I<ifZ SSSS3S 



M, ut binae iftae lineae aequaliter ad curvae tangentem 

 in M inclinentur. Quem in finem pono A F ~/, ut fit 



T F = T P — A P -4- A F zn t — x -{-/. 



Qjiare cum fit tMMZzMTN, requiritur ut fit 



MF=:TFzz:t — x-1-/. 



Elt autem 



M F = ■/ (/ H- P F) = / (/2 -f. 0^2 _ 2 / X H- /2) , 



et t=:^-^9 unde fequitur: 



yj^H- x^ _ a / X +// z= 12i.2j:L^±^li^' . 



Hinc reperitur 



y^^dy^ — do^P^-^i^xydxdy—zfydxdy^^zOs feu. 



y(3y^ — doi^)-{-z(x — /)Dx3/— o. 

 Ponatur 9y = p9a:, ut fiat 



y(p^— i)-H2(x— /)/3 = o, feu 



_^2£|£— /) unde differentiando nafcitur 



/ — i — p^ 



Hinc nancifcimur 



n {x—f) i^-^p-) dp — pdx^p"^ — 1)= pdx {p^ -h i) (p^— i). 

 Unde concluditur aut jd^ -f- 1 zz: o , quod praeberet valorem 

 ipiius p impofTibilem , aut 



2 {x — /) dp = p{p' — i) 3 X, h. e. 

 Al^ — - ^ '^ ^ ^, , , et inteffrando 



X—J p(l — p2)' o 



l (x — /) zz Z (i -H jd) -h Z (i — p) — 2 f p 4- U. 

 Proinde 



x--/=: g"7»'^ zz «^ — a, feu 



o d 0? zz (a — /-h x) 3/^, 



Y a undo 



