174 



— ^ c i/ [ j2 -H (x -/^)] [f 4- (x - g)2] 

 zz: [c-~2CH-i)x^-+- 2 (/— cg) (c— i) x-hf^-i-(r ^—2cfg., 



feu 



2c/[j^-f-(x— /)^J [/ -f- (x - g)^-] 



I=:(C-H- l)jr-f- 2 CX^ 2 C (/-^.§)X-i- 2 Cfg. 



Sumantur denuo quadrata, atque legitimis fadis reduCtioni- 

 bus et divilione per y^ inftituta, reperitur: 



(c2_j)2^2_^4c(c — i)2r^-4c(c — i)2(/4-g)3C 

 -i-4c/g(c=^-Hi) — 4-c^(f + g")=:o. 



Hinc iam patet, problemati nonniii lineas fecundi ordini? 

 vel feSiones conicas fatisfacere. Quo nunc conftans arbi- 

 traria c determinetur, abfciffae a vertice curvae computen- 

 tur, vt cafu xmo lit quoque /==0: tum quoniam in ae» 

 quatione integrali 



U-f->/(j2-}-u2) = Ci;^-c/(/2-|-2;2J 



effe nequit c zn o , in ultima aequatione liabemus : 

 unde refultat 



r — /^-+-g^ -i^-i/f /*^2/^g°-^g^ l) /g-f-ga j^(/a — gS ) 



2/g — ♦^ V 4/2 g2 -' 2/g 



Una itaque radix eft czz|-, altera c zz: ^. Pro priore ae- 

 quatio noftra eft: 



(g2 —J2]2 O ^_ 4 g f g -/)g ^ 4 g (g H-/) (g — /1!^ y Hj 



feu dividendo per i^-iil^ , 



(g +/)V -H 4/ g 3[^ — 4/g (/H- g) ^ == o. 



Cum in hac aequatione literae / et § eodem prorfus modo 

 contineantur, ad eandem quoque exprefTionem perveniffemus,. 



fi 



