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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 80v

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: 0.77.

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

The machine reads it as

  1. sit
  2. a = C
  3. sue
  4. Hic multa bona et vix pro differentialibus per exponentiales
  5. Ergo Xla = y Ib.
  6. eromi porra
  7. Y et qomitti possunt si intervallatam
  8. sentium in axe aequantur unilate
  9. 9.(do.y
  10. itaque si an et bus sunt constali test irunt ictae aequationes ad rectam
  11. X
  12. Sit X a Ergo
  13. Seu
  14. XS dx 2X = y
  15. a la
  16. dX : X = γ dX = X dy: XX: a
  17. dx X: to = ydX = X dy.
  18. Hinc Si Ponamus crescentibus X decrescerere is
  19. erit fydx =xdy = Xy. set fiet
  20. aequatione differentiali dx X = ydx- xdy satisfiet
  21. per absolutam XX = XY, id est x = y quo
  22. etiam est ad rectam; syp
  23. e
  24. sed secq est si crescente x crescat etiam y, tunc enim
  25. aequatio e explicanda est per v = a
  26. a
  27. ixge R.
  28. Generalius
  29. un
  30. fiet
  31. t
  32. X.y X. y = a pX. V)
  33. dabit.
  34. e
  35. L
  36. va
  37. Ry log. X. Y = X7. loga.
  38. a
  39. hoc est logo x. s =, X. y. log. a: Xy
  40. ca
  41. cgtn Xeta
  42. W
  43. ax
  44. tog. a d. eXy: X. y
  45. similiter si sit
  46. a
  47. N. y (X. y) = a) h. 7
  48. in b
  49. an
  50. s
  51. _ 5 d. 5.y: X. G = loqu a X. Y + logb Xy, : X. y, sed
  52. u
  53. unt
  54. logarithmice
  55. taur
  56. adeoqu
  57. d. Xy: X. y = X y log.a: Xy. seu _ d. X. y : X. y =
  58. r
  59. IX
  60. e
  61. fiet
  62. quonum raro ad hanc formam reduci possunt aequationes differen
  63. Possunt aeq rationes esse huienadicclaresie
  64. kales.
  65. compositae ex pluribus logarithmicis, r quantitatibus vert
  66. a
  67. a
  68. gratia ponamus scribi _(d Xig: X. Y + X. y d. X. y : X. Y
  69. X. V
  70. sed hunc ne sempee ees rdu differentialis primi graedus ordinarie nec
  71. non habetur potest reduci ad tatem aequationem
  72. a n
  73. a
  74. exponentiales
  75. na
  76. X. y in X. y (X. y) = a num. a (X. y: a
  77. imo hinc patet omnem aequationem etiam communem reduci posse ad expo
  78. antiatem, sit enim XX + ry =aa. fiet Rumb (xribanum b
  79. num ((xx: b) in num. 6 (y3: C) = num. aa, et ita ora semper ad duos
  80. terminos reduci possunt

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 80v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0160?run=74