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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 160r, page id 00068196:0317
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=317
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.
x+I = A+ ID Xt m - fD+ nD Xt n ∞ n
C11)+ l   ln C Cmp
107 + na, 20Z+2a 10Z+1a, 30Z+ 3la
50F1)
lfS+ mD
b = 4027+ 4142+ 42aa. D = h02Z + siaZ + 52aa
2ozt2a, 30z+3 a
2 10. 30a
-00. 50m
F, 20.30a
-00. 50n
- 10.30 a
11. 20
IL 1. 20
= 10. 31 a = 00. 51m
H1. 30
= 20.31a = 005In
21. 30
(F102n
170.304  11. 20 a
20.30a dtp
1.300
H. 3 S
18ga
pro3la
l2. 30
M -  00. St. 1 m) m-n
em
410. 30 (l-m)
20 = 4.
A. K
10_ (m -x)
2) CLm)
(10. 11. 31 (L n) (10(m- 1) +30 (1- m)
. nAI. 10.30 ((- 1) (1 (m nD 131 (1 1))
in hac aequatione
substitui deb et
valor ipsorum
20 et 21 inventus
Unde fiet
f0+nD
= 11. 31 a -00. 52m
= 21. 31a - 00. 52N
lam
H1. da
2. 31a
M - n
1 - m)
11. 31_ (m. n)
+10 _ (m -n
1314Cl - m)
(eo pi ltaz. tua x Bo nostua
(31 10. 30 (l- n) (1(m - n) + 31 (L m))
= M. l 30. 11. 31 (L- 1) (10 Cm. n) + 30 (l m)
An), C (10. 2 +11.30) (10 m- 1) 130(L. n2) (1 (m - n) + s. (2 m. 3)
( 1) ( (10. 31 + 11.30) (10 (m n) 430 (1 - m) (a lm. u) 31
fiet 10 (m -n) +30(l -m), 11. 31, 1om - 1on + 30 L - 3om = 10. 3l, 18(m- n) u(m - n)
Totu aequatio dividi potest per 1- n
II (m - n) + 31 (L- m), 10. 30, 1m = Un +31 L - 3m. 1130 30(l - m 31 (L- m
Seu 10(m -n) = CL- m) , 1. 31=
 Cm- n) +31 (r m), 10. 30
(5) (23a
4o taz. Mfan  1  sE corpuics u
40fZZ +41 faz + 42 faa  10. 7973 + 10. 21 aaZ + 11. 21  son Vt simjisi ma
(1)
50lZ2 + 51laz. + 52 laa
-00. 50l
+10, 20a
Bl - m
c
1031, 10 (m - n) + 30 ((-m), 11 (m- n) + 31 ((- m)
11. 30
Si fierit 11. 31 = 10. 30 et 10. 31 +11. 30 =
10.30 = 11. 31
Nongs
IIY + 131 a =
(sed ita nimium supponitur
feret 10 Cm - n) + 3ol lam m) = +, uCm - n) + 31 C l - m
sifieret 10. 31 +21. 30 = 2 f1B. 11. 3031) 16.31 + 11. 30 (2.10. 31. 3031 = (4)0. 11. 30. 31)
fiet 10. 31 = 11.30. quod non lic fiat 10. 31 = 11.30 quod non . est
si sot 31 = 0 fiet 11 (m- n+ 10. 30 = 11. 30 (10 (m - 1) + 30(l - m) 11 (m - n) sd ha lice
p- m
. l- m = A
compendii H(m - n) + 3C (L- m) vocetur 131 a, et  13a = 31X= ur
fiet, r = 1oY + 30s, 11. 31 + 131 a 10. 30 = (10. 31 + 11. 30) (- 10Y + 30A) B1 a
seu (. 10.10. 11. 31YY, -2. 1, 90. 11. 31 rA + ((0. 30. B31 a 10. 31. 131ar 10.30. 11. 13I ar
1050
+38. 11. 131a) + 16, 30 31. 31 ad
10. 3H t 31 (ar +131a) = 2 10 34 11. 31 rR  - 30HIAY. finz, 10 31 +u. 30 - x10 30. n7
30. 30. I1. 31 AA
31X
se W. 31 = 11. 30
baque non surcedit inquisitio
Xap. S0+ p
FH. 2a
11. 3 a
11. 31 -10.30
00. 30=