                 all
                 solids
                 or
                 bodies
                 vveigh
                 lesse
                 in
                 the
                 vvater
                 than
                 in
                 the
                 aire
                 ,
                 and
                 so
                 much
                 the
                 lesse
                 it
                 vvill
                 be
                 ,
                 by
                 hovv
                 much
                 the
                 vvater
                 is
                 grosse
                 and
                 thick
                 ,
                 because
                 the
                 vveight
                 findes
                 a
                 greater
                 resistance
                 ,
                 and
                 therefore
                 the
                 vvater
                 supports
                 more
                 than
                 aire
                 ;
                 and
                 further
                 ,
                 because
                 the
                 vvater
                 by
                 the
                 ponderositie
                 is
                 displeased
                 ,
                 and
                 so
                 strives
                 to
                 be
                 there
                 againe
                 ,
                 pressing
                 to
                 it
                 ,
                 by
                 reason
                 of
                 the
                 other
                 vvaters
                 that
                 are
                 about
                 it
                 ,
                 according
                 to
                 the
                 proportion
                 of
                 
                 his
                 weight
                 .
                 Archimedes
                 demonstrateth
                 ,
                 that
                 all
                 bodies
                 weigh
                 lesse
                 in
                 the
                 water
                 (
                 or
                 in
                 like
                 liquor
                 )
                 by
                 how
                 much
                 they
                 occupie
                 place
                 :
                 and
                 if
                 the
                 water
                 weigh
                 a
                 pound
                 weight
                 ,
                 the
                 magnitude
                 in
                 the
                 water
                 shall
                 weigh
                 a
                 pound
                 lesse
                 than
                 in
                 the
                 aire
                 .
              
               
                 Now
                 by
                 knowing
                 the
                 proportion
                 of
                 water
                 and
                 mettles
                 ,
                 it
                 is
                 found
                 that
                 Gold
                 loseth
                 in
                 the
                 water
                 the
                 19
                 part
                 of
                 his
                 weight
                 ,
                 Copper
                 the
                 9
                 part
                 ,
                 Quicksilver
                 the
                 15
                 part
                 ,
                 Lead
                 the
                 12
                 part
                 ,
                 Silver
                 the
                 10
                 part
                 ,
                 Iron
                 the
                 8
                 part
                 ,
                 Tinne
                 the
                 7
                 part
                 and
                 a
                 little
                 more
                 :
                 wherefore
                 in
                 materiall
                 and
                 absolute
                 weight
                 ,
                 Gold
                 in
                 respect
                 of
                 the
                 water
                 that
                 it
                 occupieth
                 weigheth
                 18
                 ,
                 and
                 ¾
                 times
                 heavier
                 than
                 the
                 like
                 quantitie
                 of
                 water
                 ,
                 that
                 is
                 ,
                 as
                 18
                 ¾
                 to
                 the
                 Quicksilver
                 15
                 times
                 ,
                 Lead
                 11
                 and
                 ⅗
                 ,
                 Silver
                 10
                 and
                 ⅔
                 ,
                 Copper
                 9
                 and
                 1
                 /
                 10
                 ,
                 Iron
                 8
                 and
                 ½
                 ,
                 and
                 Tinne
                 8
                 and
                 1
                 /
                 ●
                 .
                 Contrarily
                 in
                 respect
                 of
                 greatnesse
                 ,
                 if
                 the
                 water
                 be
                 as
                 heavy
                 as
                 the
                 Gold
                 ,
                 then
                 is
                 the
                 water
                 almost
                 19
                 times
                 greater
                 than
                 the
                 magnitude
                 of
                 the
                 Gold
                 ,
                 and
                 so
                 may
                 you
                 judge
                 of
                 the
                 rest
                 .
              
            
             
               
                 18.
                 
                 How
                 is
                 it
                 that
                 a
                 ballance
                 having
                 like
                 weight
                 in
                 each
                 scale
                 ,
                 and
                 hanging
                 
                   in
                   aequilibrio
                
                 in
                 the
                 aire
                 ,
                 being
                 placed
                 in
                 another
                 place
                 ,
                 (
                 without
                 removing
                 any
                 weight
                 )
                 it
                 shall
                 cease
                 to
                 hang
                 
                   in
                   aequilibrio
                
                 sensibly
                 :
                 yea
                 by
                 a
                 great
                 difference
                 of
                 weight
                 ?
              
               
                 THis
                 is
                 easie
                 to
                 be
                 resolved
                 by
                 considering
                 different
                 mettles
                 ,
                 which
                 though
                 they
                 
                 vveigh
                 equall
                 in
                 the
                 aire
                 ,
                 yet
                 in
                 the
                 vvater
                 there
                 vvill
                 be
                 an
                 apparant
                 difference
                 ;
                 as
                 suppose
                 so
                 that
                 in
                 the
                 scale
                 of
                 each
                 Ballance
                 be
                 placed
                 18
                 pound
                 vveight
                 of
                 severall
                 metalls
                 ,
                 the
                 one
                 Gold
                 ,
                 and
                 the
                 other
                 Copper
                 ,
                 vvhich
                 being
                 
                   in
                   aequilibrio
                
                 in
                 the
                 aire
                 ,
                 placed
                 in
                 the
                 vvater
                 ,
                 vvill
                 not
                 hang
                 so
                 ,
                 because
                 that
                 the
                 Gold
                 los●eth
                 neare
                 the
                 18
                 part
                 of
                 his
                 vveight
                 ,
                 vvhich
                 is
                 about
                 1
                 pound
                 ,
                 and
                 the
                 Copper
                 loseth
                 but
                 his
                 9
                 part
                 ,
                 vvhich
                 is
                 2
                 pound
                 :
                 vvherefore
                 the
                 Gold
                 in
                 the
                 vvater
                 vveigheth
                 but
                 17
                 pound
                 ,
                 and
                 the
                 Copper
                 16
                 pound
                 ,
                 vvhich
                 is
                 a
                 difference
                 most
                 sensible
                 to
                 confirme
                 that
                 point
                 .
              
            
             
               
                 19.
                 
                 To
                 shew
                 what
                 waters
                 are
                 heavier
                 one
                 than
                 another
                 ,
                 and
                 how
                 much
                 .
              
               
                 PHysicians
                 have
                 an
                 especiall
                 respect
                 unto
                 this
                 ,
                 judging
                 that
                 vvater
                 vvhich
                 is
                 lightest
                 is
                 most
                 healthfull
                 and
                 medicinall
                 for
                 the
                 body
                 ,
                 &
                 Sea-men
                 knovv
                 that
                 the
                 heaviest
                 vvaters
                 do
                 beare
                 most
                 ,
                 and
                 it
                 is
                 knovvne
                 vvhich
                 water
                 is
                 heaviest
                 thus
                 .
                 Take
                 a
                 piece
                 of
                 wax
                 ,
                 and
                 fasten
                 Lead
                 unto
                 it
                 ,
                 or
                 some
                 such
                 like
                 thing
                 that
                 it
                 may
                 but
                 precisely
                 swimme
                 ,
                 for
                 then
                 it
                 is
                 equal
                 to
                 the
                 like
                 magnitude
                 of
                 water
                 ,
                 then
                 put
                 it
                 into
                 another
                 vessell
                 which
                 hath
                 contrary
                 water
                 ,
                 and
                 if
                 it
                 sinke
                 ,
                 then
                 is
                 that
                 water
                 lighter
                 than
                 the
                 other
                 :
                 but
                 if
                 it
                 sinke
                 not
                 so
                 deep
                 ,
                 then
                 it
                 argueth
                 the
                 water
                 to
                 be
                 heavier
                 or
                 more
                 grosser
                 than
                 the
                 first
                 water
                 ,
                 or
                 one
                 may
                 take
                 a
                 piece
                 of
                 vvood
                 ,
                 and
                 marke
                 the
                 quantitie
                 of
                 sinking
                 of
                 it
                 into
                 severall
                 waters
                 ,
                 by
                 vvhich
                 you
                 may
                 judge
                 
                 which
                 is
                 lightest
                 or
                 heaviest
                 ,
                 for
                 in
                 that
                 which
                 it
                 sinkes
                 most
                 ,
                 that
                 is
                 infallibly
                 the
                 lightest
                 ,
                 and
                 so
                 contrarily
                 .
              
            
             
               
                 20.
                 
                 How
                 to
                 make
                 a
                 Pound
                 of
                 water
                 weigh
                 as
                 much
                 as
                 
                   10
                   ,
                   2●
                   ,
                   ●0
                
                 ,
                 or
                 a
                 hundred
                 pound
                 of
                 Lead
                 ;
                 nay
                 as
                 much
                 as
                 a
                 thousand
                 ,
                 or
                 ten
                 thousand
                 and
                 pound
                 weight
                 ?
              
               
                 THis
                 proposition
                 seems
                 very
                 impossible
                 ,
                 yet
                 water
                 inclosed
                 in
                 a
                 vessell
                 ,
                 being
                 constrained
                 to
                 dilate
                 it selfe
                 ,
                 doth
                 weigh
                 so
                 much
                 as
                 though
                 there
                 were
                 in
                 the
                 concavitie
                 of
                 it
                 a
                 solid
                 body
                 of
                 water
                 .
              
               
                 There
                 are
                 many
                 wayes
                 to
                 experiment
                 this
                 proposition
                 ,
                 but
                 to
                 verifie
                 it
                 ,
                 it
                 may
                 be
                 sufficient
                 to
                 produce
                 two
                 excellent
                 ones
                 onely
                 :
                 which
                 had
                 they
                 not
                 been
                 really
                 acted
                 ,
                 little
                 credit
                 might
                 have
                 been
                 given
                 unto
                 it
                 .
              
               
                 The
                 first
                 way
                 is
                 thus
                 .
                 Take
                 a
                 Magnitude
                 which
                 takes
                 up
                 as
                 much
                 place
                 as
                 a
                 hundred
                 or
                 a
                 thousand
                 pound
                 of
                 water
                 ,
                 and
                 suppose
                 that
                 it
                 were
                 tied
                 to
                 some
                 thing
                 that
                 it
                 may
                 hang
                 in
                 the
                 aire
                 ;
                 then
                 make
                 a
                 Ballance
                 that
                 one
                 of
                 the
                 scales
                 may
                 inviron
                 it
                 ,
                 yet
                 so
                 that
                 it
                 touch
                 not
                 the
                 sides
                 of
                 it
                 :
                 but
                 leave
                 space
                 enough
                 for
                 one
                 pound
                 of
                 water
                 :
                 then
                 having
                 placed
                 100
                 pound
                 weight
                 in
                 the
                 other
                 scale
                 ,
                 throw
                 in
                 the
                 water
                 about
                 the
                 Magnitude
                 ,
                 so
                 that
                 one
                 pound
                 of
                 water
                 shall
                 weigh
                 downe
                 the
                 hundred
                 pound
                 in
                 the
                 other
                 Ballance
                 .
              
               
            
          
           
             
               PROBLEM
               .
               LXXXVI
               .
               Of
               sundry
               Questions
               of
               Arithmetick
               ,
               and
               first
               of
               the
               number
               of
               sands
               .
            
             
               IT
               may
               be
               said
               incontinent
               ,
               that
               to
               undertake
               this
               were
               impossible
               ,
               either
               to
               number
               the
               Sands
               of
               Lybia
               ,
               or
               the
               Sands
               of
               the
               Sea
               ;
               and
               it
               vvas
               this
               that
               the
               Poets
               sung
               ,
               and
               that
               vvhich
               the
               vulgar
               beleeves
               ;
               nay
               ,
               that
               vvhich
               long
               ago
               certaine
               Philosophers
               to
               Gelon
               King
               of
               Sicily
               
               reported
               ,
               that
               the
               graines
               of
               sand
               vvere
               innumerable
               :
               But
               I
               ansvvere
               vvith
               Archimedes
               ,
               that
               not
               only
               one
               may
               number
               those
               vvhich
               are
               at
               the
               border
               and
               about
               the
               Sea
               ;
               but
               those
               vvhich
               are
               able
               to
               fill
               the
               vvhole
               vvorld
               ,
               if
               there
               vvere
               nothing
               else
               but
               sand
               ;
               and
               the
               graines
               of
               sands
               admitted
               to
               be
               so
               small
               ,
               that
               10
               may
               make
               but
               one
               graine
               of
               Poppy
               :
               for
               at
               the
               end
               of
               the
               account
               there
               need
               not
               to
               expresse
               them
               ,
               but
               this
               number
               30840979456
               ,
               and
               35
               Ciphers
               at
               the
               end
               of
               it
               .
               Clavius
               and
               Archimedes
               make
               it
               somevvhat
               more
               ;
               because
               they
               make
               a
               greater
               firmament
               than
               
                 Ticho
                 Brahe
              
               doth
               ;
               and
               if
               they
               augment
               the
               Vniverse
               ,
               it
               is
               easie
               for
               us
               to
               augment
               the
               number
               ,
               and
               declare
               assuredly
               how
               many
               graines
               of
               sand
               there
               are
               requisite
               to
               fill
               another
               vvorld
               ,
               in
               comparison
               that
               our
               visible
               vvorld
               vvere
               but
               as
               one
               graine
               of
               sand
               ,
               an
               atome
               or
               a
               point
               ;
               for
               there
               is
               nothing
               to
               do
               but
               to
               multiply
               the
               number
               by
               it selfe
               ,
               vvhich
               vvill
               amount
               to
               ninety
               places
               ,
               vvhereof
               tvventie
               are
               these
               ,
               95143798134910955936
               ,
               and
               70
               Ciphers
               at
               the
               end
               of
               it
               :
               vvhich
               amounts
               to
               a
               most
               prodigious
               number
               ,
               and
               is
               easily
               supputated
               :
               for
               supposing
               that
               a
               graine
               of
               Poppy
               doth
               containe
               10
               graines
               of
               sand
               ,
               there
               is
               nothing
               but
               to
               compare
               that
               little
               bovvle
               of
               a
               graine
               of
               Poppy
               ,
               vvith
               a
               bovvle
               of
               an
               inch
               or
               of
               a
               foot
               ,
               &
               that
               to
               be
               compared
               vvith
               that
               of
               the
               earth
               ,
               and
               then
               that
               of
               the
               earth
               vvith
               that
               o
               the
               firmament
               ;
               and
               so
               of
               the
               rest
               .
            
             
               
               
                 2.
                 
                 Divers
                 metalls
                 being
                 melted
                 together
                 in
                 one
                 body
                 ,
                 to
                 finde
                 the
                 mixture
                 of
                 them
                 .
              
               
                 THis
                 wat
                 a
                 notable
                 invention
                 of
                 Archimedes
                 ,
                 related
                 by
                 Vitrivius
                 in
                 his
                 Architecture
                 ,
                 where
                 he
                 reporteth
                 that
                 the
                 Gold-smith
                 which
                 King
                 Hiero
                 imployed
                 for
                 the
                 making
                 of
                 the
                 Golden
                 Crowne
                 ,
                 which
                 was
                 to
                 be
                 dedicated
                 to
                 the
                 gods
                 ,
                 had
                 stolen
                 part
                 of
                 it
                 ,
                 and
                 mixed
                 Silver
                 in
                 the
                 place
                 of
                 it
                 :
                 the
                 King
                 suspicious
                 of
                 the
                 work
                 proposed
                 it
                 to
                 Archimedes
                 ,
                 if
                 by
                 Art
                 he
                 could
                 discover
                 without
                 breaking
                 of
                 the
                 Crowne
                 ,
                 if
                 there
                 had
                 been
                 made
                 mixture
                 of
                 any
                 other
                 metall
                 with
                 the
                 Gold.
                 The
                 way
                 which
                 he
                 found
                 out
                 was
                 by
                 bathing
                 himselfe
                 ;
                 for
                 as
                 he
                 entred
                 into
                 the
                 vessell
                 of
                 water
                 ,
                 (
                 in
                 which
                 he
                 bathed
                 himselfe
                 )
                 so
                 the
                 water
                 ascended
                 or
                 flew
                 out
                 over
                 it
                 ,
                 and
                 as
                 he
                 pulled
                 out
                 his
                 body
                 the
                 water
                 descended
                 :
                 from
                 which
                 he
                 gathered
                 that
                 if
                 a
                 Bowle
                 of
                 pure
                 Gold
                 ,
                 Silver
                 ,
                 or
                 other
                 metall
                 were
                 cast
                 into
                 a
                 vessell
                 of
                 water
                 ,
                 the
                 water
                 proportionally
                 according
                 to
                 the
                 thing
                 cast
                 in
                 would
                 ascend
                 ;
                 and
                 so
                 by
                 way
                 of
                 Arithmetick
                 the
                 question
                 lay
                 open
                 to
                 be
                 resolved
                 :
                 who
                 being
                 so
                 intensively
                 taken
                 with
                 the
                 invention
                 ,
                 leapes
                 out
                 of
                 the
                 Bath
                 all
                 naked
                 ,
                 crying
                 as
                 a
                 man
                 transported
                 ,
                 
                   I
                   have
                   found
                   ,
                   I
                   have
                   found
                   ,
                
                 and
                 so
                 discovered
                 it
                 .
              
               
                 Now
                 some
                 say
                 that
                 he
                 took
                 two
                 Masses
                 ,
                 the
                 one
                 of
                 pure
                 Gold
                 ,
                 and
                 the
                 other
                 of
                 pure
                 Silver
                 ;
                 each
                 equall
                 to
                 the
                 weight
                 of
                 the
                 Crowne
                 ,
                 and
                 therefore
                 unequall
                 in
                 magnitude
                 or
                 greatnesse
                 ;
                 
                 and
                 then
                 knowing
                 the
                 severall
                 quantities
                 of
                 water
                 which
                 was
                 answerable
                 to
                 the
                 Crown
                 ,
                 and
                 the
                 severall
                 Masses
                 ,
                 he
                 subtilly
                 collected
                 ,
                 that
                 if
                 the
                 Crowne
                 occupied
                 more
                 place
                 within
                 the
                 water
                 than
                 the
                 Masse
                 of
                 Gold
                 did
                 :
                 it
                 appeared
                 that
                 there
                 was
                 Silver
                 or
                 other
                 metall
                 melted
                 with
                 it
                 .
                 Now
                 by
                 the
                 rule
                 of
                 position
                 ,
                 suppose
                 that
                 each
                 of
                 the
                 three
                 Masses
                 weighed
                 18
                 pound
                 a
                 piece
                 ,
                 and
                 that
                 the
                 Masse
                 of
                 Gold
                 did
                 occupie
                 the
                 place
                 of
                 one
                 pound
                 of
                 water
                 ,
                 that
                 of
                 Silver
                 a
                 pound
                 and
                 a
                 halfe
                 ▪
                 and
                 the
                 Crown
                 one
                 pound
                 and
                 a
                 quarter
                 only
                 :
                 then
                 thus
                 he
                 might
                 operate
                 the
                 Masse
                 of
                 Silver
                 which
                 weighed
                 18
                 pounds
                 ,
                 cast
                 into
                 the
                 water
                 ,
                 did
                 cast
                 out
                 halfe
                 a
                 pound
                 of
                 water
                 more
                 then
                 the
                 Masse
                 of
                 Gold
                 ,
                 which
                 weighed
                 18
                 pound
                 ,
                 and
                 the
                 Crowne
                 which
                 weighed
                 also
                 18
                 pound
                 ,
                 being
                 put
                 into
                 a
                 vessell
                 full
                 of
                 water
                 ,
                 threw
                 out
                 more
                 water
                 than
                 the
                 Masse
                 of
                 Gold
                 by
                 a
                 quarter
                 of
                 a
                 pound
                 ,
                 (
                 because
                 of
                 mixt
                 metall
                 which
                 was
                 in
                 it
                 :
                 )
                 therefore
                 by
                 the
                 rule
                 of
                 proportion
                 ,
                 if
                 halfe
                 a
                 pound
                 of
                 water
                 (
                 the
                 excesse
                 )
                 be
                 answerable
                 to
                 18
                 pound
                 of
                 Silver
                 ,
                 one
                 quarter
                 of
                 a
                 pound
                 of
                 excesse
                 shall
                 be
                 answerable
                 to
                 9
                 pound
                 of
                 Silver
                 ,
                 and
                 so
                 much
                 was
                 mixed
                 in
                 the
                 Crowne
                 .
              
               
                 Some
                 judge
                 the
                 way
                 to
                 be
                 more
                 facill
                 by
                 weighing
                 the
                 Crowne
                 first
                 in
                 the
                 aire
                 ,
                 then
                 in
                 the
                 water
                 ;
                 in
                 the
                 aire
                 it
                 weighed
                 18
                 pound
                 ,
                 and
                 if
                 it
                 were
                 pure
                 Gold
                 ,
                 in
                 the
                 water
                 it
                 would
                 weigh
                 but
                 17
                 pound
                 ;
                 if
                 it
                 were
                 Copper
                 it
                 would
                 weigh
                 but
                 16
                 pound
                 ;
                 but
                 because
                 vve
                 vvill
                 suppose
                 that
                 Gold
                 and
                 Copper
                 is
                 mixed
                 together
                 ,
                 it
                 vvill
                 vveigh
                 lesse
                 then
                 17
                 pound
                 ,
                 
                 yet
                 more
                 than
                 16
                 pound
                 ,
                 and
                 that
                 according
                 to
                 the
                 proportion
                 mixed
                 :
                 let
                 it
                 then
                 be
                 supposed
                 that
                 it
                 vveighed
                 in
                 the
                 vvater
                 16
                 pound
                 and
                 3
                 quarters
                 ,
                 then
                 might
                 one
                 say
                 by
                 proportion
                 ,
                 if
                 the
                 difference
                 of
                 one
                 pound
                 of
                 losse
                 ,
                 vvhich
                 is
                 betvveen
                 16
                 and
                 17
                 )
                 be
                 ansvverable
                 to
                 18
                 pound
                 ,
                 to
                 vvhat
                 shall
                 one
                 quarter
                 of
                 difference
                 be
                 ansvverable
                 to
                 ,
                 vvhich
                 is
                 betvveen
                 17
                 and
                 16
                 ¾
                 ,
                 and
                 it
                 vvill
                 be
                 4
                 pound
                 and
                 a
                 halfe
                 ;
                 and
                 so
                 much
                 Copper
                 vvas
                 mixed
                 vvith
                 the
                 Gold.
                 
              
               
                 Many
                 men
                 have
                 delivered
                 sundry
                 vvayes
                 to
                 resolve
                 this
                 proposition
                 since
                 Archimedes
                 invention
                 ,
                 and
                 it
                 vvere
                 tedious
                 to
                 relate
                 the
                 diversities
                 .
              
               
                 
                   Baptista
                   Benedictus
                
                 amongst
                 his
                 Arithmeticall
                 Theoremes
                 ,
                 delivers
                 his
                 vvay
                 thus
                 :
                 if
                 a
                 Masse
                 of
                 Gold
                 of
                 equall
                 bignesse
                 to
                 the
                 Crovvne
                 did
                 vveigh
                 20
                 pound
                 ,
                 and
                 another
                 of
                 Silver
                 at
                 a
                 capacity
                 or
                 bignesse
                 at
                 pleasure
                 ,
                 as
                 suppose
                 did
                 vveigh
                 12
                 pound
                 ,
                 the
                 Crovvne
                 or
                 the
                 mixt
                 body
                 would
                 vveigh
                 more
                 than
                 the
                 Silver
                 ,
                 and
                 lesser
                 than
                 the
                 Gold
                 ,
                 suppose
                 it
                 vveighed
                 16
                 pound
                 vvhich
                 is
                 4
                 pound
                 lesse
                 than
                 the
                 Gold
                 by
                 8
                 pound
                 ,
                 then
                 may
                 one
                 say
                 ,
                 if
                 8
                 pound
                 of
                 difference
                 come
                 from
                 12
                 pound
                 of
                 Silver
                 ,
                 from
                 vvhence
                 comes
                 4
                 pound
                 vvhich
                 vvill
                 be
                 6
                 pound
                 and
                 so
                 much
                 Silver
                 vvas
                 mixed
                 in
                 it
                 ,
                 &c.
                 
              
            
             
               
               
                 3.
                 
                 Three
                 men
                 bought
                 a
                 quantitie
                 of
                 wine
                 ,
                 each
                 paid
                 alike
                 ,
                 and
                 each
                 was
                 to
                 have
                 alike
                 ;
                 it
                 happened
                 at
                 the
                 last
                 partition
                 that
                 there
                 were
                 21
                 Barrells
                 ,
                 of
                 which
                 7
                 were
                 full
                 ,
                 7
                 halfe
                 full
                 ,
                 and
                 7
                 empty
                 ,
                 how
                 must
                 they
                 share
                 the
                 wine
                 and
                 vessells
                 ,
                 that
                 each
                 have
                 as
                 many
                 vessells
                 one
                 as
                 another
                 ,
                 &
                 as
                 much
                 wine
                 one
                 as
                 another
                 ?
              
               
                 THis
                 may
                 be
                 answered
                 two
                 wayes
                 as
                 followeth
                 ,
                 and
                 these
                 numbers
                 2
                 ,
                 2
                 ,
                 3
                 ,
                 or
                 3
                 ,
                 3
                 ,
                 1
                 ,
                 may
                 serve
                 for
                 direction
                 ,
                 and
                 signifies
                 that
                 the
                 first
                 person
                 ought
                 to
                 have
                 3
                 Barrells
                 full
                 ,
                 and
                 as
                 many
                 empty
                 ones
                 ,
                 and
                 one
                 which
                 is
                 halfe
                 full
                 ;
                 so
                 he
                 shall
                 have
                 7
                 vessells
                 and
                 3
                 Barrels
                 ,
                 and
                 a
                 halfe
                 of
                 liquor
                 ;
                 and
                 one
                 of
                 the
                 other
                 shall
                 in
                 like
                 manner
                 have
                 as
                 much
                 ,
                 so
                 there
                 will
                 remaine
                 for
                 the
                 third
                 man
                 1
                 Barrell
                 full
                 ,
                 5
                 which
                 are
                 halfe
                 full
                 ,
                 and
                 1
                 empty
                 ,
                 and
                 so
                 every
                 one
                 shall
                 have
                 alike
                 both
                 in
                 vessells
                 and
                 wine
                 .
                 And
                 generally
                 to
                 answer
                 such
                 questions
                 ,
                 divide
                 the
                 number
                 of
                 vessells
                 by
                 the
                 number
                 of
                 persons
                 ,
                 and
                 if
                 the
                 Quotient
                 be
                 not
                 an
                 intire
                 number
                 ,
                 the
                 question
                 is
                 impossible
                 ;
                 but
                 when
                 it
                 is
                 an
                 intire
                 number
                 ,
                 there
                 must
                 be
                 made
                 as
                 many
                 parts
                 as
                 there
                 are
                 3
                 persons
                 ,
                 seeing
                 that
                 each
                 part
                 is
                 lesse
                 than
                 the
                 halfe
                 of
                 the
                 said
                 Quotient
                 :
                 as
                 dividing
                 21
                 by
                 3
                 there
                 comes
                 7
                 for
                 the
                 Quotient
                 ,
                 which
                 may
                 be
                 parted
                 in
                 these
                 three
                 parts
                 ,
                 2
                 ,
                 2
                 ,
                 3
                 ,
                 or
                 3
                 ,
                 3
                 ,
                 1
                 ,
                 each
                 of
                 which
                 being
                 lesse
                 than
                 ha●fe
                 of
                 7.
                 
              
            
             
               
               
                 4.
                 
                 There
                 is
                 a
                 Ladder
                 which
                 stands
                 upright
                 against
                 a
                 wall
                 of
                 10
                 foot
                 high
                 ,
                 the
                 foot
                 of
                 it
                 is
                 pulled
                 out
                 6
                 foot
                 from
                 the
                 wall
                 upon
                 the
                 pavement
                 :
                 how
                 much
                 hath
                 the
                 top
                 of
                 the
                 Ladder
                 descended
                 ?
              
               
                 THe
                 ansvver
                 is
                 ,
                 2
                 foot
                 :
                 for
                 by
                 Pythagoras
                 rule
                 the
                 square
                 of
                 DB
                 ,
                 the
                 Hypothenusal
                 is
                 
                 equall
                 to
                 the
                 square
                 of
                 DA
                 6
                 ,
                 &
                 AB
                 10.
                 
                 Novv
                 if
                 DA
                 be
                 6
                 foot
                 ,
                 and
                 AB
                 10
                 foot
                 ,
                 the
                 squares
                 are
                 36
                 and
                 100
                 ,
                 vvhich
                 36
                 taken
                 from
                 100
                 rests
                 64
                 ,
                 vvhose
                 Roote-quadrate
                 is
                 8
                 so
                 the
                 foot
                 of
                 the
                 Ladder
                 being
                 novv
                 at
                 D
                 ,
                 the
                 toppe
                 vvill
                 be
                 at
                 C
                 ,
                 2
                 foot
                 lovver
                 than
                 it
                 vvas
                 vvhen
                 it
                 vvas
                 at
                 B.
                 
              
            
          
           
             
               PROBLEM
               .
               LXXXVII
               .
               Witty
               suits
               or
               debates
               between
               Caius
               and
               Sempronius
               ,
               upon
               the
               forme
               of
               f●gures
               ,
               which
               Geometricians
               call
               Isoperimeter
               ,
               or
               equall
               in
               circuit
               or
               compasse
               .
            
             
               MArvell
               ●ot
               at
               it
               if
               I
               make
               the
               Mathematicks
               take
               place
               at
               the
               Ba●●e
               ,
               and
               if
               I
               set
               
               forth
               here
               B●rtoleus
               ,
               who
               witnesseth
               of
               himselfe
               ,
               that
               being
               then
               an
               ancient
               Doctor
               in
               the
               Law
               ,
               he
               himselfe
               took
               upon
               him
               to
               learne
               the
               elements
               and
               principles
               of
               Geometry
               ,
               by
               which
               he
               might
               set
               forth
               certaine
               Lawes
               touching
               the
               divisions
               of
               Fields
               ,
               Waters
               ,
               Islands
               ,
               and
               other
               incident
               places
               :
               now
               this
               shall
               be
               to
               shew
               in
               
               passing
               by
               ,
               that
               these
               sciences
               are
               profitable
               and
               behovefull
               for
               Judges
               ,
               Counsellors
               ,
               or
               such
               ,
               to
               explaine
               many
               things
               which
               fall
               out
               in
               Lawes
               ,
               to
               avoid
               ambiguities
               ,
               contentions
               ,
               and
               suits
               often
               .
            
             
               
                 1.
                 
                 Incident
                 .
              
