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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 154v, page id 00068201:0308
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loX + AX + n =
10. 30 X + 1. 3oX + 12. 30 = Coinced. cam ( 20. 40 X + 20. 91X + 21. 41 -.
20  + 21 =0
40 X +41
20X +2IX +22 =0
+0X r41
10 X + uX +1 =0
30X 17+C
10. 30 X + 11. 30X4 12. 30X
4 1091. + 11. 31. u + 12.
1073 + uX +12X + 13
 30X +3
10.30x = 11. 30X + 1230X +13, 30X
+10. 31X F 11. 3IX +1231XF131
10X+ XFLX LBXL4
4 30X+31
1030X + 11. 30X4123OK + 13. 2X + 1t. 30X
+ 10. 31. 411. 31.. + p. 31. 4133, - +1.3)
28
Et itue forio
co. 40X + 20. 41X + 20. 42X
+ 21. 40X + 21. 41 X + 21. 92X
+ 12. 40 X + 27. 41 X +2
40X + 4IX +42X+43
∞X + 21X +22
20. 40X 120. 4( +20. Ae X + 10. 13X
+21. 40. 2.91.. 2. 42 - + 2. 43X
2.40- 22 4 = 2042. +22. 43S
Ad reddendum calculum uniformem possermus pro 10, 1, 12, 13, 14 ponere
11, 12, 13, 14, 13; et pro 40, 41, 42, 43, ponere 42, 43, 44,45, et ita pro
novissimis duab quasi fuisset 11 X+ + 12X + 13X + IX Y15, et 42 X + 43N + 44X + 45
Et ita pro duabus aequationibus novissimis scribemus:
1P. 20 X rr2. 30X + 13 30X p 1430( 4r5 30 X L 1 30
urgo X + 1230 Xti3. 30 X+14. 30 X +15. 30 X + 6. 30 X2
103] - 11.31 .. 12. 31-. 13. 31. 14. 31.. 15. 31.. 5
2agX +. 4) X 42o qat2o. qs X t20. +bX 120. 3 X) - 0
21. g1. 21. 42. 21. 47. 21. 44.. 21. 45. 21- 4
22. 40. 22.41. 22. 42. 22. 43. 22. 44. 22. 45.)
ubi 10, et 16 et 40 et 41, et 4b et 47  quivalent nihilo, tantum tamen
tantumque adhibentur ad servandam uniformitatem calculi
Fortasse tamen hoc supplenento non erit opus, itaque consideremus solas aequa
tones dextras, quia in illis incognitarum numerus crescit, qui in sinistris manet,
et sit 20.40 X + 20. 4) X + 21. 41 (   50a X + 51 a X + sea
21. 40
et siet 40 = 50a :20 41 = 52a: 21
unde _ 20. 20. 52 + 21. 21.50 = 20. 21. 51
20. 407 + 2t. 40X + 22. 90X
E  ~ solx + siX + 52 X+ 53
+ 20. 4 X + 21. 91X +22.41 b
30 = 50: 20 4t = 20. 40  f 20. 4) X + 20,q2X. 
21.40
+ 212X
2 soR Ns X rIXESIX +54
22. 40 5. 41. +22. 42
40 = 50: 20 42 = 54: 22 42. 20. 20. 41 + 21. 50 = 20. 51 21. 12. 41+ 21. 54 = 72. 53
fit 41 = 20.51 - 21.50, : 20.20 = 22. 33- 21.54,: 22. 22
202.G4 +,22. 50 +20. 21. 22. 51 - 21. 21. 22.50 = 20.22.52
20. 54 + 22. 50 + f 20. 51 -2150 +- 22. 53 - 21. 54 = 52
2.20.20
sad in his non satis apparet ordo.
2- 22. 22
20. 42 + 21. 41 + 22. 40 = 32 20. 43+ 21. 42 + 22. 41 = 53
41 = 5i = 20. 42 - 22. 40, : 21 = 53 -=20. 43- 21. 42, : 22
fil 22. 52 - 20. 22, 42. - 22. 22 40 = 21. 53 - 20. 21. 43 - 21. 21, 42
seu 42 = 22. 528 = 21. 53 - 22. 22. 40 + 20. 21. 43,:, 20. 22 - 21. 2)
20 ve (2091 X + 21. 41 X
20. 40 X + 21. 40X + 22. 40X
+ 20. 41. . + 3. 41.. + 22.41.
20X + 4X +  40X + 41X142
20X+21X +2
+ el.40 221.tes
+22. 40. frc. 41