7$ DE METHODO MAX. ET M1N.

Ex quo jam apparet, fi insuper fuerit R = o j tum etiam, quar-tam integrationem locum habere, & ira porro.

Casus IV.

66. Si fuerit Vf= o , ita Ut sit ^2= Ndy + Fdp + Qdq*4- R d r -f- S ds -f - Scc.

Aquatio pro curva quassita ante prodiit o = N — — -f.’A d Q d' K. . ^ s

4 -

&c. qure multiplicetur per dy =;Ndy - R dp - Qdq —■*

d x* d x l d x*

pdx , & tum addatur dZ —

Rdr —— S d s — Scc. prodibit.

° = ^ Z - ft ,F + t%Z-t*£+

- P dp — Qd q Rdr — S d s

cujus integrale assignari potest; erit enim

■ A+z—Pf+itfc

q dK q ddS

dx dx*

-— Rr +

o

Scc.

dx d x*

d x

rd_Sd x

vel o -=A+z

pd*S

— Q.dp pddK — 3p3K 4 - Kddp' d x % -

+

d x

d p d d S 4 ~ d S d dp -

Sd*p

d x*

Scc. cujus termini,

quomodo ulterius progrediantur, si in d Z insint sequentia diffe-rcntialia Tdt } Udu Scc. sponte patet.

C A

SUS

V.

67. Si sit & M~o> ScN= o; ita Ut sit dZ~Pdp -piQdq R dr Sds + &c. _

Quia est N = o 3 una integratio per casum primum institua-tur i