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Leibniz-Handschriften zur Mathematik LH 35, 5, 23, fol. 4v

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.

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. 3r); this page is its left half.

The machine reads it as

  1. Habemus erge jam tros aequationes ad Logarithmicam curvam
  2. quae sunt:
  3. X aegu Y Sidy: y et V. raequ. sh. r(sit a aequ
  4. Posita faequ r ftah: h)
  5. et X aequ. log. y. posito log. Y esse 0.
  6. Sed possunt adhuc aliae inveniri aequationes per series in finitas
  7. et quidem quia M P erat Z. est Peaequ rr: Y + Z. et PB aequ r (aZ. r
  8. est autem in integris PZ aequ Y= Z + Z + Z etc. vel q
  9. vle esse Ergo PB aequ Z - yt + 73. A
  10. 2t
  11. 5Y
  12. etc
  13. ar3
  14. itaque Numerus cujus Logarithmus est 0 sit Y. et quivis alius
  15. quidam numerus propositus sit Y+Z. ipsis Logarithmus Hyperbolicus
  16. potentia
  17. posita Hyperbolae rr) erit
  18. 2
  19. = +
  20. posita MP _ q et PB, X.
  21. est investigare Logarithmum.
  22. et + 23 -
  23. Er
  24. r
  25. 74
  26. + 2
  27. et c. aequ. X
  28. Et ita ex dato Numero facile
  29. Videamus jam quomodo ope alterius seriei infinitae ex dato
  30. Logarithmo possit inveniri numerus: Quaeritur scilicet
  31. linea in qua sit dx aequ dx r + Z aequ. dZ r. Scribatur
  32. Zaequ. (a) + bX + cX + _x + f x ete et rZaquta + lX + CX et
  33. et rdZe aego 0 + rbdx +2rXd t 3re xdx +0 fXdx etC
  34. 49
  35. dx rFZ aequ() dx + bx dx + Cxdx + ex dx etc
  36. +r
  37. et comparando singulos terminos valorum O et D fet poterit poni a
  38. 1. 2Y
  39. et ita porro in infinitum, et habebimus:
  40. Z aequ X + X + X
  41. 12Y 12382
  42. + X
  43. + Y
  44. 723473 123,4574
  45. 12. 3Y
  46. +. etc.
  47. posito X Logarithmo, et Y+ Z bg Numero.
  48. numerus sive hibcoqu tunc erit Y=Z aq seu fiet Zgo
  49. et erit 1 seu Z aqu e seu haequ Y - r + Y - Y + Y
  50. seu h: Y aequ. -
  51. 1.2 1. 2.3
  52. 1. 2 1. 2.3 1.2.3
  53. Bere
  54. Eadem methodo potuissemus invenire valorem ipsius X, ex Z. nam
  55. scribatur X aequ (a) + bZ + cZ + ez3 + f29.
  56. dx aequ 0 +ibdZ + 2C247 13C2 47 + 9533 42
  57. dx rtZ aeq. (4.brdz+ 2eiZtZ +ser z 12sr2 42
  58. 11
  59. dz Y
  60. fiet b aeq. 1.
  61. Faequ +
  62. 473
  63. = 1b212+2cZ47131743
  64. Y dque x X X
  65. Caeq+
  66. caequie
  67. et ita porro
  68. seu Xaeq (D) + 2 = Z
  69. + 53
  70. +
  71. 12
  72. et
  73. C
  74. eaequ
  75. Cnonstum
  76. cessunt
  77. numer
  78. Et quidem in valore ipsius q rationali per X ponitur a esse 0. alioqui alia
  79. a seu constens supernumerria assumta ponitur esse oAat in vulore ipsius X per Z
  80. omitti quidem sed tamen et retineri potest.
  81. Hinc si Logarithmus X sit tenitas, seu si CF aequ CM, erit FH
  82. sit aqu
  83. aegu
  84. falioqui alius
  85. prodint sertes,

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 23, fol. 4v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068041:0008?run=73