AD CURVAS INVENIENDAS ABSOLUTA, ii 5

valores §.30 indicati substituantur. Quoniam autem insuper in hsecdifferentialia ingrediuntur dn^ dndn !', &c. ponamus eo-rum valores ex m» oriundos tantisper, donec eos inveniamus ,este hos :

dndn'd n"

n v. «,

n v. 6n v. y

dn" = nv.dr{ v ■ = nv. edri' = »y. £

Hinc itaque erunt valores disterentiales

dri" = nv. *dri"* = nv. $&C.

d.Zdx = »y. (Z« -f- )

dx

d.zldx = (z'6 4- 4 -—)

d x d x '

d.i' d* = ^ si'y + ir — -|1 + ^ )

</. Z"' d x = # y. d xd. Z n ' d x = # y. x L n, sd. t' dx = »y. ^x. Z v £

&C.

Ut nunc valores litterarum «, 6, y, </, k, &c. definiamus 7notandum est este d n, <3?n 7 , &c. valores distcrentiales

quantitatum n, n', n% &c. Est vero

n = /"sz]

n' = f[_ Z~]dx + [ Z ] d x

n 9 = J"\_Z~\dx -j— \_^~\d x -j- £Z im Jdx

n r// = s[Z)dx -\-\_z~\dx + \_z!-\dx + l&ldx

&c.

ibi/'[Z]^A:,per hypothesin, a particula n y non afficitur. Va-ores igitur distcrentiales formularum [Zjdx } [Z' J dx , [Z"y*&c.imt investigandi, qui erunt

* 0

P

2

df. [ Z] dx