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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 28
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33
(b)
10 + 1X + 12X + 13X + 14X aequ. N. et 20 + 21X + 2X aequ. N
unde multiplicando per cuucem secundum altissimos fit.
- 14. 20X - 14. 21. X3
y. N. Unde ut ex aequ. 7. et 26. fit aequ. 30.
ita ex aequationibus (33) et (26) fiet aequatio 136) tantum pro , in aequ (30)
pro 10, 11, 12, 13. scribendo 10. 22, U. 22, +422, H3. E
+10. 21. 2222 +10. 22. 22. 22 X (26) ubi
- 11. 20. 22. 22
= 13, 20, 20, 22
- 14 20. 20. 21
- 12, 20, 22. 22
+ 14. 20.20. 22. aequ. N.
= 13. 20, 21. 22
= 1420. 21. 21
et fiet.
quantitas.
ubi sola litera ir assurgit ad cubum.
si (33) et (26) fuuxissemus per crucem
sccundum infinos habuissemus aliam
in qua sola 20 assurrexisset
ad cubum
si simul jungamus secundum infimos et summos, possemus statim habere
aequationem secundum cujus summus terminus sit X. hoc modo:
+ 10a + I aX F 12 a X + 13a X + 14 a X
+2ob X + 2bx + 22 b x ( oqu. N
+20c = 21CX + 22CX
unde faciendo b aqu - 14. a aqu. 22. Caequ 10. 22: 20 fiet:
+ 11. 20. 22 + 12. 20. 22 X + 13. 20.227
= 10. 21. 22 =14. 20.20. - 14. 20.210
= 10 22. 22.
cui si adscribamus.
+B20a + _21 a X
5
aequ. N.
+ 22 a XX. et faciamus a aequ = 11. 2021 to  5. 22
fiet: + 12, 20. 20. 22. + 13, 20. 20. 22 X
= 14. 20. 20. 20
= 10. 20. 22. 2V
- 14. 20. 20. 21. aequ. N
- 11. 20. 22. 22
-
- 11. 20. 21. 22 + 10 21. 22. 22.
+ 10. 21. 21. 22
eosse
20
Notandum semper 20. tractanit 2r. et  uti in aequ. (36) tran
ctatur 22, e 20, ita in aeqo (37) tractari 20, 22. Nempe
etiam 14 10, 11, 12, 13, 14 mutando in 14, 13, 12, 11, 10. ubi 12 manet
demonstratio est quia pro X scribendo talis fit transcuntatio
manente eodem slculo.
Ex aequationibus 26 et 35. statim possumus obtinere aequa
tionem ultimam qualis ea esse oportet sine ulla depressione
uti ex aqu.  e E6) et (4) seu (21) et 4) fit aequ. 25. nempe
in aequo 25. pus 10, 11, 12, scribendo - 10. 21. 22
et fiet : = 10. 22. 22. 22
4
+ 11. 20. 22)
10a + ua X + 12 a X + 13a X + 14 a X
5
+ 10bX + 11bX + (26X3 + 13bX  + 14bX
+10CX + 1ICX + 12CX + 13CX + 14c7
20l + 21lX + 22 lx
+ 20mX + 2 m X F22 m. X
+20n X +2In X 3 = 22AX
= 10. 22. 22 4 13, 20. 22
+20pX + 21pX + 22pX a
+ 12. 20, 22 ) - 14. 20. 21
= 20qX + 219X + 219X)
1∞. 20. 20
faciemus a aequ. 20 et laequ - 10. et caequ22 et qq aequ- 14 secundum 7
secundum 
et m aequ = 11. 20  - l0 b + 10. 21,: 20 secundum 2 et p aequ. (- 13. 21 - 14b +14. 21, 22 secuntrum 6
et n aequ.  - 12. 20. 20 - 11. 20 b (= 10. 20. 22 + 10. 20 22) + 11. 20. 21 + 10. 21 b - 10. 21. 21, : 20. 20 secundum 3
et n aequ ( 14. 20. 22) - 13. 22 b = 12. 22. 22 (+ 14. 20. 22) + 13. 21. 27 + 14. 21b -1421. 21 22. 22 secundum 5
qu 10. sigus it. Et +1H. 20. 20i  1200n a. 2LEV(1 L ,  2t. 2f 10. 1g. 20. 20. . 21  1010 e1. 22. V2) (10M. 20 21. 22. 2 (1013, 10. 202113+ (0. 14. 20. 20.212D: 412222 2 2Z2. V) 13 2
13, 20. 20. 21. 22 = 14. 20. 20. 21. 21, : +10. 21. 22. 22 = 11. 20. 22.22 413. 20. 2022-14. 20. 202)
identica, vemi quidem, sed inutilis. quod mirum est; puto autem id exinde profectum, quod invita arbitrariasmet ali e qutioi
aequis