Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  PROPOSITIO XX. PROBLEMA IV.
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                  DE MUNDI
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                  SYSTEMATE</s>
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                  Invenire & inter ſe comparare Pondera corporum in Terræ hujus
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                  regionibus diverſis.
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                  <s>Quoniam pondera inæqualium crurum canalis aqueæ
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                  ACQqca
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                  æqualia ſunt; & pondera partium, cruribus totis proportionalium
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                  & ſimiliter in totis ſitarum, ſunt ad invicem ut pondera totorum,
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                  adeoque etiam æquantur inter ſe; erunt pondera æqualium & in
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                  cruribus ſimiliter ſitarum partium reciproce ut crura, id eſt, reci­
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                  proce ut 230 ad 229. Et par eſt ratio homogeneorum & æqua­
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                  lium quorumvis & in canalis cruribus ſimiliter ſitorum corporum.
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                  Horum pondera ſunt reciproce ut crura, id eſt, reciproce ut di­
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                  ſtantiæ corporum a centro Terræ. Proinde ſi corpora in ſupre­
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                  mis canalium partibus, ſive in ſuperficie Terræ conſiſtant; erunt
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                  pondera eorum ad invicem reciproce ut diſtantiæ eorum a centro.
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                  Et eodem argumento pondera, in aliis quibuſcunque per totam
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                  Terræ ſuperficiem regionibus, ſunt reciproce ut diſtantiæ loeorum
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                  a centro; & propterea, ex Hypotheſi quod Terra Sphærois ſit,
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                  dantur proportione.
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                  <s>Unde tale confit Theorema, quod incrementum ponderis per­
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                  gendo ab Æquatore ad Polos, ſit quam proxime ut ſinus verſus
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                  Latitudinis duplicatæ, vel, quod perinde eſt, ut quadratum ſinus
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                  recti Latitudinis. </s>
                  <s>Et in eadem circiter ratione augentur arcus
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                  graduum Latitudinis in Meridiano. </s>
                  <s>Ideoque cum Latitudo
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                  Lu­
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                  tetiæ Pariſiorum
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                  ſit 48
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                  gr.
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                  50′, ea loeorum ſub Æquatore 00
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                  gr.
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                  00′,
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                  & ea loeorum ad Polos 90
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                  gr.
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                  & duplorum ſinus verſi ſint 11334,
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                  00000 & 20000, exiſtente Radio 10000, & gravitas ad Polum ſit
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                  ad gravitatem ſub Æquatore ut 230 ad 229, & exceſſus gravi­
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                  tatis ad Polum ad gravitatem ſub Æquatore ut 1 ad 229: erit ex­
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                  ceſſus gravitatis in Latitudine
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                  Lutetiæ
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                  ad gravitatem ſub Æquatore,
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                  ut 1X(11334/20000) ad 229, ſeu 5667 ad 2290000. Et propterea gravitates
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                  totæ in his locis erunt ad invicem ut 2295667 ad 2290000. Quare
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                  cum longitudines pendulorum æqualibus temporibus oſcillantium
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                  ſint ut gravitates, & in Latitudine
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                  Lutetiæ Pariſiorum
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                  longitudo
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                  penduli ſingulis minutis ſecundis oſcillantis ſit pedum trium Pa­
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                  riſienſium & linearum 8 1/9: longitudo penduli ſub Æquatore ſu­
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                  perabitur a longitudine ſynchroni penduli
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                  Pariſienſis,
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                  exceſſu li­
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                  neæ unius & 87 partium milleſimarum lineæ. Et ſimili computo
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                  confit Tabula ſequens.
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