i* *>¥£ ( o ) §>e£<- 



fumma produclorum ex binis zr8 9.34-* + 9'i7.34-* 



-f-8.17.34^^9^34-* 



produ&um omnium s; 8.9. 17. 34*« — 8". 3*. 17 4 . 



Hinc pronunciari poffe videtur, minimos numeros in- 

 tegros problemati fatisfacientes etfe 272- 306 *, 578; 

 frados autem hos £; T + 7 ; &. 



Caeterum hic notafle iuuabit , fi tres numeri integri 

 x, y, z defiderentur, vt tantum haec formula xy + xz\~yz 

 fiat numerus quadratus , eos in genere ita exhiberi 

 poffe , vt fit : 



x-^ry=z(a-b)^(d-ef 



j+s^^^ + ^/f 

 z-irx^ic-af+if-df 



vnde fit x-+-y-\-z — aa-\-bb-\-cc — ab — bc-ac 

 -\-dd-\-ee^ff—de — ef—df^ ipfique numeri ita fe 

 habebunt : 



xzz(a-b)(a-c)-+-(d-e)(d-f) 

 yzz(b-c)(b~a)-+-(e-f)(e-d) 

 z -(c-a)(c-b)-+-(f-d)(f-e) 

 vnde fit : 



V(xy-+-yz-\-xz) — a(e-f)-+-b(f-d)-\-c(d-e') 

 Vel fimplicius haec folutio ita enunciari poteft , vt fit: 



x — lm-\-pq\ ) yzz mn-+-qr\ zzzinl-+-rp 

 fumtis his fenis numeris /, m, n et p, q, r 9 ita vt fit : 



l-+-m-+-n — o et p-+-q-+-r~o 

 tum vero erit : 



y(xy*+-yz-+-xz)—lq-mpz=mr~nqzz\np-lr. 



III. 



