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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 31
# Folio 5r, page id 00068244:0009
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si 
N 1+V = 1+ C y + C. C-1 y + e. C- 1. e 2 y dtc et quolibis termino vocato si erit sepers B = A
1. 2. 3
Quolobet jam termino appellato A, et l  , 0 vel 1 vel 2 vel 3 appellato V, est
es
-36. C. d. . 14 = 997. oppeals. B, B Ed, erit B = yA. C. B, : v+ 1  et C - B. C- v- 1: v+2
Ex priore aequatione est: vB+ B= eA vA. fit v- eA B. A+B ex posteriore vC+ C = BC BV-B
seu v= BC - 2C - B∞. B +C. Ergo A+B: Bt C:: est- B: CB. BriC Hinc si relationem
inter quatuor terminos velimus adhibere possumus tollere ev, et e, et y
rursus si sit 1+ Z = 1 + hZ + h. ha 1 97 + R. h - 1. h- 2 G3 esc  et terminos hos appellemus L, M. dtc
1. 2. 3
1.2 
fiet: M = Z L. e - V,: V + 1
Ergo 1+G in 1+Z = AL + BM etc + AM + B N. et C + GN+ BP dec seu EL +A Mi
B2
in
c
126
complehendendo sub A_ omnes ubi rescondentes in se se invicem ducuntur, sub AM, omnes ubi i
qui ieono quorum loca unitate differunt sea primus in secundum, secundus in certium, in
Et ita porro. Oi AL t sron aliter hic exprimitur At BM= XyALCBFV
Unde etiam haberi posset relatio inter AL, BM, etc ex quatuor terminis asspintis.
se ducuntur
loco AL smbea possumus AL +    AL. Ey 2. E. v. h V
rec beni
AM = 2. AL. 6- B, v11 Z- AL. y. E vAZ . V
LB = y. AL. C- B: vtI.
v+1
AN= ZZ AL. h= hati. v. 11YC BB2,. AL Y9. P. V. E. V. L A
LC = yy AL. E. B. C. v- 1. BH Vst va.   h v. h. B 1
AP + LD
(IVAI
= A Jus. e. B. (v. 1. E. v.r +
VE1. 2. B13S Z3. h v. h. B1. h. v  
+ esc
+ dc
+ dsc
vt1. V+1
itaque
sine B. + AC + LD + LE dt C 14 e. V eav. ea va1 2, e. v. . P- 1. e. vot  dsc: H. sed eo casu si incissimus
AL 3. C- v
v+I
v+ 2. v+ 3.
a primo seu si A et L = 1, et v = 0. redit res 14y = 1+ ey + e. C.) y 
3+2.
 Ut 1y et 1+Z per ompendum in se invicem
multiplicemus, considerem, 1B + y + D2 y + 13y + 14 y dtc per 20 + 21 Z + 22 f +238 ec
1+Y in 14 Z =
fiet:  tron y 2 + 1y dtc
12. 20
12. 21
11. 20
Gtacta hor lao 1s 20 - 1.) . e - _ h. t 11. 0 -   1 ) 1x 22  hbot b. 2 11  - h h. B C. 1
2.2
13. 20
M100 e 2
Est autem hoc loco 10. 20-1) 10. 21 - er 1t 20 = _)10. gl = h. h. 1. 11. 21 = h. e 12. 20 - C. e-1
1 21 =  h.  1g0= C
10. 23 = h. h - 1. h- 2.. 14. 22 = C. h. h- 1 12. 21 = 8. 8- 1. 1 19. 20 = 8. C- 1. C- 2.)
10 22 = h. R=1
1. 23
1. 1. 2
10. 24 = h. hat. h- 2. h. 3 11. 23 = P. h. h - 1. fur 12.22 = c. C- 1. h. h - 1 13. 21 = C. (-1. P- 2. h 14, 20 = 8. (-1. C-2. (-3
. 2. 3.
1. 1. 2. 
P.1.2,3
l. 1. 2. 3
1. 1. 2. 2
fit ergo: 1 + h y X br. h a1 Y + h. h - 1. her 1,3 h. h - 1. h. 2. b. 3 1
45 _E.F.
ee
1. 2. 3.4
ubi videndum an possit relatio inter
e et h, reperiri talis, ut relatio
inter p. Q. A detur
10. 20 + 10. 21 7 + 14. 2Y
10- 2279 11.  1y
2. 3
C. h. h -1
1. 1. 2
c.  1. H
1. 1. 2
C. P-1. C-2
20. 10 y
1. 2.3
20. 11 yy
10. 23. 23 11. 21792 20. 12 y3
el
et
etc
1. 2. 3. 4
e. h. h- 1. h- 2 
1. 1. 2. 3
C. e 1. h. h- 1
1. D 2. 2
C. C- 1. C- h
1. 1. 2.3
(-1. C-2. C-3.
1. 2. 3.4
1. 2. 3.4
.
149. 11X