Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                  <s>
                    <pb xlink:href="039/01/335.jpg" pagenum="307"/>
                    <lb/>
                  mergatur, & altitudo aquæ ſtagnantis ſupra fundum vaſis ſit
                    <emph type="italics"/>
                  GR
                    <emph.end type="italics"/>
                  :
                    <lb/>
                    <arrow.to.target n="note283"/>
                  velocitas quacum aqua quæ in vaſe eſt, effluet per foramen
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                    <lb/>
                  in aquam ſtagnantem, ea erit quam aqua cadendo & caſu ſuo de­
                    <lb/>
                  ſcribendo altitudinem
                    <emph type="italics"/>
                  IR
                    <emph.end type="italics"/>
                  acquirere poteſt. </s>
                  <s>Nam pondus aquæ
                    <lb/>
                  omnis in vaſe quæ inferior eſt ſuperficie aquæ ſtagnantis, ſuſtine­
                    <lb/>
                  bitur in æquilibrio per pondus aquæ ſtagnantis, ideoque motum
                    <lb/>
                  aquæ deſcendentis in vaſe minime accelerabit. </s>
                  <s>Patebit etiam &
                    <lb/>
                  hic Caſus per Experimenta, menſurando ſcilicet tempora qui­
                    <lb/>
                  bus aqua effluit.
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                  </s>
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                <p type="margin">
                  <s>
                    <margin.target id="note283"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Hinc ſi aquæ altitudo
                    <emph type="italics"/>
                  CA
                    <emph.end type="italics"/>
                  producatur ad
                    <emph type="italics"/>
                  K,
                    <emph.end type="italics"/>
                  ut ſit
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  in duplicata ratione areæ foraminis in quavis fundi parte
                    <lb/>
                  facti, ad aream circuli
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  : velocitas aquæ effluentis æqualis erit
                    <lb/>
                  velocitati quam aqua cadendo & caſu ſuo deſcribendo altitudinera
                    <lb/>
                    <emph type="italics"/>
                  KC
                    <emph.end type="italics"/>
                  acquirere poteſt.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Et vis qua totus aquæ exilientis motus generari poteſt,
                    <lb/>
                  æqualis eſt ponderi Cylindricæ columnæ aquæ cujus baſis eſt fora­
                    <lb/>
                  men
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                  & altitudo 2
                    <emph type="italics"/>
                  GI
                    <emph.end type="italics"/>
                  vel 2
                    <emph type="italics"/>
                  CK.
                    <emph.end type="italics"/>
                  Nam aqua exiliens quo
                    <lb/>
                  tempore hanc columnam æquat, pondere ſuo ab altitudine
                    <emph type="italics"/>
                  GI
                    <emph.end type="italics"/>
                  ca­
                    <lb/>
                  dendo, velocitatem ſuam qua exilit, acquirere poteſt.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Pondus aquæ totius in vaſe
                    <emph type="italics"/>
                  ABDC,
                    <emph.end type="italics"/>
                  eſt ad ponderis
                    <lb/>
                  partem quæ in defluxum aquæ impenditur, ut ſumma circulorum
                    <lb/>
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                  ad duplum circulum
                    <emph type="italics"/>
                  EF.
                    <emph.end type="italics"/>
                  Sit enim
                    <emph type="italics"/>
                  IO
                    <emph.end type="italics"/>
                  media pro­
                    <lb/>
                  portionalis inter
                    <emph type="italics"/>
                  IH
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  IG
                    <emph.end type="italics"/>
                  ; & aqua per foramen
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  egrediens,
                    <lb/>
                  quo tempore gutta cadendo ab
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  deſcribere poſſet altitudinem
                    <emph type="italics"/>
                  IG,
                    <emph.end type="italics"/>
                    <lb/>
                  æqualis erit Cylindro cujus baſis eſt circulus
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  & altitudo eſt 2
                    <emph type="italics"/>
                  IG,
                    <emph.end type="italics"/>
                    <lb/>
                  id eſt, Cylindro cujus baſis eſt circulus
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  & altitudo eſt 2
                    <emph type="italics"/>
                  IO,
                    <emph.end type="italics"/>
                    <lb/>
                  nam circulus
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  eſt ad circulum
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  in ſubduplicata ratione
                    <lb/>
                  altitudinis
                    <emph type="italics"/>
                  IH
                    <emph.end type="italics"/>
                  ad altitudinem
                    <emph type="italics"/>
                  IG,
                    <emph.end type="italics"/>
                  hoc eſt, in ſimplici ratione me­
                    <lb/>
                  diæ proportionalis
                    <emph type="italics"/>
                  IO
                    <emph.end type="italics"/>
                  ad altitudinem
                    <emph type="italics"/>
                  IG
                    <emph.end type="italics"/>
                  : & quo tempore gutta
                    <lb/>
                  cadendo ab
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  deſcribere poteſt altitudinem
                    <emph type="italics"/>
                  IH,
                    <emph.end type="italics"/>
                  aqua egrediens
                    <lb/>
                  æqualis erit Cylindro cujus baſis eſt circulus
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  & altitudo eſt
                    <lb/>
                  2
                    <emph type="italics"/>
                  IH
                    <emph.end type="italics"/>
                  : & quo tempore gutta cadendo ab
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  per
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  deſcribit
                    <lb/>
                  altitudinum differentiam
                    <emph type="italics"/>
                  HG,
                    <emph.end type="italics"/>
                  aqua egrediens, id eſt, aqua tota in
                    <lb/>
                  ſolido
                    <emph type="italics"/>
                  ABNFEM
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                  æqualis erit differentiæ Cylindrorum, id eſt,
                    <lb/>
                  Cylindro cujus baſis eſt
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  & altitudo 2
                    <emph type="italics"/>
                  HO.
                    <emph.end type="italics"/>
                  Et propterea
                    <lb/>
                  aqua tota in vaſe
                    <emph type="italics"/>
                  ABDC
                    <emph.end type="italics"/>
                  eſt ad aquam totam cadentem in
                    <lb/>
                  ſolido
                    <emph type="italics"/>
                  ABNFEM
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  HG
                    <emph.end type="italics"/>
                  ad 2
                    <emph type="italics"/>
                  HO,
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                  id eſt, ut
                    <emph type="italics"/>
                  HO+OG
                    <emph.end type="italics"/>
                    <lb/>
                  ad 2
                    <emph type="italics"/>
                  HO,
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  IH+IO
                    <emph.end type="italics"/>
                  ad 2
                    <emph type="italics"/>
                  IH.
                    <emph.end type="italics"/>
                  Sed pondus aquæ totius in
                    <lb/>
                  ſolido
                    <emph type="italics"/>
                  ABNFEM
                    <emph.end type="italics"/>
                  in aquæ defluxum impenditur: ac pro-</s>
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