MAX. &T Miti. R B L A T I V A> Hf

descendens a gravitate uniformis deorsum, in directione abscis-sorum sollicitatum in medio quocunque resistente celerrime de-labitur , inter omnes alias curvas super quibus descendendoeandem acquirit celeritatem. Est enim s <v celeritas corporisin quocunque curva? puncto , & W exprimit resistentiam medii.Quod nunc primum ad proprietatem communem v =sdx(g-^PV\/( i +/’/'))> ponamus esle dfV = Ud v, atquehaec formula ad Casum quartum pertinebit; erit namque n =v, & z~g~ f- W \/( j +- pp) ,ac dz = Udv- / (I + pp )

+ —, unde erit L — W(i +pp), M<= o, N=Oj

JV±dp

v' (i Hr pp )

& P =5 ■—Sumatur ergo integrale fXJdx\f{i -spp),-f (t ri-??) .

r . sUdx v’ ( I “E PP ) __ TT

sitque, casu quo x=d ponitur, e — "

ac ponatur V = He sUdx v (1 +pp \ Ex his erit formu-

lae v valor differentialis = ny,ix(

di

wvp

n v. d.

wvp

dx V ( i -f- pp )Porro maximi minimive formula

)

\‘(i+ppy

s dxy Ojf- pp ) pertinebit ac } Casum quintum*, eritque Z

yc t -f • pp)

y" v

, &

ideoque n —D, Zc E

^ I q-?? )

VOin].. M=o, N=C,,

& P

äd y

. Deinde vero, oh v ~ sdx ( g +

Wty(i+p/>S)TemZzy^g + W v (I +pp),&d L Z 1

ürf« Vf < + PP) + - js+tJ ) ! unde [H = W O +7P). ■[W]=o.cJri=o, &CP]=. 7r l^ F) • si

JUdxy 1 (i+?p)dxy/(i+pp) _ r

post integrationem fiat x—a.—Je Hy y — ’’

sitqu<f