Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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& erit
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G
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commune centrum gravitatis particularum
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A
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&
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B.
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Vis
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AXAZ
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(per Legum Corol.2.) reſolvitur in vires
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AXGZ
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&
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AXAG
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& vis
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BXBZ
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in vires
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BXGZ
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&
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BXBG.
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Vires autem
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AXAG
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&
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BXBG,
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ob proportionales
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A
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ad
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B
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&
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BG
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ad
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AG,
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æquantur;
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adeoque cum dirigantur in partes contrarias, ſe mutuo deſtruunt. </
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Reſtant vires
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AXGZ
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&
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BXGZ.
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Tendunt hæ ab Z verſus cen
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trum
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G,
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& vim —
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A+BXGZ
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componunt; hoc eſt, vim eandem ac
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ſi particulæ attractivæ
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A
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&
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B
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conſiſterent in eorum communi gra
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vitatis centro
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G,
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Globum ibi componentes. </
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LIBER
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PRIMUS.</
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>Eodem argumento, ſi adjungatur particula tertia
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C,
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& compo
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natur hujus vis cum vi —
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A+BXGZ
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tendente ad centrum
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G
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; vis
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inde oriunda tendet ad commune centrum gravitatis Globi illius
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G
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& particulæ
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C
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; hoc eſt, ad commune centrum gravitatis trium par
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ticularum
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A, B, C
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; & eadem erit ac ſi Globus & particula
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C
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conſi
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ſterent in centro illo communi, Globum majorem ibi componentes. </
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Et ſic pergitur in infinitum. </
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>Eadem eſt igitur vis tota particula
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rum omnium corporis cujuſcunque
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RSTV
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ac ſi corpus illud, ſer
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vato gravitatis centro, figuram Globi indueret.
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E. D.
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Corol.
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Hinc motus corporis attracti
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Z
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idem erit ac ſi corpus
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attrahens
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RSTV
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eſſet Sphæricum: & propterea ſi corpus illud
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attrahens vel quieſcat, vel progrediatur uniformiter in directum;
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corpus attractum movebitur in Ellipſi centrum habente in attra
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hentis centro gravitatis. </
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PROPOSITIO LXXXIX. THEOREMA XLVI.
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Si Corpora ſint plura ex particulis æqualibus conſtantia, quarum vi
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res ſunt ut diſtantiæ loeorum a ſingulis: vis ex omnium viri
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bus compoſita, qua corpuſculum quodcunque trahitur, tendet ad
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trahentium commune centrum gravitatis, & eadem erit ac ſi
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trahentia illa, ſervato gravitatis centro communi, coirent & in
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Globum formarentur.
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>Demonſtratur eodem modo, atque Propoſitio ſuperior. </
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Corol.
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Ergo motus corporis attracti idem erit ac ſi corpora tra
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hentia, ſervato communi gravitatis centro, coirent & in Globum
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formarentur. </
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<
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>Ideoque ſi corporum trahentium commune gravita
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tis centrum vel quieſcit, vel progreditur uniformiter in linea recta:
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corpus attractum movebitur in Ellipſi, centrum habente in com
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muni illo trahentium centro gravitatis. </
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