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

Prop. LXXXVIII. Theor. XLV.
Si particularum aequalium corporis cujuscun{que} vires attractivae sint ut distantiae locorum a particulis: vis corporis totius tendet ad ipsius centrum gravitatis; & eadem erit cum vi globi ex materia consi∣mili & aequali constantis & centrum habentis in ejus centro gra∣vitatis.

Corporis RSTV particulae A, B trahant corpusculum aliquod Z viribus quae, si particulae aequantur inter se, sint ut distantiae AZ, BZ; sin particulae statu∣antur

[illustration]
inaequales, sint ut hae particulae in distantias suas AZ, BZ respective ductae. Et ex∣ponantur hae vires per contenta illa A×AZ & B×BZ. Jun∣gatur AB, & secetur ea in G ut sit AG ad BG ut particula B ad particulam A; & erit G commu∣ne centrum gravitatis particula∣rum A & B. Vis A×AZ per Legum Corol. 2. resolvitur in vires A×GZ & A×AG, & vis B×BZ in vires B×GZ & B×BG. Vires autem A×AG & B×BG, ob proportionales A ad B & BG ad AG, aequantur, adeo{que}, cum dirigantur in partes contrarias, se mutuo destruunt. Restant vires A×GZ & B×GZ. Tendunt hae ab Z versus centrum G, & vim A+B×GZ componunt; hoc est, vim eandem ac si particulae attractivae A & B consisterent in eorum communi gravitatis centro G, globum ibi componentes.

Page 217

Eodem argumento si adjungatur particula tertia C; & com∣ponatur hujus vis cum vi A+B×GZ tendente ad centrum G, vis inde oriunda tendet ad commune centrum gravitatis globi il∣lius G & particulae C; hoc est, ad commune centrum gravitatis trium particularum A, B, C; & eadem erit ac si globus & parti∣cula C consisterent in centro illo communi, globum majorem ibi componentes. Et sic pergitur in infinitum. Eadem est igitur vis tota particularum omnium corporis cujuscun{que} RSTV ac si corpus illud, servato gravitatis centro, figuram globi indueret. Q.E.D.

Corol. Hinc motus corporis attracti Z idem erit ac si corpus attrahens RSTV esset Sphaericum: & propterea si corpus illud attrahens vel quiescat, vel progrediatur uniformiter in directum, corpus attractum movebitur in Ellipsi centrum habente in attra∣hentis centro gravitatis.

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