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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 72r, page id 00068195:0143
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Bi
1
etIC =2, 21Zeu
9H =10 90C 9. 10
eonumo posapomum Fundamenta calculi Literalis
pro Algorithmo quatuor specierum, et Regulae tureae
Aequalia sunt quae sibi  substitui possunt salva quantitate
et ce designantur hoc modo a = b, id est d et b sibi aequalia sunt c
valoret 1+122
mutur 
21=8
r=13
8+- 9
Axiomata, in quibus contipetur vis characterum 10+ 10=20
2t123 31
qu = 100  
20+10 = 30
uso Doni-
=A 4+) 23.
demognatur ex sef. aaequamur
et b = a veluti V = 10 et 10 = X, 1or2- f1173.
ant
mt (2) Aequivalent a = C, et a +b = C+b. Veluti a = 2 Ergo a +3 = 2+3-5
100+1 = 101
demus
x
ajule. e
demanstratur hac ex ninalam
Aequivalent a = C et ab = cb, veluti, a = Z Ergo, ab = 2b, si b = 3
fiet a. 3 =. 2.3 = 6
(4) +at b = b + a an demons
b
1
Hrque demonstrata ex dif aequalia
ama
Et L3, 3+1 = 4 ex
Initio omitti solet +, ita e a + b, idem est a
ab = ba seu 2.3 = 3. 2 =6 vel numem
+1, a = a
a - a =0
a=
minatus
matus
B l
6) quivi)
=I a Hnc - ab =-aid
vel deter minatius
4a-b, ab
a:b, 
20
t andus tuis quibis aut etias
a+b, c = aC + bc, velut 2+3, 4 = 2. 4 + 3.9
(St a+0-a
ua
Numeri vel
postatatum a+b, ab, a- b, a:b possunt
exprinu per C, oet aliam literam,
quamanquenondum ad aliam significa
tionem determinatam
2: b = 14: b (per 8) - (per 7) a, 1: b
aliam
A, aquimmabibpor
id aequale dici potest exprimi potrest per literam nondem ad signiticationem determira
11) a: D=
tam
1. b. hoc forte ismonstres ex
Theoremata quaedam hinc demonstrata
(1) si a = b et b = c erit a = c Nam si in a = b pro b (per definitionem
12
a b
si a = l et b = m fit atb = l+m Nam F (per 2) a + b = l + = (per des.
equalium) substituas e fit a = c
3) a bc = a cb = b ac = bc a = cab = eba, Sumatur una ex his aequalitatibus
ut abc = bca, sit bc- d firt ad da quae sic demonstrabitur:
aequalium) l+ m
ab sit bc = d, erit abc = ad = da a (per 7) da = bcR. sic
et abc = cba. Nam cba = (per 7) bca = da = ad = abC. Eodemus
Et generaliter hinc celligitur
omnes ect producentium multiplicantium transpositiones esse permissas
modo et caeterae demonstrari possunt.
1)
4) C, a tb = ca + 5b Nam C, a + b = (per 7) a+b, C = (per 6) aC + bc =
sic 4, 23 = 4. 2 + 4. 3 = 8+ 12 = 20
-a, b = - a b Nam = a, b = (per 10) - 1, a, b = - 1, ab = (per 10) - ab
(per 7) ca + cb
ita - 2, 3 = -6, Hoc est quod dicunt - in + facere -, seu -1, +1 =
(6) b, - a = = ab Nam (per ) b, - a = (per 7) - a, b = (per th. 5) - ab. Hoc
est quod dicunt + in = faere =, seu +1, -1
iC