r JD CURVAS INVENIENDAS ABSOLUTA. §5Exemplum III.

17. Denotet JT superfetem solidi rotundi ex conversione curva a hcirca axem A Z orti, qua <y?#/sydx\/(i+pp)> hujusquesuperficiei sunclio fit quacunque Z, invenire curvam , in qua prodata abscissa A Z = a, maximum minimumve fit { Z d x.

Ob dZ ^=Ldn , erit L functio ipsius n = sydxfi (1 +pp)i& ob du = y dx fi { 1 + pp') fiet [ZJ =y fi (1 +pp ), &

^[Z] = dy fi(1 +pp) + - unde erit [M] = o,

c^]==vci+^)i [i 3 ] = v"( i+fi)" ? rdiquI valorcs

[QJ 3 [-R], [ 5 *], &c. omnes erunt =0. Quocirca pro curvaqusesita ista habebitur aequatio : o = (H — sL dx'yfi {i-\-pp)

'— _L d, -r (H — sLdx). Ponatur, brevitatis gra-

dx fi( i+tf) J

tia, H — sLdx= Vi erit Vdxfi ( i+pp')Vpp dx _j_ Vydp f y p dy

ypy

fii^+Pi)

+

+

fi(i+pp)

fi ( 1 + M )*, seu V d x =

■Ldx.

(i + PPs ::

^ + = dbjr=

Ponamus este Z — n, ita ut maximum este debeat sdxsydx%/( i-{-pp)> erit L = 1 & sLdx =x, atque V =a—x 3

bb i? = a. Erit (4— x) dx = s'Vt fiL — ypdx.SiV

1+?? .

'a—~x=ui erit -A-——^=—/ctW 5 atque habebituristaaequatio,0 = udu—ydy + Jllsj f eu u d u * dy - V

Ponatur «==« erit du-=e dt , 8 c ddu = o

= e*{ddt +dV ), feu ddf=. — dt 1 ;porro dy=ie t (dz-^-zdt)

t

& ddy===.e{ddz L J i-zdtdZ’')i quibus substitutis, oritur

—-

o.