QVORVNB. PROBL. DIOFHJNTJEORVM. i6j 



Ex quibus valoribus litterae p> q, r, s ita definiuntur , 

 vt fit : 



pzz%n(ac-\-bd) (dd-\-^cc) 

 qzzn($bc—ad) (dd-\- 3 c c)-n(a 'a-\-zbby 

 rz=H(</</+3 cc)— «(3 bc-ad) (aa-\-$ bb) 

 szz^n(ac-\-bd) {aa-\-$bti) 



Atque hinc tandem radices cuborum quaefitorum A, B, 

 C, D erunt : 



A zz n ( 3 ac-\- 3 bc—ad-\- 3 bd)(dd-\- 3 O") - f(tftf + 3 ^)* 

 B zzn(3ac—^bc-\-ad-\-2bd)(dd-\-^cc)\-n(aa\-^bb)* 

 C :=: n(dd-\-^ccf—n(^ac-\-^bc-ad-\-^bd)(aa-\-^bb) 

 Y)—n{dd-\-zcc?-\-n(j$ac-'zfc-\-ad-\zbd)(aa-\$bb) 



quibus valoribus obtinetur , vt fit : 



A^-j-B^-hC-D 1 



et cnm folutio nulla reftri&ione fit limitata , vtique 

 latiflime patet omnesque cuborum terniones complcdi- 

 tur , quorum fumma iterum eft cubus. 



Coroll. 1. 



17. Deriuemus hinc fbrmulas magis ipeciales, ac 

 primo quidem fit dzzo; eritque 



kzz$n(a-\-b)c — n(aa-\- sbb)* 

 B zz^h(a — b)c z -\- n (a a -{- 3 bb)* 

 Qzz9nc*—$nc{a-\b)(aa-\-zbb) 

 TXzz 9 nc*-\ 3 nc (a — b)(a a -\- 3 bb), 



Si hic 



