D I O r H A N T AE A. 53 



vnJe numerorum x «t y chanider in hoc co.^fiflit , 

 vt X X — X y +j'j fit quiiJratiim ; cuiiismodi nums- 

 ri cum facilc inueniantjr j fit x x — xj i-yj — zz ; 

 erit-]ue 



t. — 'L^^Ld^ - — ^ . fcu 1 - ^^ ; 



tinc fit 



(x: -/) (- + x-ij] ~ [z^x-jy^zz-x-j) {z -.V) (z+j-2x') 



^z+j-x^^iz-x-j) 



Tnde M-JH-i^) — g-t-y — y 

 Deinde eft 



hincquc tandcm elicitur 



_t_ . (z -(- a — y) fa s_— _*+:>) 



u (2 _j- 3^ — x; (2 a H^ * — >)■ 



Sicquc pro x ct y eiusmoJi numeris inucntis , vt 

 fit rationaliter V (.v x — xy -j-jy) zz. z capiatur : 

 t^iz + x-fiiz-x+y^^xx + rj + ix-j^z 

 u~ {z+y-x]i2z-y + x)z^xx+yy-{x~y]z. 

 hinc obtinctur 



ttxx+uuyy-:{xx+yy)[xx-ixy+yy-\-(x+y)zY 

 uuxx + ttyyz^[xx+yy)[xx-^xy+yy-{x+y)z)' 

 \el etiam hoc niodo 



ttxx + u uYy—-Xxx+yy) [x+y + z)\\z- x-y ]' 

 uu XX + ttyy—\' xx+yy){ x +y - z )\ ^z + x+y /. 



Num autcm quo facilius .valorcs pro .v et y idoneos 



G 3 repe- 



