(^35) 

 §• 35» Q"od fi iam hoc Lemma ad noftriim cafum 



accommodemus, erit p — aYx^y et 7 — ^/x^j^, tum vero 

 habebimus p-f-^zrc et produdum pqznabxy^ ita \t nunc 

 fit f:^c et g zzz a If X y^ quibus notatis formula generalis in 

 Lemmate data nobis ftatim fuppeditat hanc aequationem ratio- 

 nalera : 



fl^x'^/-+-^^jf>"' =z c^ — \c^-"-abxy -4- ^ii^^ c*"-* a" b^ x'y' 



X(X — 4)(X — 51 ^X-S ^3 ^3 j^3y3 _^ etc. 



I. 2. 3. 



quae ergo aequatio manifefto pertinet ad ordinem X""*. 



§. 3<5'. Percurramus nunc aliquot cafus fimpliciorcs, 

 fitque i°.ix—2^ V — I et X nz 3, ita vt aequatio pro Hy- 



perbolis irrationalis fit b ■]/ x xy ~\- b Y xy y ~ c, atque ac- 

 quatio rationalis hinc nata erit: 



a^ X xy -\- P xyy zzi c^ — ^ c a b x y, 



ct fpatium quaefitum inter curuam et fuas aflymtotas conten- 



tum erit = ^. 2°. Sit jm. — 3 et y ~ i , ideoquc X — 4, 



4 4 



vt aequatio pro curuis fit a ]/ x^ y -]- b y xy^ z:=. c, quae ad 



rationalem perduda fit : 



a* x^y -h b"^ xy^ — c"^ — ^ c^ a b xy ~{~ z a* b' x^ y*^ 



et fpatium quaefitum hinc erit — ^. o°' Sit f-i — 3 et 



vrr 2, ideoque X— 5, vt aequatio fit 

 5 5 



a y x^yy -{- b ■]/ X xy^ — c, 



quae ad rationalem perduda fit: 



^5 ;^3^^ _j_ ^5 jj. j^^3 __ ^5 — $ c^ ab xy -h Sc a^ b* x'-y*^ 

 ct fpatium quaefitum ~ i^. 4°. Sit [Ji. ~ 4 et j' — i , ideo- 

 que X — 5j crit aequatio: 



a 



