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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 73v, page id 00068195:0146
# Scan: The same scan as fol. 72v (00068195:0144), where its text is given.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=146
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 58 lines, status machine
# Lines: 58 recognised, mean confidence 0.88
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

1.1 = 1. Nam 1. A = 1 sit a t  n = (per AX. 8) sit a = 1 fit 1. 1 = 1
t
E 1: 1 = 1. Nam sit a =1 A aeqvalibent 1: 1 = a: a, sed aequiralet a: a  =
(per ax. 1) ergo 1: 1 = 1
0 =0. Nam O∞ t. 1 Ergo it Nam a 0-0 = 0 (per ax. 9) = 0+0 (per ax. 5)
aequival:
unde Ergo Epet ex 0-0 = 0+ 0. Ergo (per ax. 2) -0= +0
-a =a e a a et a = d aequivalent. Nam aequiralent - a = a et +a - a, = 2a
∞1
aquin (per ax. 2.) aequi. o=2a aequival. 0. 2= a aequival  t.2 = a qu 16 al. O= a
(11) 1: b, 1: d = 1: bl. Nam 1: b, 1: l, bl= 1: b, 1: l, b, l = (perl3) b, 1. b, l1. l =
per 12) b: b, l: L = (per 11) 1, 1 = Cper 8) 1)b. Ergo jungendo
prima ultimi 1: b, 1: l, bl = 1. Hinc forro (per th. 12) 1: b, 1: l, bl, : bl = 1:, bl.
Ergo (per 11) 1: b, 1: l = 1: bl
(12) a: b, l: m = al:, bm. Nam(per 12) a: b, l.m = a, 1: b, l, 1. m = (per th. 3)
al, 1: b, 1:  = (per th. 11) al, 1: bM = (per 12) al: bm
ver 12
(13) Ca: b) + (c: b) = atC : b Nam a: b = 600 a, 1: b et
c: b = c, 1. b Et (a, 1. 6) + (C, 1.b) = (per 6) atc, 1. b = (per 12) ate, : b
Aequivalent
et
(18) s  a: b = l: m erit a + b, : b = l+ m, : m. Nam
a: b = l: m aequivalet (per 2) (a: b) +1 = (L: m) + 1 A quod aequivalet
(per 11) (a: b) + b: b = (l: m) + m: m quod aequivalet (per th. 13)
a +b, : b = l + m,: m
(7) a0 = 0. Nam a0 = (per 9) a, a - a = (perth. 4) aa + (a, - a) = (per 6)
aa =aa = C per 9)0
(8) - a, - b =  t ab Nam - ab + (a, - b) = (per th. 5) 
+ (-a, b) + (- a, - b) = = a, b - b = (per 9) a0 = (per th. 7.) O-sr
=(per 9) - ab + ab. Ergo prima novissimis aequando- ab + (a, - b):d
= -ib + ab Ergo (per 2) -a, - b = ab. Hoc est quod vulgo
dicunt, - in = facere +, seu = 1, -1 = 1, ita - 2, -3 =6
(9) a : b, c = ac: b Nam a : b, c = teb, ac (per 12) 1: b, a, c
=(pertZ) i ac  1:b
1: b, ac (= (per 12) ac: b Ia 2: 3, 4 = 2. 4: 3 = 8: 3
a. C:C = (per
= a. Nam ac: C  aC (per, C
bm  dt:  1: b, 1: t = p Nam 1.b, 1: l, bl = bs stib. :l, b, l = b, 1.b. l. iel a
10) aC: C
14) () a . Aequivalent a a = C et a: b = C :b. Nam
e
a: b = c: b aequivalet  (per 12) ipsi a, 1.b = c, 1: b qua
per 3) aequivalet ipsi a = c sic si a = 2 erit a: 3 = 2: 3
(15) (14) Aequivalent a: b = l: m et am = bl. Nam sper 3
16
aer
aequivalent a bb a: b = l: m et abm: b = _ lbm:m
id est (per th. 10) am = l b
) Aequivalent a: b = l: m et a: l = b: m. Nam (e
(por 3) aequivalent a: b, = l: m, et a . b, b.l= l.m, b il id est
th. 15
(per 10) aam = bl et (er itemque hoc et (per 11) a: l = b: n
et (per th. 15
18) Aequiasi a: b = l: m eritt a: b = a + l:, b +m. Nam, quia
(per dof. aequal.),
a: b = l: m (ex hypothesi) erit qm b (per th. 14) am = bl. Ergo (per 2) a0 + a =
ab + bl  id est, a, b+m = b. 4+ Er (per th. 14) a: b = a + l,:, b +m
17) si a. b = d l. m erit a