CAPUT //.

45

114. Corollarium Z.

Cognito autem exponente differentiali logarithmi naturali» datae cu-juscunque variabilis u, fi is ducatur in modulum autlogarithmorum vulga-rium (43. §.)» aut aliorum logarithmorum artificialium, obtinebitur expo-nens difterentialis Jogarithmi vulgaris, aut alterius logarithmi artificialisejusdem variabilis u (109. no. §.).

115. P r 0 b 1 c m a.

Conjideratis finu et cofinu arcus variabilis <f> inftar duarum /uisSienum ejus-dem arcus , invenire exponentes rationum’differentialium iis funSHonibusdebitarum .

Solutio.

Funftiones ejusmodi habentur in (59. §.), et illarum differentiae m

(56. §. 6. n. 57. §. 2 . n.): nimirum pro certis coefficientibus M, N, O,-

p, q, r, etc. independentibus a A(f debet effe ASin(p:=:A<PCof(p + MA<p 2,NA<p 3 +OA(p 4 + etc., et A Cof<p=— A<p Sintp + p A <p 2 + q A(p 3 +r A<? 4•f etc. Quidquid fit ergo (p, variabilis absoluta, aut funftio quaecunquealicujus variabilis abfolutae; erit per (89. §-).

e Sin (f>~e (p Cof(f>. eCof=: — etpSintp.

116. Corollarium 1.

Cum fit Sin v - —1— Cof<p et€ofv<p=i—Sin §; obtinebimus per(91. II5. §.) fequentes exponentes differentiales:

eSin v (p=e(pSintp. *Cofv <P~—e<pCof<p.

117. Corollarium 2.

Eft porro Tang<p=^|, et. Cot per (108. HZ- §-)

debebit igitur effe.

» Tang <p —~^T = «<P Sec $*.

« Cot <P———-PCofieccP».

H8- Corollarium 3.

Denique eft Sec(prsCoftp- 1 , et Colee----Sin-"'; per (104.1 15 -$•)inveniemus ergo

e Sec - — = e Tang tp Sec tp.

- c°kc - -- - e Cot <p Cole* -.

k Z

1x9. Co-