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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 44r, page id 00068196:0087
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In numeris s, B = bxade pe V, B - 1. Ergo b = 5b (b. C- 1) Erx sb x ad (b= (bdi-issen ad b, ut b -1 a 
Ergo SBx da = BX dx : (b lX -1)
in numeris d, X. B = X lb) + b dx. Ergo Lib dx = fe X db) = X, b - s b dx
ad saqulbus est ad sx  x
 aim s (tdex pragressionis Geomessicae, ad eoque summabilis; tty b . bs a e . (. L 3
Ergo sit
ut pax -1 ad dx Ergo SX bxde sua B) dx
Rursus d Xx, b = (2 xdx + dx dX) bF + XX d(b). Ergo (XX. d) (b) = XX. b - 2 sX b dx = sb du ax = (XX. b 
Et ita habentur ha summae. A)  b - V s  (bx- Ergo b Ergo dei
rgo ent fb SXX. b ex = XX A - 2B H . dx L2
A-52
=(dx: B nosito B- (dX: s ar-, 2
Carsnu
In numeris d, b = Bx+x - bx = b =, b -1. (Ergo b. = sb= bb - 1). Et posita
de constante, erit b (dx: , bar - 1) = SbX dx
d, X. b = X d,B) + b dx seu X d (bY) = dCX. bF) = b dx = X. b, bd -1. quam multipti
aequationem Multiplicando per dx:, bX -1. fet et productum utrinque summando fiet
X. bE dx = X. B dx (, b.  - 1) = S b dxdx(i, b  - d) ac denique per canonem praecedentem
pro sbx ponendo valorem, fiet (x. BB a (Xde X b tx. ()
fet pro sb x ponendo valorem fict, l. X. b dx = X. b (dx:, b = - 1) - B (dx:, b  - 1). (+ be drdn :, bt - 1
+b dxdx.
+b. dedx
d, XX. B = XX llb7  2b. X lx = XX b. (b.= - 1) + 2b: pdxC Empo Xx b = RX. b = (37 - 1)) g 2. X. b (1r: 9b = - ) bs l. 1 2)
di niniurdele
-b dx (ax:, fdu
dex d, X. b =- X db) + 3b. Xx x (= X. b ( (b7 - 1) 43 b  XXdx Ly. X b = (X W(t Y 1) 12 + 3HX. b du P X  sudx
+ b dx. Ergo (x. b dx = X. b (dx :3 b  - 1) = 3 XX. b dx: , b x - 1) 3 + 3. 2. X. b (dx:, b7 - 1)  - 3. 2 b (dx:, bX- 1) 2 +
3 (X dx(dx: bdX - 1)3 = 3 X b= (dx:, b  - 1)  + 3 bX dx (dX: , bX.1)3 = BX Axdx (dX:, bx- 1): eu ordinando
et per compendium dx dx:, bax - 1 appellando B, fiet
(X b dx = X( X3 bs B i 3XX b  + 3. 2 X. BX
(LXdx = b= B
SX. bE x = x. bxB - b BB
IXX. Bdx = XX. BB - 2X. bX BB + 2 X 93
_ axDB
X. b dx = X bF B - 3Xx. H 3B + 3 2 X. b. B3 - 3.2. 76 X. 94
+3  b x3
p. Lxdu: 
dx bY = Xt bB +A X ax6X aplxtaX b  rb 
Ergo sx Vx - X 68. 4X  28B, 43 NX V 84 3. 2x b 197 + 3. 21 fr95
F+. 3. Xb x B3 - 7E1B2
-31X. b  BD + 32b 4- 133 b B.
= b dxdxBD
(x b k = X bB - 4 X b  + 4 3 XrbB3 - 4. 3 LXb Ct + 43 2b95
=6Y X(. a BB H4 X B deb - a (3. b dx 4
+4 X. S ax xb F est B apax B
bx dx BB
aid alaxo.
26XX6 d BB +6. 2XV axB - 6. 2. GX A. B1.
+6 bXdxdx B3
+x6 deBB 24 (Ax B
1b dx D
ita continuando poterit inveniri
regula continuationis