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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 139r, page id 00068198:0277
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# Lines: 67 recognised, mean confidence 0.80
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si
sit log. a 1hil
a a = Z X = sdz:
du = dx a seu d, a = dx a
Sit log. b = 1 et log. a = 0
s
sa
s
s
D
N. X qV j X: a
a
ba
dx = dZ. Z
7:a. Ergo
X: a logb = log. a = log. Z - log. a. et
 seu per aeq. 1. et 2 fit X: a = log. Z. seu
X: a = 5 dZ: Z et +X. Z: a = dZ. adeoque ex 7 et 3
1Xia (∞)
fit dx b: a
X: a
1
=dZ. Ergo denique ax bia
0)
c2d
seu ax b:a =  a. b: a (+ C)
pore b: a. Xa  = Z: a X: atlogX = log. Z
1391
(. X: a
seu X: a  sax :X = (dz. Z. seu dx: a + Gdlx: X = dz. 2
(C
et fit dZ = Z ex Z: a + 4,Z. X dx. Ergo summando et
q explicando in aeq. 5. summata per aequ. li fiet
X: a
dx
a bia. X: a = (b: a X: a dx u+  b: a.
X:a  e 16
Ergo per 6 juncta aequalo calculi praecedentis
fit
il
a
a
b:a. X: a dx =  b: a. X - a b: a.
1
=Xda
Generalius sit 1= XanC) qua fiet utique
R.a
dque = s a + n Z. X ax seu Z= (Z: a dx + n5Z. X ax. seu ex1
2
a
b: a X: a = b: a  X: a dx + b: a  X: a Pax
a
o
(4
id  n
Hinc habetur illud memoriale omnes dari summas talium
talis
b: a X: a. ax, qualiscunque sit n, modo sit
rationalis integra, datur enim cum n = 1, ev anescente
X. a, tunc eum habetur summ per aeq. 10 calculi primi;
ergo et datur si n sit 1. Hinc ergo porro datur si
n sit 2, et ex hac si n sit 3. et ita porro Hinc et
vicissim datur si n sit sit - 1. quia posita n = 0 in aeq. 4
ergo et si n; sit = 2, etc
sed quid si n sit fractio.
ut praeparemgue aditum ad alteriora, resumamus
ert et proriontneti a tit srat