CAPVT'V.

131

. Scholion.

884. Cum ergo pro M et N quascunqu 6functiones ipsius x accipere“ liceat, innumerabiles hincnacti fumus aequationum differentio - differentialiuiflformas , quas ope multiplicatoris 77? N j inte-

grare possumus. Forma scilicet generalis, quae hocmultiplicatore integrabitis redditur , est Yt vidimus* ' ~ ... 2 f ti - x

ä#+sfe('>'M+ sN ^)+,-l E (*MrfN-WM+ 2 CMf "Ä

ipso intcgrali existente :

Kdj 23 d x 2

^ *3#* + i «f£ + Cf

. rHdxM

)

vbi perspicuum est partem exponentialem constanti Caffectam \trinque omitti poste, cum ea sola ifftproprietate sit praedita. Qiiodsi partem exponentia-

Hdx

M

lern ad algebraicam reducamus ponendo e

- zHdx d L ^ »t MdL , . Mddi

ent -m- — 7- et Nrr: rrzr; hmeque rfN — 7^-^

M

d L d MiLdjc

- LM d L r ,iLL dxi

et Nr:vnde

i.Ldx

ista forma

ddyü X

ddv , dy / d M i dL ) , i.,fddL , dLdW dL 2 . 2CLd*\

dx -d^"l M ^ L *J'Ldx iLMdx Lldx “t wT '

quae per - 4 - 7x7^" multiplicata integral 6

praebet:

M d y 1 , MydLdy , i „ s MdL 2 , r 1 T \

7 dH + + *y y 1 TTTdT 2 -+* L L >

,7- , r. dM_i dL 2 dX - », Kjf

Vel si ponamus ¥ — — — K — vt fit M~lT

erit nostra aequatio differentio - differentiatis

1 dy d K V (J dL _ d L* , dKdL , 2 CLLd*'

dx ir -

. . “ ^ — _i . a JL±± 1

J^d x. iLLdx KLdx ~*

K K

’■)