Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/336.jpg" pagenum="308"/>
                    <lb/>
                    <arrow.to.target n="note284"/>
                  inde pondus aquæ totius in vaſe eſt ad ponderis partem quæ in
                    <lb/>
                  defluxum aquæ impenditur, ut
                    <emph type="italics"/>
                  IH+IO
                    <emph.end type="italics"/>
                  ad 2
                    <emph type="italics"/>
                  IH,
                    <emph.end type="italics"/>
                  atque adeo ut
                    <lb/>
                  ſumma circulorum
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad duplum circulum
                    <emph type="italics"/>
                  EF.
                    <emph.end type="italics"/>
                    <lb/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note284"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. Et hinc pondus aquæ totius in vaſe
                    <emph type="italics"/>
                  ABDC,
                    <emph.end type="italics"/>
                  eſt ad
                    <lb/>
                  ponderis partem alteram quam fundum vaſis ſuſtinet, ut ſumma
                    <lb/>
                  circulorum
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                  ad differentiam eorundem circulorum.
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  5. Et ponderis pars quam fundum vaſis ſuſtinet, eſt ad
                    <lb/>
                  ponderis partem alteram quæ in defluxum aquæ impenditur, ut
                    <lb/>
                  differentia circulorum
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                  ad duplum circulum minorem
                    <lb/>
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                  ſive ut area fundi ad duplum foramen.
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  6. Ponderis autem pars qua ſola fundum urgetur, eſt ad
                    <lb/>
                  pondus aquæ totius quæ fundo perpendiculariter incumbit, ut cir­
                    <lb/>
                  culus
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad ſummam circulorum
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                  ſive ut circulus
                    <lb/>
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad exceſſum dupli circuli
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ſupra fundum. </s>
                  <s>Nam ponderis
                    <lb/>
                  pars qua ſola fundum urgetur, eſt ad pondus aquæ totius in vaſe,
                    <lb/>
                  ut differentia circulorum
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                  ad ſummam eorundem cir­
                    <lb/>
                  culorum, per Cor.4; & pondus aquæ totius in vaſe eſt ad pondus
                    <lb/>
                  aquæ totius quæ fundo perpendiculariter incumbit, ut circulus
                    <lb/>
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad differentiam circulorum
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EF.
                    <emph.end type="italics"/>
                  Itaque ex æquo
                    <lb/>
                  perturbate, ponderis pars qua ſola fundum urgetur, eſt ad pondus
                    <lb/>
                  aquæ totius quæ fundo perpendiculariter incumbit, ut circulus
                    <lb/>
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad ſummam circulorum
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  vel exceſſum dupli cir­
                    <lb/>
                  culi
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ſupra fundum.
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  7. Si in medio foraminis
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.336.1.jpg" xlink:href="039/01/336/1.jpg" number="188"/>
                    <lb/>
                  locetur Circellus
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  centro
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  deſcri­
                    <lb/>
                  ptus & horizonti parallelus: pondus
                    <lb/>
                  aquæ quam circellus ille ſuſtinet, majus
                    <lb/>
                  eſt pondere tertiæ partis Cylindri a­
                    <lb/>
                  quæ cujus baſis eſt circellus ille & al­
                    <lb/>
                  titudo eſt
                    <emph type="italics"/>
                  GH.
                    <emph.end type="italics"/>
                  Sit enim
                    <emph type="italics"/>
                  ABNFEM
                    <emph.end type="italics"/>
                    <lb/>
                  cataracta vel columna aquæ cadentis
                    <lb/>
                  axem habens
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                  ut ſupra, & conge­
                    <lb/>
                  lari intelligatur aqua omnis in vaſe, tam
                    <lb/>
                  in circuitu cataractæ quam ſupra cir­
                    <lb/>
                  cellum, cujus fluiditas ad promptiſſimum
                    <lb/>
                  & celerrimum aquæ deſcenſum non requiritur. </s>
                  <s>Et ſit
                    <emph type="italics"/>
                  PHQ
                    <emph.end type="italics"/>
                  co­
                    <lb/>
                  lumna aquæ ſupra circellum congelata, verticem habens
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  & alti­
                    <lb/>
                  tudinem
                    <emph type="italics"/>
                  GH.
                    <emph.end type="italics"/>
                  Et quemadmodum aqua in circuitu cataractæ con­
                    <lb/>
                  gelata
                    <emph type="italics"/>
                  AMEC, BNFD
                    <emph.end type="italics"/>
                  convexa eſt in ſuperficie interna
                    <emph type="italics"/>
                  AME,
                    <lb/>
                  BNF
                    <emph.end type="italics"/>
                  verſus cataractam cadentem, ſic etiam hæc columna
                    <emph type="italics"/>
                  PHQ
                    <emph.end type="italics"/>
                  </s>
                </p>
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