               
                 CAius
                 had
                 a
                 field
                 which
                 was
                 directly
                 square
                 ,
                 having
                 24
                 measures
                 in
                 Circuit
                 ,
                 that
                 was
                 6
                 on
                 each
                 side
                 :
                 Sempronius
                 desiring
                 to
                 fit
                 himselfe
                 ,
                 prayed
                 Caius
                 to
                 change
                 with
                 him
                 for
                 a
                 field
                 which
                 should
                 be
                 equivalent
                 unto
                 his
                 ,
                 and
                 the
                 bargaine
                 being
                 concluded
                 ,
                 he
                 gave
                 him
                 for
                 counterchange
                 a
                 piece
                 of
                 ground
                 which
                 had
                 just
                 as
                 much
                 in
                 circuit
                 as
                 his
                 had
                 ,
                 but
                 it
                 was
                 not
                 square
                 ,
                 yet
                 Quadrangular
                 and
                 Rectangled
                 ,
                 having
                 9
                 measures
                 in
                 length
                 for
                 each
                 of
                 the
                 two
                 longest
                 sides
                 ,
                 and
                 3
                 in
                 breadth
                 for
                 each
                 shorter
                 side
                 :
                 Now
                 Caius
                 which
                 was
                 not
                 the
                 most
                 subtillest
                 
                 nor
                 wisest
                 in
                 the
                 world
                 accepted
                 his
                 bargaine
                 at
                 the
                 first
                 ,
                 but
                 afterward●
                 having
                 conferred
                 with
                 a
                 Land-measures
                 and
                 Mathematician
                 ,
                 found
                 that
                 he
                 was
                 over-reached
                 in
                 his
                 bargaine
                 ,
                 and
                 that
                 his
                 field
                 contained
                 36
                 square
                 measures
                 ,
                 and
                 the
                 other
                 field
                 had
                 but
                 27
                 measures
                 ,
                 (
                 a
                 thing
                 easie
                 to
                 be
                 knowne
                 by
                 multiplying
                 the
                 length
                 by
                 the
                 breadth
                 :
                 )
                 Sempronius
                 contested
                 with
                 him
                 in
                 suite
                 of
                 Law
                 ,
                 and
                 argued
                 that
                 figures
                 which
                 have
                 equall
                 Perimeter
                 or
                 circuit
                 ,
                 are
                 equall
                 amongst
                 themselves
                 :
                 my
                 field
                 ,
                 saith
                 he
                 ,
                 hath
                 equall
                 circuit
                 with
                 yours
                 ,
                 therefore
                 it
                 is
                 equall
                 unto
                 it
                 in
                 quantitie
                 .
                 Now
                 this
                 was
                 sufficient
                 to
                 delude
                 a
                 Judge
                 which
                 was
                 ignorant
                 in
                 Geometricall
                 proportions
                 ,
                 but
                 a
                 Mathematician
                 will
                 easily
                 declare
                 the
                 deceit
                 ,
                 being
                 assured
                 that
                 figures
                 which
                 are
                 Isoperemiter
                 ,
                 or
                 equall
                 in
                 circuit
                 ,
                 have
                 not
                 alwayes
                 equall
                 capacitie
                 or
                 quantitie
                 :
                 seeing
                 that
                 with
                 the
                 same
                 circuit
                 ,
                 there
                 may
                 be
                 infinite
                 figures
                 made
                 which
                 shall
                 be
                 more
                 and
                 more
                 capable
                 ,
                 by
                 how
                 much
                 they
                 have
                 more
                 Angles
                 ,
                 equall
                 sides
                 ,
                 and
                 approach
                 nearer
                 unto
                 a
                 circle
                 ,
                 (
                 which
                 is
                 the
                 most
                 capablest
                 figure
                 of
                 all
                 ,
                 )
                 because
                 that
                 all
                 his
                 parts
                 are
                 extended
                 one
                 from
                 anothes
                 ,
                 and
                 from
                 the
                 middle
                 or
                 Centre
                 as
                 much
                 as
                 may
                 be
                 :
                 so
                 we
                 see
                 by
                 an
                 infa●lible
                 rule
                 of
                 experience
                 ,
                 that
                 a
                 square
                 is
                 more
                 capable
                 of
                 quantitie
                 than
                 a
                 Triangle
                 of
                 the
                 same
                 circuit
                 ,
                 and
                 a
                 Pentagone
                 more
                 than
                 a
                 square
                 ,
                 and
                 so
                 of
                 others
                 ,
                 so
                 that
                 they
                 be
                 regular
                 figures
                 that
                 have
                 their
                 sides
                 equall
                 ,
                 
                 otherwise
                 there
                 might
                 be
                 that
                 a
                 regular
                 Triangle
                 ,
                 having
                 24
                 measures
                 in
                 circuit
                 might
                 have
                 more
                 capacitie
                 than
                 a
                 rectangled
                 Parallelogram
                 ,
                 which
                 had
                 also
                 24
                 measures
                 of
                 circuit
                 ,
                 as
                 if
                 it
                 were
                 11
                 in
                 length
                 ,
                 and
                 1
                 inbreadth
                 ,
                 the
                 circuit
                 is
                 still
                 24
                 ,
                 yet
                 the
                 quantitie
                 is
                 but
                 11.
                 and
                 if
                 it
                 had
                 6
                 every
                 way
                 ,
                 it
                 gives
                 the
                 same
                 
                   Perimeter
                   ,
                   viz.
                
                 24.
                 but
                 a
                 quantitie
                 of
                 36
                 as
                 before
                 .
              
            
             
               
                 2.
                 
                 Incident
                 .
              
               
                 SEmpronius
                 having
                 borrowed
                 of
                 Caius
                 a
                 sack
                 of
                 Corne
                 ,
                 which
                 was
                 6
                 foot
                 high
                 and
                 2
                 foot
                 broad
                 ,
                 and
                 when
                 there
                 was
                 question
                 made
                 to
                 repay
                 it
                 ,
                 Sempronius
                 gave
                 Caius
                 back
                 two
                 sacks
                 full
                 of
                 Corne
                 ,
                 which
                 had
                 each
                 of
                 them
                 6
                 foot
                 high
                 &
                 1
                 foot
                 broad
                 :
                 who
                 beleeved
                 that
                 if
                 the
                 sackes
                 were
                 full
                 he
                 was
                 repaid
                 ,
                 and
                 it
                 seems
                 to
                 have
                 an
                 appearance
                 of
                 truth
                 barely
                 looked
                 on
                 .
                 But
                 it
                 is
                 most
                 evident
                 in
                 demonstration
                 ,
                 that
                 the
                 2
                 sacks
                 of
                 Corn
                 paid
                 by
                 Sempronius
                 to
                 Caius
                 ,
                 is
                 but
                 halfe
                 of
                 that
                 one
                 sack
                 which
                 he
                 lent
                 him
                 :
                 for
                 a
                 Cylinder
                 or
                 sack
                 having
                 one
                 foot
                 of
                 diameter
                 ,
                 and
                 6
                 foot
                 of
                 length
                 ,
                 is
                 but
                 the
                 4
                 part
                 of
                 another
                 Cylinder
                 ,
                 whose
                 length
                 is
                 6
                 foot
                 ,
                 and
                 his
                 diameter
                 is
                 2
                 foot
                 :
                 therefore
                 two
                 of
                 the
                 lesser
                 Cylinders
                 or
                 sackes
                 ,
                 is
                 but
                 halfe
                 of
                 the
                 greater
                 ;
                 and
                 so
                 Caius
                 was
                 deceived
                 in
                 halfe
                 his
                 Corne.
                 
              
            
             
               
                 3.
                 
                 Incident
                 .
              
               
                 SOme
                 one
                 from
                 a
                 common
                 Fountaine
                 of
                 a
                 City
                 hath
                 a
                 Pipe
                 of
                 water
                 of
                 an
                 inch
                 diameter
                 ;
                 
                 to
                 have
                 it
                 more
                 commodious
                 ,
                 he
                 hath
                 leave
                 to
                 take
                 as
                 much
                 more
                 water
                 ,
                 whereupon
                 he
                 gives
                 order
                 that
                 a
                 Pipe
                 be
                 made
                 of
                 two
                 inches
                 diameter
                 .
                 Now
                 you
                 will
                 say
                 presently
                 that
                 it
                 is
                 reason
                 to
                 be
                 so
                 bigge
                 ,
                 to
                 have
                 just
                 twice
                 as
                 〈…〉
                 before
                 :
                 but
                 if
                 the
                 Magistrate
                 
                 of
                 the
                 Citie
                 understood
                 Geometricall
                 proportions
                 ,
                 he
                 would
                 soon
                 cause
                 it
                 to
                 be
                 amended
                 ,
                 &
                 shew
                 that
                 he
                 hath
                 not
                 only
                 taken
                 twice
                 as
                 much
                 water
                 as
                 he
                 had
                 before
                 ,
                 but
                 foure
                 times
                 as
                 much
                 :
                 for
                 a
                 Circular
                 hole
                 which
                 is
                 two
                 inches
                 diameter
                 is
                 foure
                 times
                 greater
                 than
                 that
                 of
                 one
                 inch
                 ,
                 and
                 therefore
                 vvill
                 cast
                 out
                 four
                 times
                 as
                 much
                 vvater
                 as
                 that
                 of
                 one
                 inch
                 ,
                 and
                 so
                 the
                 deceit
                 is
                 double
                 also
                 in
                 this
                 .
              
               
                 Moreover
                 ,
                 if
                 there
                 vvere
                 a
                 heap
                 of
                 Corne
                 of
                 20
                 foot
                 every
                 vvay
                 ,
                 vvhich
                 vvas
                 borrovved
                 to
                 be
                 paid
                 next
                 yeare
                 ▪
                 the
                 party
                 having
                 his
                 Corne
                 in
                 heapes
                 of
                 12
                 foot
                 every
                 vvay
                 ,
                 and
                 of
                 10
                 foot
                 every
                 vvay
                 ,
                 proffers
                 him
                 4
                 heapes
                 of
                 the
                 greater
                 or
                 7
                 heaps
                 of
                 the
                 lesser
                 ,
                 for
                 his
                 ovvne
                 heap
                 of
                 20
                 every
                 vvay
                 ,
                 vvhich
                 vvas
                 lent
                 :
                 here
                 it
                 seems
                 that
                 the
                 proffer
                 is
                 faire
                 ,
                 nay
                 vvith
                 advantage
                 ,
                 yet
                 the
                 losse
                 vvould
                 be
                 neare
                 1000
                 foot
                 .
                 Infinite
                 of
                 such
                 causes
                 do
                 arise
                 from
                 Geometricall
                 figures
                 ,
                 vvhich
                 are
                 able
                 to
                 deceive
                 a
                 Judge
                 or
                 
                 Magistrate
                 ,
                 vvhich
                 is
                 not
                 somevvhat
                 seene
                 in
                 
                   Mathematicall
                   Documents
                
                 .
              
            
          
           
             
               PROBLEM
               .
               LXXXVIII
               .
               Containing
               sundry
               Questions
               in
               matter
               of
               Cosmography
               .
            
             
               FIrst
               ,
               it
               may
               be
               demanded
               ,
               vvhere
               is
               the
               middle
               of
               the
               vvorld
               ?
               I
               speak
               not
               here
               Mathematically
               ,
               but
               as
               the
               vulgar
               people
               ,
               vvho
               ask
               ,
               vvhere
               is
               the
               middle
               of
               the
               vvorld
               ?
               in
               this
               sence
               to
               speak
               absolutely
               there
               is
               no
               point
               vvhich
               may
               be
               said
               to
               be
               the
               middle
               of
               the
               surface
               ,
               for
               the
               middle
               of
               a
               Globe
               is
               every
               vvhere
               :
               notvvithstanding
               the
               
                 Holy
                 Scriptures
              
               speake
               respectively
               ,
               and
               make
               mention
               of
               the
               middle
               of
               the
               earth
               ,
               and
               the
               interpreters
               apply
               it
               to
               the
               Citie
               of
               Jerusalem
               placed
               in
               the
               middle
               of
               Palestina
               ,
               and
               the
               habitable
               vvorld
               ,
               that
               in
               effect
               taking
               a
               mappe
               of
               the
               vvorld
               ,
               and
               placing
               one
               foot
               of
               the
               Compasses
               upon
               Jerusalem
               ,
               and
               extending
               the
               other
               foot
               to
               the
               extremity
               of
               
                 Europe
                 ,
                 Asia
              
               ,
               and
               Afric●
               ,
               you
               shall
               see
               that
               the
               Citie
               of
               Jerusalem
               is
               as
               a
               Centre
               to
               that
               Circle
               .
            
             
               
                 2.
                 
                 Secondly
                 ,
                 how
                 much
                 is
                 the
                 depth
                 of
                 the
                 earth
                 ,
                 the
                 height
                 of
                 the
                 heavens
                 ,
                 and
                 the
                 compasse
                 of
                 the
                 world
                 ?
              
               
                 FRom
                 the
                 surface
                 of
                 the
                 earth
                 unto
                 the
                 Centre
                 according
                 to
                 ancient
                 traditions
                 ,
                 is
                 3436.
                 miles
                 ,
                 so
                 the
                 vvhole
                 thicknesse
                 is
                 6872
                 miles
                 ,
                 
                 of
                 which
                 the
                 whole
                 compasse
                 or
                 circuit
                 of
                 the
                 earth
                 is
                 21600
                 miles
                 .
              
               
                 From
                 the
                 Centre
                 of
                 the
                 earth
                 to
                 the
                 Moone
                 there
                 is
                 neare
                 56
                 Semidiameters
                 of
                 the
                 earth
                 ,
                 which
                 is
                 about
                 192416
                 miles
                 .
                 unto
                 the
                 Sunne
                 there
                 is
                 1142
                 Semidiameters
                 of
                 the
                 earth
                 ,
                 that
                 is
                 in
                 miles
                 3924912
                 ;
                 from
                 the
                 starry
                 firmament
                 to
                 the
                 Centre
                 of
                 the
                 earth
                 there
                 is
                 14000
                 Semidiameters
                 ,
                 that
                 is
                 ,
                 48184000
                 miles
                 ,
                 according
                 to
                 the
                 opinion
                 and
                 observation
                 of
                 that
                 learned
                 
                   Ticho
                   Brahe
                
                 .
              
               
                 From
                 these
                 measures
                 one
                 may
                 collect
                 by
                 Arithmeticall
                 supputations
                 ,
                 many
                 pleasant
                 propositions
                 in
                 this
                 manner
                 .
              
               
                 First
                 ,
                 if
                 you
                 imagine
                 there
                 were
                 a
                 hole
                 through
                 the
                 earth
                 ,
                 and
                 that
                 a
                 Milstone
                 should
                 be
                 let
                 fall
                 down
                 into
                 this
                 hole
                 ,
                 and
                 to
                 move
                 a
                 mile
                 in
                 each
                 minute
                 of
                 time
                 ,
                 it
                 would
                 be
                 more
                 than
                 two
                 dayes
                 and
                 a
                 halfe
                 before
                 it
                 would
                 come
                 to
                 the
                 Centre
                 ,
                 and
                 being
                 there
                 it
                 would
                 hang
                 in
                 the
                 aire
                 .
              
               
                 Secondly
                 ,
                 if
                 a
                 man
                 should
                 go
                 every
                 day
                 20
                 miles
                 ,
                 it
                 would
                 be
                 three
                 yeares
                 wanting
                 but
                 a
                 fortnight
                 ,
                 before
                 he
                 could
                 go
                 once
                 about
                 the
                 earth
                 ;
                 and
                 if
                 a
                 Bird
                 should
                 fly
                 round
                 about
                 it
                 in
                 two
                 dayes
                 ,
                 then
                 must
                 the
                 motion
                 be
                 450
                 miles
                 in
                 an
                 houre
                 .
              
               
                 Thirdly
                 ,
                 the
                 Moone
                 runnes
                 a
                 greater
                 compasse
                 each
                 houre
                 ,
                 than
                 if
                 in
                 the
                 same
                 time
                 she
                 should
                 runne
                 twice
                 rhe
                 Circumference
                 of
                 the
                 whole
                 earth
                 .
              
               
                 Fourthly
                 ,
                 admit
                 it
                 be
                 supposed
                 that
                 one
                 
                 should
                 go
                 20
                 miles
                 in
                 ascending
                 towards
                 the
                 heavens
                 every
                 day
                 ,
                 he
                 should
                 be
                 above
                 15
                 years
                 before
                 he
                 could
                 attaine
                 to
                 the
                 Orbe
                 of
                 the
                 Moone
                 .
              
               
                 Fifthly
                 ,
                 the
                 Sunne
                 makes
                 a
                 greater
                 way
                 in
                 one
                 day
                 than
                 the
                 Moone
                 doth
                 in
                 20
                 dayes
                 ,
                 because
                 that
                 the
                 Orbe
                 of
                 the
                 Sunnes
                 circumference
                 is
                 at
                 the
                 least
                 20
                 times
                 greater
                 than
                 the
                 Orbe
                 of
                 the
                 Moone
                 .
              
               
                 Sixthly
                 ,
                 if
                 a
                 Milstone
                 should
                 descend
                 from
                 the
                 p●ace
                 of
                 the
                 Sunne
                 a
                 thousand
                 miles
                 every
                 houre
                 ,
                 (
                 which
                 is
                 above
                 15
                 miles
                 in
                 a
                 minute
                 ,
                 farre
                 beyond
                 the
                 proportion
                 of
                 motion
                 )
                 it
                 would
                 be
                 above
                 163
                 dayes
                 before
                 it
                 would
                 fall
                 dovvne
                 to
                 the
                 earth
                 .
              
               
                 Seventhly
                 ,
                 the
                 Sunne
                 in
                 his
                 proper
                 sphere
                 moves
                 more
                 than
                 seven
                 thousand
                 five
                 hundred
                 and
                 seventy
                 miles
                 in
                 one
                 minute
                 of
                 time
                 :
                 novv
                 there
                 is
                 no
                 Bullet
                 of
                 a
                 Cannon
                 ,
                 Arrovv
                 ,
                 Thunderbolt
                 ,
                 or
                 tempest
                 of
                 vvinde
                 that
                 moves
                 vvith
                 such
                 quicknesse
                 .
              
               
                 Eightly
                 ,
                 it
                 is
                 of
                 a
                 farre
                 higher
                 nature
                 to
                 consider
                 the
                 exceeding
                 and
                 unmoveable
                 quicknesse
                 of
                 the
                 starry
                 firmament
                 ,
                 for
                 a
                 starre
                 being
                 in
                 the
                 Aequator
                 ,
                 (
                 which
                 is
                 just
                 between
                 the
                 Poles
                 of
                 the
                 world
                 )
                 makes
                 12598666
                 miles
                 in
                 one
                 houre
                 which
                 is
                 two
                 hundred
                 nine
                 thousand
                 nine
                 hundred
                 and
                 seventy
                 foure
                 miles
                 in
                 one
                 minute
                 of
                 time
                 :
                 &
                 if
                 a
                 Horseman
                 should
                 ride
                 every
                 day
                 40
                 miles
                 ,
                 he
                 could
                 not
                 ride
                 such
                 a
                 compasse
                 in
                 a
                 thousand
                 yeares
                 as
                 the
                 starry
                 firmament
                 moves
                 in
                 one
                 houre
                 ,
                 which
                 is
                 more
                 than
                 if
                 one
                 
                 should
                 move
                 about
                 the
                 earth
                 a
                 thousand
                 times
                 in
                 one
                 houre
                 ,
                 and
                 quicker
                 than
                 possible
                 thought
                 can
                 be
                 imagined
                 :
                 and
                 if
                 a
                 starre
                 should
                 flye
                 in
                 the
                 aire
                 about
                 the
                 earth
                 with
                 such
                 a
                 prodigious
                 quicknesse
                 ,
                 it
                 would
                 burne
                 and
                 consume
                 all
                 the
                 world
                 here
                 below
                 .
                 Behold
                 therefore
                 how
                 time
                 passeth
                 ,
                 and
                 death
                 hasteth
                 on
                 :
                 this
                 made
                 Copernicus
                 ,
                 not
                 unadvisedly
                 to
                 attribute
                 this
                 motion
                 of
                 
                   Primum
                   mobile
                
                 to
                 the
                 earth
                 ,
                 and
                 not
                 to
                 the
                 starry
                 firmament
                 ;
                 for
                 it
                 is
                 beyond
                 humane
                 sense
                 to
                 apprehend
                 or
                 conceive
                 the
                 rapture
                 and
                 violence
                 of
                 that
                 motion
                 being
                 quicker
                 than
                 thought
                 ;
                 and
                 the
                 word
                 of
                 God
                 testifieth
                 that
                 the
                 Lord
                 made
                 all
                 things
                 in
                 
                   number
                   ,
                   measure
                   ,
                   weight
                
                 ,
                 and
                 time
                 .
              
            
          
           
             
               PROBLEM
               .
               XCII
               .
               To
               finde
               the
               Bissextile
               yeare
               ,
               the
               Dominicall
               letter
               ,
               and
               the
               letters
               of
               the
               moneth
               .
            
             
               LEt
               123
               ,
               or
               124
               ,
               or
               125
               ,
               or
               26
               ,
               or
               27
               ,
               (
               which
               is
               the
               remainder
               of
               1500
               ,
               or
               1600
               )
               be
               divided
               by
               4
               ,
               which
               is
               the
               number
               of
               the
               Leape-yeare
               ,
               and
               that
               which
               remaines
               of
               the
               division
               shewes
               the
               leap-yeare
               ,
               as
               if
               one
               remaine
               ,
               it
               shewes
               that
               it
               is
               the
               first
               yeare
               since
               the
               Bissextile
               or
               Leap-year
               ,
               if
               two
               ,
               it
               is
               the
               second
               year
               &c.
               and
               if
               nothing
               remaine
               ,
               then
               it
               is
               the
               Bissextile
               or
               Leap-yeare
               ,
               and
               the
               Quotient
               shews
               you
               how
               many
               Bissextiles
               or
               Leap-yeares
               there
               are
               conteined
               in
               so
               many
               yeares
               .
            
             
               
               
                 To
                 finde
                 the
                 Circle
                 of
                 the
                 Sun
                 by
                 the
                 fingers
                 .
              
               
                 LEt
                 123
                 ,
                 24
                 ,
                 25
                 ,
                 26
                 ,
                 or
                 27
                 ,
                 be
                 divided
                 by
                 28
                 ,
                 (
                 which
                 is
                 the
                 Circle
                 of
                 the
                 Sunne
                 or
                 whole
                 revolution
                 of
                 the
                 Dominicall
                 letters
                 )
                 and
                 that
                 which
                 remaines
                 is
                 the
                 number
                 of
                 joynts
                 ,
                 which
                 is
                 to
                 be
                 accounted
                 upon
                 the
                 fingers
                 by
                 
                   Filius
                   esto
                   Dei
                   ,
                   coelum
                   bonus
                   accipe
                   gratis
                
                 :
                 and
                 where
                 the
                 number
                 ends
                 ,
                 that
                 finger
                 it
                 sheweth
                 the
                 yeare
                 which
                 is
                 present
                 ,
                 and
                 the
                 words
                 of
                 the
                 verse
                 shew
                 the
                 
                   Dominicall
                   letter
                
                 .
              
               
                 Example
                 .
              
               
                 DIvide
                 123
                 by
                 28
                 for
                 the
                 yeare
                 (
                 and
                 so
                 of
                 other
                 yeares
                 )
                 and
                 the
                 Quotient
                 is
                 4
                 ,
                 and
                 there
                 remaineth
                 11
                 ,
                 for
                 which
                 you
                 must
                 account
                 11
                 words
                 :
                 
                   Filius
                   esto
                   Dei
                   ,
                   &c.
                
                 upon
                 the
                 joynts
                 beginning
                 from
                 the
                 first
                 joynt
                 of
                 the
                 Index
                 ,
                 and
                 you
                 shall
                 have
                 the
                 answer
                 .
              
               
                 For
                 the
                 present
                 to
                 know
                 the
                 
                   Dominicall
                   letter
                
                 for
                 each
                 moneth
                 ,
                 account
                 from
                 January
                 unto
                 the
                 moneth
                 required
                 ,
                 including
                 January
                 ,
                 and
                 if
                 there
                 be
                 8
                 ,
                 9
                 ,
                 7
                 ,
                 or
                 5
                 ,
                 you
                 must
                 begin
                 upon
                 the
                 end
                 of
                 the
                 finger
                 from
                 the
                 thumbe
                 and
                 account
                 ,
                 
                   Adam
                   degebat
                   ,
                   &c.
                
                 as
                 many
                 words
                 as
                 there
                 are
                 moneths
                 ,
                 for
                 then
                 one
                 shall
                 have
                 the
                 letter
                 which
                 begins
                 the
                 moneth
                 ;
                 then
                 to
                 know
                 what
                 day
                 of
                 the
                 moneth
                 it
                 is
                 ,
                 see
                 how
                 many
                 times
                 7
                 is
                 comprehended
                 in
                 the
                 number
                 of
                 dayes
                 ,
                 and
                 take
                 the
                 rest
                 ,
                 suppose
                 4
                 ,
                 account
                 upon
                 the
                 first
                 finger
                 within
                 &
                 without
                 by
                 the
                 joynts
                 ,
                 
                 unto
                 the
                 number
                 of
                 4
                 ,
                 which
                 ends
                 at
                 the
                 end
                 of
                 the
                 finger
                 :
                 from
                 whence
                 it
                 may
                 be
                 inferred
                 that
                 the
                 day
                 required
                 was
                 Wednesday
                 ,
                 Sunday
                 being
                 attributed
                 to
                 the
                 first
                 joynt
                 of
                 the
                 first
                 finger
                 or
                 Index
                 :
                 and
                 so
                 you
                 have
                 the
                 present
                 yeare
                 ,
                 the
                 Dominicall
                 letter
                 ,
                 the
                 letter
                 which
                 begins
                 the
                 Moneth
                 ,
                 and
                 all
                 the
                 dayes
                 of
                 the
                 Moneth
                 .
              
            
          
           
             
               PROBLEM
               .
               XCIII
               .
               To
               finde
               the
               New
               and
               Full
               Moone
               in
               each
               Moneth
               .
            
             
               ADde
               to
               t●e
               Epact
               for
               the
               yeare
               ,
               the
               Moneth
               from
               March
               ,
               then
               subtract
               that
               surplus
               from
               30
               ,
               and
               the
               rest
               is
               the
               day
               of
               the
               Moneth
               that
               it
               vvill
               be
               New
               Moone
               ,
               and
               adding
               unto
               it
               14
               ,
               you
               shall
               have
               that
               Full
               Moone
               .
            
             
               
                 Note
              
               
                 THat
                 the
                 Epact
                 is
                 made
                 alwayes
                 by
                 adding
                 11
                 unto
                 30
                 ,
                 and
                 if
                 it
                 passe
                 30
                 ,
                 subtract
                 30
                 ,
                 and
                 adde
                 11
                 to
                 the
                 remainder
                 ,
                 and
                 so
                 
                   ad
                   infinitum
                
                 :
                 as
                 if
                 the
                 Epact
                 were
                 12
                 ,
                 adde
                 11
                 to
                 it
                 makes
                 23
                 for
                 the
                 Epact
                 next
                 year
                 ,
                 to
                 vvhich
                 adde
                 11
                 makes
                 34
                 ,
                 subtract
                 30
                 ,
                 rests
                 4
                 the
                 Epact
                 for
                 the
                 yeare
                 after
                 ,
                 and
                 15
                 for
                 the
                 yeare
                 follovving
                 that
                 ,
                 and
                 26
                 for
                 the
                 next
                 ,
                 and
                 7
                 for
                 the
                 next
                 ,
                 &c.
                 
              
            
          
           
             
             
               PROBLEM
               .
               XCIV
               .
               To
               finde
               the
               Latitude
               of
               ●
               Countrey
               .
            
             
               THose
               that
               dwell
               between
               the
               North-Pole
               and
               the
               Tropicke
               of
               Cancer
               ,
               have
               their
               Spring
               and
               Summer
               between
               the
               10
               of
               March
               ,
               and
               the
               13
               of
               September
               :
               and
               therefore
               in
               any
               day
               between
               that
               time
               ,
               get
               the
               sunnes
               distance
               by
               instrumentall
               observation
               from
               the
               zenith
               at
               noone
               ,
               and
               adde
               the
               declination
               of
               the
               sun
               for
               that
               day
               to
               it
               :
               so
               the
               Aggragate
               sheweth
               such
               is
               the
               Latitude
               ,
               or
               Poles
               height
               of
               that
               Countrey
               .
               Now
               the
               declination
               of
               the
               sunne
               for
               any
               day
               is
               found
               out
               by
               Tables
               calculated
               to
               that
               end
               :
               or
               Mechanically
               by
               the
               Globe
               ,
               or
               by
               Instrument
               it
               may
               be
               indifferently
               had
               :
               and
               here
               note
               that
               if
               the
               day
               be
               between
               the
               13
               of
               September
               and
               the
               10
               of
               March
               ,
               then
               the
               sunnes
               declination
               for
               that
               day
               must
               be
               taken
               out
               of
               the
               distance
               of
               the
               sunne
               from
               the
               zenith
               at
               noone
               :
               so
               shall
               you
               have
               the
               Latitude
               ,
               as
               before
               .
            
          
           
             
               PRBOLEM
               XCV
               .
               Of
               the
               Climates
               of
               countreys
               ,
               and
               to
               finde
               in
               what
               C●imate
               any
               countrey
               is
               under
               .
            
             
               CLimates
               as
               they
               are
               taken
               Geographically
               signifie
               nothing
               else
               but
               when
               the
               l●ngt●
               
               of
               the
               longest
               day
               of
               any
               place
               ,
               is
               half
               an
               houre
               longer
               ,
               or
               shorter
               than
               it
               is
               in
               another
               place
               (
               and
               so
               of
               the
               sh●rtest
               day
               )
               and
               this
               account
               to
               begin
               from
               the
               Equinoctia●l
               Circle
               ,
               seeing
               all
               Countreys
               under
               it
               have
               the
               shortest
               and
               longest
               day
               that
               can
               be
               but
               12
               houres
               ;
               But
               all
               other
               Countreys
               that
               are
               from
               the
               Equinoctiall
               Circle
               either
               towards
               the
               North
               or
               South
               of
               it
               unto
               the
               Poles
               themselves
               ,
               are
               said
               to
               be
               in
               some
               one
               Climate
               or
               other
               ,
               from
               the
               Equinoctiall
               to
               either
               of
               the
               Poles
               Circles
               ,
               (
               which
               are
               in
               the
               Latitude
               of
               66
               degr
               .
               30
               m.
               )
               between
               each
               of
               which
               Polar
               Circles
               and
               the
               Equinoctial
               Circle
               there
               is
               accounted
               24
               Climates
               ,
               which
               differ
               one
               from
               another
               by
               halfe
               an
               hours
               time
               :
               then
               from
               each
               Polar
               Circle
               ,
               to
               each
               Pole
               there
               are
               reckoned
               6.
               other
               Climates
               which
               differ
               one
               from
               another
               by
               a
               moneths
               time
               :
               so
               the
               whole
               earth
               is
               divided
               into
               60
               Climates
               ,
               30
               being
               allotted
               to
               the
               Northerne
               Hemisphere
               ,
               and
               30●
               to
               the
               Southerne
               Hemispheare
               .
               And
               here
               note
               ,
               that
               though
               these
               Climats
               which
               are
               betweene
               the
               Equinoctiall
               and
               the
               Polar
               Circles
               are
               equall
               one
               unto
               the
               other
               in
               respect
               of
               time
               ,
               to
               wit
               ,
               by
               halfe
               an
               houre
               ;
               yet
               the
               Latitude
               ,
               breadth
               ,
               or
               internall
               ,
               conteined
               between
               Climate
               and
               Climate
               ,
               is
               not
               equall
               :
               and
               by
               how
               much
               any
               Climate
               is
               farther
               from
               the
               Equinoctiall
               than
               another
               Climate
               ,
               by
               so
               much
               the
               lesser
               is
               the
               intervall
               between
               that
               Climate
               and
               the
               next
               :
               so
               those
               that
               are
               nearest
               the
               Equinoctial
               are
               largest
               ,
               
               and
               those
               which
               are
               farthest
               off
               most
               contracted
               :
               and
               to
               finde
               what
               Climate
               any
               Countrey
               is
               under
               :
               subtract
               the
               length
               of
               an
               Equinoctiall
               day
               ,
               to
               wit
               ,
               12
               houres
               from
               the
               length
               of
               the
               longest
               day
               of
               that
               Countrey
               ;
               the
               remainder
               being
               doubled
               shews
               the
               Climate
               :
               So
               at
               London
               the
               longest
               day
               is
               neare
               16
               houres
               and
               a
               halfe
               ;
               12
               taken
               from
               it
               there
               remaines
               4
               houres
               and
               a
               halfe
               ,
               which
               doubled
               makes
               9
               halfe
               houres
               ,
               that
               is
               ,
               9
               Climates
               ;
               so
               London
               is
               in
               the
               9
               climate
               .
            
