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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 9
# Folio - , page id 00067968:0041
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si a = l et b - m erit a - b
si a = l et bem erit a - b = l- m. si aequalibus detrahas aequalia restant aequalia
num a - b = a - b. (per ident.) et in posterione
pro a substituendo l, et pro b substituendo m
aequalia (ex hyp. 1. 2) quod licat (per ..) fiet
a - b = l- m
Z. E. D
coroll. si a = l fiat a - b = l - b
constat ex propiiupro M ponendo b
si a = l et a+ b = l. + m fiet b = n
Nam b +a = M + l,  (per transpos. add)
Er ergo (per praeced.) b+ a - a = m + l- C
Ergo b = m Q. E. D
Ca corulli si a - l et a rb = leb erit
coroll si, a + b = a + m erit b = m
constat ex prop. pro l ponendo a
si a = l et a - b = l- m erit b = m
4 - b = - b- a Nam
si a - b = l - m et b = m erit a = l
Nam adtibs aequalibus fit a - b. + b = l - m + M
id est a = L. E. D
si a = b = l - m et sit a = l erit b = M
adt detructis aequalibus fiet - a + a - b =
-l+ l- m idest - b = - m. Unde per ...
est b = m
=a - b = -b - a. sea transpositio
Nam si = a - b = c et - b - a = d fiet
+ a - a - b + b = a + C + b et 1b b a +a
= b + d + a Ergo a + C+ b =0. Et similiter
+ b = b = a + a =  b + d + a = 0.
Ergo a +c+ b = b+d + a Ergo c = d, Q. E.d
0 - a - a seu e non su
Nam 0 a = b
Nam o a =  00+0 - a
sit 0- a = C Ergo  0- a ta = c+ a.
0= a = c. Ergo + b +0 - a = b + c. Sed
Ergo 0 = c+ a
ma = - a
b+0 = b (ex def. Nihili) Ergo b - a = b + c. seu
per.. 1) C = -a Z. E. d
19= =0, Nam 40+0 =0-0 sd +0
urobique ablici A et fit
ea  a0 b irit na-
hoc demonstrri non pt, nisi ponendo anc
o- a = -a. li ona=c sit oaram cta
fit s eta Nar
pa ergo e 10+0a = 0+C
non sit b aa - a +Y
ona = - a +b b- a
 b1o A= ba
on a C fit b40C
4+0 a =  a+C.  sd b +0=b
ergo a- a =a+C
ast
1b
a + b =  +b -a
Assumatur pro vero fC. ta atb b+a+ a + b
Ergo b+b = b1 at a+b- bebrara =ata
+a b = xb a - a + b + a = + b - a + a seu
Ergo bab= Ba
=a 1a +b = b - a + a seu b = b quod est verum
Inde cotinere converso L b a+ at b = b - a +q
b2b e B b = b et   + Ergo 0+ b = b+0.
ergo
4 + a + b = b - a + a. Ergo - a + b + a = b - a + a
a b- c erit c- 1 a + b
et u si C = a + b erit -c = - a - b
si C= a +b erit - C= = (a +b) ex lege substitationis
 sed  (a+ b) = - a ub (ex significaoe vinculi)
Ergo si c= atb erit - c = - a b
Si - a - b eut = - b - a
Nam sit nab =c fit a.
sit a+b = C sit = a - b = = C (per..) erit et b+a =C
aeb auaub esit ea
ergo -ba a = =C Ergo - a -b = - b - a q. E. d.
0 - a = = a Nam a +0 - a = + a = a = 0. Ergo
a+0-a = 0 2 = a= 0 quod est verum jum
invertomus incipiendo a finelli a-a = 0 Ergo a +0-a = - a2 a
Ergo a + - a = a - a. Ergo at
hic nod hac consequont ut demonstretur st praesupponi
a+6
videlu a oua=a
ergo = a +b = b-a
s
t0-d - 8-a