418 CAPUT XVIII. DE MOTU CORPORUM

atque

/•, ... v r rr, f Gtt (l — aau) co(H

p = 5 cof£ + {bb — ff) co ftj cofB ^-----—

S$u' (i — ctan 1 ) co Q't

+-j- )

q= scof, + c»-..) cof^cora (

Ht/ (r — blm') cof §'t

• - , •)

r> rn , / f , N C, r Gtt (i - ccu) eofFtv = # coi $ + (aa - hb) coi £ cof»; ^ ^ —

H»/ (l — ceu') co Q‘t

)

C 0 R 0 L L, 2 .

9 T 3‘ Angulorum etiam $t et ^ titerque quantitate conflante auge-ri poteft, ac fi eorum loco feribamus $t + g et dt + h, integralia conti-nebunt fex conflantes arbitrarias g, h, E, F, G, H, ideoque erunt inte-gralia completa haruin fex aequationum diflferentialium:

aadx — ifgdt (r co f», — q cofA); dp = dt (a cof»; — >/ cof A)

Mrfy — ifgdt (p cofS 1 — r cof£); dq = dt (x cofA — s; cof£)tttiL — ifgdt (q cof£ - cof»;); dr = dt (y cof£— x cof»,).

C 0 R O L L. 3 .

91 $. Si corpus initio quieverit, ut in problemate afiumfimus, itant tum fuerit x — o,y=ozlz=zo\ poni debet E — o, q — o, eth — v; reliquas autem conilantes ex fitu corporis initiali'definiri oportet.

C O R O L L. 4 .

91 5 . Nempe fi pro initio , quo t = o, ponantur anguli ZDA — s,ZDB = ni, e,20c^n; ut fit

r \ — cofA r — cof?

fm (1 _ m) .= -—-; fin (m - n) = ——-S- ;

fiuc Im»; fm», finA

^ - cof„

fin(n - l) — ~~p y~r —r—

t