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 10, 2024.

Pages

Lemma III.
Eaedem rationes ultimae sunt etiam aequalitatis, ubi parallelogramom∣rum latitudines AB, BC, CD, &c. sunt inaequales, & omnes minuuntur in infinitum.

Sit enim AF aequalis latitudini maximae, & compleatur pa∣rallelogrammum FAaf. Hoc erit majus quam differentia figurae inscriptae & figurae circumscriptae, at latitudine sua AF

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in infinitum diminuta, minus fiet quam datum quodvis rectan∣gulum.

Corol. 1. Hinc summa ultima parallelogrammorum evanescenti∣um coincidit omni ex parte cum figura curvilinea.

Corol. 2. Et multo magis figura rectilinea, quae chordis evanes∣centium arcuum ab, bc, cd, &c. comprehenditur, coincidit ul∣timo cum figura curvilinea.

Corol. 3. Ut & figura rectilinea quae tangentibus eorundem arcuum circumscribitur.

Corol. 4. Et propterea hae figurae ultimae (quoad perimetros acE,) non sunt rectilineae, sed rectilinearum limites curvilinci.

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