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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 62v

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: 0.84.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 63r); this page is its left half.

The machine reads it as

  1. C1
  2. et 1l + 12 m + 13 = 0
  3. et 2al + 22 m + 23 =0
  4. ducantur in se invicem fil . 21. I + iu Im 4 1. 23 + 1. 23 m + 13. 23 -0
  5. +12. 22 mmr + A1. 22 Cm + 13, 24C +13. 22 M
  6. sint jam 11. 12, datae, reliquae quaesitae, ut supersint solum U et nun de l’etm
  7. ergo fit 12. 21 + 11. 22 20 et 11. 23+ 13, 1 = 0 et 12, 23 + 13. 2 20
  8. perE
  9. fit Ce per per 4, 23. HL. N 21 ) et 23 B. H 22
  10. fit per 4, C 22 1d. 1 t per 5, 2
  11. ergo
  12. fit per. 5 23 = -6 13: 1 21 et per 6 fit 23 = -13: 12 22
  13. eidE per 8 et 7. fit 22= 12: 15 21 sed ex aeq. 4 fit 22 = - 12: 11 21.
  14. Ergo fit 1 +12: 11 21 = - _ 1: 1121. U Quod vel est absurdum
  15. vel docet debere aut 12 aut 21 e quari nihilo. 12: H 13 esse = 0
  16. vel docet debere esse 12: 11 21 =0. quod fit vel 22 e vel 2)
  17. =0
  18. j quia ergo 21 - 30. 11. 8 12 jam substituamque, fiet
  19. (14) Ssn
  20. O.H. H + 23= 6. 1: 12 et 2 8 22 = 1-0 per gen
  21. et 23= (2 70. 13: 12 per 7 et 14. Quibus valoribus substitutis
  22. in ag. 3. fili. 0.112: 12 U D - ∞ mm Be - 0. 13: 12 =0
  23. et divisis omnibus per 0. fit 11: l =mm = 132: 12 20
  24. seu 112 H - 12 mm = 132 (2 a
  25. Sed perplexu res est, utrum hoc procedat
  26. sane videamus an l + m + n attolli possunt ad quadratum
  27. una sola multiplicatione per a l + bm + cn, fet enem:
  28. al + + bmm + cnn + a im + aln + bmn + cnn = 0
  29. + b.. + c ln + C..
  30. ribi fiat AB a- g, et b --c. Ergo a = b
  31. ubi vel erit n = 0 vel fiet a = = c, et b = - c adeoque a = b
  32. r
  33. ma
  34. ubi ut toteantur C et
  35. non esed sed ut tollatur lm, etiam fieri debet a = - b.
  36. quod est absurdum, nisi B = 0, adesque et a = 0, et c quoque = 0.
  37. quod absundum

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 62v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0124?run=73