MfJL=jc)3c, m}x — dy, et Mm — ■/ (dy- -*-}rdo(^)=id s, 

 pofito nempe arcu curvae zz: s. Du£tis iam normalibus ad 

 curvam in M, m, in punSho R libi invicem occurrentibus , 

 erit M R radius curvaturae, pofitoque angulo MKm~d(^, 

 erit Mm~c)s — MK.d(p. Quare cum per hypothefm 

 iit MR— /5 hanc pro curva aequationem habemus: 



a ^ z= / (df-^f ^:xr)—yd(p. 

 Pofito angulo^ fub quo radius ve£tor et radius ofculi fe in- 

 vicem fecant, feu A M R = v[/, vt fiat AmK. — \\j -{- d \\^, 

 erit in triangulis AMO, KmO) angulus externus 



AOR = v}>H-9a: = \p-f-avp-f-acI), 

 unde fequitur d(p~dx — d \\^. Eft autem angulus 



m M fJL = poo — O M [Ji = vp, 

 ideoque tang. \jy = -^^^, et cof. \p — ^j unde reperitur 



d. tang. vj. JyJjil^^l^, 

 pofito nempe d x conftante; proinde 



a Vjy = a . tang. Vt> . COf- V[. = dxiyBdy-ay^, ^ 



Nancifcimur hinc 



Tifh-T^^y^^T^ylj- dxjdsi^yddy-hdy^) dx{2dy^-+-y^dxi — yddy) ' 



et aequatio ad curvam haec eft: 



unde porro fit 



1 

 (5 j- -f- j^ 9 x^)' = j 3 X (2 3 j^ -f- j- 9 ar^ —j d d y), 



quae pofito d y ~ p d x, abit in fequentem 



3 



dx(p~ -hy^)^z:y (2 p^^d x-+-y^ dx—y d p), iiYe 

 3 

 "dy (p--^ y^)-~y (^p-dy-^y^dy—ypdp), ob Dxi:^. 



Quae 



