Simili argumentatione probari potest, quod si gravitas particu∣larum Fluidi diminuatur in triplicata ratione distantiarum a centro; & quadratorum distantiarum SA, SB, SC, &c. reciproca (nem∣pe SA cub./SAq., SA cub./SBq., SA cub./SCq.) sumantur in progressione Arithme∣ca; densitates AH, BI, CK, &c. erunt in progressione Geome∣trica. Et si gravitas diminuatur in quadruplicata ratione distan∣tiarum, & cuborum distantiarum reciproca (puta SAqq./SA cub., SAqq./SB cub., SAqq./SC cub., &c.) sumantur in progressione Arithmetica; densitates AH, BI, CK, &c. erunt in progressione Geometrica. Et sic in infinitum. Rursus si gravitas particularum Fluidi in omnibus di∣stantiis eadem sit, & distantiae sint in progressione Arithmetica, densitates erunt in progressione Geometrica, uti Vir Cl. Edmundus Halleius invenit. Si gravitas sit ut distantia, & quadrata distan∣tiarum sint in progressione Arithmetica, densitates erunt in pro∣gressione Geometrica. Et sic in infinitum. Haec ita se habent ubi Fluidi compressione condensati densitas est ut vis compressio∣nis, vel, quod perinde est, spatium a Fluido occupatum reciproce ut haec vis. Fingi possunt aliae condensationis leges, ut quod cu∣bus vis comprimentis sit ut quadrato-quadratum densitatis, seu triplicata ratio Vis aequalis quadruplicatae rationi densitatis. Quo in casu, si gravitas est reciproce ut quadratum distantiae a centro, densitas erit reciproce ut cubus distantiae. Fingatur quod cubus vis comprimentis sit ut quadrato-cubus densitatis, & si gravitas est reciproce ut quadratum distantiae, densitas erit reciproce in
Philosophiæ naturalis principia mathematica autore Js. Newton ...
About this Item
- Title
- Philosophiæ naturalis principia mathematica autore Js. Newton ...
- Author
- Newton, Isaac, Sir, 1642-1727.
- Publication
- Londini :: Jussu Societatis Regiae ac Typis Josephi Streater ...,
- 1687.
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- Subject terms
- Mechanics -- Early works to 1800.
- Celestial mechanics -- Early works to 1800.
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http://name.umdl.umich.edu/A52251.0001.001
- Cite this Item
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"Philosophiæ naturalis principia mathematica autore Js. Newton ..." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A52251.0001.001. University of Michigan Library Digital Collections. Accessed May 29, 2025.
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Page 301
sesquiplicata ratione distantiae. Fingatur quod vis comprimens sit in duplicata ratione densitatis, & gravitas reciproce in ratione duplicata distantiae, & densitas erit reciproce ut distantia. Ca∣sus omnes percurrere longum esset.