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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 10
# Folio 8v, page id 00068007:0016
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XtuxI) +X + IX + 12X + 13X +14X +15 = 0
+x3
145
=X = 21a
- 2∞
= 11. 21 = 11. 2D
+21 +21. 2 F21. 2
+ 11. 21
2. 2
412
X + 21X + 22 =.
X +
Ergo X=
+ecy +5i
E_
ay- d
at 0b4 ex + dX
s-
seu compendio 
2
e + fx + EX
y
X Mlq X + AX + 1X + 14 X + 13 =0 X + 2IX + 22 = quadrando fit
N + 1 X + 12X + 13X, +14X + 1520
Et ex 3a per 2 fit. +
(seu XX = -21X - 22
X +21X + 22 = 0 fX = 213 2F = 2. 21. 22 + 22. 22
- 213XX = 21. 21 22X) +2.21.2 + 22822 fit X3= - 2IXX = E2X
Ex4 sit X = +2. 4. 2XX + 2222.
42. 2. 2
f 22.22.
e frI. ux +  Y. 2V
guu fel. 2. 22 (42. 1. E. 22.
-re
f22. 22
+ II. C + 11. 22CE
1, 146+ 4 - 2 -8
2l - 1 - 4 +2 +4
+ 2
X 6 XX
+21 X + 2P. 22
Aursus ex 5 per 2 fit - 21. 41 2: - 721. 2222
422. 22.
Et ex 6per 2 sib X = , 21. 21 X + 21. 22
Ergo ex aeq, 1. per 7, 4, 82. fiet
E 21.21 
12, 1+4 =2
13, - 1
614
5
- 22
 21 X + 21. 22
-321.2 . = 2.71. 22
+ 28
- 11. 23.
+, 1I. 21. 22.
+12. 21.
- 12. 22.
- 13. 21.
+ 14.
- 11. 21:22
+11. 22
+ 12. 21.22
= 13. 22
+15
(10)
142
(20 = 30X + 31  ypendio
34X + 35 =0
X+21X + 22 =0
tit _ 14- 21. 4 + 22
e
(1
seu 25.0- 21. 24. 35 + 342920
sit 20ux + ux=
dividatur 1 per 2fit residuus 36 + 21X = 0 et sit 1127 = st. Ed 14 22 operatio 30 + 3IX L LX a33X , qX ss 
Dimilendus 10 + uX+ X +13X +1 4X + 15K,
0
et fit 15.22 =35. 22 1 34. 2 Hinc 31= 11 Ex alibi a me calculatis
VXX+LXN =0 IXLuXtM=0
14. 22 = 32. 2 +33. 4 + 34. 20  dividatur 1 per 2. erit operatio 30X + 3IX + 32X3+ 33X + 34X+ 35
14. 27 = 34. 22 +35 435. 20
13. 22 = 3322434. 21+35. 20
(1. 22 Dl.2C+32. 21 +33 20
et siei residuns 34∞ + 35X 34X + 35 =0 lex,
32 = 10. 10. 2 - 10.19. 21 + 1.11. 20 - 10. 12. 20, : 102 103. 22 - 10. 1. 2s + 11. 11. 207: 10
10. 2 30. 22+31. 21 +32. 20
it lex operationis erit: 
erit
10, 20 = 10. 3
10. 21 = 10. 31 + 11. 3 1, 29
22 = 10. 32
+I1. 32 +12. 31+
10, 24 = 10. 39 + 11. 39+ 12. 326
10. 23 = 10.
10. 25 = 10. 35 + 11. 34 +12. 33
+0 26 10 361 H 35+ n 4
30 = 20
31 = 10. 21 = 11. 20, : 10
33 = 102.23 - 10. 11. 22 + 10. 152 21 - 113. 20 + 18. 1112. 20 - 10.12. 21 + 10. 11. 12. 20,: 18
seu 5 = 10. 23 = 18. nar +. 10. 1218. 30 =  11. 20, : 103
34 = 19. 24 - 10.1. 23 + 10. unr2, = 10 lin 12 20 + 1 20 seu 34. 1. 1. 1B 12p 1 . 1,. po  - 1 0. 1. t 1. 21 4 11. 20, . 10
2
= 103. 12. 22 4 16. n. M. 21 = 10, 12. 11. 11. 20
u
(L1. 12.11. 20
1212 20 r 1. 11. 20
et 35 = 10.25 = 10. 11. 24 +1031. 21. 23 = 18. 11. 1. 1. 22 4 10, 11. 11. 1. 11. 21 = 15. 20.
1. 12.
1. 1. 12, 21
12. 23
1215. 22
p. 12. 11. 21
12. 12. 21 12. H1. 11. 21
itaque 2 = 20. 1031 = 10. 21 - 11.20  1832 = 15. 22 - (17. 10n. 21 + 15. 20
12. 2 210. 1. 12. 2) . 11320 10. 34 = 152. 24 - 1. 172 o. A. 12. 4
14.  + 10. 111. 23 - 10. 18 1. 22 4 10, 11. 11. 11.11. 21 = 1P3. 20 1 1212. 20
(0 12. 21 210. 11. 12. 20
11. 12. 11. 1.
12. 11. 11. 11.2
3.10. 11220
rouni Iimmaus bly 2 dogato pe ast trot e non anierur a cor au ta erero avu e n rmet.
II. 2
21.21
= - 4+4
1F +t 2
11. H1. 11. 12. 20 N apparet. quod prodiant omne