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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 72r

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: 0.82.

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The machine reads it as

  1. Invenire tres quantitates continue proportionalis quorum humma rit ∞ a, et (uboruum Xb.
  2. sint quantitates X, y, Z, erit qu X + y + Z∞ a, et Z ∞ a - x - y, porro sit brevitatio
  3. causa a - y ∞ V, erit 2∞ V - X, que duita
  4. in
  5. ergo
  6. et
  7. re
  8. Vn = Xn∞ yy Eivo Xu - vX + yy ∞v.
  9. X∞ =V + V200- yy prima
  10. 2 = X ∞ LV - V v0-yy tertia couantitas
  11. Carum Cubi igitur hunt
  12. 00 + - 0012 00-77 +1=0800 -yy + etc:
  13. s
  14. 23 - 20014 00-yy + 1107200-yy = et:
  15. 2
  16. +
  17. = V
  18. e
  19. + 3VX , 02 - yy ∞ b
  20. live y + 2 -3Vyy ∞b, et lubrtitutis citerii erit
  21. V+ a - 3 aay = 3 aYY - - 3ayY + 3y - b. ∞0
  22. Eive a3 - 3aay + 3y2-b∞ 0
  23. Tive V = aay + = a - =b = ∞ 10.
  24. Mea methodus.
  25. 1)
  26. XAy+Z = a X + y + 33 = b NG et XZ = yy
  27. sit xy + XZ + gZ = M Ergo per 3 et 4 fit Xy + yy + y2 = m. et per 1 et 5 fit ay = m
  28. )
  29. rursus generaliter a = b- eM (per 142, 4.) jam Xry9 Z+ 3Ma + 8XyZ 2per e.
  30. jam ex Tabula Theomematum mea per 1. 2. 4 s. b e2) (7) Sa y()
  31. A
  32. a = b∞ 3ma +3Xy
  33. day
  34. 3
  35. (per 6) (per 3)
  36. Artis est ita calculum
  37. instituere, literasque
  38. ita assumere ut in
  39. calculo irrationales
  40. destruantur. Quoi
  41. hos loco fit
  42. seu 3 -ay + a - b =

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 72r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0143?run=74