t8a SOLVTIO GENEKAtn 



qua autem ita in vnam compingetur , vt vterque 

 factor feorfim x-\-y et xx — xy -\-yy vel quadratum 

 effe debeat, vel triplum quadratum. 



I. Sit primum vterque fa&or quadratus ; ac po- 

 natur xx— xy-\-yyzz. (pp— pq-\-qqY , eritque vel 

 xzrpp—ipq et yzzpp — qq , vel xzzipq—pp 

 et yzzqq — pp. Priori cafu ergo oporttt vt fit 

 x-\-yzzipp~ipq — qq quadratum. Quae forma 

 cum fit zz 3pp — {p~\-qf-> ^ ponatur.mrr, oporteret 

 effe ^ppzzi p-\- qf- -\-rr zz fummae duorum quadra- 

 torum , quod eft impofTibile. Relinquitur ergo alter 

 cafus , quo x -\-yzzq q -\- i p q -npp zz. (q -\-p) 2 - 3 pp 

 :zz quadratum , ,cui fatisfitponeado 



pzimn et .qz^mm ~-?2.mn-\-mn 

 xzz ipq-ppzz 4.mn{zmvi—$mn-\-nn) 

 yzz q q —p pzz ( 3 711 m -\- nn) ($mm — ^.mn-Vnn) 

 ■zz\ (m — »)(3 m — n)(z m m -\- n n) 



II. Tum vero ponatur r xx— xy-\-yy ~ triplo 

 qmdrato z 3(pp—pq-\-<M) 2 eritque, cui triplici mo- 

 do fatisfit: 



j xzzipp-ipq- qq xzzipp-ipq-qq "' xzzpp\ipq~2qq 

 ' yzz pp+ipq-iqq ' yzz pp-\pq+qq ' 'yzz-pp\+pq~ gq 

 Cafu primo fit : 



x -\-yzz 3 Dp- 3 q q zz 3 plo quadrato, feu pp -qqz qua- 

 drato : vnde fit pzzmm-\-nn \ et q zz % mn 3 

 ideoque 

 x zz 1 (m*— im"-n— im n z - \- «*) 

 y zz m"-\- 4. m z n — 6 m m n n— \- 4 m n'\- n* 



Cafu 



