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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 89r, page id 00068201:0177
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si sint quatuor lterae les a. b. c et tres aequationes tunc valor unis literae
Ita habebitur:
beq 10 + 1 a + 12 b + BC 
et ooqu. 20 + 2 a + 22 b + 23C. 0aequ 30 + 31a +32b + BC
tione 6 in qua
nempe ex praecedenti, quo omissa c, invenimus aequationem in qua aberat tam
a quam b. Nunc ergo ex aequ. 6 facierius aliquam in qua habebitur
valor ipsius C, tantum pro 10 ponendo. 10+ 13C : pro 20 20 + 23C, pro 30, 30 + 33C
+10 int2t. 32 420 in t3c. 12 + 30 in +1A. 22. aqu0
et habebimus: 1e 1+13C
eodem modo mutatis mutandis habetur valor a et b
pro a, mutatur 73 (n 1 et contra, pro b, mulatur 3 in 2 et contta
C+
jam inquarta aequatione 40 + 41a +42b + 43C aequ. 0. substitu.
untur inventi valores, quod fit multiplicaone per crucem, ut paulo aute
opus vero erit collocale valorem, ipsius C in ordinem, et fier
1XC 110. 21. 32 = +13. 21.32 C. aq. 0. Unde apparet quanta facilitate
Notabile in
- 10.31. 22
+20, 31. 12
= 20. 11. 3
+ 30. II. 2
30. 21. 12
- 13. 31. 22
423. 31. 12
-23. 11. 32
+33. 11. 21
- 33. 21. 12
ex aequ. 6. fiat aequ. 2 tantum enim
aad formulam aequationis 7 adjiciatur
alia formula, hoc uno ab ipsa differens
20. 30
quod loco 10
13C 23C 33C ubi contingis ipsiu
contra. Ergo si eadem dentur
set +10. 21. 33 12. 21. 330. ag. 0. Et eoiem modo habebitur a. valor ipsius a, ex aequ. 7
pemaente
-10. 31. 33 + 12.31. 23
+ 26. 31. 13-
-20. 11. 33
bipsia i munco
mutando 3 in 1. et contra. seu coefficientes
ipsius A in crefficientes ipsius  et contra.
et poterit scribi aequ.9.
generaliter acitem illud apparet praeclarum, in vulore ipsius C non ingredi
+ 30. HI. 23
= 30. 21. 13 4 32. 71. 12
in absolutum terminum nillqu ingrediatur coefficiem
ipsius c. eodem modo in caeteris aequatione pro b. (nempe in aqu 8) vulorem
quod in aequatione pro Csnequ)
absolutum Terminum non ingreditur coefficiens ipsius b.
iseud vero adhuc praeclarius, quod quain stis aequationibus 7. 8. 9.
t quantitas multiplicans literas a vel b vel c; est ubique eadem
quoque in contracium mulata sint,
possunt potius signa mutari in absoluti termino. Itaque distinctius sic scitemus
solis te sign et ne signa
Le +1.
si gua petenda ex sinistris
characteribus jn miniorbus sine inerioritus
signa nominuloris omnia tantantur
mutantur mutatis signis Numeras
joris valoris C
quod si ordinemque secundum
charncteres den sinisttos ita stabit:
a, 11. 22. 23C
-11. 23, 32
 27. 32
13. 23 31
Si in ulla 1. 2.
+ 10.2, 32 aequ.0
+ 12.
2
-11. 20.32
1z. 29. 31
5eq. 0
= 1 2130.
diperini o  
=0. 21.33 49.0
+ R10 23. 31
1. 3. 0
23 31 42
1o2 20 A)B reviter
103 (0 C +, aequ. 0. add
2020b+ aquo
Catao 10 + 41a + 110+ +C 59. 0.
hec 400 ( a0 a + n OB, 1B3G) ay o-
+ 41F) 410a
1308 0. 123.
eter aequaliones tres autio suntat
jum jungatur equatio
lles eperauilo
ibere.
+11. 203
r13 2. 30
10. 22. 33  aequ. 0
+ 10. 2322
+2.1032
17. 2032
+ 435)
ita in O supsletur 0, in D, 2. in Q, 2: in D 3 8
Ex aeg.. 1I erventa fit aegi. 0. cutus oumia perse pallut autem in sigo
ubique praeter 1.2.3
+428