          
           
             
               PROBLEM
               .
               XCVI
               .
               Of
               Longitude
               and
               Latitude
               of
               the
               Earth
               and
               of
               the
               Starres
               .
            
             
               LOngitude
               of
               a
               Countrey
               ,
               or
               place
               ,
               is
               an
               arcke
               of
               the
               Aequator
               conteined
               between
               the
               Meridian
               of
               the
               Azores
               ,
               and
               the
               Meridian
               of
               the
               place
               ,
               and
               the
               greatest
               Longitude
               that
               can
               be
               is
               360
               degrees
               .
            
             
               
                 Note
                 .
              
               
                 That
                 the
                 first
                 Meridian
                 may
                 be
                 taken
                 at
                 pleasure
                 upon
                 the
                 Terrestriall
                 Globe
                 or
                 Mappe
                 ,
                 for
                 that
                 some
                 of
                 the
                 ancient
                 Astronomers
                 would
                 have
                 it
                 at
                 Hercules
                 Pillars
                 ,
                 which
                 is
                 at
                 the
                 straights
                 at
                 
                   Gibraltar
                   :
                   Ptolomy
                
                 placed
                 it
                 at
                 the
                 
                   Canary
                   Isl●nds
                
                 ,
                 but
                 now
                 in
                 these
                 latter
                 times
                 it
                 is
                 held
                 to
                 be
                 neare
                 the
                 Azores
                 .
                 But
                 why
                 it
                 was
                 first
                 placed
                 by
                 Ptolomy
                 at
                 the
                 
                   Canary
                   Islands
                
                 ,
                 were
                 because
                 that
                 in
                 his
                 time
                 these
                 Islands
                 were
                 the
                 farthest
                 westerne
                 parts
                 of
                 the
                 world
                 that
                 vvas
                 then
                 discovered
                 .
                 And
                 vvhy
                 it
                 reteines
                 his
                 place
                 novv
                 at
                 Saint
                 Michaels
                 neare
                 the
                 
                 Azores
                 ,
                 is
                 that
                 because
                 of
                 many
                 accurate
                 observations
                 made
                 of
                 late
                 by
                 many
                 expert
                 Navigators
                 and
                 Mathematicians
                 ,
                 they
                 have
                 found
                 the
                 Needle
                 there
                 to
                 have
                 no
                 variation
                 ,
                 but
                 to
                 point
                 North
                 and
                 South
                 :
                 that
                 ,
                 is
                 to
                 each
                 Pole
                 of
                 the
                 world
                 :
                 and
                 why
                 the
                 Longitude
                 from
                 thence
                 is
                 accounted
                 Eastwards
                 ,
                 is
                 from
                 the
                 motion
                 of
                 the
                 Sunne
                 Eastward
                 ,
                 or
                 that
                 Ptolomy
                 and
                 others
                 did
                 hold
                 it
                 more
                 convenient
                 to
                 begin
                 from
                 the
                 Westerne
                 part
                 of
                 the
                 world
                 and
                 so
                 account
                 the
                 Longitude
                 Eastward
                 from
                 Countrey
                 to
                 Countrey
                 that
                 was
                 then
                 knowne
                 ;
                 till
                 they
                 came
                 to
                 the
                 Easterne
                 part
                 of
                 Asia
                 ,
                 rather
                 than
                 to
                 make
                 a
                 beginning
                 upon
                 that
                 which
                 was
                 unknowne
                 :
                 and
                 having
                 made
                 up
                 their
                 account
                 of
                 reckoning
                 the
                 Longitude
                 from
                 the
                 Westerne
                 part
                 to
                 the
                 Eastern
                 part
                 of
                 the
                 world
                 knowne
                 ,
                 they
                 supposed
                 the
                 rest
                 to
                 be
                 all
                 sea
                 ,
                 which
                 since
                 their
                 deaths
                 hath
                 been
                 found
                 almost
                 to
                 be
                 another
                 habitable
                 world
                 .
              
            
             
               
                 To
                 finde
                 the
                 Longitude
                 of
                 a
                 Countrey
                 .
              
               
                 IF
                 it
                 be
                 upon
                 the
                 Globe
                 ,
                 bring
                 the
                 Countrey
                 to
                 the
                 Brasen
                 Meridian
                 ,
                 and
                 whatsoever
                 degree
                 that
                 Meridian
                 cuts
                 in
                 the
                 Equinoctiall
                 ,
                 that
                 degree
                 is
                 the
                 Longitude
                 of
                 that
                 Place
                 :
                 if
                 it
                 be
                 in
                 a
                 Mappe
                 ,
                 then
                 mark
                 what
                 Meridian
                 passeth
                 over
                 it
                 ,
                 so
                 have
                 you
                 the
                 Longitude
                 thereof
                 ,
                 if
                 no
                 Meridian
                 passe
                 over
                 it
                 ,
                 then
                 take
                 a
                 paire
                 of
                 Compasses
                 ,
                 and
                 measure
                 the
                 distance
                 betweene
                 the
                 Place
                 and
                 the
                 next
                 Meridian
                 ,
                 and
                 apply
                 it
                 
                 to
                 the
                 divided
                 parallel
                 or
                 Aequator
                 ,
                 so
                 have
                 you
                 the
                 Longitude
                 required
                 .
              
            
             
               
                 Of
                 the
                 Latitude
                 of
                 Countreys
                 .
              
               
                 LAtitude
                 of
                 a
                 Countrey
                 is
                 the
                 distance
                 of
                 a
                 Countrey
                 from
                 the
                 Equinoctiall
                 ,
                 or
                 it
                 is
                 an
                 Arke
                 of
                 the
                 Meridian
                 conteined
                 between
                 the
                 Zenith
                 of
                 the
                 place
                 and
                 the
                 Aequator
                 ;
                 which
                 is
                 two-fold
                 ,
                 viz.
                 either
                 North-Latitude
                 or
                 South-Latitude
                 ,
                 either
                 of
                 which
                 extendeth
                 from
                 the
                 Equinoctiall
                 to
                 either
                 Pole
                 ,
                 so
                 the
                 greatest
                 Latitude
                 that
                 can
                 be
                 is
                 but
                 90
                 degrees
                 :
                 If
                 any
                 Northern
                 Countrey
                 have
                 the
                 Artick
                 Circle
                 verticall
                 ,
                 which
                 is
                 in
                 the
                 Latitude
                 of
                 66.
                 gr
                 .
                 30.
                 m.
                 the
                 Sun
                 will
                 touch
                 the
                 Horizon
                 in
                 the
                 North
                 part
                 thereof
                 ,
                 and
                 the
                 longest
                 day
                 will
                 be
                 there
                 then
                 24
                 houres
                 ,
                 if
                 the
                 Countrey
                 have
                 lesse
                 Latitude
                 than
                 66.
                 degrees
                 30.
                 m.
                 the
                 Sun
                 will
                 rise
                 and
                 set
                 ,
                 but
                 if
                 it
                 have
                 more
                 Latitude
                 than
                 66.
                 gr
                 .
                 30
                 m.
                 it
                 will
                 be
                 visible
                 for
                 many
                 dayes
                 ,
                 and
                 if
                 the
                 Countrey
                 be
                 under
                 the
                 Pole
                 ,
                 the
                 Sun
                 will
                 make
                 a
                 Circular
                 motion
                 above
                 the
                 Earth
                 ,
                 and
                 be
                 visible
                 for
                 a
                 half
                 yeare
                 :
                 so
                 under
                 the
                 Pole
                 there
                 will
                 be
                 but
                 one
                 day
                 ,
                 and
                 one
                 night
                 in
                 the
                 whole
                 yeare
                 .
              
               
                 
              
            
             
               
               
                 To
                 finde
                 the
                 latitude
                 of
                 Countreys
                 .
              
               
                 IF
                 it
                 be
                 upon
                 a
                 Globe
                 ,
                 bring
                 the
                 place
                 to
                 the
                 Brasen
                 Meridian
                 ,
                 and
                 the
                 number
                 of
                 degrees
                 
                 which
                 it
                 meeteth
                 therewith
                 ,
                 is
                 the
                 Latitude
                 of
                 the
                 place
                 .
                 Or
                 with
                 a
                 paire
                 of
                 Compasses
                 take
                 the
                 distance
                 between
                 the
                 Countrey
                 and
                 the
                 Equinoctiall
                 ,
                 which
                 applied
                 unto
                 the
                 Equinoctiall
                 will
                 shew
                 the
                 Latitude
                 of
                 that
                 Countrey
                 ;
                 which
                 is
                 equall
                 to
                 the
                 Poles
                 height
                 ;
                 if
                 it
                 be
                 upon
                 a
                 Mappe
                 .
                 Then
                 mark
                 what
                 parallel
                 passeth
                 over
                 the
                 Countrey
                 and
                 where
                 it
                 crosseth
                 the
                 Meridian
                 ,
                 that
                 shall
                 be
                 the
                 Latitude
                 :
                 but
                 if
                 ●o
                 parallel
                 passeth
                 over
                 it
                 ,
                 then
                 take
                 the
                 distance
                 betweene
                 the
                 place
                 and
                 the
                 next
                 parallel
                 ,
                 which
                 applied
                 to
                 the
                 divided
                 Meridian
                 from
                 that
                 parallel
                 will
                 shew
                 the
                 Latitude
                 of
                 that
                 place
                 .
              
            
             
               
                 To
                 finde
                 the
                 distance
                 of
                 places
                 .
              
               
                 IF
                 it
                 be
                 upon
                 a
                 Globe
                 :
                 then
                 with
                 a
                 paire
                 of
                 Compasses
                 take
                 the
                 distance
                 betweene
                 the
                 two
                 Places
                 ,
                 and
                 apply
                 it
                 to
                 the
                 divided
                 Meridian
                 or
                 Aequator
                 ,
                 and
                 the
                 number
                 of
                 degrees
                 shall
                 shew
                 ●e
                 distance
                 ;
                 each
                 degree
                 being
                 60.
                 miles
                 .
                 ●f
                 it
                 be
                 in
                 a
                 Mappe
                 (
                 according
                 to
                 Wrights
                 pro●ection
                 )
                 
                 take
                 the
                 distance
                 with
                 a
                 paire
                 of
                 Com●asses
                 between
                 the
                 two
                 places
                 ,
                 and
                 apply
                 this
                 distance
                 to
                 the
                 divided
                 Meridian
                 on
                 the
                 Mappe
                 right
                 against
                 the
                 two
                 places
                 ;
                 so
                 as
                 many
                 degrees
                 as
                 is
                 conteined
                 between
                 the
                 feet
                 of
                 the
                 Compasses
                 so
                 much
                 is
                 the
                 distance
                 between
                 the
                 two
                 places
                 .
                 If
                 the
                 distance
                 of
                 two
                 places
                 be
                 required
                 in
                 a
                 particular
                 Map
                 then
                 with
                 the
                 Compasses
                 take
                 the
                 distance
                 between
                 the
                 two
                 places
                 ,
                 and
                 apply
                 it
                 to
                 the
                 scale
                 of
                 Miles
                 ,
                 so
                 have
                 you
                 the
                 distance
                 ,
                 if
                 the
                 scale
                 be
                 too
                 short
                 ,
                 take
                 the
                 scale
                 between
                 the
                 Compasses
                 ,
                 and
                 apply
                 that
                 to
                 the
                 two
                 places
                 as
                 often
                 as
                 you
                 can
                 ,
                 so
                 have
                 you
                 the
                 distance
                 required
                 .
              
            
             
               
                 Of
                 the
                 Longitude
                 ,
                 Latitude
                 ,
                 Declination
                 ,
                 and
                 distance
                 of
                 the
                 Starres
                 .
              
               
                 THe
                 Declination
                 of
                 a
                 starre
                 is
                 the
                 nearest
                 distance
                 of
                 a
                 Star
                 from
                 the
                 Aequator
                 ;
                 the
                 Latitude
                 of
                 a
                 Starre
                 is
                 the
                 nearest
                 distance
                 of
                 a
                 Sarre
                 from
                 the
                 Ecliptick
                 :
                 the
                 Longitude
                 of
                 a
                 Starre
                 is
                 an
                 Ark
                 of
                 the
                 Ecliptick
                 conteined
                 between
                 the
                 beginning
                 of
                 Aries
                 ,
                 and
                 the
                 Circle
                 of
                 the
                 Starres
                 Latitude
                 ,
                 which
                 is
                 a
                 circle
                 drawne
                 from
                 the
                 Pole
                 of
                 the
                 Ecliptick
                 unto
                 the
                 starre
                 ,
                 and
                 so
                 to
                 the
                 Ecliptick
                 .
                 The
                 distance
                 between
                 two
                 Sarres
                 in
                 Heaven
                 is
                 taken
                 by
                 a
                 Crosse-staffe
                 or
                 other
                 Instrument
                 ,
                 and
                 upon
                 a
                 Globe
                 it
                 is
                 done
                 by
                 taking
                 between
                 the
                 feet
                 of
                 the
                 Compasses
                 the
                 two
                 Starres
                 ,
                 and
                 applying
                 it
                 
                 to
                 the
                 Aequator
                 ,
                 so
                 have
                 you
                 the
                 distance
                 betweene
                 those
                 two
                 starre●
                 .
              
            
             
               
                 How
                 is
                 it
                 that
                 two
                 Horses
                 or
                 other
                 creatures
                 being
                 foaled
                 or
                 brought
                 forth
                 into
                 the
                 world
                 at
                 one
                 and
                 the
                 same
                 time
                 ,
                 that
                 after
                 certaine
                 dayes
                 travell
                 the
                 one
                 lived
                 more
                 dayes
                 than
                 the
                 other
                 ,
                 notwithstanding
                 they
                 dyed
                 together
                 in
                 one
                 and
                 the
                 sam●
                 moment
                 also
                 ?
              
               
                 THis
                 is
                 easie
                 to
                 be
                 answered
                 :
                 let
                 one
                 of
                 them
                 travell
                 toward
                 the
                 West
                 and
                 the
                 other
                 towards
                 the
                 East
                 :
                 then
                 that
                 which
                 goes
                 towards
                 the
                 West
                 followeth
                 the
                 Sunne
                 :
                 and
                 therefore
                 shall
                 have
                 the
                 day
                 somewhat
                 longer
                 than
                 if
                 there
                 had
                 been
                 no
                 travell
                 made
                 ,
                 and
                 that
                 which
                 goes
                 East
                 by
                 going
                 against
                 the
                 Sunne
                 ,
                 shall
                 have
                 the
                 day
                 shorter
                 ,
                 and
                 so
                 in
                 respect
                 of
                 travell
                 though
                 they
                 dye
                 at
                 one
                 and
                 the
                 selfe
                 same
                 houre
                 and
                 moment
                 of
                 time
                 ,
                 the
                 one
                 shall
                 be
                 older
                 than
                 the
                 other
                 .
              
               
                 From
                 which
                 consideration
                 may
                 be
                 inferred
                 that
                 a
                 Christian
                 ,
                 a
                 Jew
                 ,
                 and
                 a
                 Saracen
                 ,
                 may
                 have
                 their
                 Sabbaths
                 all
                 upon
                 one
                 and
                 the
                 same
                 day
                 though
                 notwithstanding
                 the
                 Saracen
                 holds
                 his
                 Sabath
                 upon
                 the
                 Friday
                 ,
                 the
                 Jew
                 upon
                 the
                 Saturday
                 ,
                 and
                 the
                 Christian
                 upon
                 the
                 Sunday
                 :
                 For
                 being
                 all
                 three
                 resident
                 in
                 one
                 place
                 ,
                 if
                 the
                 Saracen
                 and
                 the
                 Christian
                 begin
                 their
                 travell
                 upon
                 the
                 Saturday
                 ,
                 the
                 Christian
                 going
                 West
                 ,
                 and
                 the
                 Saracen
                 Eastwards
                 ,
                 shall
                 compasse
                 the
                 
                 Globe
                 of
                 the
                 earth
                 ,
                 thus
                 the
                 Christian
                 at
                 the
                 conclusion
                 shall
                 gaine
                 a
                 day
                 ,
                 and
                 the
                 Saracen
                 shall
                 lose
                 a
                 day
                 ,
                 and
                 so
                 meet
                 with
                 the
                 Jew
                 every
                 one
                 upon
                 his
                 owne
                 Sabbath
                 .
              
            
             
               
                 Certaine
                 fine
                 observations
                 .
              
               
                 1
                 UNder
                 the
                 Equinoctiall
                 the
                 Needle
                 hangs
                 
                   in
                   equilibrio
                
                 ,
                 but
                 in
                 these
                 parts
                 it
                 inclines
                 under
                 the
                 Horizon
                 ,
                 and
                 being
                 under
                 the
                 Pole
                 it
                 is
                 thought
                 it
                 will
                 hang
                 verticall
                 .
              
               
                 2
                 In
                 these
                 Countreys
                 which
                 are
                 without
                 the
                 Tropicall
                 Circles
                 ,
                 the
                 Sunne
                 comes
                 East
                 and
                 West
                 every
                 day
                 for
                 a
                 halfe
                 yeare
                 ,
                 but
                 being
                 under
                 the
                 Equinoctiall
                 the
                 Sun
                 is
                 never
                 East
                 ,
                 nor
                 West
                 ▪
                 but
                 twice
                 in
                 the
                 yeare
                 ,
                 to
                 wit
                 ,
                 the
                 10.
                 of
                 March
                 and
                 the
                 13
                 of
                 September
                 .
              
               
                 3
                 If
                 a
                 ship
                 be
                 in
                 the
                 Latitude
                 of
                 23
                 gr
                 .
                 30
                 m.
                 that
                 is
                 ,
                 if
                 it
                 have
                 either
                 of
                 the
                 Tropicks
                 verticall
                 :
                 then
                 at
                 what
                 time
                 the
                 Sunnes
                 Altitude
                 is
                 equall
                 to
                 his
                 distan●e
                 from
                 any
                 of
                 the
                 Equinoctiall
                 points
                 ,
                 then
                 t●e
                 Sunne
                 is
                 due
                 East
                 or
                 West
                 .
              
               
                 4
                 If
                 a
                 ship
                 be
                 betweene
                 the
                 Equinoctiall
                 and
                 either
                 of
                 the
                 Tropicks
                 ,
                 the
                 Sunne
                 will
                 come
                 twice
                 to
                 one
                 point
                 of
                 the
                 compasse
                 in
                 the
                 forenoone
                 ,
                 that
                 is
                 ,
                 in
                 one
                 and
                 the
                 same
                 position
                 .
              
               
                 5
                 Vnder
                 the
                 Equinoctiall
                 neare
                 Guinea
                 there
                 is
                 but
                 two
                 sorts
                 of
                 windes
                 all
                 the
                 year
                 ,
                 6
                 moneths
                 a
                 Northerly
                 winde
                 ,
                 and
                 6
                 moneths
                 a
                 Southerly
                 winde
                 ,
                 and
                 the
                 flux
                 of
                 the
                 Sea
                 is
                 accordingly
                 .
              
               
                 6
                 If
                 two
                 ships
                 under
                 the
                 Equinoctiall
                 be
                 100.
                 leagues
                 asunder
                 ,
                 and
                 should
                 sayle
                 Northerly
                 
                 untill
                 they
                 were
                 come
                 under
                 the
                 Articke
                 circle
                 ,
                 they
                 should
                 then
                 be
                 but
                 50
                 leagues
                 asunder
                 .
              
               
                 7
                 Those
                 which
                 have
                 the
                 Artick
                 circle
                 ,
                 verticall
                 :
                 when
                 the
                 Sunne
                 is
                 in
                 the
                 Tropick
                 of
                 Cancer
                 ,
                 the
                 Sun
                 setteth
                 not
                 ,
                 but
                 toucheth
                 the
                 western
                 part
                 of
                 the
                 Horizon
                 .
              
               
                 8
                 If
                 the
                 complement
                 of
                 the
                 Sunnes
                 height
                 at
                 noon
                 be
                 found
                 equall
                 to
                 the
                 Sunnes
                 Declination
                 for
                 that
                 day
                 ,
                 then
                 the
                 ●quinoctiall
                 is
                 verticall
                 :
                 or
                 a
                 shippe
                 making
                 such
                 an
                 observation
                 ,
                 the
                 Equinoctiall
                 is
                 in
                 the
                 Zenith
                 ,
                 or
                 direct
                 over
                 them
                 ,
                 by
                 which
                 Navigators
                 know
                 when
                 they
                 crosse
                 the
                 line
                 ,
                 in
                 their
                 travels
                 to
                 the
                 Indies
                 ,
                 or
                 other
                 parts
                 .
              
               
                 9
                 The
                 Sunne
                 being
                 in
                 the
                 Equinoctiall
                 ,
                 the
                 extremity
                 of
                 the
                 stile
                 in
                 any
                 Sunne-dyall
                 upon
                 a
                 plaine
                 ,
                 maketh
                 a
                 right
                 line
                 ,
                 otherwise
                 it
                 is
                 
                   Eclipticall
                   ,
                   Hyperbolicall
                   ,
                   &c.
                
                 
              
               
                 10
                 When
                 the
                 shadow
                 of
                 a
                 man
                 ,
                 or
                 other
                 thing
                 upon
                 a
                 Horizontall
                 〈◊〉
                 is
                 equall
                 unto
                 it
                 in
                 length
                 ,
                 then
                 is
                 the
                 Sunne
                 in
                 the
                 middle
                 point
                 between
                 the
                 Horizon
                 and
                 the
                 Zenith
                 ,
                 that
                 is
                 ,
                 45
                 degrees
                 high
                 .
              
            
          
           
             
               PROBLEM
               .
               XCVII
               .
               To
               make
               a
               Triangle
               that
               shall
               have
               three
               right
               Angles
               .
            
             
               OPen
               the
               C●passes
               at
               p●easure
               :
               and
               upon
               A
               ,
               describe
               an
               Arke
               BC.
               then
               at
               the
               same
               opening
               ,
               place
               one
               of
               the
               feet
               in
               B
               ,
               and
               describe
               
               the
               Ark
               AC
               .
               Lastly
               ,
               place
               one
               of
               the
               feet
               of
               the
               Compasses
               in
               C.
               and
               describe
               the
               Arke
               AB·
               so
               shall
               you
               have
               the
               
               sphericall
               
                 Aequilaterall
                 Triangle
                 ABC
              
               ,
               right
               angled
               at
               A
               ,
               at
               B
               ,
               and
               at
               C.
               that
               is
               ,
               each
               angle
               comprehended
               9●
               .
               degrees
               :
               which
               can
               never
               be
               in
               any
               plaine
               Triangle
               ,
               whether
               it
               be
               
                 Equilaterall
                 ,
                 Isocelse
                 ,
                 scaleve
                 ,
                 Orthogonall
                 ,
              
               or
               Opigonall
               .
            
          
           
             
               PROBLEM
               .
               XCVIII
               .
               To
               divide
               a
               line
               in
               as
               many
               equall
               parts
               as
               one
               will
               ,
               without
               compasses
               ,
               or
               without
               seeing
               of
               it
               .
            
             
               THis
               Proposition
               hath
               a
               fallacie
               in
               it
               ,
               &
               cannot
               be
               practised
               but
               upon
               a
               Maincordion
               :
               for
               the
               Mathematicall
               line
               which
               proceeds
               from
               the
               flux
               of
               a
               point
               ,
               cannot
               be
               divided
               in
               that
               wise
               :
               One
               may
               have
               therefore
               an
               Instrument
               which
               is
               called
               Maincordion
               ,
               because
               there
               is
               but
               one
               cord
               :
               and
               if
               you
               desire
               to
               divide
               your
               line
               into
               3
               parts
               ,
               run
               your
               finger
               upon
               the
               frets
               untill
               you
               sound
               a
               third
               in
               musick
               :
               if
               you
               would
               have
               the
               fourth
               part
               of
               the
               line
               ,
               
               then
               finde
               the
               fourth
               sound
               ,
               a
               fifth
               ,
               &c.
               so
               shall
               you
               have
               the
               answer
               .
            
          
           
             
               PROBLEM
               .
               XCIX
               .
               To
               draw
               a
               line
               which
               shall
               incline
               to
               another
               line
               ,
               yet
               never
               meet
               :
               against
               the
               Axiome
               of
               Parallels
               .
            
             
               THis
               is
               done
               by
               help
               of
               a
               Conoeide
               line
               ,
               produced
               by
               a
               right
               line
               upon
               one
               &
               the
               same
               plaine
               ,
               held
               in
               great
               account
               amongst
               the
               Ancients
               ,
               and
               it
               is
               drawne
               after
               this
               manner
               .
            
             
               Draw
               a
               right
               line
               infinitely
               ,
               and
               upon
               some
               end
               of
               it
               ,
               as
               at
               I
               ,
               draw
               a
               perpendicular
               line
               I
               
               A.
               augment
               it
               to
               H.
               then
               from
               A.
               draw
               lines
               at
               pleasure
               to
               intersect
               the
               line
               
                 I.
                 M.
              
               in
               each
               of
               which
               lines
               from
               the
               right
               line
               ,
               IM
               .
               transferre
               
                 IH
                 .
                 viz.
                 KB
                 .
                 LC.OD.PE.QF.MG
                 .
              
               then
               from
               those
               points
               draw
               the
               line
               H.B.C.D.E.F.G.
               which
               will
               not
               meet
               with
               the
               line
               IM
               .
               and
               yet
               incline
               nearer
               and
               nearer
               unto
               it
               .
            
          
           
             
             
               PROBLEM
               .
               C.
               To
               observe
               the
               variation
               of
               the
               compasses
               ,
               or
               needle
               in
               any
               places
               .
            
             
               FIrst
               describe
               a
               Circle
               upon
               a
               plaine
               ,
               so
               that
               the
               Sun
               may
               shine
               on
               it
               both
               before
               noone
               and
               afternoone
               :
               in
               the
               centre
               of
               which
               Circle
               place
               a
               Gn●●on
               or
               wire
               perpendicular
               as
               AB
               ,
               and
               an
               houre
               before
               noone
               marke
               the
               extremitie
               of
               the
               shadow
               of
               AB
               ,
               which
               suppose
               it
               be
               at
               C.
               describe
               a
               Circle
               at
               that
               semidiamiter
               CDF
               .
               then
               after
               noone
               mark
               when
               the
               top
               of
               the
               shadow
               of
               AB
               .
               toucheth
               the
               Circle
               ,
               which
               admit
               in
               D
               ;
               divide
               the
               distance
               CD
               into
               two
               equall
               parts
               ,
               which
               suppose
               at
               E.
               draw
               the
               line
               EAF
               .
               which
               is
               the
               Meridian
               line
               ,
               or
               line
               of
               North
               &
               South
               :
               now
               
               if
               the
               Arke
               of
               the
               Circle
               CD
               .
               be
               divided
               into
               degrees
               .
               place
               a
               Needle
               GH
               ,
               upon
               a
               plaine
               set
               up
               in
               the
               Centre
               ,
               and
               marke
               how
               many
               degrees
               the
               point
               of
               the
               Needle
               G
               ,
               is
               from
               E.
               so
               much
               doth
               the
               Needle
               vary
               from
               the
               North
               in
               that
               place
               .
            
          
           
             
             
               PROBLEM
               .
               CI.
               How
               to
               finde
               at
               any
               time
               which
               way
               the
               wind
               is
               in
               ones
               Chamber
               ,
               without
               going
               abroad
               ?
            
             
               VPon
               the
               Plancking
               or
               floore
               of
               a
               Chamber
               ,
               Parlor
               ,
               or
               Hall
               ,
               that
               you
               intend
               to
               have
               this
               device
               ,
               let
               there
               come
               downe
               from
               the
               top
               of
               the
               house
               a
               hollow
               post
               ,
               in
               which
               place
               an
               Iron
               rod
               that
               it
               ascend
               above
               the
               house
               10
               ,
               or
               6
               
               foot
               with
               a
               vane
               or
               a
               scouchen
               at
               it
               to
               shew
               the
               winds
               without
               :
               and
               at
               the
               lower
               end
               of
               this
               rod
               of
               Iron
               ,
               place
               a
               Dart
               which
               may
               by
               the
               moving
               of
               the
               vane
               with
               the
               wind
               without
               ,
               turne
               this
               Dart
               which
               is
               within
               :
               about
               which
               upon
               the
               plaister
               must
               be
               described
               a
               Circle
               divided
               into
               the
               32
               points
               of
               the
               Mariners
               Compasse
               pointed
               and
               distinguished
               to
               that
               end
               ,
               then
               may
               it
               be
               marked
               by
               placi●
               to
               Compasse
               by
               it
               ;
               for
               having
               noted
               the
               North
               point
               ,
               the
               East
               ,
               &c
               ▪
               it
               is
               easie
               to
               note
               all
               the
               rest
               of
               the
               points
               :
               and
               so
               at
               any
               time
               comming
               into
               this
               Roome
               ,
               you
               have
               nothing
               to
               do
               but
               to
               look
               up
               to
               the
               Dart
               ,
               which
               will
               point
               you
               out
               what
               way
               the
               winde
               bloweth
               at
               that
               instant
               .
            
          
           
             
             
               PROBLEM
               .
               CII
               .
               How
               to
               draw
               a
               parallel
               sphericall
               line
               with
               great
               ease
               ?
            
             
               FIrst
               draw
               an
               obscure
               line
               GF
               .
               in
               the
               middle
               of
               it
               make
               two
               points
               AB
               ,
               (
               which
               serves
               for
               Centres
               then
               place
               one
               foot
               of
               the
               Compasses
               in
               B
               ,
               and
               extend
               the
               other
               foot
               to
               A
               ,
               and
               describe
               the
               
                 semicircle
                 AC
              
               .
               then
               place
               one
               foot
               of
               the
               Compasses
               in
               A
               ,
               and
               extend
               the
               other
               foot
               to
               C
               ,
               and
               describe
               the
               
                 semicircle
                 CD
              
               .
               Now
               place
               the
               Compasses
               in
               B
               ,
               and
               extend
               the
               other
               foot
               unto
               D
               ,
               and
               describe
               the
               
                 semicircle
                 DF
              
               ,
               and
               so
               
                 ad
                 infinitum
              
               ;
               which
               being
               done
               neatly
               ,
               that
               there
               be
               
               no
               right
               line
               seene
               nor
               where
               the
               Compasses
               were
               placed
               ,
               will
               seeme
               very
               strange
               how
               possibly
               it
               could
               be
               drawne
               with
               such
               exactnes
               ,
               to
               such
               which
               are
               ignorant
               of
               that
               way
               .
            
          
           
             
             
               PROBLEM
               .
               CIII
               .
               To
               measure
               an
               in
               accessible
               distance
               ,
               as
               the
               breadth
               of
               a
               River
               with
               the
               help
               of
               ones
               hat
               onely
               .
            
