Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

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Dentur duo corpora A & B; ſit hujus velocitas b; illius celeritas a; velo-
22524. citas reſpectiva, ſi in contrarias partes ferantur eſt a + b ; hanc 33475. mus d. Summa virium eſt Aaa + Bbb, quam, manente velocitate reſpecti-
va, diximus omnium minimam poſitis A, B: : b, a , id eſt Aa = Bb.
44499.
Poſitis enim talibus velocitatibus, augeatur a quantitate quacunque e; vis
corporis A erit nunc Aaa + 2A ae + Aee. Corporis B velocitas, quia
manet velocitas reſpectiva d = a + b, erit b-e; nam a + e + b - e = a + b; er-
go vis corporis B erit Bbb - 2Bbe + Bee, & ſumma virium eſt Aaa
+ Bbb + Aee + Bee + 2Aae - 2Bbe.
Sed propter Aa = Bb ſeſe mutuo duo ultimi termini deſtruunt, & ſum-
ma valet Aaa + Bbb + Aee + Bee, quæ primam excedit. Similis eſt de-
monſtratio ſi augeatur velocitas b, minutâ, eâdem quantitate, velocitate a; un-
de patet demonſtratio n. 499.
Poſuimus A, B: :b, a; componendo A + B, B: :b + a = d, a; ergo
55525. a = {Bd/A + B}, ſimiliter b = {Ad/A + B}; idcirco ſumma virium Aaa + Bbb =
{ABBdd + BAAdd/B + Aq} dividendo numeratorem & denominatorem per
B + A, quantitas hæc æqualis eſt {ABdd/B + A} ut in n. 510. monuimus.

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