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Leibniz-Handschriften zur Mathematik LH 35, 9, 19, fol. 5r

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: 0.72.

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. 6v); this page is its right half.

The machine reads it as

  1. ei
  2. sit aequatio differentialis, inter X, y, et dx, dius
  3. AB, X, BC y.. 1CDax D2Cdy.
  4. sit X+y = 7G. et 1CE sit co
  5. L 2C2)
  6. V
  7. est erit ap dy - dz = co
  8. et XdX + ydy = Z dZ
  9. sit jam aequatio differentialis quaecunque ex numero implicatarm
  10. verbi gratia b XG rdus Xdx + ydy = X du
  11. id agtu id quaeritur, ut obtineatur aequatio diffferentialis pura
  12. patet tolli posse duas X et y itemque alterntiam ex duabus
  13. dus vel ax. Et prodibit aequatio in qua sole erit
  14. evunt _y, du du, deo. Nam ex aequ
  15. ex aequ. 3 fit Xdx
  16. r
  17. noch
  18. L
  19. 2C
  20. K
  21. a+
  22. -qudu dy + y ay
  23. Nam
  24. Ergo
  25. Nam ex aeg. 1 fit:
  26. (6) l
  27. seu
  28. yy du. Unde ope aequationum 6 et 8
  29. D ait
  30. V
  31. q2 ay = ZZ d72 seu y = Z 1 dy - dz
  32. b
  33. quan aequationem substitureado in aequ. b. sit
  34. ima t +deZ d
  35. bc
  36. ed
  37. ex rav. ex aeg. 3 fit =
  38. 3
  39. cXd
  40. = 277 Laty - dze dza + 77 dus (229
  41. l
  42. dy: du eo-dus +du
  43. id
  44. L
  45. sublatis jam irrationalibus
  46. et mulliplicationib,s vel divisionibus facitis, ponamus aequitionem
  47. Ci
  48. nest
  49. 2. et horum
  50. =cua. G. B etit angulus cti.
  51. 2
  52. s
  53. a
  54. potentias arteffcium Tantum opus est artificium tate desiderari
  55. prot
  56. vlile pri
  57. prodires
  58. ut nova assumatur litera unica
  59. e
  60. est
  61. barn da
  62. quae sola ipsis co, et dy
  63. evanescant. verbi gratia sit aequatu
  64. dicis
  65. et
  66. dus simul
  67. dZ + dy a = DQ a
  68. 2a
  69. (2) a
  70. sd a
  71. et si ponamus du esse semper aequalem sibi seu costantem fiet,
  72. Z.2
  73. Q= dn a, seu S -sq = ma. seu SB- sz =
  74. seu posibs y uniformiter crescentibus ausuler i arue circuli seu in constante ordinu
  75. da
  76. ductu, denta area ex Z ipsi basi seu au applicatis aequabitur quadrato psim
  77. dimidiato. quod si non sit qedus constans sed osunatur pore

Cite

Leibniz-Handschriften zur Mathematik LH 35, 9, 19, fol. 5r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068144:0009?run=73