14

CAPUT I.

3. Et (i pro quocunque indeterminato numero n, literis k, 1 , m, etc.quantitates independetites a variabili z denotantibus, potiamr Z" — a"+ na n - 1 bz + k z 2 4* lz 3 + m z 4 4-etc.; poliibPes debebunteffe alii coeffi-cjentes «. /3, y, etc. independentes a variabili z, pro quibus fleretZ" + I —Z'\ Z — n n + I +(n+ 1) a 11 bz + «z 2 + / 3 z 3 + y z 4 + etCy ob (1

Hinc vero (2) (Z) et ^Zl. §.) evidenter sequitur, quod demonftraridebebat.

33. Corollarium 1*

Differentia cujuslibet funftionis u = A + B v + C v 2 + D v 3 + Ev 4 -f- etc.variabilis v erit Ayr= A + B(v-t-Av) + C(v 4 -Av) 2 4 'D(v+Av) 3 + E(v-j-Av) 4+ etc. —u (20. §.) =(13 +2 Cv + 3 Dv 2 + 4 Ev 3 4 -etc. 3 A ■ +a A v 2 4-/3 A v 3+ y A v* + etc., pro quibusdam coefficientibus «, / 3 , y, etc. iudependentibusa differentia Av (32. §.).

34. Coro 1 larium a. 1

Datis quoque binis funftionibus <p == K + E w + M w 2 + Nw 3 + etc.i»t=;pe-(-qe 2 + re 3 4 -se 4 +etc., poflibiles erunt coefficientes a, / 3 , y, etc.independentes a quantitate e, pro quibus fieret <£> K+ L p e+ ct e 5 +.3 e 3+ ye 4 + etc. (32. §.).

35. Problema.

Invenire feriem aequalem logarithmo /unSionis u — x-f-z pertinenti adfyflema indeterminatum.

Solutio.

1. Sint A, B, C, D, etc. coefficientes, pro quibus et quovis valore va.riabilis 2 debeat fieri.

Jog u~A.z + Bz 2 4 -Cz 3 + Dz 4 + - - - + Pz r -f Qz r + I . .. >

2. Extare debeuunt coefficientes cc, /3, y, S, etc. independentes a diffe-rentia A z variabilis z, pro quibus fieret (33. §.)

A logun=(A + 2 Bz + 3CZ 1 4 - 4 D z? -j-f- r Pz r-I + (r 4 -i) Qz r ) Az

4 - oc A z 2 4 - /3 A z 3 4 - y A z 4 4 - i A z 5 4 - etc.

3. Eft autem A log u log u 1 — log u (20. §.) “ log (1 4 * z 4 - A z)

— log(i+z) (19. §-) — Iog(l + ) :

etiam

A log

A A zI -\-z

4 -

B Az 2, CAz 3(x 4 -z) 2 + ( i 4-z; 3

ob (1.) deberet ergo effe

DA_z 4

(i4-z) 4

4- etc.

4. Quam-