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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 6
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pag. 4.)
sen (()= b (c) + (b)C
Quid multa. jam habemus l = b () (b (C) + (b)C). Nam 
Nam pag. 1. in jam inveneramus si b = c esse b (c) + (b)C = 0 Namtit = b b) + (6) b = 0 + 0 =0
Sin b -() ( c = 1b) fit b (C) + (b) C = bb + cb) (b) = b + (b) = 1. itaque jam tandem
omni ambignitate remota fiet X = (b (5) Hb) C) + b(9) + (b) c (d). videamus jam A
an Posita b = c sit X = 1, et posita b = c = b) sit X = (d). Nempe
si b =c fit X = (b 1b) + 1b) b) + b1) +b) B. (d) = (0) + 01d) = 1 + 0 = 1
Si b) =c fit X = (b b + (b), 6)) +, bb + (6)16) (d) = (b +(b)) + b + b) (3) = (1) +, 1(d) =0 + (d)= d
seu b = (c)
Aeque ita habetur quaesitum
si sit    ( + L n + (2) (d)
et y = (x) fiet y = (n + ( (d)) = 1 - n - (12) Cd = (1) - 1)(d) = () (e ) 1- D) =  d(4
jam ergo Et y = ((b (8) + 1b) c) + b C) + Cb) C 1d))
italu + (n)(d) = (d. itaque y = (b(C) + (b)C) d X = n + (n) d) () = 1 - n et (d  1- d fiet
YL L _ n + 1+ nd _d Bn =  (∞ CC +1 + nd + (d)
 -) + sid
2= b() AbsC i sit X = (B) + N(d) et y = (X) fit y = 1 - (d4 d) = ( + cd) = 1 1  nd
si X = () + R1d) fit 1E A +  - dd et X = (pd) et y = pd
itaque tandem X = b() + (6) C5 D) et (b (C) + (HC, d) et y~ b(c) + (6) c
Restat ut B  melius quam intio, et sine omni ambignitate seu dispunctiortate
p+ b(c) PC p+ Z + d + 1 LyX)0 = 500- ∞ 10y + 10X
A habentur y et X. Ergo p - + 2d 100 Zd + 10 (2d) et e
d - 1.
Et quidem reperio. hine si ba c = b fiert  p (d), sin _ (C)  b p. cum sit Z =  fiet p = (d)
exprimamus, si licet.
sin c = (b) _ fit Z = 1 et p = 100d + 19d) - 10 - d 100) - 10 = - 10, 1 d) = - 10 d et firt
p = 100d - 10d - d =  d, 100 - 11 = d. verum est ergo quod diximus initio si b - b
ext  fore p = (d) sin C = (b) fore p = d. videamus an hinc sequatur
esse H(C) + P1d) = 1 sune si  cab sit sit per compend b(C) + p(d) = W. fiet
nam fieret (d) = 1. cum tamen sen (d) d =0 cum possit esse quaecunque.
non brevior ipsius p valor haberi possit si 6 = b fit p = 1d)
Nesero an
sin c = (b) fit p = d
Novum et mirabile Analyseos genus est  ex ejusmodi conditionalibus ducere, absolutas
possum semper, sed non sine ambignitte visicum descenditur ad vruteo rationales
b(C) + p(d) =1 sit c- b fit b b) Hdd) = o+  = cet sed hoc non est 1 sed e vel L
At paulo difficitius est omnem evilare ambignitatem
+
et
si b c- b firi Z =0 si c = (b) sit Z=1
0+d
si Zao fit p(d) si Et vicissim si zu efit c- b si Z unde Z = b (1) + 6) C
si Z- 1 est c = 1b) Ergo n Z- 0 est p -1d) si Z = 1 est p = d et rursus
=1 -Z.d +7d (b)C + (p)d An utiliter qursus ad hibe bitur
D) = 1-Z, tud
si p- d est Z = 1. Ergo  ut ante Z  fiebat ex C et b, ita nunc ex p at (d)
Ergo fit Z= Cd) EP) + op. Hinc si ex ob  c = b sit. p -(d) et ob c= (b) fit p= d, fiet
jam Hine vicissim si Z = 0 est c-b
invertendo si p = (d) est Z= 0
Ita tandem aequaio theorema aliquod conveniens sum assecutus.
jam quia (p) = 1- p fiet b() dp + (d) - (d) p = Z seu dp + 1 + dx p d = Z seu p- Z  d +:, 2d -1
seu p = Z-(d)3:, d - (d) sed d - cd) = d - 1 + d et (() = 1 - d fil Z+d - 1, :, 2d -1 = p vrl
b(C) +1b)C =  dp + (d) (B)
sed praestat tamen prior
prop
imd si quaritur quantitus  sit 0 si = b et quaesit 1 si c - (b) R. Erit b (C) +b)C = Z. Ihtiopes
marum sequetu
quod est in integris. Sedmoxsesso lvimus ergo sequentia
ido
to
4to
V
...
90Zd
conditionas
niepps.
invertu
-- 2. g
irit (BX) + bC
2 Erit (2) + Zd = X = (Zd)
2 Erit (Z)d +Ze B
si exo 1:-  c= 1 2 Euto (2) D) +Zd = p. hac novum et
idiiu 1.  e
..-
D......
1- Z- d sole
fo .......
y. quanditas quae sito si c b et e si c b) fit lilcte t b e vg
L. c. d. e 47dC
y= deZ)de 2.
X= Z (cd C) +(Z) d. C
= Ze + (2C. d.e
e
..
ed irso
M al
be  b
DC
i
  cons.  pagi
un valo
em ipsius
ii b c= b) = B) e b = H- dcito fuy -o A x = Y
etxace
nso q+ b+ d) + b7d + b) dte+ ad
si c = (b) = d et 6 () d) sit P i b briu
sibec conveniunt fini
in (0 =4 + b) +b) d + + 1hl0
pyto
eddempositosi ex 1 fit N - 1 Si C-
sin.
ixtie
ave
.-10 erit X 10
 non queniunt frat
re fit que
1= b01 1V) de Hb +6)0) (O= B
 seu fit q ea B, diC, ut  ex b, C,t
o = g + bdHb)d + et d
firt
shalibet 3 quoniunt fiet utige
oy oo=q+ 2b te fit q20
Hu si cxb) et D ~osit y 20 et X =C quade in e b
D21 fit Y= e et X ) stt (din B et d non conveniunt fit
Iam supra si cab =d fit y = 0 et X = 1
o= 9 4b)+ e et sit q= e
et HGdx Huc si b et E quenant est 9 - B. sin
Hac methodo Poteris =Cadt e + esde) bet cnonquamm est que, ergo fit
cb. (d) fit y = C et X= (C) Fy= a)e+ ()de
pergi ad commuam in qua est r, et
s res dignissima est quae producatur, si
modo otium esset
= (2) β + ZC posito B forman
ex e, D, E, ut P est b,C,
suporest ut quaeram
a fi 3 plo quonaus 2 a 7
sit