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 June 4, 2024.

Pages

Prop. VII. Prob. II.
Gyretur corpus in circumferentia circuli, requiritur lex vis centripe∣tae tendentis ad punctum aliquod in circumferentia datum.

Esto circuli circumferentia SQPA, centrum vis centripetae S, corpus in circumferentia latum

[illustration]
P, locus proximus in quem mo∣vebitur Q. Ad diametrum SA & rectam SP demitte perpendi∣cula PK, QT, S per Q ipsi SP parallelam age LR occurrentem circulo in L & tangenti PR in R, & coant LQ, PR in Z. Ob similitudinem triangulo um ZQR, ZTP, SPA erit RP quad. (hoc est QRL) ad QT quad. ut SA quad. ad SP quad. Ergo QRL×SP quad./SA quad. aequatur QT quad. Ducantur haec aequa∣lia

Page 46

in SP quad./QR, & punctis P & Q coeuntibus, scribatur SP pro RL Sic fiet SPqc/SAq aequale QTq×SPq / QR Ergo (per Corol. Theor. V.) vis centripeta reciproce est ut SP qc/SAq, id est (ob datum SA quad) ut quadrato-cubus distantiae SP. Quod erat inveniendum.

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