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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 12
# Folio 12v, page id 00068009:0024
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 11r); this page is its left half.
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(10) Sil y a et a - b, il y aura = a =- b
Care il y aura (par 1) a a
Car a = a = b - b  doni (par
VF) s’il y a a a = b, IkG aura a = b
cae Car (par ap. y). a - a = b - b.
donc (par 10) a = Donc (par ax. 1) a- a =
(1R) S il y a a - b = 0 il y aura a = b
aejlulos de purtcete’e Car ( pas A) il y aura
a - b + b = 0 + b donc (par ax 3 et 4) a = b
(3) S’il y a - a = - b il y aura a = b
car a - a = b - b  donc (par ax. 11) a - a = b -a
donc (par ax. 10) a= b (par 11) a = b
(14) s’il y a c - a = c - b il y aura   a = b
a= Car ( par 10) il y a - a = - b (donc par 13)
il y aura a =b Autrement.
s s’il y a c - a = c - b, il y aura c  ta =
C- b + a c a t a = C - c -
adjontons de part et d’autre - c + a, il (par 4)
donc il y aura +C - C = a + a = c - c + b = a
et (par ax. 3) il y aura 0 = b -a, ( donc
par 12) il y aura l =b
(15) S’il y a, ac = bc, il y aura a = b
Car aC = bC (par 3) et a
et bc = b  jam c
2E
(5) aC = a. Car a C = a E (par 10) = a (par 9) L. E. d.
16) s’il y a ac = bc, il y aura a =b.
dire
Car  (par 8) il y aura ac = bc ; st  15) a = b
s’il y a a = b il y aura a = b, car
Car (par 7) il y aura ac = bc dons (par 5) a = b
(18) F’it y a  = G, il y aura a = b
Car (par 8) il y aura ac
18) s’ily a a = , il y aura a = b
Car (par 7) il y aura ab = ab donc (par 15) il y aura b = a
19) 5’il y a a = es, il y aura a - b.
Car (par 8) il y aura  = f donc (par 15)
il y aura à = C ou bien (par ax. 7)
=
aC
Car (par ax. 7) il y aura C = 1. C et (par 8)
Il y aura tC = e donc il y aura à = 
ac
et par consequent a =b
(2) 5 - 12 +t = - 1
=a, b = - ab Nam -a = -1, a. Ergo - a 1b = - 1, a, b = -1, ab = - ab
a  ee a. 1 - a
c a _ =a  1 = a . Nam = a 2,1- 1 = 0
a -a, 1+ = 0 =  ta 
on  (pur 3) e be. 6 = b Gou (par 3) c: b.
a - 1 = a Nam = - a, 1 - 1 = - a1 + (- a -1) = - a + (- a - 1) = 0 = - a + a
ae a
t, + 1
-a Nam a = - a - c. Ego a: -, - - a, -1: - 1 = = a
Ergo (per .. ..)  - a  -1 = a
b= na ib. Nam aba a1, b. Egua: b- 4:, - l, b sed a: -1- a Eugo a  b. = na ib
ene a, - b = ab. N
a: 1 = a
car a  it a. = 1. a. 1 = a
42C = a, 675
a
aCb.C) A +. 1. C C car t. C
ae CkC = a : (b. c) = ac. b
Car 1. (1:C) =1C: c(r. C) 1C = C (per ..)
d b
= a. t
: lb: c)
c = ac car
= a.
4. c = a. c.  = ac. + = 
al
_  = à
ia
4)
lb. a=  20) ab (par ap. 11) - 1
Et L a = a (par ex 12.) = 1. don 1 par prop 6. crol . 7)  a
sod B FC, b
Car 4.
Car foit 4 = d, il y aura  = d (par 15)
a. -
ac
(ur et
et
de
ac
ab
:c = 
soit  soit L c 4= e
l
4: c = d: c. =-
6
Modusb inveniendi demonstrationem, sa
eb  demonstratio hujus veritato
_  :b = ab scribe : b = 
et beb = b mais  b. b =
donc a :b = ab
ons spar
donc a = b a ab P abc. b = acb
a. (V.C) = ac  b a: (b. C) = ac :b
car a: (b: c) = a c: c lb: c) C (b. C) = b ednc
aC: c (b: C) = ac: b
= ad
bc
e car 4 :c = abd. c60 = ab. bc
bc
et CEt. C) = 1 donc 1: Cl:C) = C 1 = C
Alter a . c - a,
coroll. ac - 4.
a
a