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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 13
# Folio 6r, page id 00068010:0011
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(6) Theor. si a = - b erit b = -a
Nam quia a = - b (ex hyp). Ergo
(per 10) addendo aequalibus istisque aequalia b et
b (per 3) fietit (per 10) aequalia:
a + b = - b + b. Ergo (per ((ic) a + b = 0
seu (per 15) a = 0 - b, seu
(per 9) a = b. nu 
17 pheotadi
a -a =0
Nam -a sit f. Ergo ex hypothesi
-a = La opsiot 5- f a 14
Nam a sit =f jam (per 3)5.f0
Er Nam -a designetur per f. seu sit
=a = f jam l f - f = 0 (per 3.) Ergo
pro f ponendo aequale ipsi (ex hyp) - a fiet
=a = -a = 0
sheoro)
Q. E. d
18-- a =  + a
Nam = a = = a = 0 (per 17) et 0 =
=a + a (per 11). Ergo (per 5) - a - - a = a + a
Etg Unde utrobique addendo a fient (per 10)
aequalia +ara 2- a = -d + a + a.
Unde (per 11) cecaaC QED
0- - a = 0 + a seu (per 9) - - a = +a
E
(18  Addenda ascibuntur signis.
retentis. sit  f cui addi debet
a - b fiet f+ a - b
sit a - b = e. ergo si f addi debet es
efit f+C (per 6) Ergo pro e substituendo mimorum abjicere ab una parte
tuendo valorem  (per 2) qui est a- b
+(ex byp.) fiet f+ a = b Q. E. d
19) Adde Subtrahenda asribuntur
signis mutatis + in d vel - in +
At F cui detrahi debet a- b fiet
= a
- a-b = f + a - b
Nam f- a b - f - a  b et
mo (21(18) Qua Explic. Quod de S toto sub
formula sub vinculo comprehensa
significatur, intelligendum est de
singulis membris vinculo conclusis
ut a ut - (a = b) aignificatur a
vel  a - b significat - a - - b
(22)Addenda ascribuntum signis
(per per
retentis. seu sit f + (a - b) = f +a
mant
Nam f,  (a -b) = 4 +a + b = Mperto (per 19
Sran b
19) Theor. - ta = -a aut + - a = -a
(19)C
+da
e-
Aa t
 patet ex 8
patet  8.
n
(20) in omni aequatione licet
et signo contrario affectum ponere
in altera
sit a f+ a - b = h. dico
fore f = h - a + b. Nam in
aequatione (ex hypothes vera) f+ a - b -
addatur utrobique -a + b, fiet indes
futa - b - a +b = h = a + b, id
est (per 11) f= h - a + b
G. E. d