Full text: Gravesande, Willem Jacob: Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam

Ex hiſce patet actione corporis hujus vim, ideoque velo-
oitatem, non minui ſine ipſius obſtaculi, aut partium hoc
componentium; translatione ex hac actione oriunda.

208.1.

523.

209. SCHOLIUM 1.
Demonſtrationes n. 499. 510

Dentur duo corpora A & B; ſit hujus velocitas b; illius celeritas a; velo-
citas reſpectiva, ſi in contrarias partes ferantur eſt a + b ; hanc dici- mus d. Summa virium eſt Aaa + Bbb, quam, manente velocitate reſpecti-
va, diximus omnium minimam poſitis A, B: : b, a , id eſt Aa = Bb.

209.1.

524.
475.
499.

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
a = {Bd/A + B}, ſimiliter b = {Ad/A + B}; idcirco ſumma virium Aaa + Bbb =
{ABBdd + BAAdd/ B + A q } dividendo numeratorem & denominatorem per
B + A, quantitas hæc æqualis eſt {ABdd/B + A} ut in n. 510. monuimus.

209.1.

525.

210. Demonſtrationes Algebraicæ n. 513. 516.

Geometrice demonſtravimus regulas n. 513. & 516. algebraice quam ſa-
cillime deducuntur ex propoſitione numeri 512.

Sit corpus A motum velocitate a; corpus B agitatum velocitate b: velo-
citas reſpectiva eſt a - b ſi corpora ad eandem partem tendant ; hæc ictu de- ſtruitur quare eſt ſumma mutationum in velocitatibus corporum poſt ictum. B eſt ad A ut mutatio velocitatis in A, ad mutationem velocitatis in B ; & componendo A + B, A: :a - b, ad mutationem in velocitate corporis B, quæ

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