QVAE FWENTPR tLVS QVAM DET. Ht 



definire fbrmulas notabiliores, quae per eius refolutionemi 

 sedduntur quadrata. 



Solutio. 



In genere ergo quadratum erit haec forma : 

 PP+ NL(xx + yy\-zz- 2xy-2yz-2xz~ia(x-\-y-\rz) **)) 



Sit M-i— r et capiatur ? — x ~\-y-\-z-\-a , erit 

 i) 4rXy + 4.xz-t-4.jz + 4. a (x+y+z)-{-aa-{-bzzn'> 



Capiatur P— x-\-j-\- z -a, erit 



2) 4 xy -+- 4 * s +- 4 y # -+- # * -4- £ — n 

 Capiatur ?—x-\-y-z-\-a, erit 



3) ^xy-i-^a(x-\-y)-\-aa-\-b^Q 



4) 4* £+-4 *(*-*- 2)-+- <?<*-+-£ — □' 



5) +yz-\-4.a(.y-\-z)-\-aa-\-b~Q 



Capiatur ?z=:x-\-y — z—a, erit 



6) /\.xy-\-^az-\-aa-\-b — n 



7) 4x*'-f-4<y-+*tf«'-+-^=:a : 

 S) 4/«-+-4.«x-+-«*-+-^zza». 



Coroll. r^ 



3<J. Ad formtilas has facillime foluendas , f>on?U 

 tur tertia ^.xy-\-4-a(x-^-y)-\-aa-\-b , aeqtialis quft- 

 drato cuipiam «« et ob 4^ -\-a)(j -\-a)zLuu-b-\- $aa ',, 



feu (.v-f-<7)(j/-f-<3ryzr:^(««-^-+- 3 # tf) 



Ex fa&oribus numeri \(uu-b-\- %ad) commodifllme dc-- 

 finiumur numeri duo X et y\, tertitts autem «^ colligitur 



