Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 695 · Oldenburg, fol. 52v

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: 0.85.

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. 53r); this page is its left half.

The machine reads it as

  1. diversis
  2. Quantitatum ex defferentibus in definitis in se invicem ductis factarum
  3. ut.
  4. aequatio
  5. et Lyxp2y + V x
  6. d yx. erit ydx + 8 x dy.
  7. Dyx +
  8. Hinc si
  9. +gyx+ fxXer
  10. a + by +CX + (y + fX + dyX M 10. statim habetur
  11. tangens curvae ad quam est ista aequatio. Nam ponendo A, Bp y.
  12. et A2B Y y + dy. (silicet quia
  13. seu 1cd.
  14. B2Bp dy)
  15. seueD
  16. itemque ponendo
  17. 1B16) X et 2B2C+ X + dX (scilicet. quia 2CDp, dx) et
  18. quia eadem aequatu exprimit quoque relationem inter A2B et 2b2C
  19. quae eam exprimebat inter AcB, et 1B, C, hunc in aquatione
  20. illa pro y et x substituendo y + ay et x + ax. fiet:
  21. a + by + CX + cyx + e y
  22. + fX
  23. +9Vx + hyx
  24. bdy + c dx + ayax + e ydy +2fXaX + rgxydys + 2hXy AX
  25. + axdy
  26. a
  27. +a
  28. 9y dx +hx dus
  29. + d dxdus + eaus +f dx tgdy X +hdx
  30. +29 dy) dx + Exdxdus
  31. ubi abjectis illis quae sunt supra primam lineam quippe nihito aequalibus
  32. per aequationem praecedentem, et abjectis illis quae sunt infra
  33. secundam, quia in illis duae indifinitae parvae in se invicem dicuntur,
  34. hinc restabit tantum aequatio haec.
  35. b dy + cdX + by dx
  36. b xdys
  37. e.
  38. 0 quicquid sclicet reperitur
  39. inter lineam primam et secundam, et mutata aequatione
  40. in rationem seu analogiam, fiet
  41. idest
  42. ∞-dy
  43. quia
  44. c
  45. -dy.
  46. ex
  47. C + dy + 25X +gy + 2hXy ec
  48. b + dx +2ey +29xy + h X ds
  49. = 1B2B seu - 1CD
  50. seu
  51. AD2C
  52. vid
  53. FiB) erii c+ dy hc - T. B
  54. d B1C
  55. b + dx ex B
  56. quod coincidit cum regula Plusiana, ostenditque eam statim occurrere hanc

Cite

LBr. 695 · Oldenburg, fol. 52v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-860722:0104?run=74