Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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denſiorem verſus centrum, vel ſubductæ relinquant tenuiorem; &
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hæ (per Prop. </
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>LXXV) trahent Sphæras alias quotcunque concentri
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cas ſimilares
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GH, IK, LM,
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&c. </
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>ſingulæ ſingulas, viribus reci
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proce proportionalibus quadrato diſtantiæ
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SP.
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Et componendo
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vel dividendo, ſumma virium illarum omnium, vel exceſſus ali
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quarum ſupra alias, hoc eſt, vis quas Sphæra tota ex concen
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tricis quibuſcunque vel concentricarum differentiis compoſita
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AB,
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trahit totam ex concentricis quibuſcunque vel concentricarum dif
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ferentiis compoſitam
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GH,
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erit in eadem ratione. </
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>Augeatur nu
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merus Sphærarum concentricarum in infinitum ſic, ut materiæ den
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ſitas una cum vi attractiva, in progreſſu a circumferentia ad cen
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trum, ſecundum Legem quamcunque creſcat vel decreſcat: &, ad
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dita materia non attractiva, compleatur ubivis denſitas deficiens, eo
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ut Sphæræ acquirant formam quamvis optatam; & vis qua harum
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una attrahet alteram erit etiamnum (per argumentum ſuperius) in
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eadem illa diſtantiæ quadratæ ratione inverſa.
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E. D.
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LIBER
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PRIMUS.</
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Corol.
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1. Hinc ſi ejuſmodi Sphæræ complures, ſibi invicem per
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omnia ſimiles, ſe mutuo trahant; attractiones acceleratrices ſingula
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rum in ſingulas erunt, in æqualibus quibuſvis centrorum diſtantiis,
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ut Sphæræ attrahentes. </
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Corol.
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2. InQ.E.D.ſtantiis quibuſvis inæqualibus, ut Sphæræ attra
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hentes applicatæ ad quadrata diſtantiarum inter centra. </
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Corol.
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3. Attractiones vero motrices, ſeu pondera Sphærarum in
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Sphæras erunt, in æqualibus centrorum diſtantiis, ut Sphæræ attra
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hentes & attractæ conjunctim, id eſt, ut contenta ſub Sphæris per
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multiplicationem producta. </
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Corol.
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4. InQ.E.D.ſtantiis inæqualibus, ut contenta illa applicata
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ad quadrata diſtantiarum inter centra. </
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