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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 13
# Folio 12v, page id 00068010:0024
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26) = b = - 1, b signifiat b poni subtractive adhoc, seu multiplicam per numorum significantem unitatem subtraction
ut scilicet b per hoc tollatur ex magnitudine cui ad ubi ponitur -b
ponitu
26 diguam subtractionis, seu Minus, est
contrarium signe + et quod fuit positum aufert
(27) a a ∞0 seu pituto
(28) ot a a seu 0 non auget
(29) Et  a - b significat vel b tolli ab a
ex a, debere ex eo in quo ponitur Ra 
(27)  b - b = 0
) sa bre si ab aequalibus auferas
aequalia residua sunt aequalia. sit a = l
et b = m erit a - b = l - m
Nam a - b = a - b. _ in posteriore pro a
ponatur l et pro b ponatur in Aaequalia ex hypothesi
pro aequalibus (per 2) fiet a - b = l - m Q. E. d
(29) si a = b+ e erit a -b = e.
Nam a - b = + e - b (per CB) sa
L b. b + C (per e+ B C b ( per 7)
(29) eet si a = b + e erit a - b = e
Nam a - b = B2BB brC = b (per 28)
b +e - b = (per 7) e+b - b = (per 29) e+0
= (per 10) e
Q. E. d
e  t  (30) ab ab 1b = = ab
30) is Minus in plus facit minus
seu a,  in + b facit - ab
(28.2) Si a quantitatibus ducabus auferas
iqualia et residua sint aequalia
quantitates sunt aequales
31) plus in minus facitplus seu ta, in - b
Nam +a in - b =  (per 16) + a, B-1, +b
= (per 20) 2t, ab = (per 26) = ab
(( (32) Minus in CMinus facit
plus seuag a b E
32)g
Nam g Ergo Agug
Nam 29-g = g-g
(33)
(2)
si  h= = g erit q- = h
Nam h= = g (ex hyp.) Ergo FB (per 12)
9+h = g-. Ergo (per 27) 9th =0. Ergo
)(pr  (per 29) 9 = 0 -k
per mete  Eego(per 10) g= -h
L. Eud 
_g= = - g
Nam g = =h, posito h~ - g (per 33)
Ergo in _ aequ. I =- h pro h. ponendo
valorem -qfiet (per 2) fret.
g= ∞- 9  9: E- D
34) Minus in Minus est plus
seu s a in b = ab
Nam = a = - 1, a et = b = -1, b, (per 
= C per 34) +1, ab = (1 per 21) ab
n. addas aequalia (3) Axioma:  a = a
Nam si aequalibus ab e
b et in fintt a - b + b et L = m + m seu (4) Si a = b sequitur b = a
chagui
per 27) a et l
9. E. d
28. 3) Si ab aequalius auforas duas quantitates
Ergo L a; in b ( et ab, (per 20)
21, - 1, ab=  (per 26)  -i, ab
et
s a - b = l  m et sit b = m
erit d = l
et  residua euit aequalia erumt
quantitates ablatae aquales sit a
Nam =a in +b = - al in ab C per 26) - 1, a  + b = (per 20)
-1, ab ( ) = (per 26) = ab
facit = ab
Si et a - b = l-m
erit b=m
Nam ex a - b = l - in fiat (per 11)
rando aequana ex ppesi) aet
i a = b erit - a = - 
a +  b be a - b + b + m = l - M rM X
Id est (per 27) at =. l+ b ergo
caper erunt C
(32) = a - =a = 0 sit = a = n
Nam sit = a = f erit - a- - a = f-5 per 20
(per 18) M X b,  (per 20) cuife
(2) ge
= - 9
Nam - g Ergo (por v) qug
Nam f ∞9 =0 (per 17) Ergo
qug
sed 2 -g 29 = 0
g- g- -g = e.
Ergo g = - - g
Aliter a
(∞9) = (g) = 0 (pr 32) = G9 (per 21
g
Aliter (8) (9)  (p 31) = 0
g 0 = (per 32) (=9) - (9
seu  -g - -g =  (per 12) g - g. Ergo
(per 28. 2)  ag = 9. Z. E. d