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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 66r, page id 00068196:0131
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10X + 1X + iaa X + 1a  t, multiplicetur per 30X + 31a Z_+ 32 aaX+ 33 ax, 2a
prodeat 4, 20X + 2, aX + 22 aax + 23 a X  + 24 a X +25 aXX + 26a X + 27 a, debet hoc coincidientiari cum
producto = 10. 30X + 10. 31a X + 10. 32 aa X L 10. 33 a X + 1034 a X
+ 11. 30a 11. 31
prodibit 0 26. 10.70
12. 30
40. 30 = 10, 30. 40, 21 = 10. 31 + U. 30
40. 22 = 10. 32 +11. 31 + 12. 30
11. 32 +11. 33a + 11 34 a XX
12. 31
13. 30
12. 32
13. 31
_12. 33aR + 12. 34a X
13. 32. 13,3368 + 13. 34a
1430 - 14. 3,
14.32 + 14. 354
4023 = 10. 33 +H. 32 +12. 31+ 13.30. Et ita pono
Hi Atque hoc sufficit pro conone multiplicationis, sed pro eanone divisionis oportet quaerere
30, 31, 32 etc. quod est difficilius, atque ita eut procedendum, ponamus 40 = 10.
Y 88e fiet 30 = 20. unde  21 = 10. 31 + 11. 20. Et 1031 = 10. 21 - 11. 20. Hinc
10. 22 = 102. 32 + tter + 10. 11. 39 + 10. 12. 30 = 10. 32 + 10, 11, 21 - 112.20. Et fiet
10. 12, 20
102. 32 = 10. 22 - 10. 11. 21 + 11. 20 10343 = 15. 33 + 10. 11. 32 + 18. 12. 31 + 10. 13. 30
= 10.12
Du 103. 23 = 103. 33 + 10. 11. 22 - 10. 11.21 + 113520 et fiet 10.33 = 10. 23- 10.1. 32 +19, 11. 21 - 12. 20
= 104(2. 20
F 10. 12. 21 - 10. 11. 12. 20
+ 10. 13. 20
10. 24 = 10. 34 + 103. 11. 33 + 10, 12. 32 + 103, 13. 31 + 102.14.30
fiet 10. 34 = 10. 24. - 10. 11. 23 + 10. 11. 22 - 10. 113. 21 + 157. 20
.
+ 510, 11. 12. 21, - 2. 10. 11. 12.20
+10, 11. 13, 20
- 103. 12. 22 + 102. 11. 12. 21 ∞ 10. 11. 12.20
4+ 10, 122. 20
102. 13. 21 + 102. 11. 13. 20
= 103. 14, 20
16. 35= 10, 25 - 10. 11. 24 + 18. 11. 1123 -10, 1P. 22 +10. 1, +21
= 115. 20
-10. 12212
+ 18, 12. 21
-10t. 12. 23
= 18. 1B. 22 +10. 11F, 21 = 11.2
+18. 11. 12. 32 =3. 10. 11. 12. 21 419. 11
-10t. 13. 22 + 10. 11. 13. 21 ∞10,. 11. 12.20
+ 13. 137. 21 23,10.11, 13, 20
10. 14. 2 + 2. 10. 12. 13. 20
+3. 103. 11. 14.20
-18. 15. 20
1ouch. 22 +101
-10. 14. 8
Eit 10. 11. 12,20
ubi calculum continuo, quasi
altiorsfuisset assumti multiplicantes
18, 25 = 10535 + 10. 11.34,+10. 12. 33 410.1332
en 10. 35 = 18. 25 - 187. 11.34 -10 12.33-
, 16t. 13. 32 - 10. 14. 31 - 10. 15. 30
 
E2. RZ PtS HH - 18   410. I1. B3. 2) L2.10. 11.13,20
L1d
+ 10. 113. 12. 20
0
- 10, 11. 12.20-=
+10. 11. 14. 2C
L1D. 1(312. 20
2. 16. 11. 12.20
(B, 103, 12. 13. 20
= 102. 11. 13. 20 X
= 10, 12. 13.20
+ 103. 11. 14. 20.5 ==
-10t. 15. 20 d L
E
Et ita patet propessus in infinitum. 
oanes lege
10. 13, 20
+10t, 14, 31 + 10t. 15. 30
102. 12. 23 + 193. 11. 12, 2242. 15, 11. 12. 21 +2. 10. 113.12. 20
C
16. 25- 10.11. 24 + 10. 11. II. 23 =10. 12. 23 +18, 11. 12. 22 - 15. 11.12. 21
cc4.
5
exdentur, sine potentia
nogeneorum convenientet
12
etc
sec dra.s. semper
 un eodem coniisle
gradu
 conveninut
tam formali quam cirtuali. id epan Numeri praefixi sunt tropospositiones forenam facientes
semodum literas i possibiles formam facientes. Signorum haec estregula generalis
I facilis, ut, si ex 11, 12, 13, etc. componatur paris gradus dimensio sit signum plus:
siu impar, minus.
+10 H YX
uib
Regula ergo generatis huc redit
st 10, 20 X + hI a XFaaX + 2XX424CX FVaKX tESax +ya CSoSan Iarsm Eushra aeia
pt
20X + na XX + 12aa X + 13a3
equ. Bo L 3ia X 3r aa X + 33a  taa
fiet 10. 20 10.21 10.22 10.23 10.24 10.25 10.26
e
aequ.
aequ.
1030 10. 31 10. 32
11. 30 11. 31
Homogenectum formalem
v
12. 30
et
aeq.
aequ.
10.33
I1. 32
12. 31
13.30
1034
11. 33
1232
13.31
14. 30
aequ.
10. 35
11. 34
12.33
13. 31
10. 36
II. 8
2. 34
11. 2f
12. 35
1.
21
10. 35a + 10. 3a t 10 ra  Cuu  mondes
L1. 37
10X uax+ B aax + 13ar3
ubi ad generalitem pro 
pro 3, 2, l etc licobit ponere C, e1, e-2
m, m -1, n - 2
pro 4, 3, 2, 1, ek
pro 7, 6, 5,4, et C
eam etmul; et m., et
+3 Et fict 50 =20 10. 31 = 10. 21 - 11. 20 16392 = 10. 22. 10. 11 2H. 1,
15. 30. 15. 31 103. 33 = 10. 23, 16, 11. 22+ (10. 11 - 18, 1221 F . 11. 4 2. 10. 11. 12 -11. 13)20
14, 31
virtuaum. ipsa 20, 21, 2C, etc non constituunt
utati ordine litranum il,athete camisa
x
12. N L 2. 15. 1112 -18. 13)21L (11L 3.10. 11. 12
+2, 10. 1I. 13 F10, 12- 163. 14)20
seu
seguum +gaias.