j59 



tum enim habeblinus 



p — (« — h) [C/-f "^fP 'ï -+-/A] —./■(/■+ of, 

 q =Z (l> — a) [(£/ -f-2/) b h ya] — j; (/-|- ç//. 

 lisdefn aequationibus quoque salisiiet , ponendo . 

 X — (affg — V/ >' — //gg (/-h â')*, 

 ?y = 2/y cy+ ^^) (<^</ -f- h/) . 

 utraque enim formula, si hi valores in ea substituantur , fit quadra- 

 tum , radice existente : 



p — (agrj — b//) \ag (2/M- çD + bff] — ffgg C/+ gf 



q = ibff— cujg) [i>j\2,j 4-,/) + ngg] - ffgg (./M- ??)' 



unde , quia _/ et <y etiam négative sumere licet , quatuor soliitiones 

 oriuiitur. 



P y o b I e 1)1 a IV. 

 §. 12. Invenire valores pro munero m it(i comparnins. iif for- 

 mula x** — |— mxxyy -f- y quadratum reddi jiossit. 



S I u t i 0. 



Statuatur x"^ -\- m xx yy -];- y"^ z= zz , quod ita rcpraesen- 

 tarl poteiit : ' ' 



z s r= (a; a; -}- z/ y'f -\- n x x y y 

 ■t- posito soilieet /« m 7i -f- 2. Hinc autem sequitur fore 

 *' n — m ~ 2 — îl^lifiL:JI-I2l\ 



XX y y 

 Addatur utrinque /». eritque 



m -4- 2 = ^t. — (XX — j^ ^ 



Statuatur nunc x z^ pq et y zzz rs , et formentur sequenles quatuor 

 aequationes ; 



I. z ~jr- XX -^ yy z=z aqqss , 



III. s — ,x:r — 2/z/ — 0pprr, 



III. z -I- a;a^ — 2/'/ i;^ yppss , 



IV. z — avr -f- z/// — ^qqrr , 

 Ita ut nunc habeamus m-2-a^ et m- 21:75, ideoque yS-cn^-^^. 



Illae autem quatuor aequationes totidem praebent determinationes, 

 guarum una est : 



