Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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<
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>Jam illud concedi æquum eſt, quod Mathematicis rationibus
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colligitur & certiſſime demonſtratur; Corpora nempe omnia, quæ
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moventur in linea aliqua curva in plano deſcripta, quæque radio
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ducto ad punctum vel quieſcens vel utcunque motum deſcribunt
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areas circa punctum illud temporibus proportionales, urgeri a
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Viribus quæ ad idem punctum tendunt. </
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<
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>Cum igitur in confeſſo
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ſit apud Aſtronomos, Planetas primarios circum Solem, ſecunda
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rios vero circum ſuos primarios, areas deſcribere temporibus pro
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portionales; conſequens eſt ut Vis illa, qua perpetuo detorquen
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tur a Tangentibus rectilineis, & in Orbitis curvilineis revolvi co
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guntur, verſus corpora dirigatur quæ ſita ſunt in Orbitarum cen
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tris. </
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<
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>Hæc itaque Vis non inepte vocari poteſt, reſpectu quidem
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corporis revolventis, Centripeta; reſpectu autem corporis cen
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tralis, Attractiva; a quacunQ.E.D.mum cauſa oriri fingatur. </
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<
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>Quin & hæc quoque concedenda ſunt, & Mathematice demon
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ſtrantur: Si corpora plura motu æquabili revolvantur in Circulis
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concentricis, & quadrata temporum periodieorum ſint ut cubi di
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ſtantiarum a centro communi; Vires centripetas revolventium
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fore reciproce ut quadrata diſtantiarum. </
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<
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>Vel, ſi corpora revol
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vantur in Orbitis quæ ſunt Circulis finitimæ, & quieſcant Orbita
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rum Apſides; Vires centripetas revolventium fore reciproce ut
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quadrata diſtantiarum. </
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<
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>Obtinere caſum alterutrum in Planetis
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univerſis conſentiunt Aſtronomi. </
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<
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>Itaque Vires centripetæ Plane
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tarum omnium ſunt reciproce ut quadrata diſtantiarum ab Or
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bium centris. </
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<
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>Si quis objiciat Planetarum, & Lunæ præſertim,
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Apſides non penitus quieſcere; ſed motu quodam lento ferri in
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conſequentia: reſponderi poteſt, etiamſi concedamus hunc mo
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tum tardiſſimum exinde profectum eſſe quod Vis centripetæ pro
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portio aberret aliquantum a duplicata, aberrationem illam per
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computum Mathematicum inveniri poſſe & plane inſenſibilem
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eſſe. </
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<
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>Ipſa enim ratio Vis centripetæ Lunaris, quæ omnium ma
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xime turbari debet, paululum quidem duplicatam ſuperabit; ad
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hanc vero ſexaginta fere vicibus propius accedet quam ad tripli
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catam. </
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<
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>Sed verior erit reſponſio, ſi dicamus hanc Apſidum progreſ
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ſionem, non ex aberratione a duplicata proportione, ſed ex alia
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prorſus diverſa cauſa oriri, quemadmodum egregie commonſtratur
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in hac Philoſophia. </
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<
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>Reſtat ergo ut Vires centripetæ, quibus Pla
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netæ primarii tendunt verſus Solem & ſecundarii verſus primarios
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ſuos, ſint accurate ut quadrata diſtantiarum reciproce. </
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