Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/337.jpg" pagenum="309"/>
                    <lb/>
                  convexa erit verſus cataractam, & propterea major Cono cujus ba­
                    <lb/>
                    <arrow.to.target n="note285"/>
                  ſis eſt circellus ille
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  & altitudo
                    <emph type="italics"/>
                  GH,
                    <emph.end type="italics"/>
                  id eſt, major tertia parte
                    <lb/>
                  Cylindri eadem baſe & altitudine deſcripti. </s>
                  <s>Suſtinet autem cir­
                    <lb/>
                  cellus ille pondus hujus columnæ, id eſt, pondus quod pondere
                    <lb/>
                  Coni ſeu tertiæ partis Cylindri illius majus eſt.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note285"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  8. Pondus aquæ quam circellus valde parvus
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ſuſtinet,
                    <lb/>
                  minor eſt pondere duarum tertiarum partium Cylindri aquæ cujus
                    <lb/>
                  baſis eſt circellus ille & altitudo eſt
                    <emph type="italics"/>
                  HG.
                    <emph.end type="italics"/>
                  Nam ſtantibus jam po­
                    <lb/>
                  ſitis, deſcribi intelligatur dimidium Sphæroidis cujus baſis eſt cir­
                    <lb/>
                  cellus ille & ſemiaxis ſive altitudo eſt
                    <emph type="italics"/>
                  HG.
                    <emph.end type="italics"/>
                  Et hæc figura æqualis
                    <lb/>
                  erit duabus tertiis partibus Cylindri illius & comprehendet colum­
                    <lb/>
                  nam aquæ congelatæ
                    <emph type="italics"/>
                  PHQ
                    <emph.end type="italics"/>
                  cujus pondus circellus ille ſuſtinet.
                    <lb/>
                  Nam ut motus aquæ ſit maxime directus, columnæ illius ſuper­
                    <lb/>
                  ficies externa concurret cum baſi
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  in angulo nonnihil acuto,
                    <lb/>
                  propterea quod aqua cadendo perpetuo acceleratur & propter ac­
                    <lb/>
                  celerationem fit tenuior; & cum angulus ille ſit recto minor, hæc
                    <lb/>
                  columna ad inferiores ejus partes jacebit intra dimidium Sphæroi­
                    <lb/>
                  dis. </s>
                  <s>Eadem vero ſurſum acuta erit ſeu cuſpidata, ne horizontalis
                    <lb/>
                  motus aquæ ad verticem Sphæroidis ſit infinite velocior quam ejus
                    <lb/>
                  motus horizontem verſus. </s>
                  <s>Et quo minor eſt circellus
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  eo
                    <lb/>
                  acutior erit vertex columnæ; & circello in infinitum diminuto, an­
                    <lb/>
                  gulus
                    <emph type="italics"/>
                  PHQ
                    <emph.end type="italics"/>
                  in infinitum diminuetur, & propterea columna ja­
                    <lb/>
                  cebit intra dimidium Sphæroidis. </s>
                  <s>Eſt igitur columna illa minor
                    <lb/>
                  dimidio Sphæroidis, ſeu duabus tertiis partibus Cylindri cujus baſis
                    <lb/>
                  eſt circellus ille & altitudo
                    <emph type="italics"/>
                  GH.
                    <emph.end type="italics"/>
                  Suſtinet autem circellus vim aquæ
                    <lb/>
                  ponderi hujus columnæ æqualem, cum pondus aquæ ambientis in
                    <lb/>
                  defluxum ejus impendatur.
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  9. Pondus aquæ quam circellus valde parvus
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ſuſti­
                    <lb/>
                  net, æquale ſet ponderi Cylindri aquæ cujus baſis eſt circellus ille
                    <lb/>
                  & altitudo eſt 1/2
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                  quamproxime. </s>
                  <s>Nam pondus hocce eſt me­
                    <lb/>
                  dium Arithmeticum inter pondera Coni & Hemiſphæroidis præ­
                    <lb/>
                  dictæ. At ſi circellus ille non ſit valde parvus, ſed augeatur donec
                    <lb/>
                  æquet foramen
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  ; hic ſuſtinebit pondus aquæ totius ſibi per­
                    <lb/>
                  pendiculariter imminentis, id eſt, pondus Cylindri aquæ cujus ba­
                    <lb/>
                  ſis eſt circellus ille & altitudo eſt
                    <emph type="italics"/>
                  GH.
                    <emph.end type="italics"/>
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  10. Et (quantum ſentio) pondus quod circellus ſuſtinet,
                    <lb/>
                  eſt ſemper ad pondus Cylindri aquæ cujus baſis eſt circellus ille &
                    <lb/>
                  altitudo eſt 1/2
                    <emph type="italics"/>
                  GH,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  EFq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  EFq
                    <emph.end type="italics"/>
                  -1/2
                    <emph type="italics"/>
                  PQq,
                    <emph.end type="italics"/>
                  ſive ut circulus
                    <lb/>
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  ad exceſſum circuli hujus ſupra ſemiſſem circelli
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  quam­
                    <lb/>
                  proxime. </s>
                </p>
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