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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 2
# Folio 68v, page id 00068202:0136
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1- X A usque ad ne =   +    Z = - E + et P. e. t 1 - e. ert. 6
Ergo si C= 1, 2,3, en. fit + - = ble,: - = +  + - 2 + 3
1 
E82- e 2.9 g0. + eet e)
A. 2.3 - 3e + C. P1  23,4 - 3. 4C + 42 - C P1. e.t
+ C. eet _C. e. 3.  2 et = o+1
Si C. 2 dat 21 5. si (. 3 al 234- 234+ 21 4. 123 
2.24
sed haberi pl ex natura summmationum
in integris ses ostendi  experentia,
quaerenda demonstrati
Nam six   = 8(.C VC B  = 1- 2Z a
Z Ergo ipt E (gdZ est ire, ut asserebatur
et id pulchui lit haec demonstratio, quod nem ostendit, etsi e sit numerus
Ergo si : y ull. = 1 fit L - en = e  
fractus, imo sunu, inio quicunque
sola inductione.
cum Wvallisius cogatur esse plentus
bEodem modo sumuari pt
eodem modo summan pl
1 + - = + 8. C- t C. B. 2. C. 3 ete
1.23  1.23.4
Nam 1+X = f + e x+ e. C. 1 X 4 C, . 1. P. 3 X + e. C. 1. e. 2. C.)  erC
(Xt = ex = 1 si x- 1
t Sida X + E. X = C p  cene R+ canar em X M = (Z.   s 
Haec tam mirabilis pronuitio vera est tam in integiis quam in fractos quicunque sit punee
 sed si integeo sit experientia accurata venficari pb, sin minus appropinquatorit
ia
uti e est integer es et X est 1. prodit regula rocllisiana
1=X dx = dy si tu x - Z fit xax = aq et X = siZ et dy = Z dX: B1. Z
Si X dx - 1X- 18
Siuni ex _ IX - ZX K
Sme d = X 3 + 3X - 1 X 
1-X dx = F Y X - E X + eerat  - C t t g) etc.
Cy eut, P- 2
si oll. A 21. fit Sux ax = 3 Su Ex -13 Sume dix = 2. 95 + sm ap - Et u u uatereri
ele + mee  e et L e = e Ego l.f) BC + m. C. 1 = be.  -1 fit ge + mee -me =qe e
9b
e
mi
pui asuut
9. Hid situ grmalibu) sivere t e eree2
10 e + 2, 8. (-1 =, 11. e. e1 fit
seu fit 20 = 121 sed ila 10, 21 =0. absund
Ergo non licet . 2. 3, vel 112. 3.4. sic exprimere, ut in finitis per se finiatur, seu non
 e fC = We D 
licel pro tali producto afferre valorem universalem. Quanquam nondum rem possin negare
absolute. Si daretur generatis ista expressio simul serviret pro sixx ax licet e esset pur
negativa vel fracta. Itaque hac expressio (I-XX du = 2. 12. en. C.
hisi pro e rationali Ac proinde est expressio imperfecta. Talis earanenda
fiactetur in rationalibus daret serien infiuntam in aliis. Excoritum tale quid candem paus latima hujus
Nolabilis interm haec summatio quod - = = 2
vel hoc 192. 3. 4 - 3. 134 = 3. 12 4 - l. tag
: . 1 - 2 + 1
= 3 quae sunt pulchia Dheoremata, sed demonstratu difficilia
= 1+ - 2 = 8 L - 2 + L - 1 - L + -  2+ L - Z + 3 -  -, - 2 +  4-
=1 -  4 + = - 4 L- 4 +6 - 2 + L, -,  - = +  - 4 + +, . 3 + E - + 
1 = 1 7 = 36 a 1. 47 1 = 3 6.9
+ 5 9 = 4. 8
1 - e + C. C -1
O+ - e 2c
3 = C. 8- 1. C-2 =0
An; 1+Zn; 1. 2
L. = 3 + 3 -1 - 4. 8. 12
= e: . D. C.2  et
= 4, sit 3.21 = E. E. 1. E. 2. E~ 3 ;d E. 1, E. 2, 6.3; 4b. E. 2, 5. 5. B; 4 7. P. E-3
1-X ax =sy dx datur ergo et datum
N datur ey a d B, - Vy dg
= L4 + 6 - 4 + 1 3. 6. 9. 12 et 5- 2 et n impar
Sic ego datur (1 - X dx = y cx
1- X = Hy et X = 1 - y
2  d N, 12. 3us ad e = s, XB dx
idem tamen est, sit e quidem sit numerus 
integer sed n sit fractus
10 13 4. 7. 10. 13
1+I, 1+ Zn, 1+ 3B usque ad 1+ en
2 e, c- T, e- 2, C. 3 er 1   1t C. L 1
1. 2. 3. 4., 1, 2, 3; 1,2;
+ = 2. + = = 2. 4 L -3 + 2 - 1 - 24. 6 ralifer (X- X d
et ib booro uti 1 = = = - 2 + 1 - 1. 2 et 2 - 2 +3 - 1 - 1. 23 et
vel. Hoc esset demonstrandum:
152.3 = 251.3, + 1512
+ - = = 4
17 (, 1 + ea2
ed seem sit serhame m ebm
10. 2le + 20 ect 2oC= 11. Ele  . 2e
non valet
quasismuz sit n