             
               THe
               way
               of
               this
               is
               easie
               :
               for
               having
               ones
               hat
               upon
               his
               head
               ,
               come
               neare
               to
               the
               bank
               of
               the
               River
               ,
               and
               holding
               your
               head
               upright
               (
               which
               may
               be
               by
               putting
               a
               small
               stick
               to
               some
               one
               of
               your
               buttons
               to
               prop
               up
               the
               chin
               )
               pluck
               downe
               the
               brim
               or
               edge
               of
               your
               hat
               untill
               you
               may
               but
               see
               the
               other
               side
               of
               the
               water
               ,
               then
               turne
               about
               the
               body
               in
               the
               same
               posture
               that
               it
               was
               before
               towards
               some
               plaine
               ,
               and
               marke
               where
               the
               sight
               by
               the
               brimme
               of
               the
               hat
               glaunceth
               on
               the
               ground
               ▪
               for
               the
               distance
               from
               that
               place
               to
               your
               standing
               ,
               is
               the
               breadth
               of
               the
               River
               required
               .
            
          
           
             
               PROBLEM
               .
               CIIII.
               How
               to
               measure
               a
               height
               with
               two
               strawes
               or
               two
               small
               stickes
               .
            
             
               TAke
               two
               strawes
               or
               two
               stickes
               which
               are
               one
               as
               long
               as
               another
               ,
               and
               place
               them
               at
               right
               Angles
               one
               to
               the
               other
               ,
               as
               AB
               .
               and
               AC
               .
               then
               holding
               AB
               .
               parallel
               to
               the
               ground
               ,
               place
               the
               end
               A
               to
               the
               eye
               at
               A.
               and
               looking
               to
               the
               other
               top
               BC.
               at
               C.
               by
               going
               backward
               or
               forward
               
               untill
               you
               may
               
               see
               the
               top
               of
               the
               Tower
               or
               tree
               ,
               which
               suppose
               at
               E.
               So
               the
               distance
               from
               your
               standing
               to
               the
               Tower
               or
               Tree
               ,
               is
               equall
               to
               the
               height
               thereof
               above
               the
               levell
               of
               the
               eye
               :
               to
               which
               if
               you
               adde
               your
               ovvne
               height
               you
               have
               the
               whole
               height
               .
            
             
               
                 Otherwise
                 .
              
               
                 TAke
                 an
                 ordinary
                 
                 square
                 which
                 Carpenters
                 or
                 other
                 workemen
                 use
                 ,
                 as
                 HKL
                 .
                 and
                 placing
                 H.
                 to
                 the
                 eye
                 so
                 that
                 HK
                 .
                 be
                 levell
                 ,
                 go
                 back
                 or
                 come
                 nearer
                 untill
                 that
                 by
                 it
                 you
                 may
                 see
                 the
                 top
                 M.
                 for
                 then
                 the
                 distance
                 from
                 you
                 to
                 the
                 height
                 is
                 equall
                 to
                 the
                 height
                 .
              
            
          
           
             
             
               PROBLEM
               .
               CV
               .
               How
               to
               make
               statues
               ,
               letters
               ,
               bowles
               ,
               or
               other
               things
               which
               are
               placed
               in
               the
               side
               of
               a
               high
               building
               ,
               to
               be
               seen
               below
               of
               an
               equall
               bignesse
               .
            
             
               LEt
               BC.
               be
               a
               Pillar
               7
               yards
               high
               ,
               and
               let
               it
               be
               required
               that
               three
               yards
               above
               the
               levell
               of
               the
               eye
               
                 A
                 ,
                 viz.
              
               at
               B.
               be
               placed
               a
               Globe
               ,
               and
               9
               yards
               above
               B.
               be
               placed
               another
               ,
               &
               22.
               yards
               above
               that
               be
               placed
               another
               Globe
               :
               how
               much
               shall
               the
               Diameter
               of
               these
               Globes
               be
               ,
               that
               at
               the
               eye
               ,
               at
               A
               ,
               
               they
               may
               all
               appeare
               to
               be
               of
               one
               and
               the
               same
               Magnitude
               :
               It
               is
               thus
               done
               ,
               first
               draw
               a
               line
               as
               AK
               .
               and
               upon
               K.
               erect
               a
               perpendicular
               KX
               .
               divide
               this
               line
               into
               27
               parts
               ▪
               and
               according
               to
               AK
               .
               describe
               an
               Arke
               KY
               .
               then
               from
               
                 K
                 ▪
              
               in
               the
               perpendicular
               KX
               ,
               account●
               ▪
               par●s
               ,
               viz
               at
               L.
               which
               shall
               represent
               the
               former
               three
               yardes
               ,
               and
               draw
               the
               line
               LA.
               from
               L
               ,
               in
               the
               said
               perpendicular
               reckon
               the
               diameter
               of
               the
               lesser
               Globe
               of
               what
               Magnitude
               it
               is
               intended
               to
               be
               :
               suppose
               SL
               ,
               and
               draw
               the
               line
               SA
               .
               cutting
               the
               Arke
               VK
               .
               in
               N.
               then
               from
               K.
               in
               the
               perpendicular
               account
               9
               yards
               ,
               which
               admit
               at
               T.
               draw
               TA
               ,
               cutting
               YK.
               in
               O
               transferre
               the
               Arke
               MN
               ,
               from
               
               A
               to
               P.
               and
               draw
               AP.
               which
               will
               cut
               the
               perpendicular
               in
               V.
               so
               a
               line
               drawne
               from
               the
               middle
               of
               VF
               .
               unto
               the
               visuall
               lines
               AI
               ,
               and
               AV
               ,
               shall
               be
               the
               diameter
               of
               the
               next
               Globe
               :
               Lastly
               ,
               account
               from
               K.
               in
               the
               perpendicular
               XK
               .
               22
               parts
               ,
               and
               draw
               the
               line
               WA
               .
               cutting
               YK
               in
               Q.
               then
               take
               the
               Arke
               MN
               ,
               and
               transferre
               it
               from
               Q
               to
               R
               and
               draw
               
                 AR
                 ▪
              
               which
               will
               cut
               the
               perpendicular
               in
               X
               so
               the
               line
               which
               passeth
               by
               the
               meddle
               of
               XW
               .
               perpendicular
               to
               the
               visuall
               line
               AW
               ,
               and
               AX.
               be
               the
               Diameter
               of
               the
               third
               Globe
               ,
               to
               wit
               5
               ,
               6.
               which
               measures
               transferred
               in
               the
               Pillar
               BC.
               which
               sheweth
               the
               true
               Magnitude
               of
               the
               Globes
               1
               ,
               2
               ,
               3.
               from
               this
               an
               Architect
               or
               doth
               proportion
               his
               Images
               ,
               &
               the
               foulding
               of
               the
               Robes
               which
               are
               most
               deformed
               at
               the
               eye
               below
               in
               the
               making
               ,
               yet
               most
               perfect
               when
               it
               is
               set
               in
               his
               true
               height
               above
               the
               eye
               .
            
          
           
             
               PROBLEM
               .
               CVI.
               How
               to
               disg●is●
               or
               disfigure
               an
               Image
               ,
               as
               a
               head
               ,
               an
               arme
               ,
               a
               whole
               body
               ,
               &c.
               so
               that
               it
               hath
               no
               proportion
               the
               eares
               to
               become
               long
               :
               the
               nose
               as
               that
               of
               a
               swan
               ,
               the
               mouth
               as
               a
               coaches
               entrance
               ,
               &c
               yet
               the
               eye
               placed
               at
               a
               certaine
               point
               will
               be
               seen
               in
               a
               direct
               &
               exact
               proportion
               .
            
             
               I
               Will
               not
               strive
               to
               set
               a
               Geometricall
               figure
               here
               ,
               for
               feare
               it
               may
               seeme
               too
               difficult
               to
               understand
               ,
               
               but
               I
               will
               indeavour
               by
               discourse
               how
               Mechanically
               with
               a
               Candle
               you
               may
               perceive
               it
               sensible
               :
               first
               there
               must
               be
               made
               a
               figure
               upon
               Paper
               ,
               such
               as
               you
               please
               ,
               according
               to
               his
               just
               proportion
               ,
               and
               paint
               it
               as
               a
               Picture
               (
               which
               painters
               know
               well
               enough
               to
               do
               )
               afterwards
               put
               a
               Candle
               upon
               the
               Table
               ,
               and
               interpose
               this
               figure
               obliquely
               ,
               between
               the
               said
               Candle
               and
               the
               Bookes
               of
               Paper
               ,
               where
               you
               desire
               to
               have
               the
               figure
               disguised
               in
               such
               sort
               that
               the
               height
               passe
               athwart
               the
               hole
               of
               the
               Picture
               :
               then
               will
               it
               carry
               all
               the
               forme
               of
               the
               Picture
               upon
               the
               Paper
               ,
               but
               with
               deformity
               ;
               follow
               these
               tracts
               and
               marke
               out
               the
               light
               with
               a
               Coles
               black
               head
               or
               Ink
               :
               and
               you
               have
               your
               desire
               .
            
             
               To
               finde
               now
               the
               point
               where
               the
               eye
               must
               see
               it
               in
               his
               naturall
               forme
               :
               it
               is
               accustomed
               according
               to
               the
               order
               of
               Perspective
               ,
               to
               place
               this
               point
               in
               the
               line
               drawne
               in
               height
               ,
               equall
               to
               the
               largenesse
               of
               the
               narrowest
               side
               of
               the
               deformed
               square
               ,
               and
               it
               is
               by
               this
               way
               that
               it
               is
               performed
               .
            
          
           
             
               PROBLEM
               .
               CVII
               .
               How
               a
               Cannon
               after
               that
               it
               hath
               shot
               ,
               may
               be
               covered
               from
               the
               battery
               of
               the
               enemy
               .
            
             
               LEt
               the
               mouth
               of
               a
               Cannon
               be
               I
               ,
               the
               Cannon
               M.
               his
               charge
               NO
               ,
               the
               wheele
               L
               ,
               the
               axletree
               PB
               .
               upon
               which
               the
               Cannon
               is
               placed
               ,
               at
               
               which
               end
               towards
               B
               ,
               is
               placed
               a
               pillar
               AE·
               supported
               with
               props
               
                 D
                 ,
                 C
                 ,
                 E
                 ,
                 F
                 ,
                 G
              
               ▪
               about
               which
               the
               Axeltree
               
               turneth
               :
               now
               the
               Cannon
               being
               to
               shoot
               ,
               it
               retires
               to
               H
               ,
               which
               cannot
               be
               directly
               because
               of
               the
               Axletree
               ,
               but
               it
               make
               a
               segment
               of
               a
               circle
               ▪
               and
               hides
               himselfe
               behind
               the
               wal
               QR
               ,
               and
               so
               preserves
               it selfe
               from
               the
               Enemies
               battery
               ,
               by
               which
               meanes
               one
               may
               avoid
               many
               inconveniences
               which
               might
               arise
               :
               and
               moreover
               ,
               one
               man
               may
               more
               easily
               replace
               it
               againe
               for
               another
               shot
               by
               help
               of
               poles
               tyed
               to
               the
               wall
               ,
               or
               other
               help
               which
               may
               multiply
               the
               strength
               .
            
          
           
             
               PROBLEM
               .
               CVIII
               .
               How
               to
               make
               a
               Lever
               ,
               by
               which
               one
               man
               may
               alone
               place
               a
               Cannon
               upon
               his
               carriage
               ,
               or
               raise
               what
               other
               weight
               he
               would
               .
            
             
               FIrst
               place
               two
               thick
               boards
               upright
               ,
               as
               the
               figure
               sheweth
               ,
               pierced
               with
               holes
               ,
               alike
               opposite
               one
               unto
               another
               as
               CD
               ,
               and
               EF
               :
               &
               let
               L
               ,
               and
               M
               ,
               be
               the
               two
               barres
               of
               Iron
               which
               passeth
               through
               the
               holes
               GH
               ,
               and
               
                 F
                 ,
                 K
              
               ,
               the
               
               
               two
               supports
               ,
               or
               props
               ,
               AB
               .
               the
               Cannon
               ,
               OP
               ,
               the
               Lever
               ,
               RS
               ,
               the
               two
               notches
               in
               the
               Lever
               ,
               and
               Q
               ,
               the
               hooke
               where
               the
               burthen
               or
               Cannon
               is
               tyed
               to
               .
               The
               rest
               of
               the
               operation
               is
               ●cill
               ,
               that
               the
               youngest
               schollers
               or
               learners
               cannot
               faile
               to
               performe
               it
               :
               to
               teach
               Minerva
               were
               in
               vaine
               ,
               and
               it
               were
               to
               Mathematicians
               injury
               in
               the
               succeeding
               Ages
               .
            
          
           
             
               PROBLEM
               .
               CIX
               .
               How
               to
               make
               a
               Clock
               with
               one
               onely
               wheele
               .
            
             
               
               MAke
               the
               body
               of
               an
               ordinary
               Dyall
               ,
               and
               divide
               the
               houre
               in
               the
               Circle
               into
               12.
               parts
               :
               make
               a
               great
               wheele
               in
               height
               above
               the
               Axletree
               ,
               to
               the
               which
               you
               shall
               place
               the
               cord
               of
               your
               counterpoize
               ▪
               so
               that
               it
               may
               descend
               ,
               that
               in
               1●
               
               houres
               of
               time
               your
               Index
               or
               Needle
               may
               make
               one
               revolution
               ,
               which
               may
               be
               knowne
               by
               a
               watch
               which
               you
               may
               have
               by
               you
               :
               then
               put
               a
               balance
               which
               may
               stop
               the
               course
               of
               the
               Wheele
               ,
               and
               give
               it
               a
               regular
               motion
               ,
               and
               you
               shall
               see
               an
               effect
               as
               just
               from
               this
               as
               from
               a
               Clock
               with
               many
               wheeles
               .
            
          
           
             
               PROBLEM
               .
               CX
               .
               How
               by
               help
               of
               two
               wheeles
               to
               make
               a
               Childe
               to
               draw
               up
               alone
               a
               hogshead
               of
               water
               at
               a
               time
               :
               and
               being
               drawne
               up
               shall
               cast
               out
               it selfe
               into
               another
               vessell
               as
               one
               would
               have
               it
               .
            
             
               LEt
               R
               be
               the
               Pit
               from
               whence
               water
               is
               to
               be
               drawne
               ,
               P
               the
               hook
               to
               throw
               out
               the
               water
               when
               it
               is
               brought
               up
               (
               this
               hook
               must
               be
               moveable
               )
               let
               AB
               be
               the
               Axis
               of
               the
               wheele
               SF
               ,
               which
               wheele
               hath
               divers
               forkes
               of
               Iron
               made
               at
               G
               ,
               equally
               fastened
               at
               the
               wheele
               ;
               let
               I
               ,
               be
               a
               Card
               ,
               which
               is
               drawne
               by
               K
               ,
               to
               make
               the
               wheele
               S
               ,
               to
               turne
               ,
               vvhich
               vvheele
               S
               ,
               beares
               proportion
               to
               the
               vvheele
               T
               ,
               as
               8
               to
               ●
               .
               let
               N
               be
               a
               Chaine
               of
               Iron
               to
               vvhich
               is
               tyed
               the
               vessel
               O
               ,
               and
               the
               other
               vvhich
               is
               in
               the
               Pit
               :
               E●
               is
               a
               piece
               of
               vvood
               vvhich
               hath
               a
               mortes
               in
               1
               ,
               and
               ●
               ,
               by
               vvhich
               the
               Cord
               I
               ,
               passeth
               ,
               tyed
               at
               the
               vvall
               ,
               as
               KH
               ,
               and
               the
               other
               piece
               of
               timber
               of
               the
               little
               vvheele
               as
               M
               ,
               mortified
               in
               likevvise
               for
               the
               
               chaine
               to
               passe
               through
               :
               draw
               the
               
                 Cord
                 I
              
               ,
               by
               K
               ,
               and
               the
               wheele
               will
               turne
               ,
               &
               so
               consequently
               the
               wheele
               T
               ,
               which
               will
               cause
               the
               vessell
               O
               to
               raise
               ;
               which
               being
               
               empty
               ,
               draw
               the
               cord
               againe
               by
               Y
               ,
               and
               the
               other
               vessell
               which
               is
               in
               the
               pit
               ●ill
               come
               out
               by
               the
               same
               reason
               .
               This
               is
               an
               invention
               which
               will
               save
               labour
               if
               practised
               ;
               but
               here
               is
               to
               be
               noted
               that
               the
               pit
               must
               be
               large
               enough
               ,
               to
               the
               end
               that
               it
               conteine
               two
               great
               vessels
               to
               passe
               up
               and
               downe
               one
               by
               another
               ▪
            
          
           
             
               PROBLEM
               .
               CXI
               .
               To
               make
               a
               Ladder
               of
               Cords
               ,
               which
               may
               be
               carryed
               in
               ones
               pocket
               :
               by
               which
               one
               may
               easily
               mount
               up
               a
               Wall
               ,
               or
               Tree
               alone
               .
            
             
               TAke
               two
               Pullies
               A
               ,
               &
               D
               ,
               unto
               that
               of
               A
               ,
               let
               there
               be
               fastened
               a
               Cramp
               of
               Iron
               as
               B
               ;
               and
               at
               D
               ,
               let
               there
               be
               fastened
               a
               staffe
               of
               a
               foot
               and
               a
               halfe
               long
               as
               F
               ,
               then
               the
               Pully
               A
               :
               place
               a
               hand
               of
               Iron
               ,
               as
               E
               ,
               to
               vvhich
               tie
               a
               cord
               of
               an
               halfe
               inch
               thick
               (
               vvhich
               may
               be
               of
               silk
               because
               it
               is
               for
               the
               pocket
               :
               )
               then
               strive
               to
               make
               fast
               the
               
               Pully
               A
               ,
               by
               the
               help
               of
               the
               Crampe
               of
               Iron
               B
               ,
               to
               the
               place
               that
               you
               intend
               to
               scale
               ;
               and
               the
               staffe
               F
               ,
               being
               tyed
               at
               the
               Pully
               D
               ,
               put
               it
               betvveen
               your
               legges
               as
               though
               you
               vvould
               sit
               upon
               it
               :
               then
               holding
               
               the
               
                 Cord
                 C
              
               in
               your
               hand
               ,
               you
               may
               guide
               your selfe
               to
               the
               place
               required
               ▪
               vvhich
               may
               be
               made
               more
               facill
               by
               the
               multiplying
               of
               Pullies
               .
               This
               secret
               is
               most
               excellent
               in
               Warre
               ,
               and
               for
               lovers
               ,
               its
               supportablenesse
               avoids
               suspition
               .
            
          
           
             
               PROBLEM
               .
               CXII
               .
               How
               to
               make
               a
               Pumpe
               whose
               strength
               is
               marvelous
               by
               reason
               of
               the
               great
               weight
               of
               water
               that
               it
               is
               able
               to
               bring
               up
               at
               once
               ,
               and
               so
               by
               continuance
               .
            
             
               LEt
               
                 〈◊〉
                 〈◊〉
                 〈◊〉
                 〈◊〉
                 〈◊〉
              
               ,
               be
               the
               height
               of
               the
               case
               about
               two
               or
               three
               foot
               high
               ,
               and
               broader
               according
               to
               discretion
               :
               the
               rest
               of
               the
               Case
               or
               concavity
               let
               be
               O
               :
               let
               the
               sucker
               of
               the
               Pumpe
               vvhich
               is
               made
               ,
               be
               just
               for
               the
               Case
               or
               Pumpes
               head
               
                 〈◊〉
                 〈◊〉
                 〈◊〉
                 〈◊〉
                 〈◊〉
              
               ,
               &
               may
               be
               made
               of
               vvood
               or
               brasse
               of
               4
               inches
               thick
               ,
               having
               a
               hole
               at
               E
               ,
               vvhich
               descending
               
               
               raiseth
               up
               the
               cover
               P
               ,
               by
               which
               issueth
               forth
               the
               water
               ,
               &
               ascending
               or
               raising
               up
               it
               shuts
               it
               or
               makes
               it
               close
               :
               RS
               ,
               is
               the
               handle
               of
               the
               sucker
               tyed
               to
               the
               handle
               TX
               ,
               which
               works
               in
               the
               post
               VZ
               .
               Let
               
                 A
                 ,
                 B
                 ,
                 C
                 ,
                 D
                 ,
              
               be
               a
               piece
               of
               Brasse
               ,
               G
               the
               piece
               which
               enters
               into
               the
               hole
               to
               F
               ,
               to
               keep
               out
               the
               Aire
               .
               
                 H
                 ,
                 I
                 ,
                 K
                 ,
                 L
                 ,
              
               the
               piece
               tyed
               at
               the
               funnell
               or
               pipe
               :
               in
               which
               playes
               the
               Iron
               rod
               or
               axis
               G
               ,
               so
               that
               it
               passe
               through
               the
               other
               piece
               MN
               ,
               which
               is
               tyed
               with
               the
               end
               of
               the
               pipe
               of
               Brasse
               .
            
             
               Note
               ,
               that
               the
               lower
               end
               of
               the
               Cisterne
               ought
               to
               be
               rested
               upon
               a
               Gridiron
               or
               Iron
               Grate
               ▪
               which
               may
               be
               tyed
               in
               the
               pit
               ,
               by
               which
               means
               lifting
               up
               and
               putting
               downe
               the
               handle
               ,
               you
               may
               draw
               ten
               times
               more
               water
               than
               otherwise
               you
               could
               .
            
          
           
             
               PROBLEM
               .
               CXIII
               .
               How
               by
               meanes
               of
               a
               Cisterne
               ,
               to
               make
               water
               of
               a
               Pit
               continually
               to
               ascend
               without
               strength
               ,
               or
               the
               assistance
               of
               any
               other
               Pumpe
               .
            
             
               LEt
               IL
               ,
               be
               the
               Pit
               where
               one
               would
               cause
               water
               to
               ascend
               continually
               to
               ●●ach
               office
               
               of
               a
               house
               or
               the
               places
               which
               are
               separated
               from
               it
               :
               let
               there
               be
               made
               a
               receive●
               as
               A
               ,
               well
               closed
               up
               with
               lead
               or
               other
               matter
               that
               aire
               enter
               not
               in
               ,
               to
               which
               fasten
               a
               pipe
               of
               lead
               as
               at
               E
               ,
               which
               may
               have
               vent
               at
               pleasure
               ,
               then
               let
               there
               be
               made
               a
               Cisterne
               as
               B
               ,
               which
               may
               be
               communicative
               to
               A
               ,
               by
               helpe
               of
               the
               pipe
               G
               ,
               from
               vvhich
               Cistern
               
               B
               ,
               may
               issue
               the
               vvater
               of
               pipe
               D
               ,
               vvhich
               may
               descend
               to
               H
               ,
               vvhich
               is
               a
               little
               belovv
               the
               levell
               of
               the
               vvater
               of
               the
               pit
               as
               much
               as
               is
               GH
               .
               to
               the
               end
               of
               vvhich
               shall
               be
               soldered
               close
               a
               Cock
               vvhich
               shall
               cast
               out
               the
               vvater
               by
               KH
               .
               Novv
               to
               make
               use
               of
               it
               ,
               let
               B
               be
               filled
               full
               of
               vvater
               ,
               and
               vvhen
               you
               vvould
               have
               it
               run
               turne
               the
               Cock
               ,
               for
               then
               the
               vvater
               in
               B
               ,
               vvill
               descend
               by
               K.
               and
               for
               feare
               that
               there
               should
               be
               vacuity
               ,
               nature
               vvhich
               abhors
               it
               ,
               vvill
               labour
               to
               furnish
               and
               supply
               that
               emptinesse
               out
               of
               the
               spring
               F
               ,
               and
               that
               the
               Pit
               dry
               not
               ,
               the
               Pipe
               ought
               to
               be
               small
               of
               an
               indifferent
               capacity
               according
               to
               the
               greatnesse
               or
               smalnesse
               of
               the
               spring
               .
            
          
           
             
             
               PROBLEM
               .
               CXIIII
               .
               How
               out
               of
               a
               fountaine
               to
               cast
               the
               water
               very
               high
               :
               different
               from
               a
               Probleme
               formerly
               delivered
               .
            
             
               LEt
               the
               fountaine
               be
               BD
               ,
               of
               a
               round
               forme
               (
               seeing
               it
               is
               the
               most
               capable
               and
               most
               perfect
               figure
               )
               place
               into
               it
               two
               pipes
               conjoyned
               as
               EA
               ,
               and
               HC
               ,
               so
               that
               no
               Aire
               may
               enter
               in
               at
               the
               place
               of
               joyning
               :
               let
               each
               of
               the
               Pipes
               
               have
               a
               cock
               G
               ,
               &
               L
               :
               the
               cocke
               at
               G
               ,
               being
               closed
               ,
               open
               that
               at
               I
               ▪
               &
               so
               with
               a
               squirt
               force
               the
               water
               through
               the
               hole
               at
               H
               ,
               then
               close
               the
               Cocke
               at
               A
               ,
               &
               draw
               out
               the
               squirt
               ,
               and
               open
               the
               cock
               at
               G.
               the
               Aire
               being
               before
               rarified
               will
               extend
               his
               dimensions
               ,
               and
               force
               the
               water
               with
               such
               violence
               ,
               that
               it
               will
               amount
               above
               the
               height
               of
               one
               or
               two
               Pipes
               :
               and
               so
               much
               the
               more
               by
               how
               much
               the
               Machine
               is
               great
               :
               this
               violence
               will
               last
               but
               a
               little
               while
               if
               the
               Pipe
               have
               too
               great
               an
               opening
               ,
               for
               as
               the
               Aire
               approacheth
               to
               his
               naturall
               place
               ,
               so
               the
               force
               will
               diminish
               .
            
          
           
             
             
               PROBLEM
               .
               CXV
               .
               How
               to
               empty
               the
               water
               of
               a
               Cisterne
               by
               a
               Pipe
               which
               shall
               have
               a
               motion
               of
               it selfe
               .
            
             
               LEt
               AB
               ,
               be
               the
               vessell
               ;
               CDE
               ,
               the
               Pipe
               :
               HG
               ,
               a
               little
               vessell
               under
               the
               greater
               ,
               in
               which
               one
               end
               of
               the
               Pipe
               is
               ,
               
                 viz.
                 C
              
               ,
               and
               let
               the
               other
               end
               of
               the
               Pipe
               E.
               passing
               through
               the
               bottome
               of
               the
               vessell
               
               at
               F
               ,
               then
               as
               the
               vessell
               filleth
               so
               will
               the
               Pipe
               ,
               and
               when
               the
               vessell
               ,
               shall
               be
               full
               as
               farre
               as
               PO
               ,
               the
               Pipe
               will
               begin
               to
               runne
               at
               E
               ,
               of
               his
               owne
               accord
               ,
               and
               never
               cease
               untill
               the
               vessell
               be
               wholly
               empty
               .
            
          
           
             
               PROBLEM
               CXVI
               .
               How
               to
               squirt
               or
               spout
               out
               a
               great
               height
               ,
               so
               that
               one
               pot
               of
               water
               shall
               last
               a
               long
               time
               .
            
             
               LEt
               there
               be
               prepared
               two
               vessels
               of
               Brasse
               ,
               Lead
               ,
               or
               of
               other
               matter
               of
               equal
               substance
               as
               are
               the
               two
               vessels
               AB
               ,
               and
               BD
               ,
               &
               let
               them
               be
               joyned
               together
               by
               the
               two
               Pillars
               MN
               ,
               &
               EF
               :
               then
               let
               there
               be
               a
               pipe
               HG
               .
               which
               may
               passe
               through
               the
               cover
               of
               the
               vessell
               CD
               ,
               and
               passe
               through
               AB
               ,
               into
               G
               ,
               making
               a
               little
               bunch
               or
               rising
               in
               the
               cover
               of
               the
               vessell
               AB
               ,
               so
               that
               the
               pipe
               touch
               it
               not
               at
               the
               bottome
               :
               
               then
               let
               there
               be
               soldered
               fast
               another
               Pipe
               IL
               ,
               which
               may
               be
               separated
               from
               the
               bottome
               of
               the
               vessell
               ,
               and
               may
               have
               his
               bunchie
               swelling
               as
               the
               former
               without
               touching
               the
               bottome
               :
               as
               is
               represented
               in
               L
               ,
               and
               passing
               through
               the
               bottome
               of
               AB
               ,
               may
               be
               continued
               unto
               I
               ,
               that
               
               is
               to
               say
               ,
               to
               make
               an
               opening
               to
               the
               cover
               of
               the
               vessell
               AB
               ,
               &
               let
               it
               have
               a
               little
               mouth
               as
               a
               Trumpet
               :
               to
               that
               end
               to
               receive
               the
               water
               .
               Then
               there
               must
               further
               be
               added
               a
               very
               smal
               Pipe
               which
               may
               passe
               through
               the
               bottome
               of
               the
               vessell
               AB
               ,
               as
               let
               it
               be
               OP
               ,
               and
               let
               there
               be
               a
               bunch
               ;
               or
               swelling
               over
               it
               as
               at
               P
               ,
               so
               that
               it
               touch
               not
               also
               the
               bottome
               :
               let
               there
               be
               further
               made
               to
               this
               lesser
               vessell
               an
               edge
               in
               forme
               of
               a
               Basin
               to
               receive
               the
               water
               ,
               which
               being
               done
               poure
               water
               into
               the
               Pipe
               IL
               ,
               untill
               the
               vessell
               CD
               ,
               be
               full
               ,
               then
               turne
               the
               whole
               Machine
               upside
               downe
               that
               the
               vessell
               CD
               ,
               may
               be
               uppermost
               ,
               and
               AB
               ,
               undermost
               ;
               so
               by
               helpe
               of
               the
               pipe
               GH
               ,
               the
               water
               of
               the
               vessell
               CD
               ,
               will
               runne
               into
               the
               vessel
               AB
               ,
               to
               have
               passage
               by
               the
               pipe
               PO.
               This
               motion
               is
               pleasant
               at
               a
               feast
               in
               filling
               the
               said
               vessel
               with
               wine
               ,
               which
               will
               spout
               it
               out
               as
               though
               it
               were
               from
               a
               boyling
               fountaine
               ,
               in
               the
               forme
               of
               a
               threed
               very
               pleasant
               to
               behold
               .
            
          
           
             
             
               PROBLEM
               .
               CXVIII
               .
               How
               to
               practise
               excellently
               the
               reanimation
               of
               simples
               ,
               in
               case
               the
               plants
               may
               not
               be
               transported
               to
               be
               replanted
               by
               reason
               of
               distance
               of
               places
               .
            
             
               TAke
               what
               simple
               you
               please
               ,
               burne
               it
               and
               take
               the
               ashes
               of
               it
               ,
               and
               let
               it
               be
               calcinated
               two
               houres
               between
               two
               Creusets
               wel
               luted
               ,
               and
               extract
               the
               salt
               :
               that
               is
               ,
               to
               put
               water
               into
               it
               in
               moving
               of
               it
               ;
               then
               let
               it
               settle
               :
               and
               do
               it
               two
               or
               three
               times
               ,
               afterwards
               evaporate
               it
               ,
               that
               is
               ,
               let
               the
               water
               be
               boyled
               in
               some
               vessel
               ,
               untill
               it
               be
               all
               consumed
               :
               then
               there
               will
               remaine
               a
               salt
               at
               the
               bottome
               ,
               which
               you
               shall
               afterwards
               sowe
               in
               good
               Ground
               wel
               prepared
               :
               such
               as
               the
               Theatre
               of
               husbandry
               sheweth
               ,
               and
               you
               shall
               have
               your
               desire
               .
            
          
           
             
               PROBLEM
               .
               CVIII
               .
               How
               to
               make
               an
               infalliable
               perpetuall
               motion
               .
            
