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

Lemma VIII.
Si rectae datae AR, BR cum arcu AB, chorda AB & tangente AD, triangula tria ARB, ARB, ARD constituunt, dein puncta A, B accedunt ad invicem: dico quod ultima forma triangulorum evanescentium est similitudinis, & ultima ratio aequalitatis.

Page 31

Nam producantur AB, AD, AR ad b, d & r. Ipsi RD agatur parallela rbd, & arcui AB similis ducatur arcus Ab. Coeuntibus punctis A, B, angulus bAd

[illustration]
evanescet, & propterea triangula tria rAb, rAb, rAd coincident, sunt{que} eo nomine similia & aequalia. Unde & hisce semper similia & proportionalia RAB, RAB, RAD fient ultimo sibi invicem similia & aequalia. Q.E.D.

Corol. Et hinc triangula illa in omni de rationibus ultimis argumentatione pro se invicem usurpari possunt.

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