89 



Quacunque autcm combinatlone utamur posito V rr: (P -j- Q?/)*, 

 ob V — PP -H QR orietur ista aequatio canonica Q,yy -f- 2P;/— R— o 

 cujus deinde alteram formam Sxa; -h Ta? -t- U zz: elicere possumus, 

 quo facto , constitutis formulis directricibus y -\- y^ zn — ~ vel 

 yy^ z=: — ^ ; tura vero x -{- x^ -^z — — sive xx^ nz -^ , innumera- 

 biles alios valoi'es idoneos pro x invesdgare licebit , nisi forte nu- 

 inerus horum valorum ob indolem formulae propositae fuerit finitus. 



§. 4 5. Si ex tribus aequationibus pro litteris p, q, ?•, datis 

 lias littcras in génère detei'minare velleraus in formulas valde com- 

 plcxas incideremus, cum tamen quovis casu oblato negotium facillime 

 absolvalur. Quamobrem usum hujus solutionis in exemple speciali 

 ostendamus. 



E X e m p 1 u m 



§. 46. Proposita sit ista formula Vm 1 -f- 3x'^, quae his 

 tribus casibus x zz: , x zz: i , x zzz 2 , evadit quadratum scilicet 

 casu X ziz. Q fit V zzz 1 , casu vero x zzz i , fit V zzz 4 , et casu 

 X zzz 2 fit V :zz 4 9. Quamobrem posito P zzz p -{- qx -\- rxx ori- 

 cntur très sequentes aequationes : 



1. ?>\ X zzi Q erit -^j^ i ^zip , 



2. .. X zz: l . . -^^ 2 zzz p -\- q -{- r 



3. .. XZZZ2 .. -+- 7 z=/5 -[-2f/ -|-4/-. 



Sumamus autera omnes très radiées positive eritque p ZZZ i , duae 

 reliquae vero aequationes erunt i zzz q ~\~ r et b :zzz2q -^ Àr, mide 

 cruitur r zz; 2 et (/ zz: — 1 sicque habebimus P zzz 1 — x -i- 2xx. 



§. 4 7. Hinc igitur reperlemua QR. zz: V — P'' h. e. 

 Kt^- — x'^ -f- ix^ — Sxx-i- 2xz: — x ix — i')(x — 2')ix— 1) 

 quamobrem sumamus Q ziz (a: — \f et R zz — x ix -— 2) unde 

 Suppl. aux Mémoirts de t'^cad. 



