Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/201.jpg" pagenum="173"/>
                  & qualitates Phyſicas, ſed quantitates & proportiones Mathema­
                    <lb/>
                    <arrow.to.target n="note149"/>
                  ticas in hoc Tractatu expendens, ut in Definitionibus explicui. </s>
                  <s>In
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                  Matheſi inveſtigandæ ſunt virium quantitates & rationes illæ, quæ
                    <lb/>
                  ex conditionibus quibuſcunque poſitis conſequentur: deinde, ubi
                    <lb/>
                  in Phyſicam deſcenditur, conferendæ ſunt hæ rationes cum Phæ­
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                  nomenis, ut innoteſcat quænam virium conditiones ſingulis cor­
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                  porum attractivorum generibus competant. </s>
                  <s>Et tum demum de vi­
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                  rium ſpeciebus, cauſis & rationibus Phyſicis tutius diſputare lice­
                    <lb/>
                  bit. </s>
                  <s>Videamus igitur quibus viribus corpora Sphærica, ex particu­
                    <lb/>
                  lis modo jam expoſito attractivis conſtantia, debeant in ſe mutuo
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                  agere, & quales motus inde conſequantur. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note149"/>
                  LIBER
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                  PRIMUS.</s>
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              <subchap2>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  SECTIO XII.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  De Corporum Sphæriccrum Viribus attractivis.
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                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXX. THEOREMA XXX.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si ad Sphæricæ ſuperficiei puncta ſingula tendant vires æquales cen­
                    <lb/>
                  tripetæ decreſcentes in duplicata ratione diſtantiarum a punctis:
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                  dico quod corpuſculum intra ſuperficiem conſtitutum his viri­
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                  bus nullam in partem attrahitur.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Sit
                    <emph type="italics"/>
                  HIKL
                    <emph.end type="italics"/>
                  ſuperficies illa Sphæri­
                    <lb/>
                    <figure id="id.039.01.201.1.jpg" xlink:href="039/01/201/1.jpg" number="114"/>
                    <lb/>
                  ca, &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  corpuſculum intus conſtitu­
                    <lb/>
                  tum. </s>
                  <s>Per
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  agantur ad hanc ſuper­
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                  ficiem lineæ duæ
                    <emph type="italics"/>
                  HK, IL,
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                  arcus
                    <lb/>
                  quam minimos
                    <emph type="italics"/>
                  HI, KL
                    <emph.end type="italics"/>
                  intercipi­
                    <lb/>
                  entes; &, ob triangula
                    <emph type="italics"/>
                  HPI, LPK
                    <emph.end type="italics"/>
                    <lb/>
                  (per Corol. </s>
                  <s>3. Lem. </s>
                  <s>VII) ſimilia, arcus
                    <lb/>
                  illi erunt diſtantiis
                    <emph type="italics"/>
                  HP, LP
                    <emph.end type="italics"/>
                  pro­
                    <lb/>
                  portionales; & ſuperficiei Sphæricæ
                    <lb/>
                  particulæ quævis ad
                    <emph type="italics"/>
                  HI
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  KL,
                    <emph.end type="italics"/>
                  rec­
                    <lb/>
                  tis per punctum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  tranſeuntibus un­
                    <lb/>
                  dique terminatæ, erunt in duplicata
                    <lb/>
                  illa ratione. </s>
                  <s>Ergo vires harum particularum in corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  exercitæ
                    <lb/>
                  ſunt inter ſe æquales. </s>
                  <s>Sunt enim ut particulæ directe & quadrata
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                  diſtantiarum inverſe. </s>
                  <s>Et hæ duæ rationes componunt rationem </s>
                </p>
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          </chap>
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