             
               M●xe
               5.
               or
               6.
               ounces
               of
               ☿
               with
               is
               equall
               weight
               of
               ♃
               ,
               grinde
               it
               together
               with
               10.
               or
               12
               ounces
               of
               sublimate
               dissolved
               in
               a
               celler
               upon
               a
               Marble
               the
               space
               of
               foure
               dayes
               ,
               and
               it
               will
               become
               like
               Oile
               ,
               Olive
               ,
               which
               distill
               with
               fire
               of
               chaffe
               or
               driving
               fire
               ,
               and
               it
               will
               
               sublime
               dry
               substance
               ,
               then
               put
               water
               upon
               the
               earth
               (
               in
               forme
               of
               Lye
               )
               which
               will
               be
               at
               the
               bottom
               of
               the
               Limbeck
               ,
               and
               dissolve
               that
               which
               you
               can
               ;
               filter
               it
               ,
               then
               distill
               it
               ,
               and
               there
               will
               be
               produced
               very
               subtill
               Antomes
               ,
               which
               put
               into
               a
               bottle
               close
               stopped
               ,
               and
               keep
               it
               dry
               ,
               and
               you
               shall
               have
               your
               desire
               ,
               with
               astonishment
               to
               all
               the
               world
               ,
               and
               especially
               to
               those
               which
               have
               travelled
               herein
               without
               fruit
               .
            
          
           
             
               PROBLEM
               .
               CXIX
               .
               Of
               the
               admirable
               invention
               of
               making
               the
               Philosophers
               Tree
               ,
               which
               one
               may
               see
               with
               his
               eye
               to
               grow
               by
               little
               and
               little
               .
            
             
               TAke
               two
               ounces
               of
               
                 Aqua
                 fortis
              
               ,
               and
               dissolve
               in
               it
               halfe
               an
               ounce
               of
               fine
               silver
               refined
               in
               a
               Cappell
               :
               then
               take
               an
               ounce
               of
               
                 Aqua
                 fortis
              
               ,
               and
               two
               drams
               of
               Quick-silver
               :
               which
               put
               in
               it
               ,
               and
               mixe
               these
               two
               dissolved
               things
               together
               ,
               then
               cast
               it
               into
               a
               Viall
               of
               halfe
               a
               pound
               of
               water
               ,
               which
               may
               be
               well
               stopped
               ;
               for
               then
               every
               day
               you
               may
               see
               it
               grow
               both
               in
               the
               Tree
               and
               in
               the
               branch
               .
               This
               liquid
               serves
               to
               black
               haire
               which
               is
               red
               ,
               or
               white
               ,
               without
               fading
               untill
               they
               fall
               ,
               but
               here
               is
               to
               be
               noted
               that
               great
               care
               ought
               to
               be
               had
               in
               anointing
               the
               haire
               ,
               for
               feare
               of
               touching
               the
               flesh
               :
               for
               this
               composition
               is
               very
               Corrosive
               or
               searching
               ,
               that
               as
               soone
               as
               it
               toucheth
               the
               flesh
               it
               raiseth
               blisters
               ,
               and
               bladders
               very
               painfull
               .
            
          
           
             
             
               PROBLEM
               .
               CXX
               .
               How
               to
               make
               the
               representation
               of
               the
               great
               world
               ?
            
             
               DRaw
               salt
               Niter
               out
               of
               salt
               Earth
               ▪
               which
               is
               found
               along
               the
               Rivers
               side
               ,
               and
               at
               the
               foot
               of
               Mountaines
               ,
               where
               especially
               are
               Minerals
               of
               Gold
               and
               Silver
               :
               mix
               that
               Niter
               well
               cleansed
               with
               ♃
               ,
               then
               calcinate
               it
               hermetically
               ▪
               then
               put
               it
               in
               a
               Limbeck
               and
               let
               the
               receiver
               be
               of
               Glasse
               ,
               well
               luted
               ,
               and
               alwayes
               in
               which
               let
               there
               be
               placed
               leaves
               of
               Gold
               at
               the
               bottome
               ,
               then
               put
               fire
               under
               
               the
               Limbeck
               untill
               vapours
               arise
               which
               will
               cleave
               unto
               the
               Gold
               ;
               augment
               your
               fire
               untill
               there
               ascend
               no
               more
               ,
               then
               take
               away
               your
               receiver
               ,
               and
               close
               it
               hermetically
               ,
               and
               make
               a
               Lampe
               fire
               under
               it
               untill
               you
               may
               see
               presented
               in
               it
               that
               which
               nature
               affords
               us
               :
               as
               
                 Flowers
                 ,
                 Trees
                 ,
                 Fruits
                 ,
                 Fountaines
                 ,
                 Sunne
                 ,
                 Moone
                 ,
                 Starres
                 ,
                 &c.
                 
              
               Behold
               here
               the
               forme
               of
               the
               Limbeck
               ,
               and
               the
               receiver
               :
               A
               represents
               the
               Limbeck
               ,
               B
               stands
               for
               the
               receiver
               .
            
          
           
             
             
               PROBLEM
               .
               CXXI
               .
               How
               to
               make
               a
               Cone
               ,
               or
               a
               Pyramidall
               body
               move
               upon
               a
               Table
               without
               springs
               or
               other
               Artificiall
               meanes
               :
               so
               that
               it
               shall
               move
               by
               the
               edge
               of
               the
               Table
               without
               falling
               ?
            
             
               THis
               proposition
               is
               not
               so
               thornie
               and
               subtile
               as
               it
               seemes
               to
               be
               ,
               for
               putting
               under
               a
               Cone
               of
               paper
               a
               Beetle
               or
               such
               like
               creature
               ,
               
               you
               shall
               have
               pleasure
               with
               astonishment
               &
               admiration
               to
               those
               which
               are
               ignorant
               in
               the
               cause
               :
               for
               this
               animall
               will
               strive
               alwayes
               to
               free
               herself
               from
               the
               captivity
               in
               which
               she
               is
               in
               by
               the
               imprisonment
               of
               the
               Cone
               :
               for
               comming
               neere
               the
               edge
               of
               the
               Table
               she
               will
               returne
               to
               the
               other
               side
               for
               feare
               of
               falling
               .
            
          
           
             
               PROBLEM
               CXXII
               .
               To
               cleave
               an
               Anvill
               with
               the
               blow
               of
               a
               Pistoll
               .
            
             
               THis
               is
               proper
               to
               a
               Warrier
               ,
               and
               to
               performe
               it
               ,
               let
               the
               Anvill
               be
               heated
               red
               hot
               as
               one
               
               can
               possible
               ,
               in
               such
               sort
               that
               all
               the
               solidity
               of
               the
               body
               be
               softned
               by
               the
               fire
               :
               then
               charge
               the
               Pistoll
               with
               a
               bullet
               of
               silver
               ,
               and
               so
               have
               you
               infallibly
               the
               experiment
               .
            
          
           
             
               PROBLEM
               .
               CXXIII
               .
               How
               to
               r●st
               a
               Capon
               carried
               in
               a
               Budget
               at
               a
               Saddle-bowe
               ,
               in
               the
               space
               of
               riding
               5
               or
               6
               miles
               ?
            
             
               HAving
               made
               it
               ready
               and
               larded
               it
               ,
               stuffe
               ●t
               with
               Butter
               ;
               then
               heat
               a
               piece
               of
               steele
               which
               may
               be
               formed
               round
               according
               to
               the
               length
               of
               the
               Capon
               ,
               and
               big
               enough
               to
               fill
               the
               Belly
               of
               it
               ,
               and
               then
               stop
               it
               with
               Butter
               ;
               then
               wrap
               it
               up
               well
               and
               inclose
               it
               in
               a
               Box
               in
               the
               Budget
               ,
               and
               you
               shall
               have
               your
               desire
               :
               it
               is
               said
               that
               
                 Count
                 Mansfield
              
               served
               himse●fe
               with
               no
               others
               ,
               but
               such
               as
               were
               made
               ready
               in
               this
               kinde
               ,
               for
               that
               it
               loseth
               none
               of
               its
               substance
               ,
               and
               it
               is
               dressed
               very
               equally
               .
            
          
           
             
               PROBLEM
               .
               CXXIV
               .
               How
               to
               make
               a
               Candle
               burne
               and
               continue
               three
               times
               as
               long
               as
               otherwise
               it
               would
               ?
            
             
               VNto
               the
               end
               of
               a
               Candle
               half●burned
               stick
               a
               farthing
               lesse
               or
               more
               ,
               to
               make
               it
               hang
               
               perpendicular
               in
               a
               vessel
               of
               water
               ,
               so
               that
               it
               swimme
               above
               the
               water
               ;
               then
               light
               it
               ,
               and
               it
               
               will
               susteine
               it self
               &
               float
               in
               this
               manner
               ;
               and
               being
               placed
               into
               a
               fountaine
               ,
               pond
               ,
               or
               lake
               that
               runnes
               slowly
               ,
               where
               many
               people
               assemble
               ,
               it
               will
               cause
               an
               extreme
               feare
               to
               those
               which
               come
               therein
               in
               the
               night
               ,
               knowing
               not
               what
               it
               is
               .
            
          
           
             
               PROBLEM
               .
               CXXV
               .
               How
               out
               of
               a
               quantitie
               of
               wine
               to
               extract
               that
               which
               is
               most
               windy
               ,
               and
               evill
               ,
               that
               it
               hurt
               not
               a
               sick
               Person
               ?
            
             
               
               TAke
               two
               vials
               in
               such
               sort
               that
               they
               be
               of
               like
               greatnesse
               both
               in
               th●
               belly
               and
               the
               neck
               ;
               fill
               one
               of
               them
               of
               wine
               ,
               and
               the
               other
               of
               water
               :
               let
               the
               mouth
               of
               that
               which
               hath
               the
               water
               be
               placed
               into
               the
               mouth
               of
               that
               which
               hath
               the
               wine
               ,
               so
               the
               water
               shall
               
               be
               uppermost
               ,
               now
               because
               the
               water
               is
               heavier
               than
               the
               wine
               ,
               it
               will
               descend
               into
               the
               other
               Viall
               ,
               and
               the
               wine
               which
               is
               lowest
               ,
               because
               it
               is
               highest
               will
               ascend
               above
               to
               supply
               the
               place
               of
               the
               water
               ,
               and
               so
               there
               will
               be
               a
               mutuall
               interchange
               of
               liquids
               ,
               and
               by
               this
               penetration
               the
               wine
               wil
               lose
               her
               vapors
               in
               passing
               through
               the
               water
               .
            
          
           
             
               PROBLEM
               CXXVI
               .
               How
               to
               make
               two
               Marmouzets
               ,
               one
               of
               which
               shall
               light
               a
               Candle
               ,
               and
               the
               other
               put
               it
               out
               ?
            
             
               Upon
               the
               side
               of
               a
               wall
               make
               the
               figure
               of
               a
               Marmouzet
               or
               other
               animall
               or
               forme
               ,
               and
               right
               against
               it
               on
               the
               other
               wall
               make
               another
               ;
               in
               the
               mouth
               of
               each
               put
               a
               pipe
               or
               quill
               so
               artificially
               that
               it
               be
               not
               perceived
               ;
               in
               one
               of
               which
               place
               salt
               peter
               very
               fine
               ,
               and
               dry
               and
               pulverised
               ;
               and
               at
               the
               end
               set
               a
               little
               match
               of
               paper
               ,
               in
               the
               other
               place
               sulphur
               beaten
               smal
               ,
               then
               holding
               a
               Candle
               lighted
               in
               your
               hand
               ,
               say
               to
               one
               of
               these
               Images
               by
               way
               of
               command
               ,
               Blow
               out
               the
               Candle
               ;
               then
               lighting
               the
               paper
               with
               the
               candle
               ,
               the
               salt-peter
               wil
               blow
               out
               the
               Candle
               immediatly
               ,
               and
               going
               to
               the
               other
               Image
               (
               before
               the
               match
               of
               the
               Candle
               be
               out
               )
               touch
               the
               sulphur
               with
               it
               and
               say
               ,
               Light
               the
               Candle
               ,
               &
               it
               will
               immediatly
               be
               lighted
               ,
               which
               will
               cause
               an
               admiration
               to
               those
               which
               see
               the
               action
               ,
               if
               it
               be
               wel
               done
               vvith
               a
               secret
               dexterity
               .
            
          
           
             
             
               PROBLEM
               .
               XXVII
               .
               How
               to
               keepe
               wine
               fresh
               as
               if
               it
               were
               in
               a
               celler
               though
               it
               were
               in
               the
               heat
               of
               Summer
               ,
               and
               without
               Ice
               or
               snow
               ,
               yea
               though
               it
               were
               carried
               at
               a
               saddles
               bow
               ,
               and
               exposed
               to
               the
               Sun
               all
               the
               day
               ?
            
             
               SEt
               your
               wine
               in
               a
               viall
               of
               Glasse
               ;
               and
               place
               it
               in
               a
               Box
               made
               of
               wood
               ,
               Leather
               ,
               or
               such
               like
               :
               about
               which
               vial
               place
               Salt-peeter
               ,
               and
               it
               will
               preserve
               it
               and
               keep
               it
               very
               fresh
               :
               this
               experiment
               is
               not
               a
               little
               commodious
               for
               those
               which
               are
               not
               neare
               fresh
               waters
               ,
               and
               whose
               dwellings
               are
               much
               exposed
               to
               the
               Sunne
               .
            
          
           
             
               PUOBLEM
               .
               CXXVIII
               .
               To
               make
               a
               Cement
               which
               indureth
               or
               lasteth
               as
               marble
               ,
               which
               resisteth
               aire
               and
               water
               without
               ever
               disjoyning
               or
               uncementing
               ?
            
             
               TAke
               a
               quantity
               of
               strong
               and
               gluing
               Morter
               vvell
               beaten
               ,
               mixe
               vvith
               this
               as
               much
               nevv
               slaked
               Lime
               ,
               and
               upon
               it
               cast
               Oile
               of
               Olive
               or
               Linseed-Oile
               ,
               and
               it
               vvill
               become
               hard
               as
               Marble
               being
               applyed
               in
               time
               .
            
          
           
             
             
               PROBLEM
               .
               CXXIX
               .
               How
               to
               melt
               metall
               very
               quickly
               ,
               yea
               in
               a
               shell
               upon
               a
               little
               fire
               .
            
             
               MAke
               a
               bed
               upon
               a
               bed
               of
               metall
               with
               pouder
               of
               Sulphur
               ,
               of
               Salt-peeter
               ,
               and
               saw-dust
               alike
               ;
               then
               put
               fire
               to
               the
               said
               pouder
               with
               a
               burning
               Charcole
               ,
               and
               you
               shall
               see
               that
               the
               metall
               will
               dissolve
               incontinent
               and
               be
               in
               a
               Masse
               .
               This
               secret
               is
               most
               excellent
               ,
               and
               hath
               been
               practised
               by
               the
               reverend
               father
               Mercen●●
               of
               the
               order
               of
               the
               Minims
               .
            
          
           
             
               PROBLEM
               .
               CXXX
               .
               How
               to
               make
               Iron
               or
               steele
               exceeding
               hard
               ?
            
             
               QVench
               your
               Blade
               or
               other
               Instrument
               seven
               times
               in
               the
               blood
               of
               a
               male
               Hog
               mixt
               with
               Goose-grease
               ,
               and
               at
               each
               time
               dry
               it
               at
               the
               fire
               before
               you
               wet
               it
               :
               and
               it
               will
               become
               exceeding
               hard
               ,
               and
               not
               brittle
               ,
               which
               is
               not
               ordinary
               according
               to
               other
               temperings
               and
               quenchings
               of
               Iron
               :
               an
               experiment
               of
               small
               cost
               ,
               often
               proved
               ,
               and
               of
               great
               consequence
               for
               Armorie
               in
               warlike
               negotiations
               .
            
          
           
             
             
               PRBOLEM
               CXXXI
               .
               To
               preserve
               fire
               as
               long
               as
               you
               will
               ,
               imitating
               the
               inextinguible
               fire
               of
               Vestales
               .
            
             
               AFter
               that
               you
               have
               extracted
               the
               burning
               spirit
               of
               the
               salt
               of
               ♃
               ,
               by
               the
               degrees
               of
               fire
               ,
               as
               is
               required
               according
               to
               the
               Art
               of
               Chymistrie
               ,
               the
               fire
               being
               kindled
               of
               it selfe
               ,
               break
               the
               Limbeck
               ,
               and
               the
               Irons
               which
               are
               found
               at
               the
               bottome
               will
               flame
               and
               appeare
               as
               burning
               Coles
               as
               soone
               as
               they
               feele
               the
               aire
               ;
               which
               if
               you
               promptly
               inclose
               in
               a
               viall
               of
               Glasse
               ,
               and
               that
               you
               stop
               it
               exactly
               with
               some
               good
               Lute
               :
               or
               to
               be
               more
               assured
               it
               may
               be
               closed
               up
               with
               Hermes
               wax
               for
               feare
               that
               the
               Aire
               get
               not
               in
               .
               Then
               will
               it
               keep
               more
               than
               a
               thousand
               yeares
               (
               as
               a
               man
               may
               say
               )
               yea
               at
               the
               bottome
               of
               the
               Sea
               ;
               and
               opening
               it
               at
               the
               end
               of
               the
               time
               ,
               as
               soone
               as
               it
               feeles
               the
               Aire
               〈◊〉
               takes
               fi●e
               ▪
               with
               which
               you
               may
               light
               a
               Match
               .
               This
               secret
               merits
               to
               be
               travelled
               after
               and
               put
               in
               practice
               ,
               for
               that
               it
               is
               not
               common
               ,
               and
               full
               of
               astonishment
               ,
               seeing
               that
               all
               kinde
               of
               fire
               lasteth
               but
               as
               long
               as
               his
               matter
               lasteth
               ,
               and
               that
               there
               is
               no
               matter
               to
               be
               found
               that
               will
               so
               long
               in●●●e
               .
            
          
           
             
             
               Artificiall
               fire-Workes
               :
               Or
               the
               manner
               of
               making
               of
               Rockets
               and
               Balls
               of
               fire
               ,
               as
               well
               for
               the
               Water
               ,
               as
               for
               the
               Aire
               ;
               with
               the
               composition
               of
               Starres
               ,
               Golden-rain
               ,
               Serpen●s
               ,
               Lances
               ,
               Whee●s
               of
               fire
               and
               such
               like
               ,
               pleasant
               and
               Recreative
               .
            
             
               
                 Of
                 the
                 composition
                 for
                 Rockets
                 .
              
               
                 IN
                 the
                 making
                 of
                 Rockets
                 ,
                 the
                 chiefest
                 thing
                 to
                 be
                 regarded
                 is
                 the
                 composition
                 that
                 they
                 ought
                 to
                 be
                 filled
                 with
                 ;
                 forasmuch
                 as
                 that
                 which
                 is
                 proper
                 to
                 Rockets
                 which
                 are
                 of
                 a
                 lesse
                 sort
                 is
                 very
                 improper
                 to
                 those
                 which
                 are
                 of
                 a
                 more
                 greater
                 forme
                 ;
                 for
                 the
                 fire
                 being
                 lighted
                 in
                 a
                 great
                 concave
                 ,
                 which
                 is
                 filled
                 with
                 a
                 quick
                 composition
                 ,
                 burnes
                 with
                 great
                 violence
                 ;
                 contrarily
                 ,
                 a
                 weak
                 composition
                 being
                 in
                 a
                 small
                 concave
                 ,
                 makes
                 no
                 effect
                 :
                 therefore
                 we
                 shall
                 here
                 deliver
                 in
                 the
                 first
                 place
                 rules
                 and
                 directions
                 ,
                 which
                 may
                 serve
                 for
                 the
                 true
                 composition
                 ,
                 or
                 matter
                 with
                 which
                 you
                 may
                 charge
                 any
                 Rocket
                 ,
                 from
                 Rockets
                 which
                 
                 are
                 charged
                 but
                 with
                 one
                 ounce
                 of
                 Powder
                 unto
                 great
                 Rockets
                 which
                 requireth
                 for
                 their
                 charge
                 10
                 pound
                 of
                 Powder
                 ,
                 as
                 followeth
                 .
              
               
                 
                   For
                   Rockets
                   of
                   one
                   ounce
                   .
                
                 
                   Vnto
                   each
                   pound
                   of
                   good
                   musket
                   Powder
                   smal
                   beaten
                   ,
                   put
                   two
                   ounces
                   of
                   smal
                   Cole
                   dust
                   ,
                   and
                   with
                   this
                   composition
                   charge
                   the
                   Rocket
                   .
                
              
               
                 
                   For
                   Rockets
                   of
                   2
                   or
                   3
                   ounces
                   .
                
                 
                   Vnto
                   every
                   foure
                   ounces
                   and
                   a
                   halfe
                   of
                   powder
                   dust
                   ,
                   adde
                   an
                   ounce
                   of
                   Salt-peter
                   ,
                   or
                   to
                   every
                   4
                   ounces
                   of
                   powder
                   dust
                   ,
                   adde
                   an
                   ounce
                   of
                   Cole
                   dust
                   .
                
              
               
                 
                   For
                   Rockets
                   of
                   4
                   ounces
                   .
                
                 
                   Vnto
                   every
                   pound
                   of
                   Powder
                   dust
                   adde
                   4
                   ounces
                   of
                   Salt
                   peter
                   &
                   one
                   ounce
                   of
                   Cole
                   dust
                   :
                   but
                   to
                   have
                   it
                   more
                   slow
                   ,
                   unto
                   every
                   10.
                   ounces
                   of
                   good
                   dust
                   powder
                   adde
                   3
                   ounces
                   of
                   Salt-peter
                   ,
                   and
                   3
                   ounces
                   of
                   Cole
                   dust
                   .
                
              
               
                 
                   For
                   Rockets
                   of
                   5
                   or
                   6
                   ounces
                   .
                
                 
                   Vnto
                   every
                   pound
                   of
                   Powder
                   dust
                   ,
                   adde
                   3
                   ounces
                   and
                   a
                   halfe
                   of
                   Salt
                   peter
                   ,
                   and
                   2
                   ounces
                   and
                   a
                   halfe
                   of
                   Coledust
                   ,
                   as
                   also
                   an
                   ounce
                   of
                   Sulphur
                   ,
                   and
                   an
                   ounce
                   of
                   fyle
                   dust
                   .
                
              
               
                 
                   For
                   Rockets
                   of
                   7
                   or
                   8
                   ounces
                   .
                
                 
                   Vnto
                   every
                   pound
                   of
                   Powder
                   dust
                   adde
                   4
                   ounces
                   of
                   Salt
                   peter
                   ,
                   and
                   3
                   ounces
                   of
                   Sulphur
                   .
                
              
               
                 
                   Of
                   Rockets
                   of
                   10
                   or
                   12
                   ounces
                   .
                
                 
                   Vnto
                   the
                   precedent
                   composition
                   adde
                   halfe
                   an
                   ounce
                   of
                   Sulphur
                   ,
                   and
                   it
                   will
                   be
                   sufficient
                   .
                
              
               
                 
                   For
                   Rockets
                   of
                   14
                   or
                   15
                   ounces
                   .
                
                 
                   Vnto
                   every
                   pound
                   of
                   Powder
                   dust
                   adde
                   4
                   ounces
                   of
                   Salt
                   peter
                   ,
                   or
                   Cole
                   dust
                   2
                   ¼
                   ounces
                   of
                   
                   Sulphur
                   and
                   file
                   dust
                   of
                   1
                   ¼
                   ounce
                   .
                
              
               
                 
                   For
                   Rockets
                   of
                   1
                   ,
                   pound
                   .
                
                 
                   Vnto
                   every
                   pound
                   of
                   Powder
                   dust
                   adde
                   3
                   ounces
                   of
                   Cole
                   dust
                   ,
                   and
                   one
                   ounce
                   of
                   Sulphur
                   .
                
              
               
                 
                   Of
                   Rockets
                   of
                   2
                   ,
                   pound
                   .
                
                 
                   Vnto
                   every
                   pound
                   of
                   Powder
                   dust
                   adde
                   9
                   ½
                   ounces
                   of
                   Salt
                   peter
                   ,
                   of
                   Cole
                   dust
                   2
                   1
                   /
                   ●
                   ounces
                   ,
                   filedust
                   1
                   ●
                   /
                   2
                   ounce
                   ,
                   and
                   of
                   Sulphur
                   ¾
                   of
                   ounce
                   .
                
              
               
                 
                   For
                   Rockets
                   of
                   3
                   ,
                   pound
                   .
                
                 
                   Vnto
                   every
                   pound
                   of
                   Salt
                   peter
                   adde
                   6
                   ounces
                   of
                   Cole
                   dust
                   ,
                   and
                   of
                   Sulpher
                   4
                   ,
                   ounces
                   .
                
              
               
                 
                   For
                   Rockets
                   of
                   
                     4
                     ,
                     5
                     ,
                     6
                  
                   ,
                   or
                   7
                   ,
                   pound
                   .
                
                 
                   Vnto
                   every
                   pound
                   of
                   Salt
                   peter
                   adde
                   5
                   ounces
                   of
                   Cole
                   dust
                   ,
                   and
                   2
                   ½
                   ounces
                   of
                   Sulphur
                   .
                
              
               
                 
                   For
                   Rockets
                   of
                   
                     8
                     ,
                     9
                  
                   ,
                   or
                   10
                   pound
                   .
                
                 
                   Vnto
                   every
                   pound
                   of
                   Salt
                   peter
                   ,
                   adde
                   5
                   ½
                   ounces
                   of
                   Cole
                   dust
                   ,
                   and
                   of
                   Sulphur
                   2
                   ½
                   ounces
                   .
                
                 
                   Here
                   note
                   that
                   in
                   all
                   great
                   Rockets
                   ,
                   there
                   is
                   no
                   Powder
                   put
                   ,
                   because
                   of
                   the
                   greatnesse
                   of
                   the
                   fire
                   which
                   is
                   lighted
                   at
                   once
                   ,
                   which
                   causeth
                   too
                   great
                   a
                   violence
                   ,
                   therefore
                   ought
                   to
                   be
                   filled
                   with
                   a
                   more
                   weaker
                   composition
                   .
                
              
            
             
               
                 Of
                 the
                 making
                 of
                 Rockets
                 and
                 other
                 Fireworkes
                 .
              
               
                 FOr
                 the
                 making
                 of
                 Rockets
                 of
                 sundry
                 kindes
                 ,
                 divers
                 moulds
                 are
                 to
                 be
                 made
                 ,
                 with
                 their
                 Rolling
                 pins
                 ,
                 Breaths
                 ,
                 Chargers
                 ,
                 &c.
                 as
                 may
                 be
                 seen
                 here
                 in
                 the
                 figure
                 .
                 And
                 having
                 rolled
                 a
                 Case
                 of
                 paper
                 upon
                 the
                 Rolling
                 pin
                 for
                 your
                 mould
                 ,
                 fill
                 it
                 with
                 the
                 composition
                 belonging
                 to
                 that
                 mould
                 as
                 before
                 is
                 delivered
                 :
                 
                 now
                 may
                 you
                 load
                 it
                 on
                 the
                 top
                 ,
                 with
                 Serpents
                 ,
                 Reports
                 ,
                 Stars
                 ,
                 or
                 Golden
                 Raine
                 :
                 the
                 Serpents
                 are
                 made
                 about
                 the
                 bignesse
                 of
                 ones
                 little
                 finger
                 ,
                 by
                 rolling
                 a
                 little
                 paper
                 upon
                 a
                 small
                 stick
                 ,
                 and
                 then
                 tying
                 one
                 end
                 of
                 it
                 ,
                 and
                 filling
                 it
                 with
                 the
                 mixt
                 composition
                 somewhat
                 close
                 ,
                 and
                 then
                 tying
                 the
                 other
                 end
                 .
                 The
                 reports
                 are
                 made
                 in
                 their
                 paper-Cases
                 as
                 the
                 Serpents
                 ,
                 but
                 the
                 Paper
                 somewhat
                 thicker
                 to
                 give
                 the
                 greater
                 report
                 .
                 These
                 are
                 filled
                 with
                 
                 graine-Powder
                 or
                 halfe
                 Powder
                 and
                 halfe
                 composition
                 ,
                 and
                 tying
                 both
                 ends
                 close
                 ,
                 they
                 are
                 finished
                 .
                 The
                 best
                 kinde
                 of
                 starres
                 are
                 made
                 with
                 this
                 mixture
                 following
                 ;
                 unto
                 every
                 4
                 ounces
                 of
                 Salt-peter
                 ,
                 adde
                 2
                 ounces
                 of
                 Sulphur
                 ,
                 
                 and
                 to
                 it
                 put
                 1.
                 ounce
                 of
                 Powder-dust
                 ,
                 and
                 of
                 this
                 composition
                 make
                 your
                 starres
                 ,
                 by
                 putting
                 a
                 little
                 of
                 it
                 within
                 a
                 small
                 quantity
                 of
                 
                 towe
                 ;
                 and
                 then
                 tying
                 it
                 up
                 in
                 the
                 form
                 of
                 a
                 ball
                 as
                 great
                 as
                 an
                 Hasel-Nut
                 or
                 a
                 little
                 Wal-nut
                 ,
                 through
                 which
                 there
                 must
                 be
                 drawne
                 a
                 little
                 Primer
                 to
                 make
                 it
                 take
                 fire
                 .
                 Touching
                 the
                 making
                 of
                 the
                 Golden
                 Raine
                 ,
                 that
                 is
                 nothing
                 but
                 filling
                 of
                 Quilles
                 with
                 the
                 composition
                 of
                 your
                 Rockets
                 somewhat
                 hard
                 .
                 Now
                 if
                 the
                 head
                 of
                 a
                 Rocket
                 be
                 loaded
                 with
                 a
                 thousand
                 of
                 those
                 Quilles
                 ,
                 it
                 s
                 a
                 goodly
                 sight
                 to
                 see
                 how
                 pleasantly
                 they
                 ●pread
                 themselves
                 in
                 the
                 Aire
                 ,
                 and
                 come
                 downe
                 like
                 streames
                 of
                 Gold
                 much
                 like
                 the
                 falling
                 downe
                 of
                 Snow
                 being
                 agitated
                 by
                 some
                 turbulent
                 winde
                 .
              
            
             
               
               
                 Of
                 recreative
                 fires
                 .
              
               
                 1
                 PHil●strates
                 saith
                 ,
                 that
                 if
                 wine
                 in
                 a
                 platter
                 be
                 placed
                 upon
                 a
                 receiver
                 of
                 burning
                 Coles
                 ,
                 to
                 exhale
                 the
                 spirit
                 of
                 it
                 ,
                 and
                 be
                 inclosed
                 within
                 a
                 Cupboard
                 or
                 such
                 like
                 place
                 ,
                 so
                 that
                 the
                 Aire
                 may
                 not
                 go
                 in
                 ,
                 nor
                 out
                 ,
                 and
                 so
                 being
                 shut
                 up
                 for
                 30
                 yeares
                 ,
                 he
                 that
                 shall
                 open
                 it
                 ,
                 having
                 a
                 wax
                 Candle
                 lighted
                 ,
                 and
                 shall
                 put
                 it
                 into
                 the
                 Cubboard
                 there
                 will
                 appeare
                 unto
                 him
                 the
                 figure
                 of
                 many
                 cleare
                 starres
                 .
              
               
                 2
                 If
                 Aquavitae
                 have
                 Camphire
                 dissolved
                 in
                 it
                 ;
                 and
                 be
                 evaporated
                 in
                 a
                 close
                 Chamber
                 ,
                 where
                 there
                 is
                 but
                 a
                 Charcole
                 fire
                 ,
                 the
                 first
                 that
                 enters
                 into
                 the
                 Chamber
                 with
                 a
                 Candle
                 lighted
                 ,
                 will
                 be
                 extremely
                 astonished
                 ,
                 for
                 all
                 the
                 Chamber
                 will
                 seeme
                 to
                 be
                 full
                 of
                 fire
                 very
                 subtile
                 ,
                 but
                 it
                 will
                 be
                 of
                 little
                 continuance
                 .
              
