^6 G. H. C S T J' R D E N S 



§. 4- 



De Superfich Paraboloidis. 



dy p dy^ p^ 

 Cum aequatio Parabolae sit j* = /);c, esl ^ydy ■= pdx^ inde ^- = — et — ^ = ~^% 



rfS = i:i7rdx^{^-L 4- g) = a^^^^^(l£^'j = r^*V'(4/>*+/'») 

 S =f^y^dx^{i + %)- f^dxV{.\P='-\-f^ 

 = -i££±^' + Const. = ^ +£!I^ + const. 

 Pro « = o, fit Const. = — rTp') adeoque 

 Superficies Paraboloidis S = ^^{r^^—^ — /")• 



S. 5' 



De Superficie Sphaeroidis, 



Si Spbaeroidem quaeramus , quae oritur ex revolutione Elllpseos circa axin mino- 

 rem , debet in aequatione solita b cum a permutari , ciim hcc casu abscissae supra 

 axin minorcm constituantur. 



Coraputatis itaque abscissis a centro ElHpseos, ejus aequatio in casu proposito erit 



a- • 



•f = ,-2 C^*— *^J; adeoque: 



9.b^a^xdx za^xdx , a^xdx 



.ydy = -^— = - — ^,- ;ydy = - -^ 



_ a^^xdx ci^xdx _ axdx 







,. a^x^dx^ ,o, .»_ a^x^dx^ , , . _ o''X^dx^ -\-hHb^ ^x^)dx^ 

 crgo df = ^,-^,-_-,-; dx-Jrdy _ ^^a:--.- + -^* - i=(«»-,«; " 



- b\b^-x*) i»C«»-^^; 



