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.
Link to this Item
http://name.umdl.umich.edu/A52251.0001.001
Cite this Item
"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 14, 2025.
Pages
Prop. LXXXV. Theor. XLII.
Si corporis attracti, ubi attrahenti contiguum est, attractio longe fortior sit, quam cum vel minimo intervallo separantur ab invicem: vires particularum trahentis, in recessu corporis attracti, decrescunt in ra∣tione plusquam duplicata distantiarum a particulis.
Nam si vires decrescunt in ratione duplicata distantiarum a particulis; attractio versus corpus Sphaericum, propterea quod (per Prop. LXXIV.) sit reciproce ut quadratum distantiae at∣tracti
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corporis a centro Sphaerae, haud sensibiliter augebitur ex contactu; at{que} adhuc minus augebitur ex contactu, si attractio in recessu corporis attracti decrescat in ratione minore. Patet igi∣tur Propositio de Sphaeris attractivis. Et par est ratio Orbium Sphaericorum concavorum corpora externa trahentium. Et mul∣to magis res constat in Orbibus corpora interius constituta tra∣hentibus, cum attractiones passim per Orbium cavitates ab at∣tractionibus contrariis (per Prop. LXX.) tollantur, ideo{que} vel in ipso contactu nullae sunt. Quod si Sphaeris hisce Orbibus{que} Sphaericis partes quaelibet a loco contactus remotae auferantur, & partes novae ubivis addantur: mutari possunt figurae horum cor∣porum attractivorum pro lubitu, nec tamen partes additae vel subductae, cum sint a loco contactus remotae, augebunt notabi∣liter attractionis excessum qui ex contactu oritur. Constat igi∣tur Propositio de corporibus figurarum omnium. Q.E.D.
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