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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 37
# Folio 1v, page id 00068250:0002
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Veriamus ad exemplum.
10 + H1 X + 12 XX = mult plicetur per 30 + 31X
20 + HIX + 22 XX = 0 multiplicetur per 40 + 41 X
compositum ex duobus productis erit.
10. 30 + 11. 30X + 12. 30 X X
10. 31. 11. 31 .. + (2. 31X C=O
20. 40+ 21. 40.. 27. 40..
ubi 12,22, 31 poni pissunt = 1
et 41 = - 1
ubi ut destrnatur X, fient
aquationes tres
10. 30+ 20.40 -0 11. 38+10.31 1-0 12. 30 + 11. 31
21. 40+ 20. 41)
22. 40 +2. 415=
20. 41.. 21. 41.. +. 22 4I.. 1 nam quarta 11. 31 + 22. 91 =0 per s. patet
posito 12, 3122 =1, et 4= - 1
Harum trium aequationum ope tolli possunt incognitae assumtitiae, 30 et 40
coefficientes ipsins 30 sunt 10, ut,
40 sunt 20, 21, 22
Nextrins nempe ipsius 1
coesticientes sum
0  10-20, ((- 21
seu compendio 0, E1, S+
Habemus combinationes cum suis
incognitis assumtitiis pariter ac litera,
4 10. 21. = 10. 22.54
Unde fiet
= 11. 20.54
+10. 11 (2)
L10. 21pI
 (0. 11-20
+ 12. 20. 51
(10 Mes. 2
 10. 24. X
410. 12. 2
 O
signis debitis (ae quationem
carentem
ubi 12 et 22 = 1
et 51 = 10-20
et 52 = 11 - 21
+ 10, 19. 21 = 10. 10. 22
= 10. 21. 21
et ex i1s
+ 10, 20. 22
= I1. 11. 20 + 10. 12. 20
posito si placet
Li. 2020
+1I. 20. 21 = 12. 20. 20
10 +11 +12XX + (3X + 14X multiplcetur per 30 +31X + 32XX 133X.
f10. 21.E
90+ 41X + 42XX + 43X
ubi 14, 24, 33 =1 et 43= -1. componendo producta in unam aequatione
et 20+ 2X +22XX +23X + 24X ....
fiet 10.30 + 11. 30X. + 12, 30XX + 13 P30 X + 14. 30X
19. 31
20.40 +21.40
3
2041
10. 32
22.40
21. 41
12. 31
20. 42
10. 32
10. 33
23140
22. 41
21. q2
20. 43
13. 31 + 14. 31 XO
12. 32
11. 33
24. 40
23. 41
22. 42
21. 43
13- 32
12 33
_+24 A
22142
22143
+14, 32X.
13.33
sut septem aequationes, quibis tollendae sex lilerae 30, 31, 32, 40, 41, 42; nam
et 43= = l unde, quia et 14 = 24 = 1 fil 14. 334 29. 43 20 per se
unitas habet coefficientes 0 0 d 10-20 1- 21 12-22
Seu q1, =4l1
seu compendro, 0 0
d
0
20. habet oefficientes 10 11 12 1 13
31
a
10
+1
--
 0 10
 O c
11
habet Coefficientes 28 21 22
= a  a 12 2 0 20 21
12
52
22
0 20 21
24
13-28
3.3, coefficetiulbo
demila linga t. pteo
4222 0
linea prima et columna ultima, cam 52 omnes sentone ex coefficientibu demta linea l et est penult. ex
abilitat dervo habit tres notas sinistias, isst tres motus sinistras 2 sutama adtatrum deptrarum est 9
t22
3
d
14, 33X
24435
5
e+
8C
24. 47
23.43
f.L. 73.23
vcluditur
1423