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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 41r

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: 0.81.

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The machine reads it as

  1. