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 27, 2025.

Pages

Prop. VI. Theor. IV.
Corpora Sphaerica homogenea & aequalia, resistentiis in duplicata ra∣tione velocitatum impedita, & solis viribus insitis incitata, tem∣poribus quae sunt reciproce ut velocitates sub initio, describunt sem∣per aequalia spatia, & amittunt partes velocitatum proportionales totis.

Asymptotis rectangulis CD, CH descripta Hyperbola quavis BbEe secante perpendicula

[illustration]
AB, ab, DE, de, in B, b, E, e, exponantur velocitates initi∣ales per perpendicula AB, DE, & tempora per lineas Aa, Dd. Est ergo ut Aa ad Dd ita (per Hypothesin) DE ad AB, & ita (ex natu∣ra Hyperbolae) CA ad CD; & componendo, ita Ca ad Cd. Ergo areae ABba, DEed, hoc est spatia descripta aequantur inter se, & velocitates primae

Page 249

AB, DE sunt ultimis ab, de, & propterea (dividendo) par∣tibus etiam suis amissis AB−ab, DE−de proportionales. Q.E.D.

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