               
                 3
                 Candles
                 which
                 are
                 deceitful
                 are
                 made
                 of
                 halfe
                 powder
                 ,
                 covered
                 over
                 with
                 Tallow
                 ,
                 and
                 the
                 other
                 halfe
                 is
                 made
                 of
                 cleane
                 Tallow
                 ,
                 or
                 Waxe
                 ,
                 with
                 an
                 ordinary
                 week
                 ;
                 this
                 Candle
                 being
                 lighted
                 ,
                 and
                 the
                 upper
                 halfe
                 consumed
                 ,
                 the
                 powder
                 will
                 take
                 fire
                 ,
                 not
                 without
                 great
                 noise
                 and
                 astonishment
                 to
                 those
                 which
                 are
                 ignorant
                 of
                 the
                 cause
                 .
              
               
                 4
                 A
                 dozen
                 or
                 twenty
                 smal
                 Serpents
                 placed
                 secretly
                 under
                 a
                 Candlestick
                 that
                 is
                 indifferent
                 big
                 ,
                 which
                 may
                 have
                 a
                 hole
                 passe
                 through
                 the
                 socket
                 of
                 it
                 to
                 the
                 Candle
                 ,
                 through
                 which
                 a
                 piece
                 of
                 primer
                 may
                 be
                 placed
                 ,
                 and
                 setting
                 a
                 smal
                 C●ndle
                 in
                 the
                 socket
                 to
                 burne
                 according
                 
                 to
                 a
                 time
                 limited
                 :
                 which
                 Candlestick
                 may
                 be
                 set
                 on
                 a
                 side
                 Table
                 without
                 suspition
                 to
                 any
                 ;
                 then
                 when
                 the
                 Candle
                 is
                 burned
                 ,
                 that
                 it
                 fires
                 the
                 primer
                 ,
                 that
                 immediately
                 will
                 fire
                 all
                 the
                 Serpents
                 ,
                 which
                 overthrowing
                 the
                 Candlestick
                 will
                 flye
                 here
                 and
                 there
                 ,
                 intermixing
                 themselves
                 ,
                 sometimes
                 in
                 the
                 Aire
                 ,
                 sometimes
                 in
                 the
                 Planching
                 ,
                 one
                 amongst
                 another
                 ,
                 like
                 the
                 crawling
                 of
                 Serpents
                 ,
                 continuing
                 for
                 a
                 pretty
                 while
                 in
                 this
                 posture
                 ,
                 and
                 in
                 extinguishing
                 every
                 one
                 will
                 give
                 his
                 report
                 like
                 a
                 Pistoll
                 ;
                 This
                 will
                 not
                 a
                 little
                 astonish
                 some
                 ,
                 thinking
                 the
                 house
                 will
                 be
                 fired
                 ,
                 though
                 the
                 whole
                 powder
                 together
                 makes
                 not
                 an
                 ounce
                 ,
                 and
                 hath
                 no
                 strength
                 to
                 do
                 such
                 an
                 effect
                 .
              
            
             
               
                 How
                 to
                 make
                 fire
                 run
                 up
                 and
                 downe
                 ,
                 forward
                 and
                 backward
              
               
                 TAke
                 small
                 Rockets
                 ,
                 and
                 place
                 the
                 taile
                 of
                 one
                 to
                 the
                 head
                 of
                 the
                 other
                 upon
                 a
                 Cord
                 according
                 to
                 your
                 fancie
                 ,
                 as
                 admit
                 the
                 Cord
                 to
                 be
                 ABCDEFG
                 .
                 give
                 fire
                 to
                 the
                 Rocket
                 at
                 A
                 ,
                 which
                 will
                 flye
                 to
                 B
                 ,
                 which
                 will
                 come
                 back
                 againe
                 to
                 A
                 ,
                 and
                 fire
                 another
                 at
                 C
                 ,
                 that
                 will
                 flie
                 at
                 D
                 ,
                 which
                 will
                 fire
                 another
                 there
                 ,
                 and
                 fl●e
                 to
                 E
                 ,
                 and
                 that
                 to
                 F
                 ,
                 and
                 so
                 from
                 F
                 ,
                 to
                 G
                 ,
                 and
                 at
                 G
                 ,
                 may
                 be
                 placed
                 a
                 pot
                 of
                 fire
                 ,
                 
                   viz.
                   GH
                
                 .
                 which
                 fired
                 will
                 make
                 good
                 sport
                 ▪
                 bec●u●e
                 the
                 Serpents
                 which
                 are
                 in
                 it
                 will
                 variously
                 ●ntermix
                 themselves
                 in
                 the
                 Aire
                 ,
                 and
                 upon
                 the
                 ground
                 ,
                 and
                 every
                 one
                 will
                 extinguish
                 with
                 a
                 report
                 :
                 and
                 here
                 may
                 you
                 note
                 that
                 upon
                 the
                 
                 Rockets
                 may
                 be
                 placed
                 fierie
                 Dragons
                 ,
                 Combatants
                 ,
                 or
                 such
                 like
                 to
                 meet
                 one
                 another
                 ,
                 having
                 
                 lights
                 placed
                 in
                 the
                 Concavity
                 of
                 their
                 bodies
                 which
                 will
                 give
                 great
                 grace
                 to
                 the
                 action
                 .
              
            
             
               
                 How
                 to
                 make
                 Wheels
                 of
                 fire
                 .
              
               
                 TAke
                 a
                 Hoop
                 ,
                 and
                 place
                 two
                 Lath●
                 acrosse
                 one
                 the
                 other
                 ;
                 upon
                 the
                 crossing
                 of
                 which
                 make
                 a
                 hole
                 ,
                 so
                 that
                 it
                 may
                 be
                 placed
                 upon
                 a
                 pin
                 to
                 turne
                 easily
                 ,
                 as
                 the
                 figure
                 Q.
                 sheweth
                 upon
                 the
                 sides
                 of
                 which
                 hoope
                 or
                 round
                 Circle
                 place
                 your
                 Rockets
                 ,
                 to
                 which
                 you
                 may
                 place
                 Lances
                 of
                 fire
                 between
                 each
                 
                 Rocket
                 :
                 let
                 this
                 wheele
                 be
                 placed
                 upon
                 a
                 standard
                 as
                 here
                 is
                 represented
                 ,
                 and
                 place
                 a
                 piece
                 of
                 Primer
                 from
                 one
                 Lance
                 to
                 another
                 ,
                 then
                 give
                 fire
                 at
                 G
                 ,
                 which
                 will
                 fire
                 F
                 ,
                 that
                 B
                 ,
                 that
                 will
                 fire
                 
                 D
                 ,
                 that
                 C
                 ,
                 and
                 that
                 will
                 fire
                 the
                 Rocket
                 at
                 A
                 ▪
                 then
                 immediatly
                 the
                 wheel
                 will
                 begin
                 to
                 move
                 ,
                 and
                 represent
                 unto
                 the
                 spectators
                 a
                 Circle
                 of
                 changeable
                 fire
                 ,
                 and
                 if
                 pots
                 of
                 fire
                 be
                 tied
                 to
                 it
                 ,
                 you
                 will
                 have
                 fine
                 sport
                 in
                 the
                 turning
                 of
                 the
                 wheele
                 and
                 casting
                 out
                 of
                 the
                 Serpents
                 .
              
            
             
               
                 Of
                 night-Combatants
                 .
              
               
                 CLubbes
                 ,
                 Targets
                 ,
                 Faulchons
                 ,
                 and
                 Maces
                 charged
                 with
                 severall
                 fires
                 ,
                 do
                 make
                 your
                 night-Combatants
                 ,
                 or
                 are
                 used
                 to
                 make
                 place
                 amongst
                 a
                 throng
                 of
                 people
                 .
                 The
                 Clubbes
                 at
                 the
                 ends
                 are
                 made
                 like
                 a
                 round
                 Panier
                 with
                 
                 small
                 sticks
                 ,
                 filled
                 with
                 little
                 Rockets
                 in
                 a
                 spirall
                 forme
                 glu●d
                 and
                 so
                 placed
                 that
                 they
                 fire
                 but
                 one
                 after
                 another
                 ;
                 the
                 Ma●es
                 are
                 of
                 divers
                 fashions
                 ,
                 some
                 made
                 oblong
                 at
                 the
                 end
                 ,
                 some
                 made
                 of
                 a
                 sp●rall
                 forme
                 ,
                 but
                 all
                 made
                 hollow
                 to
                 put
                 in
                 several
                 composition
                 ,
                 and
                 are
                 boared
                 in
                 divers
                 places
                 ,
                 which
                 are
                 for
                 sundry
                 Rockets
                 ,
                 and
                 Lances
                 of
                 weak
                 composition
                 to
                 be
                 fired
                 at
                 pleasure
                 :
                 The
                 Faulchons
                 are
                 made
                 of
                 wood
                 in
                 a
                 bowing
                 forme
                 like
                 the
                 figure
                 A
                 ,
                 having
                 their
                 backes
                 large
                 to
                 receive
                 many
                 Rockets
                 ,
                 the
                 head
                 of
                 one
                 neare
                 the
                 neck
                 of
                 another
                 ,
                 glued
                 and
                 fastned
                 well
                 together
                 ,
                 so
                 that
                 one
                 being
                 spent
                 another
                 may
                 be
                 fired
                 .
                 〈◊〉
                 Targets
                 
                 are
                 made
                 of
                 wooden
                 thinne
                 boards
                 ,
                 which
                 are
                 channeled
                 in
                 spiral
                 lines
                 to
                 containe
                 primer
                 
                 to
                 fire
                 the
                 Rockets
                 one
                 after
                 another
                 ,
                 which
                 is
                 all
                 covered
                 with
                 thinne
                 covering
                 of
                 wood
                 ,
                 or
                 Pastboard
                 ,
                 boared
                 with
                 holes
                 spirally
                 also
                 ;
                 which
                 Rockets
                 must
                 be
                 glued
                 and
                 made
                 fast
                 to
                 the
                 place
                 of
                 the
                 Channels
                 :
                 Now
                 if
                 two
                 men
                 ,
                 the
                 one
                 having
                 a
                 Target
                 in
                 his
                 hand
                 ,
                 and
                 the
                 other
                 a
                 Falchon
                 ,
                 or
                 Mace
                 of
                 fire
                 ,
                 shall
                 begin
                 to
                 fight
                 ,
                 it
                 will
                 appeare
                 very
                 pleasant
                 to
                 the
                 Spectators
                 :
                 for
                 by
                 the
                 motion
                 of
                 fighting
                 ,
                 the
                 place
                 will
                 seem
                 to
                 be
                 ful
                 of
                 streames
                 of
                 fire
                 :
                 and
                 there
                 may
                 be
                 adjoyned
                 to
                 each
                 Target
                 a
                 Sunne
                 or
                 a
                 burning
                 Comet
                 with
                 Lances
                 of
                 fire
                 ,
                 which
                 will
                 make
                 them
                 more
                 beautifull
                 and
                 resplendent
                 in
                 that
                 acti●n
                 .
              
            
             
               
                 Of
                 standing
                 Fires
                 .
              
               
                 SVch
                 as
                 are
                 used
                 for
                 recreation
                 ,
                 are
                 
                   Collossus
                   ,
                   Statues
                   ,
                   Arches
                   ,
                   Pyramides
                   ,
                   Chariots
                   ,
                
                 
                 
                 Chaires
                 of
                 triumph
                 and
                 such
                 like
                 ,
                 which
                 may
                 be
                 accommodated
                 with
                 Rockets
                 of
                 fire
                 ,
                 and
                 beautified
                 with
                 sundry
                 other
                 artificiall
                 fires
                 ,
                 as
                 pots
                 of
                 fire
                 for
                 the
                 Aire
                 which
                 may
                 cast
                 forth
                 several
                 figures
                 ,
                 Scutchions
                 ,
                 Rockets
                 of
                 divers
                 sorts
                 ,
                 Starres
                 ,
                 Crownes
                 ,
                 Leaters
                 ,
                 and
                 such
                 like
                 ,
                 the
                 borders
                 of
                 which
                 may
                 be
                 armed
                 with
                 sundry
                 Lances
                 of
                 fire
                 ,
                 of
                 small
                 flying
                 Rockets
                 with
                 reports
                 ,
                 flames
                 ,
                 of
                 small
                 birds
                 of
                 Cypres
                 ,
                 Lan●hornes
                 of
                 fire
                 ,
                 Candles
                 of
                 divers
                 uses
                 ,
                 and
                 colours
                 in
                 burning
                 :
                 and
                 whatsoever
                 the
                 fancie
                 of
                 an
                 ingenious
                 head
                 may
                 allude
                 unto
                 .
              
            
             
               
                 Of
                 Pots
                 of
                 fire
                 for
                 the
                 Aire
                 ,
                 which
                 are
                 throwne
                 out
                 of
                 one
                 Case
                 one
                 after
                 another
                 of
                 a
                 long
                 continuance
                 .
              
               
                 MAke
                 a
                 long
                 Trunk
                 as
                 AG
                 ,
                 and
                 by
                 the
                 side
                 AH
                 ,
                 let
                 there
                 be
                 a
                 Channel
                 which
                 may
                 be
                 fiered
                 with
                 slow
                 primer
                 or
                 composition
                 ;
                 then
                 having
                 charged
                 the
                 Trunk
                 AG
                 ,
                 with
                 the
                 Pots
                 of
                 fire
                 for
                 the
                 Aire
                 at
                 IGEC
                 ,
                 and
                 make
                 the
                 Trunk
                 AG
                 ,
                 very
                 fast
                 unto
                 a
                 Post
                 as
                 IK
                 ,
                 give
                 fire
                 at
                 the
                 top
                 as
                 at
                 A
                 ,
                 which
                 burning
                 downewards
                 will
                 give
                 fire
                 to
                 C
                 ,
                 and
                 so
                 throw
                 out
                 that
                 Pot
                 in
                 the
                 Aire
                 ,
                 vvhich
                 being
                 spent
                 ,
                 in
                 the
                 meane
                 time
                 the
                 fire
                 vvil-burne
                 from
                 B
                 to
                 D
                 ,
                 and
                 so
                 fire
                 E
                 ,
                 and
                 throvv
                 it
                 out
                 also
                 into
                 the
                 Ayre
                 ,
                 and
                 so
                 all
                 the
                 rest
                 one
                 after
                 another
                 vvill
                 be
                 throvvne
                 out
                 :
                 and
                 if
                 the
                 Pots
                 of
                 fire
                 for
                 the
                 Aire
                 vvhich
                 are
                 cast
                 out
                 ,
                 be
                 filled
                 vvith
                 diverse
                 Fire-vvorkes
                 ,
                 they
                 vvill
                 be
                 so
                 much
                 the
                 
                 more
                 pleasant
                 to
                 the
                 
                 beholders
                 .
                 These
                 Trunks
                 of
                 fire
                 doe
                 greatly
                 adorne
                 a
                 Firevvorke
                 ,
                 and
                 may
                 conveniently
                 be
                 placed
                 at
                 each
                 angle
                 of
                 the
                 vvhole
                 vvorke
                 .
              
            
             
               
                 Of
                 Pots
                 of
                 fire
                 for
                 the
                 ground
                 .
              
               
                 MAny
                 Pots
                 of
                 fire
                 being
                 fired
                 together
                 do
                 give
                 a
                 fine
                 representation
                 ,
                 and
                 recreation
                 to
                 the
                 spectators
                 ,
                 and
                 
                 cause
                 a
                 vvonderfull
                 shout
                 amongst
                 the
                 common
                 people
                 vv
                 ch
                 are
                 standers
                 by
                 ;
                 for
                 those
                 Pots
                 being
                 filled
                 vvith
                 Balles
                 of
                 fire
                 and
                 flying
                 Serpents
                 for
                 the
                 Aire
                 ,
                 they
                 vvill
                 so
                 intermix
                 one
                 vvithin
                 another
                 ,
                 in
                 flying
                 here
                 and
                 there
                 a
                 little
                 above
                 the
                 ground
                 ,
                 and
                 giving
                 such
                 a
                 volley
                 of
                 reports
                 that
                 the
                 Aire
                 vvill
                 rebound
                 vvith
                 their
                 noise
                 ,
                 and
                 the
                 vvhole
                 place
                 be
                 filled
                 vvith
                 sundry
                 
                 streames
                 of
                 pleasant
                 fire
                 ;
                 which
                 serpents
                 will
                 much
                 occupie
                 these
                 about
                 the
                 place
                 to
                 defend
                 themselves
                 in
                 their
                 upper
                 parts
                 ,
                 when
                 they
                 will
                 no
                 lesse
                 be
                 busied
                 by
                 the
                 balls
                 of
                 fire
                 ,
                 which
                 seeme
                 to
                 annoy
                 their
                 feet
                 .
              
            
             
               
                 Of
                 Balles
                 of
                 f●re
                 .
              
               
                 THese
                 are
                 very
                 various
                 according
                 to
                 a
                 mans
                 fancy
                 ;
                 some
                 of
                 which
                 are
                 made
                 with
                 very
                 small
                 Rockets
                 ,
                 the
                 head
                 of
                 one
                 tyed
                 to
                 the
                 neck
                 of
                 another
                 :
                 the
                 ball
                 being
                 made
                 may
                 be
                 covered
                 over
                 with
                 pitch
                 except
                 the
                 hole
                 to
                 give
                 fire
                 to
                 it
                 ;
                 this
                 Ball
                 will
                 make
                 fine
                 sport
                 amongst
                 the
                 standers
                 by
                 ,
                 which
                 will
                 take
                 all
                 a
                 fire
                 ,
                 and
                 rolle
                 sometimes
                 this
                 way
                 ,
                 sometimes
                 that
                 way
                 ,
                 between
                 the
                 legs
                 of
                 those
                 that
                 are
                 standers
                 by
                 ▪
                 if
                 they
                 take
                 not
                 heed
                 ,
                 for
                 the
                 motion
                 will
                 be
                 very
                 irregular
                 ,
                 and
                 
                 in
                 the
                 motion
                 will
                 cast
                 forth
                 severall
                 fires
                 with
                 reports
                 .
                 In
                 the
                 second
                 kind
                 there
                 may
                 be
                 a
                 channell
                 of
                 Iron
                 placed
                 in
                 divers
                 places
                 in
                 spirall
                 manner
                 ,
                 against
                 which
                 may
                 be
                 placed
                 as
                 many
                 small
                 petards
                 of
                 paper
                 as
                 possible
                 may
                 be
                 ,
                 the
                 Channell
                 must
                 be
                 full
                 of
                 slow
                 comp●sition
                 ,
                 and
                 may
                 be
                 covered
                 a●
                 the
                 former
                 ,
                 and
                 made
                 fit
                 with
                 his
                 Rockets
                 in
                 the
                 middle
                 :
                 this
                 Ball
                 may
                 be
                 shot
                 out
                 of
                 a
                 
                 morter
                 Peece
                 ,
                 or
                 charged
                 on
                 the
                 top
                 of
                 a
                 Roc●et
                 :
                 for
                 in
                 its
                 motion
                 it
                 will
                 flye
                 here
                 and
                 there
                 ,
                 and
                 give
                 many
                 reports
                 in
                 the
                 Aire
                 :
                 because
                 of
                 the
                 discharge
                 of
                 the
                 petards
                 .
              
            
             
               
                 Of
                 fire
                 upon
                 the
                 Water
                 .
              
               
                 Places
                 which
                 are
                 〈◊〉
                 upon
                 Rivers
                 or
                 great
                 Ponds
                 ,
                 are
                 proper
                 to
                 make
                 Recreative
                 fres
                 on
                 :
                 and
                 if
                 it
                 be
                 required
                 to
                 make
                 some
                 of
                 consequence
                 ,
                 such
                 may
                 conveniently
                 be
                 made
                 upon
                 two
                 Bo●ts
                 ,
                 upon
                 which
                 may
                 be
                 built
                 two
                 
                   Beasts
                   ,
                   Turrets
                   ,
                   Pagins
                   ,
                   Castles
                   ,
                
                 or
                 such
                 like
                 ,
                 
                 to
                 receive
                 or
                 hold
                 the
                 diversity
                 of
                 Fire
                 workes
                 that
                 may
                 be
                 made
                 within
                 it
                 ,
                 in
                 which
                 may
                 play
                 〈◊〉
                 fires
                 ,
                 Petards
                 ,
                 &c.
                 and
                 cast
                 out
                 many
                 simple
                 Granadoes
                 ,
                 Balls
                 of
                 fire
                 to
                 burne
                 in
                 the
                 
                 water-Serpents
                 and
                 other
                 things
                 ,
                 and
                 often
                 times
                 these
                 boates
                 in
                 their
                 incounters
                 may
                 hang
                 one
                 in
                 another
                 ,
                 that
                 so
                 the
                 Combatants
                 with
                 the
                 Targets
                 ,
                 and
                 Maces
                 may
                 fight
                 ;
                 which
                 will
                 give
                 great
                 ▪
                 content
                 to
                 the
                 eyes
                 of
                 those
                 which
                 are
                 lookers
                 on
                 ,
                 and
                 in
                 the
                 conclusion
                 fire
                 one
                 another
                 ,
                 (
                 for
                 which
                 end
                 they
                 were
                 made
                 :
                 )
                 by
                 which
                 the
                 dexterity
                 of
                 the
                 one
                 may
                 be
                 knowne
                 in
                 respect
                 of
                 the
                 other
                 ,
                 and
                 the
                 triumph
                 and
                 victory
                 of
                 the
                 fight
                 gotten
                 .
              
            
             
               
                 Of
                 Balles
                 of
                 fire
                 which
                 move
                 upon
                 the
                 water
                 .
              
               
                 THese
                 may
                 be
                 made
                 in
                 forme
                 of
                 a
                 Ball
                 stuffed
                 with
                 other
                 little
                 Balls
                 ,
                 glued
                 round
                 about
                 and
                 filled
                 with
                 composition
                 for
                 the
                 water
                 ,
                 which
                 fiered
                 ,
                 will
                 produce
                 marvellous
                 and
                 admirable
                 effects
                 ,
                 for
                 which
                 there
                 must
                 be
                 had
                 little
                 Cannons
                 of
                 white
                 Iron
                 ,
                 as
                 the
                 ends
                 of
                 small
                 funnels
                 ;
                 these
                 Iron
                 Cannons
                 may
                 be
                 pierced
                 in
                 sundry
                 places
                 ,
                 to
                 which
                 holes
                 ,
                 may
                 be
                 set
                 small
                 Balles
                 ful
                 of
                 composition
                 for
                 the
                 water
                 which
                 small
                 Balls
                 must
                 be
                 peirced
                 deep
                 and
                 large
                 ,
                 and
                 covered
                 with
                 Pitch
                 ,
                 except
                 the
                 hole
                 :
                 in
                 which
                 hole
                 must
                 
                 be
                 first
                 placed
                 a
                 little
                 quantitie
                 of
                 grain-Powder
                 ;
                 and
                 the
                 rest
                 of
                 the
                 hole
                 filled
                 up
                 with
                 composition
                 ;
                 and
                 note
                 further
                 that
                 these
                 Iron
                 Cannons
                 ,
                 must
                 
                 be
                 filled
                 with
                 a
                 slow
                 composition
                 ;
                 but
                 such
                 which
                 is
                 proper
                 to
                 burne
                 in
                 the
                 water
                 :
                 then
                 must
                 these
                 Cannons
                 with
                 their
                 small
                 Balls
                 be
                 put
                 so
                 together
                 that
                 it
                 may
                 make
                 a
                 Globe
                 ,
                 and
                 the
                 holes
                 in
                 the
                 Cannons
                 be
                 answerable
                 to
                 the
                 hollow
                 Balls
                 ,
                 and
                 all
                 covered
                 over
                 with
                 Pitch
                 and
                 Tallow
                 ;
                 afterwards
                 pierce
                 this
                 Ball
                 against
                 the
                 greatest
                 Cannon
                 (
                 to
                 which
                 all
                 the
                 lesser
                 should
                 answer
                 )
                 unto
                 the
                 composition
                 ,
                 then
                 fire
                 it
                 ,
                 and
                 when
                 it
                 begins
                 to
                 blow
                 ,
                 throw
                 it
                 into
                 the
                 water
                 ,
                 so
                 the
                 fire
                 comming
                 to
                 the
                 holes
                 will
                 fire
                 the
                 graine
                 Powder
                 ,
                 the
                 which
                 will
                 cause
                 the
                 Balls
                 to
                 separate
                 and
                 fly
                 here
                 and
                 there
                 ,
                 sometimes
                 two
                 at
                 a
                 time
                 ,
                 sometimes
                 three
                 ,
                 sometimes
                 more
                 ,
                 which
                 will
                 burne
                 within
                 the
                 water
                 with
                 great
                 astonishment
                 and
                 content
                 to
                 those
                 which
                 see
                 it
                 .
              
            
             
               
                 Of
                 Lances
                 of
                 fire
                 .
              
               
                 STanding
                 Lances
                 of
                 fire
                 ,
                 are
                 made
                 commonly
                 with
                 hollow
                 wood
                 ,
                 to
                 containe
                 sundry
                 Petards
                 ,
                 or
                 Rockets
                 ,
                 as
                 the
                 figure
                 here
                 sheweth
                 ,
                 by
                 which
                 is
                 easie
                 to
                 invent
                 others
                 occording
                 to
                 ones
                 fancy
                 .
                 These
                 Lances
                 have
                 wooden
                 handles
                 ,
                 that
                 so
                 they
                 may
                 be
                 fastned
                 at
                 some
                 Post
                 ,
                 so
                 that
                 they
                 be
                 not
                 overthrowne
                 in
                 the
                 flying
                 out
                 of
                 the
                 Rockets
                 or
                 Petards
                 :
                 there
                 are
                 lesser
                 sorts
                 of
                 Lances
                 whose
                 cases
                 are
                 of
                 three
                 or
                 foure
                 fouldings
                 of
                 Paper
                 of
                 a
                 foote
                 long
                 ,
                 and
                 about
                 the
                 bignesse
                 of
                 ones
                 finger
                 ,
                 which
                 are
                 filled
                 with
                 a
                 composition
                 for
                 Lances
                 .
                 But
                 if
                 these
                 Lances
                 be
                 filled
                 with
                 a
                 composition
                 ,
                 
                 then
                 (
                 unto
                 every
                 4
                 ouncs
                 of
                 powder
                 add●
                 2
                 ounces
                 of
                 Salt-Peter
                 ,
                 and
                 unto
                 that
                 adde
                 1
                 
                 ounce
                 of
                 Sulphur
                 )
                 it
                 will
                 make
                 a
                 brick
                 fire
                 red
                 before
                 it
                 be
                 halfe
                 spent
                 ,
                 if
                 the
                 Lance
                 be
                 fiered
                 and
                 held
                 to
                 it
                 :
                 and
                 if
                 20
                 such
                 Lances
                 were
                 placed
                 about
                 a
                 great
                 Rocket
                 and
                 shot
                 to
                 a
                 house
                 or
                 ship
                 ,
                 it
                 would
                 produce
                 a
                 mischievous
                 effect
                 .
              
            
             
               
                 How
                 to
                 shoot
                 a
                 Rocket
                 Horizontall
                 ,
                 or
                 otherwise
                 .
              
               
                 VNto
                 the
                 end
                 of
                 the
                 Rocket
                 place
                 an
                 Arrow
                 which
                 may
                 not
                 be
                 too
                 heavy
                 ,
                 but
                 in
                 stead
                 of
                 the
                 feathers
                 let
                 that
                 be
                 of
                 thinne
                 white
                 
                 tinne
                 plate
                 ,
                 and
                 place
                 it
                 upon
                 a
                 rest
                 ,
                 as
                 here
                 you
                 may
                 see
                 by
                 the
                 Figure
                 ,
                 then
                 give
                 fire
                 unto
                 it
                 ,
                 and
                 you
                 may
                 see
                 how
                 serviceable
                 it
                 may
                 be
                 .
                 To
                 the
                 head
                 of
                 such
                 Rockets
                 ,
                 may
                 be
                 placed
                 Petards
                 ,
                 Balls
                 of
                 fire
                 ,
                 Granadoes
                 ,
                 &c.
                 and
                 so
                 may
                 be
                 applyed
                 to
                 warlike
                 affaires
                 .
              
            
             
               
               
                 How
                 a
                 Rocket
                 burning
                 in
                 the
                 water
                 for
                 a
                 certaine
                 time
                 ,
                 at
                 last
                 shall
                 fly
                 up
                 in
                 the
                 Aire
                 with
                 an
                 exceeding
                 quickness
                 .
              
               
                 TO
                 do
                 this
                 ,
                 take
                 two
                 Rockets
                 ,
                 the
                 one
                 equall
                 to
                 the
                 other
                 ,
                 and
                 joyne
                 them
                 one
                 unto
                 another
                 in
                 the
                 middle
                 at
                 C.
                 in
                 such
                 sort
                 that
                 the
                 fire
                 may
                 easily
                 passe
                 from
                 one
                 to
                 another
                 :
                 it
                 being
                 thus
                 done
                 ,
                 tye
                 the
                 two
                 Rockets
                 at
                 a
                 stick
                 in
                 D
                 ,
                 and
                 let
                 it
                 be
                 so
                 long
                 and
                 great
                 that
                 it
                 may
                 make
                 the
                 Rockets
                 in
                 the
                 water
                 hang
                 ,
                 or
                 lye
                 upright
                 :
                 then
                 take
                 a
                 pack-thread
                 and
                 tye
                 it
                 at
                 G.
                 and
                 let
                 it
                 come
                 double
                 about
                 the
                 stick
                 DM
                 .
                 at
                 〈◊〉
                 and
                 at
                 that
                 
                 point
                 hang
                 a
                 Bullet
                 of
                 some
                 weight
                 as
                 K.
                 for
                 then
                 giving
                 fire
                 at
                 A.
                 it
                 will
                 burne
                 to
                 B.
                 by
                 a
                 small
                 serpent
                 filled
                 there
                 and
                 tyed
                 at
                 the
                 end
                 ,
                 and
                 covered
                 so
                 that
                 the
                 water
                 injure
                 it
                 hot
                 ,
                 which
                 will
                 fire
                 the
                 Rocket
                 BD
                 ,
                 and
                 so
                 mounting
                 quick
                 out
                 of
                 the
                 water
                 by
                 the
                 loose
                 tying
                 at
                 C.
                 and
                 the
                 Bullet
                 at
                 the
                 pack-thread
                 ,
                 will
                 leave
                 the
                 other
                 Rocket
                 in
                 the
                 vvater
                 :
                 and
                 so
                 ascend
                 like
                 a
                 Rocket
                 in
                 the
                 Aire
                 ,
                 to
                 the
                 admiration
                 of
                 such
                 as
                 knovv
                 not
                 the
                 secrecie
                 .
              
            
             
               
               
                 Of
                 the
                 framing
                 of
                 the
                 parts
                 of
                 a
                 Fire-Worke
                 ,
                 together
                 ,
                 that
                 the
                 severall
                 workes
                 may
                 fire
                 one
                 after
                 another
                 .
              
