§. 2. Sint XX, jj, zZy terni numeri quadrati 

 quaefiti^ ita vt effc debeat , 



I. xx-^-yj-^-zz — n2. 



11. xxyj-^-xxzz-^-jyzz — CDj 

 quariim couditionum priori fatisfiet, fumendo 



x—pp-\-qq — rr\y—2.pr et z— 2. q r', 

 tum enim erit, 



xx-\-yy^zz — {pp-\-qq-\-r ry , 

 vnde fi ponamus x .v -Hjj' -i- :2 xs rz P' , fumtis 



x-pp + qq — rr, y-2pry z-2qr,RQt P-pp-\-qq + rr. 



§. 3. Progrediamur nunc ad nlteram conditionemy 

 quac pollulat, vt fit 



X .V {yy -\-zz)-\-z zyy — Q' ; 

 quare cum fit 



yy-h-zz — ^rr^pp-^-qq), 

 hinc orietur ifta aequatio: 



Q:=:^rr{pp-\-qq){pp-\-qq-r ;f -]- 16 p p q q /•% 

 quae diuifa pcr fatflorem quadratum 4. r r dabit 



— — {pp-^qq^iPP + ^Q-fff-^^PP^i^-^y 



quam ergo fi)rmulam quadratum rcddi oportet. Ea autem euo- 

 luta literae p et ^ ad fextam potefiatem afccndcnt, litera ve- 

 ro r tantiim ad quartam, quae ergo commode inucfligari 

 poffe vidctur , fiquidem cafus fponte patet , fcilicet fi 

 rr~pp-\-qq^ dummodo fuerit p p -h q q quadratum. 

 Interim tamcn hinc ne vnicam quidem aliam folutionem 

 deriuare licet j vnde negotium prorfus alio modo aggredi 



opor 



