Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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tur jam diſtantiæ quælibet, puta
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SA, SD, SF
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in progreſſione Mu
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ſica, & differentiæ
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Aa-Dd, Dd-Ff
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erunt æquales; & propter
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ea differentiis hiſce proportionales areæ
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thlx, xlnz
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æquales erunt
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inter ſe, & denſitates
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St, Sx, Sz,
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id eſt,
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AH, DL, FN,
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conti
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nue proportionales.
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E. D.
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DE MOTU
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CORPORUM</
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LIBER
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SECUNDUS</
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Corol.
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Hinc ſi dentur Fluidi denſitates duæ quævis, puta
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AH
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&
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CK,
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dabitur area
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thkw
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harum differentiæ
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tw
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reſpondens; &
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inde invenietur denſitas
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FN
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in altitudine quacunque
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SF,
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ſumen
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do aream
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thnz
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ad aream illam datam
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thkw
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ut eſt differentia
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Aa-Ff
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ad differentiam
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Aa-Cc.
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Scholium.
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<
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>Simili argumentatione probari poteſt, quod ſi gravitas particu
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larum Fluidi diminuatur in triplicata ratione diſtantiarum a centro;
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& quadratorum diſtantiarum
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SA, SB, SC,
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&c. </
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<
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>reciproca (nem
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pe
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(SAcub./SAq), (SAcub./SBq), (SAcub./SCq)
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) ſumantur in progreſſione Arithme
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tica; denſitates
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AH, BI, CK,
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&c. </
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<
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>erunt in progreſſione Geome
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trica. </
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<
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>Et ſi gravitas diminuatur in quadruplicata ratione diſtan
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tiarum, & cuborum diſtantiarum reciproca (puta
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(SAqq/SAcub), (SAqq/SBcub),
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(SAqq/SCcub.),
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&c.) ſumantur in progreſſione Arithmetica; denſitates
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AH, BI, CK,
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&c. </
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<
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>erunt in progreſſione Geometrica. </
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<
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>Et ſic in
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infinitum. </
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<
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>Rurſus. </
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<
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>ſi gravitas particularum Fluidi in omnibus di
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ſtantiis eadem ſit, & diſtantiæ ſint in progreſſione Arithmetica,
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denſitates erunt in progreſſione Geometrica, uti Vir Cl.
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Edmundus
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Hælleius
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invenit. </
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<
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>Si gravitas ſit ut diſtantia, & quadrata diſtantia
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rum ſint in progreſſione Arithmetica, denſitates erunt in progreſ
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ſione Geometrica. </
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<
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>Et ſic in infinitum. </
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<
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>Hæc ita ſe habent ubi Fluidi
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compreſſione condenſati denſitas eſt ut vis compreſſionis, vel, quod
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perinde eſt, ſpatium a Fluido occupatum reciproce ut hæc vis. </
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Fingi poſſunt aliæ condenſationis Leges, ut quod cubus vis com
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primentis ſit ut quadrato-quadratum denſitatis, feu triplicata ra
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tio Vis æqualis quadruplicatæ rationi denſitatis. </
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<
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>Quo in caſu, ſi gra
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vitas eſt reciproce ut quadratum diſtantiæ a centro, denſitas erit
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reciproce ut cubus diſtantiæ. </
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<
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>Fingatur quod cubus vis compri
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mentis ſit ut quadrato-cubus denſitatis, & ſi gravitas eſt reciproce
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ut quadratum diſtantiæ, denſitas erit reciproce in ſuſquiplicata ra-</
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