177 



P r b l e m a II. 



\. Â. Si ex puncto Y hynerbolae ad asymtotam ducatitr recta Trt. v. 

 YZ axi CB parallela , invenire excessum asyintutae CZ *'*■ '• 

 supra curvae arcum AY , quando punctum Y in iiifini' 

 tuin proinovetur. 



S o 1 u t i o. 



Posito serniaxe ACnza, abscissa AXrzx, applicata XYrzr?/, 

 fit aequatio pro cmva 



7iy zzz Y 2ax -\- xx , 



quae pro casu x^^oo dat ny^noo, tum vero est tang.ACZm — , 

 sin. ACZ zz: -^ — , CZ zzzyVl -\- nn. Pro arcu vero , ob 



X zzi V miyy -(- aa — a et 



nn V(9y 



y lin » -+- aa 



fit elemcntum 



.sive 



ds — dy V i -\ 



5^ =: 3?/ ^ 1 H- nn 



yy_ 



yy -H 11 



•i/i a a 

 nnjyj ^- aa 



hinc 



QZ- AYzzifdy [/^+7 - ]/„»+ 1 ÎL"^ .3 



quae formula et'am ita repraesentari potest : 



CZ - AY =z y nn 4- 1 fa^ [1 _ F 1 '"^ . ■^^],. 



Ponatur , brevitatis gratia , 



nn . aa 



, — — ni et , ziz uu , 



nn ■+- I nnyy -|- aa ' 



atque ex prima positione sequitur fore 



Mémoires de l'Acad. T. IX. 



V i — m 

 23 



