Astronomia mechamca, ^ 25 1 



^^ = ^'-*- — 2r/m ^^ 9^ = 7 ^t P = f-n 47^' 



ideoque q = —, sicque excentricitas q constans. Tum erit 



df (yf— 3wi — l-ncosSy) 

 dty'2fgL= y^ ^ , seu =dq>{ff — 2fcossVm — 3/n — -f-ncos^^^). 



(iH — C08 5) 



Solutio ergo hujus casus pendet a resolutione hujus aequationis d(f = ds~\- " ^0?^^'" ^ » ex qua, 

 si -/— est quantitas valde parva, concluditur 



^ SnsiaCim — s) n sin (2 <»-♦-«) 



Reliquis autem casibus, praecipuc si m esset =0, alia tractatio requireretur, in valorem scilicet 

 ipsius 5* accuratius inquiri oporteret, quod difflcultatibus haud esset cariturum. 



166. Scholion 3. Solutio nostri problematis posterior ideo priori est anteferenda, quod 

 binarum aequationum differentio-difTerentialium propositarum una integratio successerit. In genere 

 igltur, si idem usu veniat, solutio facilior obtineri potest. Propositis enim his duabus aequationibus 



^;dd(f-Y-2dvd(p = ^gLTdt^ et ddv^vd(p^z= — gLdf^^^-h- V)^ ; 



multiplicetur prior per 2v^d(pj ut prodeat 



^^'dcf''^ 2gLdt'' {C—fTv^dcp) = 2gLdt'' (C— S), 

 posito fTv^d(p = S. Deinde priori ^ar 2vd(p^ et posteriori per 2dv multiplicata, summa praebet 



d . (wdr/-4- dv^) = — ^gLdf (Tvd(p -h Vdv -h — )• 



Quod si jam fuerit Tvd(p-\- Vdv integrabile, ponatur integrale f{Tvd(p-\- Vdv) = -3» ut habeamus 



dv^-\- vvd(p^ = 2gLde (D -h f — ^/r 

 hinc eliminando dt'^ adipiscemur ,oiJnIt>« ym>j ciuiiUwi rnfcf/noi uitiiiA .ft noiloi^ji*. .ii^» 



Statuamus c = ; — , sitque : i^uoq ? -ilunm/l 



1h-5C08« *■ 



P ^ 2 n(iH^3ia) M<-t-w)(c-^ _,Q g^ 2 — ^^^^ !i£n!>=o, 



p p* pp pp p ^ 



ut fiat formula irrationalis l^ASrN- rr^vl^^fTA 



l/(D^l_(£^_*)=i^y(C-,S-*-^^i^^i^>), hincquc 



dv qdq> tin s -i// ^ fl (3 -*- g co8 »)\ i ''*' 



i^ p \ |>(C— '5) / , 



■ 



