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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 13
# Folio 2r, page id 00068010:0003
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auteras aeqnalia, et teridua sint ae-
qualia, qpsae quantitates sunt aequa-
les. Seu: si sit a - b = l = m Et
b = m erit a = l
Nam Si aequalibus a - b = (ex hyp. D)
l- m addas aequalia (ex hgc. 2) b et m,
nempe priori b posteriori m, fient
(per 10) aeqnalia a - b + b = l - m + m
id est (per 11) a = l. _. ED.
14) Theor. Si ab aequalibus auteras
duac quantitates, et residua sint a
qualia; erunt quantitates, aequales:
seu si sit a = l et a - b = l - m; erit
b = m.
Nam a - b - l. m (per lyp. 2) Ergo
addendo utrobique aqualia V+ m
et b + m fient (per 10) aequalia
a - b + b + m = l - m + b + m. E190
sper V. punet 7.) a + m = l+ b a quibus
aequalibus si aqualia a et L
(perhyo. 1) auterantur fient (per 12)
reridua aequalia, m = b. . ED.
(15) Deor. Si a = b + e erit a - b = e.
Nam ab utroque aqualium
auferendo b fient aegnalia, a - b = b + e - b,
id eet (per 1) a - b = e _. E. D
(16) 7seor. Si a = - b erit b = - a
Nam qui a a = - b (ex hyp) C9.
addendo aequalibus irtis aequalia a e 
b et b (per 3) fient (per 10) aequa-
lia: a + b = - b + b. Ergo (per 11)
a + b = 0 seu (per 15) B = 0 -a, seu
(per 9) a -- b
. E. D,
17) Teor. - a - = a = 0
Nam- a designetur per f. seu
sit - a = f
in omni aequatione alijiere licei quod est ntratia
ostendendum et si a = b esse - a = - b
equitur ex 1
sed si - a = - b sequitur a = b