->I4? ) 85 ( 



fionem aflurgunt , quarum refolutio fines Analyfeos tran- 

 fcendere yideatur , quandoquidem hic jtautum .de foluti^- 

 nibus per ^numefos irationales agitur. 



^. 2. Prima igitur aequatio <^uarti gradus , quam 

 hij: jtra«flabo, hoc Problemate contiaejtur. 



Problema I. 



fnuenire quatiwr numcros rationales x^ y^ z, v^ vt 

 huic aequationi fatisfiat: 



x''-\ry*-hz^ — zxxyy — xxxzz — 2.yyzz'l 



•^- 2. X X w -^- zy y V V + z z zv V -\-v^ S 



culus fonnulae ^ fatis piolixae, loco hic breuitatis gratia in 

 fequentihus fcribam litteram F, 



f. 3, Pro his autera litteris ^, j, 2, v, inuentis 

 Idoneis valoribus, fimul fequentes feptem formulae fponte 

 euadent numeri quadrati, vquae funt: 



I. xxyY — zzvv^zl^xx-^-yy—zz-^-vv)* 



II. xxzz-^yyvv — \{xx-\-zz—yy-\-vvY 



III. yyzz — xxvv — '^{yy-\-zz — xx-\-vvY 



IV. xxyy — vv[xx-\-yy) — l{xx-{-yy—zz — vv)'' 



V. xxzz — vv{xx-\-zz) — l {xx-\-zz —yy — vv)* 



VI. yyzz — vv{yyj^zz) — l{Yy^zz-xx — vvY 



VII. X xyy -]rxxzz -jryyz z — ]^{x x +y y -\- z z-\-v vy. 



Ratio per fe eft manifefta, cum quarta pars formnlae no- 

 ilrae V , cuius valor per hypoihefin — o, fjngulis his 

 feptem formuJis addita, producat reuera quadrata, quorum 

 wdices hjc aflignauimus. 



