93 == 



§. 5. Veluti fi curva AU cliatn fuerit ciiculus^, hac 

 aequalioue expreflus : uu — 2.ht-tt, ob du — ^'J^f^'^ *• 

 erit. 



quibus valoribus- fubftitutis habcbimus 



^ ^ + t - L^:!^^-^!-^^^^ et 



y =: /( :: b t - 1 1) 4-XiLfL.^-l^LrziL) , 



unde eUminando z erit 



xY (^bt — tt) -|-y(6 — t) = b/(2bt — tt). 

 Hinc iam haud difficulter elicitur t; multo autem" prompli-- 

 us ex priore aequatione 



X — t— (^- ) ('"'-^^^: erit enim 



j. I b X ' b 1 ' {a cr — z z)' 



b-'*- i (a :i — z z) 



Ex allera vero aeqtiatione clicitut 



Ex priori formula coQigitur b - t — ^ /,^^a~-^ •') ^ l^incque 

 iam penitus expelletur littera t quadratis addendi>, fcilicet 

 (b.-t)^-f(/.bt tt)^ = bb = LAlz2_±Ji^)ll, five 



(b — x)'-f-jj — b6-j-2bi/(aa — zz)-^aa — -srz, 

 quac aequatio ad rationalitatem perdi fla pracbet 



{xx-\-y y -\-%% — 2 bx— aa)'n:4bb(aa — z%) , 

 quae ergo ad quartum gradura exfurgit,. 



§. <?. Maxime autcm' moleftum, atque adeo fuperflu- 

 um foret, pro quavis cmva A U tdlem aequationem jiiona- 

 lera eiicere , cum omaia fymtomatu liuiusmodi cylinirornru 



in- 



