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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 2
# Folio 69v, page id 00068202:0138
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itaque res six potius:  be + c. P. eut = 1b). e ent et (6) eret + (. d. . ea t - E (bB. e. t.1 1
imo ne sic quidem quare potrus sic:
be = C. e. C- 1. C- 
f+he
ubi est data reliquae quaesita
 Sbiee - 1 fb)e
et fiet. bse + bh +, C eC - _ 112 cC + 1 2C b)feC + hib) C - 1. hb).
fe+ h
et fint ) C = 5(B) et bf ∞ IF2C = - 1f (6) + hlb) et bh + 12C = - 1 hib)
Ex 2 et 3 per 1. fit (41 bf - 14 2 f(b) = - 1 f1b) + h(b) et (5to) bh + 12f(6) = - 1 s(b)
b unde (6to) (6) = bf (6) :b = f:,  142 - 15 + h. (7mo) = -h :, 1. 27 + 1h. ergo ex 2. funt
(1) 1. 2H + ih f = -.  + fhhh seu 1. 255 + hh + 13 ft = 0
g0) hh +, t ft + H = - ff sit h + f = f 1 - 1 se R es h. f = -1 - 1
ergo (bd) ib = 1 1,  2 + Y1 -1 seu (b) 2 b = 1 seu (b) = b
(8V0) 12s + ih f = - 12 - 1 fh ∞hh seu 1. 2 f) + 12 fh + hh seu tit 4 3 5tr + s = - f
(9nd) seu ti a f -H seu h: f = f1 - 1 (6) :b - + 1 - Y- 1, i, D + Y 1(1)
(10) seu (b): b =  1- Y- 1:,  14 f 1 siu _ (b). b = 2f - 1 : 2 seu 6): b =
((c4d) seu (b): b = ( - 2 f. 1 (D, :, p -  seu (6). b = - 1 - + hh + 3hf. + 3 H = 2, s - 255 - L
jam pergendo faciemus
(b) C. e - 1 + (). e. C- 1. -2. C. 3 = ((6). e. 8- 1. e -2
(8) e + (h)
fit h + 3 f = + L fsr b - 142  Tut
seu h: f = -1 si 4 ∞ +
et 16) : b = 1 : 1. 2
seu
(b)=
fit (6) (F) e + (B) h) + (e) ee - 2F 5 E + 2. 3(1) () (b) ee - 2 (f) (b) + (h) (6) e =E X qud vaum est
ex 2 et 3 per 1 fit ) (6. (5) - 2 +3 (5) (B) = - 2(f) (b)) + (h) (bD et (to) (b, hi f 2.3 (5) (bs = - 2 hXbD
unde (6to) (b) : b = (5) :, 2t 2 (5) + (h) = (7noo) +h) :, 2. f) + 2(H). Ergo ex 7. fit
800)  2. 3(55) + 2Ch) () = - 2 1B - E(f) (h) - (h h) seu 2. 3(ff) + 2F3(fh) + (hh) = 0 ere.
 t= e
Chh) + Et3 (h) + 2F5 fs = 243 - 235f = 2 + 5 4 2. 23 ff. fit h + 2+3 f =  +3 fs
seu ( = 2 (h) : (5) = - 2 fit (b): 1) (b) = 2 :, 2. 3 = 22 = 1 ∞:, 4+3 - 2 - 2 - 1
ergo ebD : (b) = 1. et semper huc res redit ub sit ): _b) = 1:, 4 - 3 seu 1 et (h)): (5) C-3
Ergo res tandem egregre sic constituitur
e + B. C Itaque prodit e. e.1 4 C. P 1. C. 2. el. 3 = e. 2-1. C -2
seu e. e- 1 + . C- 1. C- 3 = C. C- 1. e -2
et  jam paulo ante erat et e. e- 2 = e. e-1
Ergo e + e. e-2 + C. C - 1. C - 3 = C. C - 1. C - 2
l + C. e-1. e- 2 + C. C - 1. C-2. 6 -3
e 2
C. 8- 1. C- 2. C. 3, C-4 8. C. 1. C- 2. 6-3
+ 1
2. 2. P. 4. P. 5 expl 3. es +
XH
+ L
+ e-5 =
AXAX
C - 4
C25
C- 1. C- 2. C 3. C- 4. C- 5 C-1. P3. P-4. C5
Asterisci notant  terminos omissot, Nempe si termini sint C, e-1, e- 2, e- 3, e- 4, C -5,
sepe scribetur
X, C - 1, X, C. 3, P. 4, Cus H, H, C. L, H, P- 4, C - 5 H H, K, C. B H, C =s X, H, H, A, B-4, H (-5 ee
quod est theorema per pulchrum, et universaliter verum utcunque termini continuentur
quae est series  quae e tunc cum e est interer abit in productum continuorum, sin sit
finitorum; qun e non sit integer, tunc series ista in Onfinitur continnari pt, sed quaeritur an tunc
quantitati finitae aequetur. Vene hoc non videtur quod non puto, sed nec videtur necesse
ubi duam serierum hujusmodi una alteram dividit
e + C, X, e- 2 + C, C - 1y X, C- 3 + C, e - 1, C-2, X, e - 4 + e, C - 1, C -2, - 3, H, e - 5 = C. 2-1, e- 2, C - 5
quemadmodum e et quod
X et A, Cd C. 1, N  , _. DC
Seu 1 + 2. C-2 + P. C - 1. C-3 + N. C- 1. C- 2. 8- 4 +X. C.1. C- 2. 8- 3. C-5 = p. P. 1. P. 2. . 3. P. 4)
ent
1
a
eoner bee) b15
fit (1)  () (b) et (6) (5) = 2 +3 (C)  (2d 2 2 (f) (bD + (h) (bD et (b) h) + 2. 3 (5) 3 2his b)
Seu 1:, 3-2
Ergo tandem generaliter
e 
1-
Hinc e
seu fe
+