$4 DE METHODO MAX. ET M1N.

bent eorum diflferentialia, si sola applicata Nn, qua? est^==jy^variari & particula n v augeri ponaturerit autem hoc sensud. n = o , quia valorcm n puncto H rclpondentem inde nonaifici ponimus. Quoniam jam n est formula integralis indefi-nita, fit ea = f[Z]dx, & [ 2] sit functio ipsarum x , y, J >,^3 r, s & /, ita ut sit d\_ ZJ = C-^3 <shv-f- [_N~] dy+ [P]d/>•h^Q^dq-^^R^dr + lS^ds-^-^T^dti unde simulyaloresderivativi ipsius d[Z] } nempe</[2'], ^[2"], </[2 w ],&c.per notandi modum receptum formari poterunt. His positis,erit ut sequitur

n =f[z]dxn' = /[Z]dx-h[ZJdxn"-=f[zjdx-h[z-]dx-h[Z'-] dxn'"=/[ Z ] dx ct- [ Z] dx + [ z' ] dx -4- [Z"] dxn N —s{_ z ] dx + [ z ] dx + [ z' ] d x -p [ z" ] dx + [7l n ~\dx&c.

Jam videamus quanta incrementa singula haec membra [Z~]dx,J ~_z '2dx, [z"]^at, [ z'"~\dx, &c. ex adjecta particula n» adapplicatam Nn capiant; quX obtinebuntur ex ipsorum diffe-rentialibus, ponendo loco differentialium Yalores §. $6 Capitisprocedentis expositos: erit itaque

nv. dx.

dx ’

d. [Z] dx ■■

d;rz']dx=i».dx( [ j^-

m

^ x

d x’

4[5!] , iqs^Ix

dx* dx s

d.sZ !, i dx — n v . dx ( d ,

d\Z'"^—n v dx( EO - iÖ + «lO__ I2Ö )

d ‘ L —^ ■+■ dx + dx s- j

jrz^dx — n 2[Q ^ ,] I 3[r] -

- ^ dX n v äx( , dx dxd - + dx * dx *+ ^ '

w/n, , . rx? v i s*!']. Wx

^. L ZJ^ — n ,.dx^[N ] dx + dx > dx^dx* A.X??

d. [_Z n J dx = o,

°* & reliqua, sequenda omnia evanescent.

Ex