ponatur a — e(pp — q q) ct b — ^ e p q. critqiic 



y (a a -\- b b) — e {p p -^ q q) ^ 



confcqucnter 



k — e(pp-\-pq) ct k'~e(pq — q q) ', liioc 

 o — h_ — Tp-^pq — p p 4-<? ) 



Multiplicctur li:iec fradio fupra et infra pcr q (p — ^), Ct 

 cum --^ dcbc.it c(!b quadratum, ficri dcbet 



fiue etiam p q (pp — q q) = n-, fiue pofito p = x X ct q —yy^ 

 cb p q — X xyy — O •> nccefTc eft vt fit jr* — y* — \2 ^ quod 

 impoflibilc cflc cuique conftat. Dcmonflratum enim eft diffe* 

 rentiam duorum biquadratorum quadratum efle non poflc. 



Scholion i. 



§. 15. Plcrumque autem, fi numerum «, fcu rationem 

 corporum A et B, pro lubitu accipcre volucrimus, et rationem 

 filorum a cx. b ita definirc, vt tempora fiant rationalia , in ca- 

 lus incidcremus, qui rationcm rationalcm intcr tcmpora ofcilla- 

 tionum planc non admittunt; vnde coacti crimus pro his cafi- 

 bus longitudincm fili vtriusque fccundum pracccpta fupra data 

 quouis cafu inuelligare. 



Scholion 2. 



§. \6. Si id tantum intcndamus, vt ratio tcmporum 

 prodcat rationalis, quaccunquc fucrit relatio inter fila , Itatim 

 ponatur a -\- b — z r et y (a -[- by — li^ — 2J, critquc 

 4.fi — +rr — *-^, hinc ^a b — ^n(r r — s s), quo fubtrado 

 ab aa\-2ab-{-bb:z^^rr^ remanct 



Dd a (fl-^) 



