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 24, 2025.

Pages

Prop. VIII. Prob. III.
Moveatur corpus in circulo PQA: ad hunc effectum requiritur lex vis centripetae tendentis ad punctum adeo longinquum, ut lineae om∣nes PS, RS ad id ductae, pro parallelis haberi possint.

A circuli centro C agatur semidiameter CA parallelas istas per∣pendiculariter secans in M & N, & jungantur CP. Ob similia triangula CPM, & TPZ, vel

[illustration]
(per Lem. VIII.) TPQ, est CPq. ad PMq. ut PQq. vel (per Lem. VII.) PRq. ad QTq. & ex natu∣ra circuli rectangulum QR×RN+QN aequale est PR quadra∣to. Coeuntibus autem punctis P, Q sit RN+QN aequlis 2 PM. Ergo est CP quad. ad PM quad. ut QR×2 PM ad QT quad. ade∣o{que} QT quad./QR aequale 2 PM cub / CP quad., & QT quad.×SP quad./QR aequale 2 PM cub.×SP quad./CP quad.. Est ergo (per Corol. Theor. V.) vis cen∣tripeta reciproce ut 2 PM cub.×SP quad./CP quad. hoc est (neglecta rati∣one determinata 2 SP quad./CP quad.) reciproce ut PM cub. Q.E.I.

Page 47

Scholium.

Et simili argumento corpus movebitur in Ellipsi vel etiam in Hyperbola vel Parabola, vi centripeta quae sit reciproce ut cu∣bus ordinatim applicatae ad centrum virium maxime longinquum tendentis.

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