X94 RESOLVTIO AEQyATIONIS 



13. Quo autem hinc pliires atque adeo infinU 

 tas folutiones eliciamus , in lubfidium vocemus for- 

 mulam s =zV{k/ -^ i ) , quippe quae metiiodo 

 Pciiiana femper infinitis modis refolui potefi , dum- 

 modo k non fuerit vel numerus ncgatiuus , vel nu- 

 merus quadratus. Qiium enim liinc fiat xj- — ;^r*- r, 

 noUram aequationera liac forma repraelentare pote- 

 rimus: 



?'-k(^ = CG' -k H') {ss-k k'). 



Hincque per fidorts irrationales fiatuamus 



Fi-Qyk-iG+HVk)(s-\-rVk)=Gs+kHr^{Gr+Us)Vk 



fic enim fimul toti aequationi latisfiet , fi quidem 

 partes rationalcs et irrationaks (eorfim acquantur. At 

 irrationales praebent : 



QczGr-l-Hx, y-+N=Aar-{-Bljr-\-Mr-\-bS'^Nsi 

 jz=:Aar-hBbr-\-Mr-+bs-{-Ns-N* 

 At partes rationales dant : 



P — Gx-i-/:Hrj feu Ax-\-Bj-+Dz=:Aas-+Abs 



-i~Ds-+kr-+kl^r 

 vnde 



xzzsia^ ^-^) 4- r (*i^-^i^^^ -Ba) 



14.. Nunc igitur loco litterarum M et N re- 



,ftituantur valores fupra inuenti , atque pro noftris 



quantitatibus quaefitis at et j fequentes reperiuntur 



formulae , fi fcilicet loco k fcribatur B' — A C : 



x = {a-+^^^^)s-+Ba-+Cb^E)i-r)-+1fE^^^ 



jzz{b-+lP^)sM^b^Aa^D)r^'^i^, 



vbi 



