# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068009:0011
# Permalink to this reading: https://leibnizlegible.com/page/00068009:0011?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 12
# Folio 6r, page id 00068009:0011
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 5v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068009&page=11
# Source image: https://digitale-sammlungen.gwlb.de/content/00068009/jpgs/default/00000011.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 70 lines, status machine
# Lines: 70 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

signes d’Egalite
segues d’Addition + a + b. B+ 2-5
de subtraction
deMultiplication.
de division:
a- b P 2 =1
a. b = ab - c 3. 2 =6 =  à b = 322
c. b - 4
6-3
On a contume d’ometre + au commencement ainsi atb, = + a + b
aFa = 2 a 2a +a = 3a et. C’est torigine des Nombres
atao
oeaa
 anaca ince
1- 2 L -1 pur 1-
 a+ b = bta a - b = b+ a
ab = ba 2.3 = 3.2 =C
020
a
1+1 = 2 2+1 = 3 3+1 =4, etC.
971 = 10 10+1 =11 etC
a
a ea
   ab = ba 3. Z 3∞6
 atb= b+a
1-1 =e Pre
-2 = - 1 Nam 1 L. Y 1H = 0-1
Axiome
() +a + b = + b + a siosi 3+3 = 2 + 3 = 5
E)
(3)
aeuc rceres
a- a = oaHI 1 - 1 = 0 2- 2 =0, etc.
O+ a = a (ot1 = 0 ot2 =0.
(4) ab = ba Ainsi 3. 2 = 2. 3 = 6
, = (2 = et A 4 (7) a, b+c = ab + ac
(5) 8g. = 8 Ainsi  01 = D 02 =0 etc.
s)
deux egaux, leun peut estre mes à la place de l’aptre dans le Calcul
ta - a
 aela AZ d CC)ahiE= ab Ainti
S)  a = b cet arc = brC et ac bc et + = b
vant
18) ( a - b vant ac = bc
2. 3 = 2. 3 = 6
Z.1 et eut etre pris à la place del autre dans le caleul
Ba - g. - b, vant R=
i Dem
tulatuDemq
ut
estre adjoulé oste, multiplier, diviser, peut istre appee considere comme une grandeur
considere comme 1C. par exemple o LrC affectée du signe +
vel -1 = +, en marque par une ge maique
que de ontandent le affectee
Ainsi on peut au licu de =D, -c + ab - a
un
mettre +f, ou quelque chose de semblable; et viceversa
proposisi hne a - b = - b + a  soa bL ut C
Soit (par la demande) -b = + c. done a b = a + = (par l’apiome 9 )
or atC = C+ a (par ax. 1.)  or c+ a = - b + a (par la
demande) donc a - b = b- a. Ce qui qu’il falloit demonstrer ou bien Z. 2. d
(parla demande)
proptoc ccar
prop. 2. 0+0 = 0 Cur soit 0 = a (il y aura donc
0+0 = 0+ a (par la supposition) Or O+ a = a (par ap. 3)
 et a = 0 (par la supposition) dons 0+0=0. Ce Q. E. d
ut soit  0-0 -0 (par ap 2)
Car +0 = 10+0 (par ap. C CA 10 = 10 - O (par ax. 2)
0 ec = +o+C (par la supposition) = C (par ax. 3) = 0 (par
udpostius a1d