Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/409.jpg" pagenum="381"/>
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                  Et propterea dico, ſecundum Regulam auream, quod ſi vis cen­
                    <lb/>
                    <arrow.to.target n="note388"/>
                  trifuga (4/505) faciat ut altitudo aquæ in crure
                    <emph type="italics"/>
                  ACca
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                  ſuperet altitu­
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                  dinem aquæ in crure
                    <emph type="italics"/>
                  QCcq
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                  parte centeſima totius altitudinis:
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                  vis centrifuga (1/289) faciet ut exceſſus altitudinis in crure
                    <emph type="italics"/>
                  ACca
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                  ſit
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                  altitudinis in crure altero
                    <emph type="italics"/>
                  QCcq
                    <emph.end type="italics"/>
                  pars tantum (1/229). Eſt igitur dia­
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                  meter Terræ ſecundum æquatorem ad ipſius diametrum per polos
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                  ut 230 ad 229. Ideoque cum Terræ ſemidiameter mediocris, juxta
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                  menſuram
                    <emph type="italics"/>
                  Caſſini,
                    <emph.end type="italics"/>
                  ſit. pedum Pariſienſium 19695539, ſeu milliarium
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                  3939 (poſito quod milliare ſit menſura pedum 5000) Terra altior
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                  erit ad Æquatorem quam ad Polos exceſſu pedum 85820, ſeu
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                  milliarum 17 1/6.
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                  </s>
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                <p type="margin">
                  <s>
                    <margin.target id="note388"/>
                  LIBER
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                  TERTIUS.</s>
                </p>
                <p type="main">
                  <s>Si Planeta major ſit vel minor quam Terra manente ejus den­
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                  ſitate ac tempore periodico revolutionis diurnæ, manebit pro­
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                  portio vis centrifugæ ad gravitatem, & propterea manebit etiam
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                  proportio diametri inter polos ad diametrum ſecundum æquato­
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                  rem. </s>
                  <s>At ſi motus diurnus in ratione quacunque acceleretur vel
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                  retardetur, augebitur vel minuetur vis centrifuga in duplicata illa
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                  ratione, & propterea differentia diametrorum augebitur vel mi­
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                  nuetur in eadem duplicata ratione quamproxime. </s>
                  <s>Et ſi denſitas
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                  Planetæ augeatur vel minuatur in ratione quavis, gravitas etiam
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                  in ipſum tendens augebitur vel minuetur in eadem ratione, &
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                  differentia diametrorum viciſſim minuetur in ratione gravitatis
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                  auctæ vel augebitur in ratione gravitatis diminutæ. Unde cum
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                  Terra reſpectu fixarum revolvatur horis 23. 56′, Jupiter autem
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                  horis 9. 56′, ſintque temporum quadrata ut 29 ad 5, & denſitates
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                  ut 5 ad 1: differentia diametrorum Jovis erit ad ipſius diame­
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                  trum minorem ut (29/5)X(5/1)X(1/229) ad 1, ſeu 1 ad 8 quamproxime. </s>
                  <s>Eſt
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                  igitur diameter Jovis ab oriente in occidentem ducta, ad ejus dia­
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                  metrum inter polos ut 9 ad 8 quamproxime, & propterea diame­
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                  ter inter polos eſt 35 1/2″. Hæc ita ſe habent ex hypotheſi quod
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                  uniformis ſit Planetarum materia. </s>
                  <s>Nam ſi materia denſior ſit ad
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                  centrum quam ad circumferentiam; diameter quæ ab oriente in
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                  occidentem ducitur, erit adhuc major.
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                  </s>
                </p>
                <p type="main">
                  <s>Jovis vero diametrum quæ polis ejus interjacet minorem eſſe
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                  diametro altera
                    <emph type="italics"/>
                  Caſſinus
                    <emph.end type="italics"/>
                  dudum obſervavit, & Terræ diametrum
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                  inter polos minorem eſſe diametro altera patebit per ea quæ
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                  dicentur in Propoſitione ſequente.
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                  </s>
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