               
                 CAuse
                 a
                 frame
                 to
                 be
                 made
                 as
                 ABCD.
                 of
                 tvvo
                 foot
                 square
                 every
                 vvay
                 ,
                 or
                 thereabouts
                 (
                 according
                 to
                 the
                 quantity
                 of
                 your
                 severall
                 vvorkes
                 )
                 then
                 may
                 you
                 at
                 each
                 angle
                 have
                 a
                 great
                 Lance
                 of
                 fire
                 to
                 stand
                 ,
                 vvhich
                 may
                 cast
                 out
                 Pots
                 of
                 fire
                 as
                 they
                 consume
                 :
                 upon
                 the
                 ledges
                 AB.BC.
                 and
                 CD
                 .
                 may
                 be
                 placed
                 small
                 Lances
                 of
                 fire
                 about
                 the
                 number
                 of
                 30
                 or
                 60
                 ,
                 some
                 sidevvise
                 ,
                 and
                 others
                 upright
                 ,
                 betvveen
                 these
                 Lances
                 may
                 be
                 placed
                 Pots
                 of
                 fire
                 sloping
                 outvvards
                 ,
                 but
                 made
                 very
                 fast
                 ,
                 and
                 covered
                 very
                 close
                 ,
                 that
                 they
                 chance
                 not
                 to
                 fire
                 before
                 they
                 should
                 ;
                 then
                 upon
                 the
                 ledges
                 
                   RE.
                   FG.HI
                
                 .
                 and
                 AD
                 may
                 be
                 placed
                 your
                 soucisons
                 ,
                 and
                 behinde
                 all
                 the
                 vvork
                 may
                 be
                 set
                 your
                 Boxes
                 of
                 Rockets
                 ,
                 in
                 each
                 of
                 vvhich
                 you
                 may
                 place
                 6
                 ,
                 9
                 ,
                 ●2
                 .
                 or
                 20
                 small
                 Rockets
                 :
                 Novv
                 give
                 fire
                 at
                 A.
                 (
                 by
                 help
                 of
                 a
                 piece
                 of
                 primer
                 going
                 from
                 one
                 Lance
                 to
                 another
                 )
                 all
                 the
                 Lances
                 vvill
                 instantly
                 at
                 once
                 be
                 lighted
                 ,
                 and
                 as
                 soone
                 as
                 the
                 Lance
                 at
                 A
                 is
                 consumed
                 ,
                 it
                 vvill
                 fire
                 the
                 Channell
                 vvhich
                 is
                 made
                 in
                 the
                 ledge
                 of
                 the
                 frame
                 vvhich
                 runnes
                 under
                 the
                 Pots
                 of
                 fire
                 ,
                 and
                 as
                 the
                 fire
                 goes
                 along
                 burning
                 ,
                 the
                 Pots
                 vvill
                 be
                 cast
                 forth
                 ,
                 and
                 so
                 the
                 rank
                 of
                 Pots
                 upon
                 the
                 sides
                 of
                 the
                 frame
                 AB.BC.
                 and
                 CD
                 .
                 being
                 spent
                 ,
                 the
                 soucisons
                 vvill
                 begin
                 to
                 play
                 being
                 fiered
                 also
                 by
                 a
                 Channel
                 vvhich
                 runnes
                 under
                 them
                 ,
                 upon
                 
                 
                 
                 the
                 ledges
                 
                   AD
                   ,
                   HI●G
                
                 ,
                 and
                 RE.
                 then
                 when
                 the
                 Soucisons
                 are
                 spent
                 upon
                 the
                 last
                 ledge
                 RE.
                 there
                 may
                 be
                 a
                 secret
                 Channel
                 in
                 the
                 ledge
                 CD
                 which
                 may
                 fire
                 the
                 Box
                 of
                 Rockets
                 at
                 K.
                 and
                 may
                 fire
                 all
                 the
                 rest
                 one
                 after
                 another
                 ,
                 which
                 Boxes
                 may
                 be
                 all
                 charged
                 with
                 severall
                 Fire-Workes
                 :
                 for
                 the
                 Rockets
                 of
                 the
                 first
                 Box
                 may
                 be
                 loaden
                 with
                 Serpents
                 ,
                 the
                 second
                 with
                 Stars
                 ,
                 the
                 third
                 with
                 Reports
                 ,
                 the
                 fourth
                 with
                 Golden
                 raine
                 ,
                 and
                 the
                 fifth
                 with
                 small
                 flying
                 Serpents
                 ;
                 these
                 mounting
                 one
                 after
                 another
                 and
                 flying
                 to
                 and
                 fro
                 will
                 much
                 inlighten
                 the
                 Aire
                 in
                 their
                 ascending
                 ,
                 but
                 when
                 these
                 Rockets
                 discharge
                 themselves
                 above
                 ,
                 then
                 will
                 there
                 be
                 a
                 most
                 pleasant
                 representation
                 ,
                 for
                 these
                 fires
                 will
                 dilate
                 themselves
                 in
                 divers
                 beautifull
                 formes
                 ,
                 some
                 like
                 the
                 branching
                 of
                 Trees
                 ,
                 others
                 like
                 fountaines
                 of
                 water
                 gliding
                 in
                 the
                 Aire
                 ,
                 others
                 like
                 flashes
                 of
                 lightning
                 ,
                 others
                 like
                 the
                 glittering
                 of
                 starres
                 ,
                 giving
                 great
                 contentment
                 ,
                 and
                 delight
                 to
                 those
                 which
                 behold
                 them
                 ;
                 But
                 if
                 the
                 worke
                 be
                 furnished
                 also
                 with
                 Balons
                 (
                 which
                 is
                 the
                 chiefest
                 in
                 recreative
                 Fire-works
                 )
                 then
                 shall
                 you
                 see
                 ascending
                 in
                 the
                 Aire
                 but
                 as
                 it
                 were
                 onely
                 a
                 quill
                 of
                 fire
                 ,
                 but
                 once
                 the
                 Balon
                 taking
                 fire
                 ,
                 the
                 Aire
                 will
                 seeme
                 more
                 than
                 100.
                 foot
                 square
                 full
                 of
                 crawling
                 ,
                 and
                 flying
                 Serpents
                 ,
                 which
                 will
                 extinguish
                 with
                 a
                 volley
                 of
                 more
                 than
                 500
                 reports
                 :
                 and
                 so
                 fill
                 the
                 Aire
                 and
                 Firmament
                 with
                 their
                 rebounding
                 clamour
                 .
              
               
               
                 The
                 making
                 of
                 which
                 with
                 many
                 other
                 rare
                 and
                 excellent
                 Fire-workes
                 ,
                 and
                 other
                 practises
                 ,
                 not
                 onely
                 for
                 recreation
                 ,
                 but
                 also
                 for
                 service
                 :
                 you
                 may
                 finde
                 in
                 a
                 book
                 intituled
                 
                   Artificiall
                   Fire-workes
                
                 ,
                 made
                 by
                 Mr.
                 Malthas
                 (
                 a
                 master
                 of
                 his
                 knowledge
                 )
                 and
                 are
                 to
                 be
                 sold
                 by
                 
                   VVilliam
                   Leake
                
                 ,
                 at
                 the
                 Crowne
                 in
                 Fleet-street
                 ,
                 between
                 the
                 two
                 Temple-Gates
                 .
              
            
          
           
             
               Conclusion
               .
            
             
               In
               this
               Booke
               we
               have
               nothing
               omitted
               what
               was
               materiall
               in
               the
               originall
               ,
               but
               have
               abundantly
               augmented
               it
               in
               sundry
               experiments
               :
               And
               though
               the
               examinations
               are
               not
               so
               full
               ,
               and
               manifold
               ;
               yet
               (
               by
               way
               of
               brevitie
               )
               we
               have
               expressed
               fully
               their
               substance
               ,
               to
               avoid
               prolixitie
               ,
               and
               so
               past
               by
               things
               reiterated
               .
            
             
               FINIS
               .
            
          
        
         
           
             
             
               Printed
               or
               sold
               by
               
                 William
                 Leak
              
               ,
               at
               the
               Crovvne
               in
               
                 Fleetstreet
                 neere
                 the
                 Temple
              
               ,
               these
               Books
               following
               .
            
             
               
                 YOrk's
                 Heraldry
                 ,
                 Folio
              
               
                 A
                 Bible
                 of
                 a
                 very
                 fair
                 large
                 Roman
                 letter
                 ,
                 4●
              
               
                 
                   Orlando
                   F●rios●
                
                 Folio
                 .
              
               
                 Callu
                 learned
                 Readings
                 on
                 the
                 Scat.
                 21.
                 
                 Hen.
                 80.
                 
                 Cap
                 5
                 of
                 Sewer●
              
               
                 Perkins
                 on
                 the
                 Laws
                 of
                 England
                 .
              
               
                 Wi●kinsons
                 Office
                 of
                 She●●●fs
                 .
              
               
                 
                   Vade
                   Mecum
                
                 ,
                 of
                 a
                 Justice
                 of
                 Peace
                 .
              
               
                 The
                 book
                 of
                 Fees.
                 
              
               
                 Peasons
                 Law.
                 
              
               
                 Mirrour
                 of
                 Just●ce
                 .
              
               
                 Topicks
                 in
                 the
                 Laws
                 of
                 England
                 .
              
               
                 
                   Sken
                   de
                   significatione
                   Verborum
                
                 .
              
               
                 Delaman's
                 use
                 of
                 the
                 Horizontal
                 Quadrant
                 .
              
               
                 Wilby's
                 2d
                 set
                 of
                 Musique
                 ,
                 345
                 and
                 6
                 Parts
                 .
              
               
                 Corderius
                 in
                 English.
                 
              
               
                 D●ctor
                 Fulk's
                 Meteors
                 .
              
               
                 Malthus
                 Fire-workes
                 .
              
               
                 Nyes
                 Gunnery
                 &
                 Fire-workes
              
               
                 C●to
                 Ma●or
                 with
                 Annotations
                 ,
                 by
                 
                   Wil.
                   Austin
                
                 Esquire
                 .
              
               
                 
                   Mel
                   Helliconium
                
                 ,
                 by
                 
                   Alex.
                   Ross●
                
              
               
                 
                   Nosce
                   teipsum
                
                 ,
                 by
                 Sr
                 
                   John
                   Davis
                
              
               
                 Animadversions
                 on
                 Lil●i●s
                 Grammer
                 .
              
               
                 The
                 History
                 of
                 Vienna
                 ,
                 &
                 Paris
              
               
                 
                   Lazarillo
                   de
                   Tormes
                
                 .
              
               
                 Hero
                 and
                 L●ander
                 ,
                 by
                 
                   G.
                   Chapman
                
                 and
                 
                   Christoph.
                   Marlow
                
                 .
              
               
                 Al●ilia
                 or
                 Philotas
                 loving
                 folly
                 .
              
               
                 Bishop
                 Andrews
                 Sermons
                 .
              
               
                 Adams
                 on
                 ●eter
                 .
              
               
                 Posing
                 of
                 the
                 Accidence
                 .
              
               
                 
                   Am●dis
                   de
                   Gaule
                
                 .
              
               
                 Guillieliam's
                 Heraldry
                 .
              
               
                 Herberts
                 Travels
                 .
              
               
                 Bacc●s
                 Tales
                 .
              
               
                 Man
                 become
                 guilty
                 ,
                 by
                 
                   John
                   Francis
                   Sen●●t
                
                 ,
                 and
                 Englished
                 by
                 Henry
                 Earl
                 of
                 Monmouth
                 .
              
               
                 The
                 Ideot
                 in
                 4
                 books
                 ;
                 the
                 first
                 and
                 second
                 of
                 Wisdom
                 ;
                 the
                 third
                 of
                 the
                 Mind
                 ,
                 the
                 fourth
                 of
                 S●●tick
                 Experiments
                 of
                 the
                 Ballance
                 .
              
               
                 The
                 life
                 and
                 Reign
                 of
                 Hen.
                 the
                 Eighth
                 ,
                 written
                 by
                 the
                 L.
                 Herbet
              
               
                 Cornwallis
                 Essays
                 ,
                 &
                 Paradoxes
                 .
              
               
                 Clenards
                 greek
                 G●ammar
                 80
              
               
                 A●laluci●
                 ,
                 or
                 the
                 house
                 of
                 light
                 :
                 A
                 discourse
                 written
                 in
                 the
                 year
                 1651
                 ,
                 by
                 SN
                 .
                 a
                 modern
                 Speculator
                 .
              
               
                 A
                 Tragedy
                 written
                 by
                 the
                 most
                 learned
                 
                   Hugo
                   Grotius
                
                 called
                 ,
                 
                   Christus
                   Patience
                
                 ,
                 and
                 translated
                 into
                 Engl.
                 by
                 
                   George
                   Sand
                
                 ▪
              
               
                 The
                 Mount
                 of
                 Olives
                 :
                 or
                 Sollitary
                 Devotions
                 ,
                 by
                 
                   Henry
                   Vaughan
                   Silurist
                
                 VVith
                 an
                 excellent
                 discourse
                 of
                 Man
                 in
                 glory
                 ,
                 written
                 by
                 the
                 Reverend
                 Anselm
                 Arch
                 Bishop
                 of
                 Canterbury
                 .
              
               
                 The
                 Fort
                 Royall
                 of
                 Holy
                 Scriptures
                 by
                 
                   I.
                   H.
                
                 
              
            
             
               
                 PLAYES
                 .
              
               
                 Hen.
                 the
                 Fourth
                 .
                 Philaster
                 .
              
               
                 The
                 wedding
                 .
                 The
                 Hollander
                 .
              
               
                 Maids
                 Tragedie
                 .
                 King
                 &
                 no
                 K.
                 
              
               
                 The
                 gratefull
                 Servant
                 .
              
               
                 The
                 strange
                 Discovery
                 .
              
               
                 Othello
                 ;
                 the
                 Moor
                 of
                 Venice
                 .
              
               
                 The
                 Merchant
                 of
                 Venice
                 .
              
            
          
        
      
       
         
           
             
             
               THE
               DESCRIPTION
               AND
               USE
               OF
               THE
               DOVBLE
               Horizontall
               Dyall
               .
               WHEREBY
               NOT
               ONELY
               THE
               Houre
               of
               the
               Day
               is
               shewn
               ;
               but
               also
               the
               
                 Meridian
                 Line
              
               is
               found
               :
               And
               most
               ASTRONOMICALL
               Questions
               ,
               which
               may
               be
               done
               by
               the
               GLOBE
               :
               are
               resolved
               .
            
             
               INVENTED
               AND
               WRITTEN
               BY
               
                 W.
                 O.
              
               
            
             
               Whereunto
               is
               added
               ,
               The
               Description
               of
               the
               generall
               HOROLOGICALL
               RING
               .
            
             
               LONDON
               ,
               Printed
               for
               WILLIAM
               LEAKE
               ,
               and
               are
               to
               be
               sold
               at
               his
               Shop
               at
               the
               signe
               of
               the
               Crown
               in
               Fleetstreet
               ,
               between
               the
               two
               Temple
               Gates
               .
               1652.
               
            
          
        
         
           
             
             
               The
               description
               ,
               and
               use
               of
               the
               double
               Horizontall
               Diall
               .
            
             
               THere
               are
               upon
               the
               Plate
               two
               severall
               Dyals
               .
               That
               which
               is
               outermost
               ,
               is
               an
               ordinary
               diall
               ,
               divided
               into
               houres
               and
               quarters
               ,
               and
               every
               quarter
               into
               three
               parts
               which
               are
               five
               minutes
               a
               piece
               :
               so
               that
               the
               whole
               houre
               is
               understood
               to
               contein
               60
               minutes
               .
               And
               for
               this
               dyall
               the
               shadow
               of
               the
               upper
               oblique
               ,
               or
               slanting
               edge
               of
               the
               style
               ,
               or
               cocke
               ,
               doth
               serve
               .
            
             
               The
               other
               diall
               ,
               which
               is
               within
               ,
               is
               the
               
                 projection
                 of
                 the
                 upper
                 Hemisphaere
                 ,
                 upon
                 the
                 plain
                 of
                 the
                 Horizon
                 :
                 the
                 Horizon
              
               it self
               is
               understood
               to
               be
               the
               innermost
               circle
               of
               the
               limbe
               :
               and
               is
               divided
               on
               both
               sides
               from
               the
               points
               of
               East
               and
               West
               into
               degrees
               ,
               noted
               with
               10.20.30
               ,
               &c.
               
               As
               far
               as
               need
               requireth
               :
               And
               the
               center
               of
               the
               Instrument
               is
               the
               Zenith
               ,
               or
               
                 Verticall
                 point
              
               .
            
             
               Within
               the
               Horizon
               the
               middle
               straight
               line
               pointing
               North
               and
               South
               upon
               which
               the
               style
               standeth
               ,
               is
               the
               Meridian
               or
               twelve
               a
               clock
               line
               :
               and
               the
               other
               short
               arching
               lines
               on
               both
               sides
               of
               it
               ,
               are
               the
               
                 houre
                 lines
              
               ,
               distinguished
               accordingly
               by
               their
               figures
               :
               and
               are
               divided
               into
               quarters
               by
               the
               smaller
               lines
               drawn
               between
               them
               :
               every
               quarter
               conteining
               15
               minutes
               .
            
             
               The
               two
               arches
               which
               crosse
               the
               houre
               lines
               ,
               meeting
               on
               both
               sides
               in
               the
               points
               of
               intersection
               of
               the
               sixe
               a
               clocke
               lines
               with
               the
               Horizon
               ,
               are
               the
               two
               semicircles
               of
               the
               Ecliptick
               or
               annuall
               circle
               of
               the
               sun
               :
               the
               upper
               of
               which
               arches
               serveth
               for
               the
               Summer
               halfe
               yeere
               ;
               and
               the
               lower
               for
               the
               Winter
               half
               yeer
               :
               and
               therefore
               divided
               into
               365
               dayes
               :
               which
               are
               also
               distinguished
               into
               twelve
               moneths
               with
               longer
               lines
               ,
               having
               their
               names
               set
               down
               :
               and
               into
               tenths
               and
               fifts
               with
               shorter
               lines
               :
               
               and
               the
               rest
               of
               the
               dayes
               with
               pricks
               as
               may
               plainly
               be
               seene
               in
               the
               diall
               .
            
             
               And
               this
               is
               for
               the
               ready
               finding
               out
               of
               the
               
                 place
                 of
                 the
                 Sun
                 every
                 day
              
               :
               and
               also
               for
               the
               shewing
               of
               the
               
                 Suns
                 yeerely
                 motion
              
               ,
               because
               by
               this
               motion
               the
               Sun
               goeth
               round
               about
               the
               heavens
               in
               the
               compasse
               of
               a
               yeer
               ,
               making
               the
               four
               parts
               ,
               or
               seasons
               thereof
               ▪
               namely
               ,
               the
               Spring
               in
               that
               quarter
               of
               the
               Ecliptick
               which
               begins
               at
               the
               
                 intersection
                 on
                 the
                 East
              
               side
               of
               the
               diall
               ▪
               and
               is
               therefore
               called
               the
               
                 Vernall
                 intersection
              
               .
               Then
               the
               Summer
               in
               that
               quarter
               of
               the
               Ecliptick
               which
               begin
               at
               the
               
                 intersection
                 with
                 the
                 Meridian
              
               in
               the
               highest
               point
               next
               the
               Zenith
               .
               After
               that
               ,
               Autumne
               in
               that
               quarter
               of
               the
               Ecliptick
               which
               beginneth
               at
               the
               intersection
               on
               the
               West
               side
               of
               the
               diall
               ,
               and
               is
               therefore
               called
               the
               
                 Au●umna●l
                 intersection
              
               and
               lastly
               ,
               the
               Winter
               in
               that
               quarter
               of
               the
               Ecliptic●
               ,
               which
               beginneth
               at
               the
               
                 intersection
                 ,
                 with
                 the
                 Meridian
              
               i●
               the
               lowest
               point
               next
               the
               Horizon
               .
            
             
               But
               desides
               this
               
                 yeerely
                 motte●
                 ,
                 the
                 Sun
              
               hath
               a
               diurnall
               ,
               or
               
                 daily
                 motion
              
               ,
               whereby
               it
               maketh
               day
               and
               night
               ,
               with
               all
               the
               diversities
               and
               inaequalities
               thereof
               :
               which
               is
               expressed
               by
               those
               other
               
                 circles
                 drawn
                 crosse
                 the
                 houre
                 lines
              
               ;
               the
               middlemost
               whereof
               ,
               being
               grosser
               then
               the
               rest
               ,
               meeting
               with
               the
               Ec●iptick
               in
               the
               points
               of
               the
               Vernall
               ,
               and
               
                 Autumnall
                 intersections
              
               ▪
               is
               the
               Equinoctiall
               :
               and
               the
               rest
               on
               both
               sides
               of
               it
               are
               called
               the
               parallels
               ,
               
                 or
                 diurnall
                 arch
                 of
                 the
                 Sun
                 ,
              
               the
               two
               outermost
               whereof
               are
               the
               Tropicks
               ,
               because
               in
               them
               the
               sun
               hath
               his
               furthe●t
               digression
               or
               Declination
               from
               the
               Aequinoctiall
               ,
               which
               is
               degrees
               23
               1
               /
               ●
               ▪
               and
               thence
               beginneth
               againe
               to
               return
               towards
               the
               Equinoctiall
               .
               The
               upper
               of
               the
               two
               Tropicks
               in
               this
               nor
               Northerne
               Hemisphere
               is
               the
               Trop●ck
               of
               Cancer
               ,
               and
               the
               sun
               being
               in
               it
               ,
               is
               highest
               into
               the
               North
               ,
               making
               
               the
               longest
               day
               of
               Summer
               :
               And
               the
               lower
               next
               the
               Horizon
               is
               the
               Tropick
               of
               Capricorne
               ;
               and
               the
               sun
               being
               in
               it
               ,
               is
               lowest
               into
               the
               South
               ,
               making
               the
               shortest
               day
               of
               winter
               .
            
             
               Between
               the
               two
               Tropicks
               and
               the
               Aequinoctiall
               ,
               infinite
               such
               
                 parallel
                 circles
              
               are
               understood
               to
               be
               conteined
               :
               for
               the
               sun
               ,
               in
               what
               point
               soever
               of
               the
               Ecliptick
               it
               is
               carried
               ▪
               describeth
               by
               his
               Lation
               a
               circle
               parallel
               to
               the
               Aequinoctiall
               :
               yet
               those
               parallels
               which
               are
               in
               the
               instrument
               ,
               though
               drawn
               but
               to
               every
               second
               degree
               of
               Declination
               ,
               may
               be
               sufficient
               to
               direct
               the
               eye
               in
               imagining
               and
               tracing
               out
               through
               every
               day
               of
               the
               whole
               yeere
               in
               the
               Ecliptick
               ,
               a
               proper
               circle
               which
               may
               be
               the
               diurnall
               
                 arch
                 of
                 the
                 sun
              
               for
               that
               day
               .
               For
               upon
               the
               right
               estimation
               of
               that
               imaginary
               parallel
               doth
               the
               manifold
               use
               of
               this
               instument
               especially
               rely
               :
               because
               the
               true
               place
               of
               the
               sun
               all
               that
               day
               is
               in
               some
               part
               or
               point
               of
               that
               circle
               .
               Wherefore
               for
               the
               bet●er
               conceiving
               and
               bearing
               in
               minde
               thereof
               ,
               every
               fift
               parallel
               is
               herein
               made
               a
               little
               g●osser
               then
               the
               rest
               .
            
             
               For
               this
               inner
               diall
               serveth
               the
               shadow
               of
               the
               upright
               edge
               of
               the
               style
               ;
               which
               I
               therefore
               call
               the
               
                 upright
                 shadow
              
               .
            
             
               And
               thus
               by
               
                 the
                 eye
                 and
                 view
                 onely
                 to
                 behold
                 and
                 comprehend
                 the
                 course
                 of
                 the
                 sun
                 ▪
                 throughout
                 the
                 whole
                 yeere
                 both
                 for
                 his
                 annuall
                 and
                 diurnall
                 motion
                 ,
              
               may
               be
               the
               first
               use
               of
               this
               instrument
               .
            
             
               II
               Use.
               To
               finde
               the
               
                 declination
                 of
                 the
                 sun
              
               every
               day
               .
            
             
               Looke
               the
               day
               of
               the
               moneth
               proposed
               in
               the
               Ecliptick
               ,
               and
               mark
               how
               many
               degrees
               the
               prick
               shewing
               that
               day
               ,
               is
               distant
               from
               the
               Equinoctiall
               ,
               either
               on
               the
               Summer
               or
               Winter
               side
               ,
               viz.
               North
               or
               South
               .
            
             
             
               Example
               1.
               
               What
               will
               the
               Declination
               of
               the
               sun
               be
               upon
               the
               eleven●h
               day
               of
               August
               ?
               look
               the
               eleventh
               day
               of
               August
               and
               you
               shall
               finde
               it
               in
               the
               sixth
               circle
               above
               the
               ●quinoctiall
               :
               Now
               because
               each
               parallel
               standeth
               (
               as
               hath
               been
               said
               before
               )
               for
               two
               degrees
               ,
               the
               sun
               shall
               that
               day
               decline
               Northwards
               12.
               degrees
               .
            
             
               Example
               2.
               
               What
               declination
               hath
               the
               sun
               upon
               the
               24
               day
               of
               March
               ?
               look
               the
               24
               day
               of
               March
               ,
               and
               you
               shall
               finde
               it
               betweene
               the
               second
               and
               third
               northern
               parallels
               ,
               as
               it
               were
               an
               half
               and
               one
               fift
               part
               of
               that
               di●tance
               from
               the
               second
               :
               Reckon
               therefore
               four
               degrees
               for
               the
               two
               circles
               ,
               and
               one
               de●ree
               for
               the
               halfe
               space
               :
               So
               shall
               the
               Suns
               declination
               be
               five
               degrees
               ,
               and
               about
               one
               fift
               part
               of
               a
               degree
               Northward
               that
               same
               day
               .
            
             
               Example
               3.
               
               What
               declination
               hath
               the
               sun
               upon
               the
               13
               day
               of
               November
               ?
               look
               the
               13
               day
               of
               November
               ,
               and
               you
               shall
               finde
               it
               below
               the
               Equinoctiall
               ten
               parallels
               ,
               and
               about
               one
               quarter
               which
               is
               20
               degrees
               and
               an
               halfe
               southward
               .
               So
               much
               is
               the
               declination
               .
               And
               according
               to
               these
               examples
               judge
               of
               all
               the
               rest
               .
            
             
               III.
               Use.
               
                 To
                 finde
                 the
                 diurnall
                 arch
                 ,
                 or
                 circle
                 of
                 the
                 suns
                 course
                 every
                 day
                 .
              
            
             
               The
               sun
               every
               day
               by
               his
               motion
               (
               as
               hath
               been
               said
               )
               describeth
               a
               circle
               parallel
               to
               the
               ●quinoctiall
               ,
               which
               is
               either
               one
               of
               the
               circles
               in
               the
               diall
               ,
               or
               some-where
               ●etween
               two
               of
               them
               .
               First
               ,
               theref●re
               se●k
               the
               day
               of
               the
               moneth
               ;
               and
               if
               it
               fall
               upon
               one
               of
               those
               parallels
               ;
               that
               is
               the
               circle
               of
               the
               suns
               course
               that
               same
               day
               :
               But
               if
               it
               fall
               betweene
               any
               two
               of
               the
               parallels
               ,
               imagine
               in
               your
               mind●
               ,
               and
               estimate
               with
               your
               eye
               ,
               another
               parallel
               th●ough
               that
               point
               betweene
               those
               two
               parallels
               keeping
               still
               the
               same
               distance
               from
               each
               of
               them
               .
            
             
             
               As
               in
               the
               first
               of
               the
               three
               former
               examples
               ,
               The
               circle
               of
               the
               Suns
               course
               upon
               11
               of
               August
               ▪
               shal
               be
               the
               very
               sixt
               circle
               above
               the
               Equinoctiall
               toward
               the
               cente●
               .
            
             
               In
               ●xample
               2.
               
               The
               circle
               of
               the
               
                 suns
                 cou●se
              
               upon
               the
               24
               of
               March
               shall
               be
               an
               imaginary
               circle
               between
               the
               second
               and
               third
               parallels
               still
               keeping
               an
               half
               of
               that
               space
               ,
               and
               one
               fifth
               part
               more
               of
               the
               rest
               ,
               from
               the
               second
               .
            
             
               In
               example
               3.
               
               The
               
                 circle
                 of
                 the
                 suns
                 course
              
               upon
               the
               13
               of
               November
               :
               shall
               be
               an
               imaginary
               circle
               between
               the
               tenth
               and
               eleventh
               parallels
               below
               the
               Equinoctiall
               ,
               still
               keeping
               one
               quarter
               of
               that
               space
               from
               the
               tenth
               .
            
             
               IIII
               Use.
               
                 To
                 finde
                 the
                 r●sing
                 and
                 setting
                 of
                 the
                 sun
                 eve●yday
                 .
              
            
             
               〈…〉
               (
               as
               was
               last
               shewed
               )
               the
               imaginary
               circle
               or
               parallel
               of
               the
               suns
               course
               for
               that
               day
               ,
               and
               marke
               the
               point
               where
               it
               meeteth
               with
               the
               horizon
               ,
               both
               on
               the
               East
               and
               W●st
               sides
               ,
               for
               that
               is
               the
               very
               point
               of
               the
               suns
               r●sing
               ,
               and
               setting
               that
               same
               day
               ,
               and
               the
               houre
               lines
               which
               are
               on
               both
               sides
               of
               it
               ,
               by
               proportioning
               the
               distance
               reasonably
               ,
               according
               to
               15
               minutes
               for
               the
               quarter
               of
               the
               houre
               ,
               will
               shew
               the
               houre
               of
               the
               suns
               rising
               on
               the
               East
               side
               ,
               and
               the
               suns
               setting
               on
               the
               West
               side
               .
            
             
               V
               Use.
               To
               know
               the
               reason
               and
               manner
               of
               the
               Increasing
               and
               decreasing
               of
               the
               nights●hroughout
               ●hroughout
               the
               whole
               yeere
               .
            
             
               When
               the
               Sun
               is
               in
               the
               Equinoctiall
               ,
               it
               riseth
               and
               setteth
               at
               6
               a
               clock
               ,
               for
               in
               the
               instrument
               the
               intersection
               of
               the
               Equinoctiall
               ,
               and
               the
               Ecliptick
               with
               the
               Horizon
               is
               in
               the
               six
               a
               clocke
               circle
               on
               both
               sides
               .
               But
               if
               the
               sun
               be
               out
               of
               the
               Equinoctial
               ,
               declining
               toward
               the
               North
               ,
               the
               intersections
               of
               the
               parallel
               of
               the
               sun
               with
               the
               Horizon
               is
               
               before
               6
               in
               the
               morning
               ,
               and
               after
               6
               in
               the
               evening
               :
               and
               the
               
                 Diurnall
                 arch
              
               greater
               then
               12
               houres
               ;
               and
               so
               much
               more
               great
               ,
               the
               greater
               the
               Northerne
               Declination
               is
               .
               Againe
               ,
               if
               the
               sun
               be
               declining
               toward
               the
               South
               ,
               the
               intersections
               of
               the
               parallel
               of
               the
               sun
               ,
               with
               the
               Horizon
               is
               after
               6
               in
               the
               morning
               ,
               and
               before
               6
               in
               the
               evening
               :
               and
               the
               
                 Diurnall
                 arch
              
               lesser
               then
               12
               houres
               ;
               and
               by
               so
               much
               lesser
               ,
               the
               greater
               the
               Southerne
               Declination
               is
               .
            
