CAPUT VL

m

Eo autem determinato cafu, quo fuerit m=n — i In (ZZ2. §.), fiet

™Ji£rch= c - ir'(>+ bC ° ! v-

333. Corollarium 3.

Et pro m:=o, ns=2 in (330. §.) elicies inde per (290. 294.5. IV.)fequentia notata digna integralia.

Si eft a >b.

fx

(a + bColip^ —

=c _ cor-i+igf!-.

(a 2 —b 2 ) (a+ bCoftp) ' / (a 2 — b 2 ) 1J

Si eft a ■< b

*<P

b. f-

=c+

(a+bCoftp ) 2

b Sin <p _ a_^ X b+aCoftp+Sintp.'/' (h 2 -n 2 )'\

2 —a 2 *) 1 v a + bColiiup y

(b 2 —a 2 Xa+b Col'<j?) \[ (b 2 -

334. Corollarium 5.

Eadem prorfus operatione, qua in refolutione problematis praece-dentis fumus uti» obtinebitur fequens transformatio.

x‘:= a -f b Cof Cp.

*<pCof(P m 1 fx — a) m e x

(a+bCoftp)' 11 b m x n ^(h 2 — a 2 + 2ax — x 2 )

Atque hinc fit perspicuum» exponentes differentiales hujus formaefecundum principia quinti capitis perfefte integrabiles futuros, fi m fitnumerus integer pofitivos, et n numerus quiscunque integer, pofitivusaut negativus. >■

335. Corollarium. 6.

Abibit autem haec formula (334 §} pro an=b in sequentem.xr=a-t-aCof(p=ra (1 —Cof<p).

£(pCofty m _ 1 (x—a) m e<

(a-faCof ®) 11 ~ a“ ' ~ 2n + r

x *• V*(2a — x)

Unde patet» pro quibus numeris m, n, quave determinata methodo ex-ponens hic differentialis perfefte eft integrabilis: nimirum per praeceptaquarti vel quinti capitis, fi m eft numerus integer pofitivus» et n aut nu-merus