86 COMMENTATIO 



quitur a centris radiorum abfolutorum curvaturae 

 iion conformari posfe hanc illamve evolutamcurvae. 

 Quoniam vero centra horum radiorum , qui dicun- 

 tur abfoluti , confiderantur tanquam fita in commu- 

 ni fectione plani osculantis et plani normalis , hoc 

 modo radius ejusmodi reperiri potest. 



Pofitis dx d*y—dy d*x-=zZ , dz d*x—dx d z zz=T 9 

 dy d*z~-*dz d x y=. X et mutatis x' , /, z' in 

 «5 /3 » y ■> est aequatio plani osculantis i) 

 X(x~*)+rtr- /3)+-ZCs-*y)c=a 

 et aequatio plani normalis vcl aequatio </$== o 

 (x — *) dx + (j — /3) dy-t- (z—y) dz=a , 

 unde derivantur 



Tdz-Zdy , . n Zdx~Xdz, 



*-«=> xdFrdx <*~*> •^255=*» l*J*> 



fi hi valores in plani normalis aequatione differen* 



tiata , quippe quae est 



{X'<*)d*x+(j -fod*y+(z~ y)d*z+dx*+dy*+dz*z=x>^ 



pofito dy* ■+- dx*+dz* = ds % - ^ fubftituantur , obti- 



netur 



CXdv-Tdx) M 

 z—y = — - ■•' D d*s , 



in qua aetione extat D ss (7V/z — Z</y) ^ 2 ^ 



H- (Zdx—Xdz)d*y , + (AV)-— ftfe) rfs, Ergo 



(Tdz-Zdy^di- n (Zdx~Xdz)d*s 

 *— «=?— ^ etjH3=a , — ^ ^ 



Jrlisce valoribus fubftitutis in S =(.v— <») 2 -t- (y— jS)*- 



-*-(* — y)% obtinetur 



• 5 4 =. 



j) Conf. a«quatio (i) in j. as t 



