III. ^V^xxvv+yjzz^ — xx-^-vv—yy — zz 



IV. 2 V { X xjj -{- X X z z + YJ z z) =: X X -^-yj + z z —-v v] 



V. 2 V {xxjj + xxvv+yyvv) — xx+jy + vv — zz 



VI. 2.V(xxzz + xxvv+zzvv) — xx+zz + vv —jy 



VII . '2.V[yjzz+jyvv + zzvv) —jj \-zz + vv — xx 

 quibus addi poteft 



VIII. zVYi — xx+jj + zz + vv. 



In hoc igitur Problemate quaterni numeri jr, j^ 2, -p, a©- 

 qualitcr ingrediuntur , cum in priore Probkmate quadrati 

 vv ratio fuiffet diuerfa. 



Solutio huiiis Problematis. 



§. 30. Solae priores formulae hic iterum fuffi- 

 ciunt ad totam folutionem abfoluendam. Cum enim for- 

 mula X xjj + zzvv debeat reddi quadratum, hoc eueniet, 

 fumendo 



xj — zv ^-^f^ i 

 tum enim erit 



V {XXJJ+-ZZVV) — ^-^^-pJiSl , 



ideoque 



z:zl{xx-\-jj-zz~vv). 

 Simili modo pro fecunda formula fi fumatur 

 j^2_22iLi£r=ll) erit 



2,J5 



y{xxzz-+-jjvv)— yJLiJ!±+ll} — 

 i^xx-^-zz—jj — vv). 



