434 DE NOVA 



ita Tt quacrl oporteat numerum ^, vt formula 

 1^*4-1 fiat quadratum. Hoc ergo facto ftatuamus; 



quod produAum cum ip(a forma propofita conue- 

 nir» , ita ptr fa<florcs irrationales oftcndimus. Quum 

 •nim (It 



Ax' - iBxj^ + Cy::^ i( Ax-Bj +j Vk) (A .v - Bj -y Vk') 

 ft Aa-%'&Mh-\-C/ — iiAa-Bb-\-byk)[Aa-Bb-byk') 



et 



pp-%%pq + ACq'=.{p'-Bq-\-qyk){p-Bq-iVk) 



Aatuamus 



Ax-ty+yVk — lAa-Bb+bVk^ip-Bq+qVk), 



tum enim fponte fiet fumsndo Vk negatiue 



Ax-By-yVk-iAa-Bb-bVk^lp-Bq-qVk) 



▼nde fufficiet altcram aequationem tantum euoluifle, 

 fi modo partes rationales ct irrationalcs feorfim in- 

 tcr fe aequentur. Prodibit igitur 



Ax-hy—{Aa-'Bb/,p-Bq)'+bq[K-'-AQ) 

 j—qiAa-hb^-^-b^p-Bq) 



qui valor in priori aequatione fubfatutus pracbet 

 Ax—Bj-^-iAa-hb^^p-Bq^-^-kbq 



hincquc xzzap — Cbq, ita vt \.Uor£5 quaefiti 

 fint 



xzzap—Cb^; yzzhp+'Aaq-iBbq, 



atque hinc adhuc alia folutio formari potefl; , qno- 

 Eiam permutatis litteri» A et C lam litterae xcty, 



quam 