             
               And
               in
               those
               places
               of
               the
               Ecliptick
               in
               which
               the
               sun
               most
               speedily
               changeth
               his
               declination
               ,
               the
               length
               also
               of
               the
               day
               is
               most
               a●tered
               :
               and
               where
               the
               Ecliptick
               goeth
               most
               parallel
               to
               the
               Equinoctiall
               changing
               the
               declination
               ,
               but
               little
               altered
               .
               As
               for
               example
               ,
               when
               the
               sun
               is
               neer
               unto
               the
               Equinoctiall
               on
               both
               sides
               ,
               the
               dayes
               increase
               and
               also
               decrease
               suddenly
               and
               apace
               ;
               because
               in
               those
               places
               the
               Ecliptick
               inclineth
               to
               the
               Equinoctiall
               in
               a
               manner
               like
               a
               streight
               line
               ,
               making
               sensible
               declination
               .
               Again
               ,
               when
               the
               sun
               is
               neere
               his
               greatest
               declination
               ,
               as
               in
               the
               height
               of
               Summer
               ,
               and
               the
               depth
               of
               Winter
               ,
               the
               dayes
               keep
               for
               a
               good
               time
               ,
               as
               it
               were
               ,
               at
               one
               stay
               ,
               because
               in
               these
               places
               the
               Ecliptick
               is
               in
               a
               manner
               parallel
               to
               the
               Equinoctiall
               ,
               the
               length
               o●
               the
               day
               also
               is
               but
               little
               ,
               scarce
               altering
               the
               declination
               :
               And
               because
               in
               those
               two
               times
               of
               the
               yeer
               ,
               the
               sun
               standeth
               as
               it
               were
               still
               at
               one
               declination
               ,
               they
               are
               called
               the
               
                 summer
                 solstice
              
               ,
               and
               
                 winter
                 solstice
              
               .
               And
               in
               the
               mean
               space
               the
               neerer
               every
               place
               is
               to
               the
               Equinoctiall
               ,
               the
               greater
               is
               the
               diversity
               of
               dayes
               .
            
             
               Wherefore
               ,
               we
               may
               hereby
               plainly
               see
               that
               the
               common
               received
               opinion
               ,
               that
               in
               every
               moneth
               the
               dayes
               doe
               equally
               increase
               ,
               is
               erroneous
               .
            
             
               Also
               we
               may
               see
               that
               in
               parallels
               equally
               distant
               from
               the
               Equinoctiall
               ,
               the
               day
               on
               the
               one
               side
               is
               equall
               to
               the
               night
               on
               the
               other
               side
               .
            
             
             
               VI.
               Vse
               .
               
                 To
                 finde
                 how
                 far
                 the
                 sun
                 riseth
                 ,
                 and
                 setteth
                 from
                 the
                 true
                 east
                 and
                 west
                 points
                 ,
                 which
                 is
                 called
                 the
                 suns
                 Amp●itude
                 ortive
                 ,
                 and
                 occasive
                 .
              
            
             
               Seek
               out
               (
               as
               was
               shewed
               in
               III
               Vse
               )
               the
               imaginary
               circle
               ,
               or
               parallel
               of
               the
               suns
               course
               ,
               and
               the
               points
               of
               that
               circle
               in
               the
               horizon
               ,
               on
               the
               East
               and
               West
               sides
               cutteth
               the
               degree
               of
               the
               
                 Amplitude
                 ortive
              
               ,
               and
               occasive
               .
            
             
               VII
               Use.
               
                 To
                 finde
                 the
                 length
                 of
                 every
                 day
                 and
                 night
                 .
              
            
             
               Double
               the
               houre
               of
               the
               sunnes
               setting
               ,
               and
               you
               shal
               have
               the
               length
               of
               the
               day
               ;
               &
               double
               the
               hour
               of
               the
               sunnes
               rising
               ,
               and
               you
               shal
               have
               the
               length
               of
               the
               right
               .
            
             
               VIII
               Vse
               .
               
                 To
                 finde
                 the
                 true
                 place
                 of
                 the
                 sun
                 upon
                 the
                 dyall
                 ,
                 that
                 is
                 ,
                 the
                 point
                 of
                 the
                 instrument
                 which
                 answereth
                 to
                 the
                 place
                 of
                 the
                 sun
                 in
                 the
                 heavens
                 at
                 any
                 time
                 ,
                 which
                 is
                 the
                 very
                 ground
                 of
                 all
                 the
                 questions
                 following
                 .
              
            
             
               If
               the
               dyall
               be
               fixed
               upon
               a
               post
               :
               Look
               what
               a
               clock
               it
               is
               by
               the
               outward
               dyall
               ,
               that
               is
               ,
               look
               what
               houre
               and
               part
               of
               houre
               the
               shadow
               of
               the
               slanting
               edge
               of
               the
               style
               sheweth
               in
               the
               outward
               limbe
               .
               Then
               behold
               the
               shadow
               of
               the
               upright
               edge
               ,
               and
               marke
               what
               point
               thereof
               is
               upon
               that
               very
               houre
               and
               part
               in
               the
               inner
               dyall
               among
               the
               parallels
               ,
               that
               point
               is
               the
               true
               place
               of
               the
               Sunne
               at
               the
               same
               instant
               .
            
             
               If
               the
               dyal
               be
               not
               fixed
               ,
               and
               you
               have
               a
               
                 Meridian
                 line
              
               no●ed
               in
               any
               window
               where
               the
               Sunne
               shineth
               :
               place
               the
               Meridian
               of
               your
               dyal
               upon
               the
               Meridian
               line
               given
               ,
               so
               that
               the
               top
               of
               the
               stile
               may
               point
               into
               the
               north
               :
               and
               so
               the
               dyal
               is
               as
               it
               were
               fixed
               ,
               wherefore
               by
               the
               former
               rule
               you
               may
               finde
               the
               place
               of
               the
               Sunne
               upon
               it
               .
            
             
               If
               the
               dyal
               be
               not
               fixed
               ,
               neither
               you
               have
               a
               Meridian
               line
               ,
               but
               you
               know
               the
               true
               houre
               of
               the
               day
               exactly
               :
               hold
               the
               dyal
               even
               and
               parallel
               to
               the
               Horizon
               ,
               moving
               
               it
               till
               the
               slanting
               edge
               of
               the
               stile
               cast
               his
               shadow
               justly
               upon
               the
               time
               or
               houre
               given
               ;
               for
               then
               the
               dyal
               is
               truly
               placed
               ,
               as
               upon
               a
               post
               .
               Seek
               therefore
               what
               point
               of
               the
               upright
               shadow
               falleth
               upon
               that
               very
               houre
               ,
               and
               there
               is
               the
               place
               of
               the
               Sun.
               
            
             
               But
               if
               your
               dyal
               be
               loose
               ,
               and
               you
               know
               neither
               the
               Meridian
               nor
               the
               time
               of
               the
               day
               .
               First
               ,
               by
               the
               day
               of
               the
               moneth
               in
               the
               Ecliptique
               ,
               finde
               the
               su●s
               parallel
               ,
               or
               d●urnall
               arch
               for
               that
               day
               ▪
               then
               holding
               the
               dyal
               level
               to
               the
               horizon
               ,
               move
               it
               every
               way
               untill
               the
               slanting
               shadow
               of
               the
               style
               in
               the
               outward
               limbe
               ,
               and
               the
               upright
               shadow
               in
               the
               Sunnes
               diurnal
               arch
               ,
               both
               shew
               the
               very
               same
               houre
               and
               minute
               ,
               for
               that
               very
               point
               of
               the
               Sunnes
               parallel
               ,
               which
               the
               upright
               shadow
               cutteth
               ,
               is
               the
               true
               place
               of
               the
               Sun
               on
               the
               dyal
               at
               that
               present
               .
            
             
               But
               note
               that
               by
               reason
               of
               the
               thicknes
               of
               the
               style
               ,
               and
               the
               bluntnesse
               of
               the
               angle
               of
               the
               upright
               edge
               ,
               the
               Sun
               cannot
               come
               unto
               that
               edge
               for
               some
               space
               before
               and
               after
               noone
               .
               And
               so
               during
               the
               time
               that
               the
               Sunne
               shineth
               not
               on
               that
               upright
               edge
               ,
               the
               place
               of
               the
               Sunne
               in
               the
               dyal
               cannot
               be
               found
               .
               Wherefore
               they
               that
               make
               this
               kinde
               of
               double
               dyal
               ,
               are
               to
               be
               careful
               to
               file
               the
               upright
               edge
               of
               the
               style
               as
               thinne
               and
               sharpe
               as
               possible
               may
               be
               .
            
             
               That
               which
               hath
               here
               bin
               taught
               concerning
               the
               finding
               out
               the
               Suns
               true
               place
               in
               the
               dyal
               ,
               ought
               perfectly
               to
               be
               understood
               ,
               that
               it
               may
               be
               readily
               ,
               and
               dexteriously
               practised
               ,
               for
               upon
               the
               true
               performance
               thereof
               dependeth
               all
               that
               followeth
               .
            
             
               IX
               Vse
               .
               
                 To
                 finde
                 the
                 houre
                 of
                 the
                 day
                 .
              
            
             
               If
               the
               dyal
               be
               fastned
               upon
               a
               post
               ,
               the
               houre
               by
               the
               outward
               dyal
               ,
               or
               limbe
               ,
               is
               known
               of
               every
               one
               ,
               and
               the
               
               upri●ht
               shadow
               in
               the
               Suns
               parallel
               ,
               or
               diurnal
               arch
               will
               also
               shew
               the
               very
               same
               houre
               .
            
             
               But
               if
               the
               dyall
               be
               loose
               ,
               either
               hold
               it
               or
               set
               it
               parallel
               to
               the
               Horizon
               ,
               with
               the
               style
               pointing
               into
               the
               north
               and
               move
               it
               gently
               every
               way
               untill
               the
               houre
               shewed
               in
               both
               dialls
               exactly
               agreeth
               ,
               or
               which
               is
               all
               one
               ,
               finde
               out
               the
               true
               place
               of
               the
               Sun
               upon
               the
               dyall
               ,
               as
               was
               taught
               in
               the
               former
               question
               ,
               for
               that
               point
               among
               the
               houre
               lines
               sheweth
               the
               houre
               of
               the
               day
               .
            
             
               X
               Vse
               .
               
                 To
                 finde
                 out
                 the
                 Meridian
                 ,
                 and
                 other
                 points
                 of
                 the
                 Compasse
                 .
              
            
             
               First
               ,
               you
               must
               seek
               the
               tru●
               houre
               of
               the
               day
               (
               by
               the
               last
               question
               )
               for
               in
               that
               situation
               the
               Meridian
               of
               the
               dyall
               standeth
               direct●y
               north
               and
               south
               :
               and
               the
               east
               pointeth
               into
               the
               east
               ,
               and
               the
               west
               into
               the
               west
               ,
               and
               the
               rest
               of
               the
               points
               may
               be
               given
               by
               allowing
               degrees
               11.
               1
               /
               ●
               unto
               every
               point
               of
               the
               compasse
               .
            
             
               XI
               Vse
               .
               
                 To
                 finde
                 out
                 the
                 Azumith
                 of
                 the
                 sun
                 ,
                 that
                 is
                 ,
                 the
                 distance
                 of
                 the
                 Verticall
                 circle
                 ,
                 in
                 which
                 the
                 sun
                 is
                 at
                 that
                 present
                 ,
                 from
                 the
                 Meridian
                 .
              
            
             
               Set
               your
               diall
               upon
               any
               plain
               or
               flat
               which
               is
               parallel
               to
               the
               horizon
               ,
               with
               the
               Meridian
               pointing
               directly
               north
               or
               south
               ,
               as
               was
               last
               shewed
               :
               then
               follow
               with
               your
               eye
               the
               upright
               shadow
               in
               a
               streight
               line
               ,
               till
               it
               cutteth
               the
               horizon
               :
               for
               the
               degree
               in
               which
               the
               point
               of
               intersection
               is
               ,
               shal
               shew
               how
               far
               the
               suns
               Azumith
               is
               distant
               from
               the
               east
               and
               west
               points
               ,
               and
               the
               complement
               thereof
               unto
               90
               ;
               shal
               give
               the
               distance
               thereof
               from
               the
               meridian
               .
            
             
               XII
               Vse
               .
               
                 To
                 finde
                 out
                 the
                 Declination
                 of
                 any
                 Wall
                 upon
                 which
                 the
                 sun
                 shineth
                 ,
                 that
                 is
                 ,
                 how
                 far
                 that
                 wall
                 swerveth
                 from
                 the
                 north
                 or
                 south
                 ,
                 either
                 eastward
                 or
                 westward
                 .
              
            
             
             
               Take
               aboard
               having
               one
               streight
               edg
               ▪
               &
               a
               line
               stricken
               perpendicular
               upon
               it
               ;
               apply
               the
               streight
               edg
               unto
               the
               wall
               at
               what
               time
               the
               sun
               shineth
               upon
               it
               ,
               holding
               the
               board
               parallel
               to
               the
               horizon
               :
               Set
               the
               dyal
               thereon
               ,
               and
               move
               it
               gently
               every
               way
               ,
               untill
               the
               same
               hour
               and
               minute
               be
               shewed
               in
               both
               dyals
               :
               and
               so
               let
               it
               stand
               :
               then
               if
               the
               dyal
               have
               one
               of
               the
               sides
               parallel
               to
               the
               Meridian
               strike
               a
               line
               along
               that
               side
               upon
               the
               board
               ,
               crossing
               the
               perpendicular
               ,
               or
               else
               with
               a
               bodkin
               make
               a
               point
               upon
               the
               board
               ,
               at
               each
               end
               of
               the
               meridian
               ,
               and
               taking
               away
               the
               instrument
               from
               the
               board
               ,
               and
               the
               board
               from
               the
               wall
               ,
               lay
               a
               ruler
               to
               those
               two
               points
               ,
               and
               draw
               a
               line
               crossing
               the
               perpendicular
               :
               for
               the
               angle
               which
               that
               line
               maketh
               with
               the
               perpendicular
               ,
               is
               the
               angle
               of
               the
               decli●nation
               of
               the
               wall
               .
               And
               if
               it
               be
               a
               right
               angle
               ,
               the
               wall
               is
               exactly
               east
               or
               west
               :
               but
               if
               that
               line
               be
               parallel
               to
               the
               perpendicular
               ,
               the
               wall
               is
               direct
               north
               or
               south
               without
               any
               declination
               at
               all
               .
            
             
               You
               may
               also
               finde
               out
               the
               declination
               of
               a
               wall
               ,
               if
               the
               dial
               be
               fixed
               on
               a
               post
               not
               very
               far
               from
               that
               wall
               ;
               in
               this
               manner
               .
               Your
               board
               being
               applyed
               to
               the
               wall
               ,
               as
               was
               shewed
               ,
               hang
               up
               a
               thred
               with
               a
               plummet
               ,
               so
               that
               the
               shadow
               of
               the
               thred
               may
               upon
               the
               board
               crosse
               the
               perpendicular
               line
               :
               make
               two
               pricks
               in
               the
               shadow
               and
               run
               instantly
               to
               the
               dyal
               and
               look
               the
               horizontal
               distance
               of
               the
               suns
               Azumith
               ,
               or
               upright
               shadow
               from
               the
               meridian
               .
               Then
               through
               the
               two
               pricks
               draw
               a
               line
               crossing
               the
               perpendicular
               :
               and
               upon
               the
               point
               of
               the
               intersection
               ,
               make
               a
               circle
               equal
               to
               the
               horizon
               of
               your
               Instrument
               ,
               in
               which
               Circle
               you
               shal
               from
               the
               line
               through
               the
               two
               pricks
               measure
               the
               Horizontal
               distance
               of
               the
               upright
               shadow
               ,
               or
               Azumith
               from
               the
               meridian
               ,
               that
               way
               toward
               which
               the
               Meridian
               is
               :
               draw
               
               a
               line
               out
               of
               the
               center
               ,
               to
               the
               end
               of
               that
               arch
               measured
               :
               and
               the
               angle
               which
               this
               last
               line
               maketh
               with
               the
               perpendicular
               ,
               shall
               be
               equall
               to
               the
               declination
               of
               the
               wall
               .
            
             
               XIII
               Vse
               .
               
                 How
                 to
                 place
                 the
                 dyall
                 upon
                 a
                 post
                 without
                 any
                 other
                 direction
                 but
                 it selfe
                 .
              
            
             
               Set
               the
               diall
               upon
               the
               post
               ,
               with
               the
               stile
               into
               the
               North
               ,
               as
               neere
               as
               you
               can
               guesse
               :
               then
               move
               it
               this
               way
               and
               that
               way
               ,
               till
               the
               same
               houre
               and
               minute
               be
               shewed
               ,
               both
               in
               the
               outward
               and
               inward
               dials
               by
               the
               severall
               shadowes
               ,
               as
               hath
               been
               already
               taught
               ,
               for
               then
               the
               diall
               standeth
               in
               its
               truest
               situation
               ;
               wherefore
               let
               it
               be
               nailed
               down
               in
               that
               very
               place
               .
            
             
               XIIII
               Vse
               .
               
                 To
                 finde
                 the
                 height
                 of
                 the
                 sun
                 at
                 high
                 noon
                 everyday
                 .
              
            
             
               Seeke
               out
               the
               diurnall
               Arch
               or
               parallel
               of
               the
               suns
               course
               for
               that
               day
               ,
               (
               by
               
                 Vse
                 III.
              
               )
               and
               with
               a
               paire
               of
               Compasses
               ,
               setting
               one
               foot
               in
               the
               center
               ,
               and
               the
               other
               in
               the
               point
               of
               intersection
               of
               that
               parallel
               with
               the
               Meridian
               ,
               apply
               that
               same
               distance
               unto
               the
               Semidiameter
               divided
               :
               for
               that
               measure
               shal
               therein
               shew
               the
               degree
               of
               of
               the
               Suns
               altitude
               above
               the
               the
               Horizon
               that
               day
               at
               high
               noon
               .
            
             
               XV
               
                 Vse
                 .
                 To
                 finde
                 the
                 height
                 of
                 the
                 sun
                 at
                 any
                 houre
                 or
                 time
                 of
                 the
                 day
                 .
              
            
             
               Seeke
               out
               the
               diurnal
               Arch
               ,
               or
               parallel
               of
               the
               suns
               course
               for
               that
               day
               :
               and
               marke
               what
               point
               of
               it
               is
               in
               the
               very
               houre
               and
               minute
               proposed
               .
               And
               with
               a
               paire
               of
               Compasses
               ,
               setting
               one
               foot
               in
               the
               Center
               ,
               and
               the
               other
               in
               that
               point
               of
               the
               parallel
               ,
               apply
               the
               same
               distance
               upon
               the
               Semidiameter
               divided
               :
               for
               that
               measure
               shall
               shew
               the
               degree
               of
               the
               suns
               altitude
               above
               the
               Horizon
               at
               that
               time
               .
            
             
             
               And
               by
               this
               meanes
               you
               may
               finde
               the
               height
               of
               the
               Sun
               above
               the
               Horizon
               at
               every
               houre
               throughout
               the
               whole
               yeere
               ,
               for
               the
               making
               of
               rings
               and
               cylinders
               and
               other
               instruments
               which
               are
               used
               to
               shew
               the
               houre
               of
               the
               day
               .
            
             
               XVI
               Vse
               .
               
                 The
                 height
                 of
                 the
                 sun
                 being
                 given
                 ,
                 to
                 finde
                 out
                 the
                 houre
                 ,
                 or
                 what
                 it
                 is
                 a
                 clocke
                 .
              
            
             
               This
               is
               the
               converse
               of
               the
               former
               :
               Seeke
               therefore
               in
               the
               Semidiameter
               divided
               ,
               the
               height
               of
               the
               sun
               given
               .
               And
               with
               a
               paire
               of
               Compasses
               ,
               setting
               one
               foot
               in
               the
               center
               ,
               and
               the
               other
               at
               that
               height
               ,
               apply
               the
               same
               distance
               unto
               the
               diurnall
               arch
               ,
               or
               parallel
               of
               the
               Sun
               for
               that
               day
               :
               for
               that
               point
               of
               the
               diurnall
               arch
               ,
               upon
               which
               that
               same
               distance
               lights
               ,
               is
               the
               true
               place
               of
               the
               sun
               upon
               the
               dial
               ;
               and
               sheweth
               among
               the
               houre
               lines
               ,
               the
               true
               time
               of
               the
               day
               .
            
             
               XVII
               Use.
               
                 Considerations
                 for
                 the
                 use
                 of
                 the
                 instrument
                 in
                 the
                 night
                 .
              
            
             
               In
               such
               questions
               as
               concerne
               the
               night
               ▪
               or
               the
               time
               before
               sun
               rising
               ,
               and
               after
               sun
               setting
               ,
               the
               instrument
               representeth
               the
               lower
               Hemisphaere
               wherein
               the
               Southerne
               pole
               is
               elevated
               .
               And
               therefore
               the
               parallels
               which
               are
               above
               the
               Aequinoctiall
               toward
               the
               center
               shall
               be
               for
               the
               Southerne
               ,
               or
               winter
               parallels
               :
               and
               those
               beneath
               the
               Aequinoctiall
               ,
               for
               the
               Northerne
               or
               Summer
               paral●els
               ;
               and
               the
               East
               shall
               be
               accounted
               for
               West
               ,
               and
               the
               West
               for
               East
               ;
               altogether
               contrary
               to
               that
               which
               was
               before
               ,
               when
               the
               Instrument
               represented
               the
               upper
               Hemisphaere
               .
            
             
               XVIII
               Use.
               
                 To
                 finde
                 how
                 many
                 degrees
                 the
                 sun
                 is
                 under
                 the
                 Horizon
                 at
                 any
                 time
                 of
                 the
                 night
                 .
              
            
             
               Seeke
               the
               Declination
               of
               the
               sun
               for
               the
               day
               proposed
               
               (
               by
               
                 Vse
                 II.
              
               )
               And
               at
               the
               same
               declination
               the
               contrary
               side
               imagine
               a
               parallel
               for
               the
               sun
               that
               night
               ▪
               and
               mark
               what
               point
               of
               it
               is
               in
               the
               very
               houre
               and
               minute
               proposed
               :
               And
               with
               a
               pair
               of
               compasses
               ,
               setting
               one
               foot
               in
               the
               center
               ,
               and
               the
               other
               in
               that
               point
               of
               the
               parallel
               ,
               apply
               that
               same
               distance
               unto
               the
               semidiameter
               divided
               :
               for
               that
               measure
               shall
               shew
               the
               degree
               of
               the
               suns
               depression
               below
               the
               Horizon
               at
               that
               time
               .
            
             
               XIX
               Use.
               
                 To
                 finde
                 out
                 the
                 length
                 of
                 the
                 C●epusculum
                 ,
                 or
                 twylight
                 ,
                 every
                 day
                 .
              
            
             
               Seek
               the
               declination
               of
               the
               sun
               for
               the
               day
               proposed
               (
               by
               
                 Vse
                 II.
              
               )
               And
               at
               the
               same
               declination
               on
               the
               contrary
               side
               imagine
               a
               parallel
               for
               the
               sun
               that
               night
               .
               And
               with
               a
               paire
               of
               compasses
               setting
               one
               foot
               in
               the
               center
               ,
               and
               the
               other
               at
               72
               degrees
               upon
               the
               semidiameter
               divided
               ,
               apply
               that
               same
               distance
               ,
               unto
               the
               suns
               nocturnall
               parallel
               :
               for
               that
               point
               of
               the
               parallel
               ,
               upon
               which
               that
               same
               distance
               shall
               light
               ,
               sheweth
               among
               the
               houre
               lines
               ,
               the
               beginning
               of
               the
               twilight
               in
               the
               morning
               ,
               or
               the
               end
               of
               the
               twilight
               in
               the
               evening
               .
            
             
               XX
               Use.
               
                 If
                 the
                 day
                 of
                 the
                 moneth
                 be
                 not
                 known
                 ,
                 to
                 finde
                 it
                 out
                 by
                 the
                 dyall
                 .
              
            
             
               For
               the
               working
               of
               this
               question
               ,
               either
               the
               diall
               must
               be
               fixed
               rightly
               on
               a
               post
               ,
               or
               else
               you
               must
               have
               a
               true
               Meridian
               line
               drawn
               in
               some
               window
               where
               the
               sun
               shineth
               ,
               wherefore
               supposing
               the
               diall
               to
               be
               justly
               set
               either
               upon
               the
               post
               ,
               or
               upon
               the
               Meridian
               .
               Look
               what
               a
               clock
               it
               is
               by
               the
               outward
               diall
               ,
               and
               observe
               what
               point
               of
               the
               upright
               shadow
               falleth
               upon
               the
               very
               same
               minute
               in
               the
               inner
               diall
               ,
               and
               through
               that
               same
               point
               imagine
               a
               parallel
               circle
               for
               the
               suns
               course
               ;
               that
               imaginary
               circle
               in
               the
               Ecliptick
               shall
               cut
               the
               day
               of
               the
               moneth
               .
            
             
               
               
                 I
                 The
                 description
                 of
                 it
                 .
              
               
                 THis
                 Instrument
                 serveth
                 as
                 a
                 Diall
                 to
                 finde
                 the
                 houre
                 of
                 the
                 day
                 ,
                 not
                 in
                 one
                 place
                 onely
                 (
                 as
                 the
                 most
                 part
                 of
                 Dials
                 do
                 )
                 but
                 generally
                 in
                 all
                 Countreys
                 lying
                 North
                 of
                 the
                 Aequinoctiall
                 :
                 and
                 therefore
                 I
                 call
                 it
                 the
                 generall
                 H●rologicall
                 ●ing
                 .
              
               
                 It
                 consisteth
                 of
                 two
                 br●zen
                 circles
                 :
                 a
                 Diameter
                 ,
                 and
                 a
                 little
                 Ring
                 to
                 hang
                 it
                 by
                 .
              
               
                 The
                 two
                 circles
                 are
                 so
                 made
                 ,
                 that
                 though
                 they
                 are
                 to
                 be
                 set
                 at
                 right
                 angles
                 ,
                 when
                 you
                 use
                 the
                 Instrument
                 :
                 yet
                 for
                 more
                 convenient
                 carrying
                 ,
                 they
                 may
                 be
                 one
                 folded
                 into
                 the
                 other
                 .
              
               
                 The
                 lesser
                 of
                 the
                 two
                 circles
                 is
                 for
                 the
                 Aequinoctiall
                 ,
                 having
                 in
                 the
                 midst
                 of
                 the
                 inner
                 side
                 or
                 thicknesse
                 ,
                 a
                 line
                 round
                 it
                 ,
                 which
                 is
                 the
                 true
                 Aequinoctiall
                 circle
                 ,
                 divided
                 into
                 twice
                 twelue
                 hours
                 ,
                 from
                 the
                 two
                 opposite
                 points
                 in
                 which
                 it
                 is
                 fastened
                 within
                 the
                 greater
                 .
              
               
                 The
                 greater
                 and
                 outer
                 of
                 the
                 two
                 circles
                 is
                 the
                 Meridian
                 :
                 One
                 quarter
                 whereof
                 ,
                 beginning
                 at
                 one
                 of
                 the
                 points
                 in
                 which
                 the
                 Aequin●cti●ll
                 is
                 hung
                 ,
                 is
                 divided
                 into
                 ninety
                 degrees
                 .
              
               
                 The
                 Diameter
                 is
                 fastened
                 to
                 the
                 Meridian
                 in
                 two
                 opposite
                 points
                 or
                 poles
                 ,
                 o●e
                 of
                 them
                 being
                 the
                 very
                 end
                 of
                 the
                 Quadrant
                 ,
                 and
                 is
                 the
                 
                   North
                   Pole.
                
                 Wherefore
                 it
                 is
                 perpendicular
                 to
                 the
                 ●quinoctiall
                 ,
                 having
                 his
                 due
                 position
                 .
                 The
                 diameter
                 is
                 broad
                 ,
                 and
                 slit
                 in
                 the
                 middle
                 :
                 and
                 about
                 the
                 slit
                 on
                 both
                 sides
                 are
                 the
                 moneths
                 and
                 dayes
                 of
                 the
                 yeer
                 .
                 And
                 within
                 this
                 slit
                 is
                 a
                 litt●e
                 sliding
                 plate
                 pierced
                 through
                 with
                 a
                 small
                 hole
                 :
                 which
                 hole
                 in
                 the
                 motion
                 of
                 it
                 ,
                 while
                 it
                 is
                 applied
                 to
                 the
                 dayes
                 of
                 the
                 yeer
                 ,
                 representeth
                 the
                 Axis
                 of
                 the
                 world
                 .
              
               
               
                 The
                 little
                 Ring
                 whereby
                 the
                 Instrument
                 hangeth
                 ,
                 is
                 made
                 to
                 slip
                 up
                 and
                 down
                 along
                 the
                 Quadrant
                 :
                 that
                 so
                 by
                 help
                 of
                 a
                 little
                 tooth
                 annexed
                 ,
                 the
                 Instrument
                 may
                 be
                 rectified
                 to
                 any
                 elevation
                 of
                 the
                 Pole.
                 
              
            
             
               
                 II.
                 The
                 use
                 of
                 it
                 .
              
               
                 IN
                 using
                 this
                 Instrument
                 ,
                 First
                 ,
                 the
                 tooth
                 of
                 the
                 little
                 Ring
                 must
                 carefully
                 be
                 set
                 to
                 the
                 height
                 of
                 the
                 Pole
                 in
                 the
                 Quadrant
                 ,
                 for
                 the
                 place
                 wherein
                 you
                 are
                 .
              
               
                 Secondly
                 ,
                 the
                 hole
                 of
                 the
                 sliding
                 plate
                 within
                 the
                 slit
                 ,
                 must
                 be
                 brought
                 exactly
                 unto
                 the
                 day
                 of
                 the
                 moneth
                 .
              
               
                 Thirdly
                 ,
                 the
                 Aeqinoctiall
                 is
                 to
                 be
                 drawn
                 out
                 ,
                 and
                 by
                 means
                 of
                 the
                 two
                 studs
                 in
                 the
                 Meridian
                 staying
                 it
                 ,
                 it
                 is
                 to
                 be
                 set
                 perpendicular
                 thereto
                 .
              
               
                 Fourthly
                 ,
                 Guesse
                 as
                 neer
                 as
                 you
                 can
                 at
                 the
                 houre
                 ,
                 and
                 turn
                 the
                 hole
                 of
                 the
                 little
                 plate
                 toward
                 it
                 .
              
               
                 Lastly
                 ,
                 Hold
                 the
                 Instrument
                 up
                 by
                 the
                 little
                 Ring
                 ,
                 that
                 it
                 may
                 hang
                 freely
                 with
                 the
                 
                   North
                   Pole
                
                 thereof
                 toward
                 the
                 North
                 :
                 and
                 move
                 it
                 gently
                 this
                 way
                 and
                 that
                 way
                 ,
                 till
                 the
                 beams
                 of
                 the
                 Sun-shining
                 thorow
                 that
                 hole
                 ,
                 fall
                 upon
                 that
                 middle
                 line
                 within
                 the
                 Aequinoctiall
                 :
                 for
                 there
                 shall
                 be
                 the
                 houre
                 of
                 the
                 day
                 :
                 And
                 the
                 Meridan
                 of
                 the
                 Instrument
                 shall
                 hang
                 directly
                 North
                 and
                 South
                 .
              
               
                 
                   These
                   Instrument
                   all
                   Dials
                   are
                   made
                   in
                   brasse
                   by
                
                 Elias
                 Allen
                 
                   dwelling
                   over
                   against
                
                 St.
                 Clements
                 
                   Church
                   without
                   Temple
                   Barre
                   ,
                   at
                   the
                   signe
                   of
                   the
                
                 Horse-shooe
                 neere
                 Essex
                 Gate
                 .
              
            
             
               FINIS