io 8 DE PR0BLEMAT1B. XNDETERMLNATIS 

 Coroll. £. 



ap. Sit azzi^ atque his conditionibus 



i—xz—yzzzn 



i—xy—yzzz.n 



j—xy — xzzzn 



fetisfiet ponendo x-\-y-\-zzzz r 



Problema 5. 



30. Propofita hac aequatione refoluenda 

 xy-+xz-+yzzza(n-\-y-+z)-\-b 

 definire formulas notabiliores , quae per eius refolutionem 

 redduntur quadrata. 



Solutio. 



Erit ergo in genere haec formula : 

 T>? + M.(xy+xz+y z) -a(x +y +- z) - b)zQuzdrato. 

 Sit M = 2, Yt habeatur : 



PP-f 2 (xy+xz+yz) - 2a(x+y+z) -2£nQuadrato. 

 Capiatur Vzzx-\-y-\-z-+a, ent 



1 ) xx+-yy-+zz+-4- (xy-+xz+yz)+aa-2bzz Quadrato. 

 Capiatur P — x -+y -z-+-a, erit 



s) xx-\-yy-+zz-+^xy — ^az-+aa-2bzza 



3) xx-+yy-+-zz-+^xz—^ay-\-aa-2bzz.n 



4) xx-+yy~\-zz-+^yz-^ax + aa— 2bzz a 

 Capiatur Pr x~ y> erit 



5) x x-\-yy •+- 2 (x-\-y)z — 2 a (x-+y -+- z)- 2 bz a 



6) xx-+zz-\-2[x-\-z)y—2a{x+-y+z)-2bzzu 

 7)jJ-\-zz-\-2(y-+z)x-2.a(x-\-y+z)-2bzzn 



Sit 



