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.
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 29, 2024.
Pages
Pro. II. Theor. II.
Corpus omne quod, cum movetur in linea aliqua curva, & radio ducto ad punctum vel immobile, vel motu rectilineo uniformiter progredi∣ens, describit areas circa punctum illud temporibus proportionales, urgetur a vi centripeta tendente ad idem punctum▪
Cas. 1. Nam corpus omne quod movetur in linea curva, de∣torquetur de cursu rectilineo per vim aliquam in ipsum agentem. (per Leg. 1.) Et vis illa qua corpus de cursu rectilineo detor∣quetur & cogitur triangula quam minima SAB, SBC, SCD &c. circa punctum immobile S, temporibus aequalibus aequalia de∣scribere, agit in loco B secundum lineam parallelam ipsi cC (per Prop. 40 Lib. I Elem. & Leg. II.) hoc est secundum lineam
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BS, & in loco C secundum lineam ipsi dD parallelam, hoc est secundum lineam CS, &c. Agit ergo semper secundum lineas tendentes ad punctum illud immobile S. Q.E.D.
Cas. 2. Et, per Legum Corollarium quintum, perinde est sive quiescat superficies in qua corpus describit figuram curvilineam, sive moveatur eadem una cum corpore, figura descripta & puncto suo S uniformiter in directum.
Scholium.
Urgeri potest corpus a vi centripeta composita ex pluribus viribus In hoc casu sensus Propositionis est, quod vis illa quae ex omnibus componitur, tendit ad punctum S. Porro si vis aliqua agat secundum lineam superficiei descriptae perpendicularem, haec faciet corpus deflectere a plano sui motus, sed quantitatem superfi∣ciei descriptae nec augebit nec minuet, & propterea in composi∣tione virium negligenda est.
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