Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Et propterea dico, ſecundum Regulam auream, quod ſi vis cen
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trifuga (4/505) faciat ut altitudo aquæ in crure
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ACca
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ſuperet altitu
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dinem aquæ in crure
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QCcq
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parte centeſima totius altitudinis:
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vis centrifuga (1/289) faciet ut exceſſus altitudinis in crure
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ACca
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ſit
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altitudinis in crure altero
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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
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Caſſini,
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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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LIBER
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TERTIUS.</
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>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. </
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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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<
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>Jovis vero diametrum quæ polis ejus interjacet minorem eſſe
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diametro altera
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Caſſinus
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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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