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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 111r

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: 0.78.

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. 112v); this page is its right half.

The machine reads it as

  1. 69 martis 1679
  2. idendum an liceat definire, Quadratices analyticarum
  3. transscendentes ope Exponentium qui nonrationalium
  4. Exempli causa quaeritur an inveniri possit series cujus feries
  5. differentialis est aope alterius assumtae exponentis inationalis
  6. 1+y
  7. sit aquatio ad curvam: fR+ +2X + 3 X + 10 f + 1y+ 1
  8. +21 X V + 22X y + 23 X aequ. 0.
  9. hujus aequatio differentialis est:
  10. e+ 1 X R+ 2 X +3 X + e dx
  11. V1Y + 12 y + 13 1
  12. et
  13. m- 1C. C
  14. +21X y +22X 3 + 20X +
  15. m
  16. 1 r.t ∞ p5qu
  17. dy
  18. a, ay
  19. npt. 1)
  20. X 21. X. V +22X V + 24)
  21. )
  22. Et fiet: d X aequ.
  23. = D = c
  24. +0 + V. E
  25. Ex qua aequ. 2. vel 3. tollamus
  26. literam X ope aequ. 1
  27. et primmus ut rem in facillimo casu experiamur, ponemus in aequi
  28. literam x ad nullam assurgere potentiam, erit 2. aequ. 3. aequ. 0.
  29. et aaeque l. aequ. M. aequ. n. aequ. 2
  30. valor ipsius a hujus modi:
  31. X aequ.
  32. d C
  33. ty
  34. aequ.
  35. unde ex aequ. 1. fiet
  36. 1 v +127 + 13y + f ago H et ex aqu. 3. fiet sequens
  37. = 21 V + 22y + 231, + 1 aequ. t
  38. h-
  39. g- 1
  40. - a. Y - 12 y - 13V
  41. c
  42. + 1, + 2y + uV + 23y
  43. albi pro X substituendo in aequ. 5. ejus valorem ex aequ. 4 habe bimus
  44. id quod statum possius ducere poteramus ex aequ. 4 hoc modo:
  45. X aqu 3 sergo ex aequ. +2 7+) (4 seu (4G- 21) 2+ at () G d2
  46. seu: dx (9 (( )IV + 12V 4 133
  47. y
  48. aequ.
  49. d
  50. -
  51. K
  52. dt
  53. in r fa rs st n a taturis
  54. uyZ.y+ny+.
  55. +G Verum 14y
  56. non est quadrata quantitas, nec putandum est in aequ. 6. posse forte
  57. dividi Numeratorem per latus nominatoris. seu per seu
  58. + 4 dF(+) t d4 dividi posse per 2. sed hoc impossibile est nam
  59. sequeretur vel 2 vel ati dividi posse per F. non 3 alioqui _ valor
  60. ipsius X ab initio non fuisset fractio, quod tamen est necessarium nam
  61. alias nunquam differentialis series fractio fiet. vel ati dividi posset
  62. per quod est impossibilae.
  63. Itaque si valorem ipsius
  64. quaerimus debemus. recurrere ad pavationem l’vel 2
  65. l
  66. . ab, et ea al e mers paisa v
  67. cy

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 111r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0223?run=74