C A P V T III.

359

qua euoluta aequatione erit

(m+ 1 )P y n dx+{m +i -n)?Sy m+l dx-y m ^d(^ ? _ 0—y m dR — y^dO ^ny^OdS S"

-y^SdR4'W/ 7H "'R</S

hinc fit P</*=~-, e - SdQ_=nQ_dS , idcoqueQ—AS 71 ct dQpznAS^'dS , quibus in membromedio substitutis fit

ES^SrfR-nAS^iS-S^R+wR^oseu - i +r, ~ A S"“' dS -+- R dS zz o , ideoque

dR = -( m 4- 1) A S n ~ :! dS

quae per S 7 ”" 4 * 1 diuisii et integrata praebetR _p (fflH-T)AS"- w -‘

S m -*" n-m -2

Ponamus A=(w+a-»)C vt sit Q=(« + 2-»)CS“et R-BS m - + - I +(;«+i)CS n - , J ideoque ?dx~RS m dS■4 -1 n — i) C S n ~~’ d S. Quocirca habebimus hanc ae-

quationem

y^S(BS m +(»-r)CS n “ J )4-^^4-a-M)CS , y-i-BS ,7I4, +(w+i)CS' I -0=

y in

quae multiplicata per — ^ --- fit integrabilis, ybi vpro $ functionem quamcunque ipsius x capere licet.

Coroll. x.