C A P UT II.

37

Av aequetur alicui feriei «v A.x+k Ax 5 + 1 Ax 3 -fetc. (84. §.); patet, de-bere dari alios finitos coefficientes M, ; N, O, etc. independentes a Ax, proquibus ob C 34 - §•) fieret Aut=Pg v A x + M A x 2 + N Ax 3 -fO Ax 4 + etc.,et ideo «u=P«v (82. §-)-

88- Corollarium 5.

Pro u~Av a -f-Bv b -|-Cv c + etc. et quavis funftione v variabilis abfo-Iutae x e fiet Pt=a A v a “ I + bBv b " 1 + cCv c_I + etc., et £u;=PeV(87- 66. §.).

89. Corollarium 6.

Hinc generatim polTumus ftatuere, exponentem rationis differentialiscujusvis fun&ionis <p datae per variabilem z, fi ejus differentia pro certisquantitatibus p, q, r, s. etc. independentibus a Az fit A<p~p Az + q Az a+ rAz 3 + sAz 4 + etc., debere efle e(p^=pez, ita ut exponens ez autunitati, aut alicui quantitati finitae aequetur, prout eft z aut variabilisabfoluta (4. §.), aut certa funftio alicujus variabilis absolutae (83- 87- §0*

90. Theorema.

Exponens rationis differentialis produiti CZ ex quacunque /unitione Zvariabilis ab/olutae x in quantitatem conflantem C aequatur producto ex ex-ponente rationis differentialis /unitionis Z in eandem conflantem C, feu efls. • C Z •—. C £ z.

D e m 0 n ft r a t i o.

Eli enim A.CZ=CAZ (21. §.) =Ce ZAx + Ck A x a + C 1 Ax>+ C m A x 4 + etc. 1,84. §.): igitur e .CZc=CeZ (82. §.).

91. Theorema.

Exponens rationis differentialis Jummae Z -)- C quantitatis conflantis C etcujus cunque /unitionis Z relatae ad variabilem ab/olutam x aequatur expo-nenti rationis differentialis ejusdem /unitionis Z, /eu efl e (Z -fC)z=£ Z.

D e m o 11 ll r a t i o.

Cum fit A(Z+C):=AZ (21. §.) — sZ Ax + k Ax 2 + 1 Ax 3 + m Ax 4+ etc. (84. §.); debet efie £(Z + C)=sZ (82. §.).

92. Theorema.

Exponens rationis differentiatis /ummae plurium/unitionum P,t), P,-Z

unius variabilis abfolutae x aequatur /ummae exponentium rationum differ en-

E z tialium

x