210 INVESTIGATIO 



Qiia nnnc R et M dantur per Q et S, et ob P=QS 

 etiam V detur per Q et S. Si haec relatio cum his 

 binis coniungatur : 



A-zr-M + C^J + O^S, etjK~ -S*-HR4-0:S 

 poterunt hinc eliminari binae quantitates S et Q, quo 

 fa<fto prodibit aeqiutio , qua V determinabitur per 

 x et y. 



Exemplum i. 



82. Exiftente dV = Pdx-f-Qdy, oporteat ejfe 

 VrrmPP-t-nQQ. 



Cum crgo CrtdV-2m?d?-\-inQdQ_, erit M- 2 m?,tt 

 N=i2«Q, feu M~zmQS ob P — QS, ita \t fic 

 VzzQQ(m$S-hn}. 



Habebimus ergo N-f- MS~2Q(wSS + ») , ideo- 

 que fpedhta S vt conrtante : 



R~/^(N-f-MS)~ 2<£(»SS-f-»)„ 



ac proinde (ai) — 4*wQ.S» 



Vnde has tres aequationes adipifcimur : 



I. V~QQfwSS-f-«) 

 II x + zmQS-imQS + O^.Skux-imQS + WS 



III. y^Sx—2QjjnSS-^n)-hO:S 

 feu y zz 2 n Q^ <D: S -S O": S. 



Qiiodfi ex II et ili eliminetur Q_, erit : 



IV. nx-mSy — («iSS-h» jO^S-wSOiS 



ex iisdem vero coniun<5tis fit Q—ff^fiJf)* qnaecum 

 pnma dac V ; 2 V \ {m$$-\r-n) ~Sx-i-y-®'. S. 



Quare 



