Leibniz-Handschriften zur Mathematik LH 35, 3 A 28, fol. 1v
Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.89.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 2r); this page is its left half.
The machine reads it as
- 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
Cite
Leibniz-Handschriften zur Mathematik LH 35, 3 A 28, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068241:0002?run=74