Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                  ad diametrum
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                  AB
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                  ut 100 ad 101: gravitas in loco
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                  Q
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                  in Terram,
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                  foret ad gravitatem in eodem loco
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                  Q
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                  in Sphæram centro
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                  C
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                  radio
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                    <emph type="italics"/>
                  PC
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                  vel
                    <emph type="italics"/>
                  QC
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                  deſcriptam, ut 126 ad 125. Et eodem argumento
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                  gravitas in loco
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                  A
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                  in Sphæroidem, convolutione Ellipſeos
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                  APBQ
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                  circa axem
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                  AB
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                  deſcriptam, eſt ad gravitatem in eodem loco
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                  A
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                  in
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                  Sphæram centro
                    <emph type="italics"/>
                  C
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                  radio
                    <emph type="italics"/>
                  AC
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                  deſcriptam, ut 125 ad 126. Eſt au­
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                  tem gravitas in loco
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                  A
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                  in Terram, media proportionalis inter
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                  gravitates in dictam Sphæroidem & Sphæram: propterea quod
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                  Sphæra, diminuendo diametrum
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                  PQ
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                  in ratione 101 ad 100,
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                  vertitur in figuram Terræ; & hæc figura diminuendo in eadem
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                  ratione diametrum tertiam, quæ diametris duabus
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                  AB, PQ
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                  per­
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                  pendicularis eſt, vertitur in dictam Sphæroidem; & gravitas in
                    <lb/>
                    <emph type="italics"/>
                  A,
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                  in caſu utroque, diminuitur in eadem ratione quam proxime.
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                  Eſt igitur gravitas in
                    <emph type="italics"/>
                  A
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                  in Sphæram centro
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                    <figure id="id.039.01.408.1.jpg" xlink:href="039/01/408/1.jpg" number="204"/>
                    <lb/>
                    <emph type="italics"/>
                  C
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                  radio
                    <emph type="italics"/>
                  AC
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                  deſcriptam, ad gravitatem in
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                    <emph type="italics"/>
                  A
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                  in Terram ut 126 ad 125 1/2, & gravitas
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                  in loco
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                  Q
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                  in Sphæram centro
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                  C
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                  radio
                    <emph type="italics"/>
                  QC
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                    <lb/>
                  deſcriptam, eſt ad gravitatem in loco
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                  A
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                  in
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                  Sphæram centro
                    <emph type="italics"/>
                  C
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                  radio
                    <emph type="italics"/>
                  AC
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                  deſcriptam,
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                  in ratione diametrorum (per Prop. LXXII.
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                  Lib. I.) id eſt, ut 100 ad 101. Conjungan­
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                  tur jam hæ tres rationes, 126 ad 125, 126
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                  ad 125 1/2, & 100 ad 101: & fiet gravitas
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                  in loco
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                  Q
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                  in Terram, ad gravitatem in loco
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                  A
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                  in Terram, ut
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                  126X126X100 ad 125X125 1/2X101, ſeu ut 501 ad 500.
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                <p type="margin">
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                    <margin.target id="note387"/>
                  DE MUNDI
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                  SYSTEMATE</s>
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                  <s>Jam cum (per Corol. 3. Prop. XCI. Lib. I.) gravitas in canalis
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                  crure utrovis
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                  ACca
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                  vel
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                  QCcq
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                  ſit ut diſtantia loeorum a centro
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                  Terræ; ſi crura illa ſuperficiebus tranſverſis & æquidiſtantibus di­
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                  ſtinguantur in partes totis proportionales, erunt pondera partium
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                  ſingularum in crure
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                  ACca
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                  ad pondera partium totidem in crure
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                  altero, ut magnitudines & gravitates acceleratrices conjunctim; id
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                  eſt, ut 101 ad 100 & 500 ad 501, hoc eſt, ut 505 ad 501. Ac
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                  proinde ſi vis centrifuga partis cujuſQ.E.I. crure
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                  ACca
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                  ex motu
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                  diurno oriunda, fuiſſet ad pondus partis ejuſdem ut 4 ad 505, eo
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                  ut de pondere partis cujuſque, in partes 505 diviſo, partes qua­
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                  tuor detraheret; manerent pondera in utroque crure æqualia, &
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                  propterea fluidum conſiſteret in æquilibrio. </s>
                  <s>Verum vis centrifuga
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                  partis cujuſque eſt ad pondus ejuſdem ut 1 ad 289, hoc eſt, vis
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                  centrifuga quæ deberet eſſe ponderis pars (4/505) eſt tantum pars (1/289).
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                  </s>
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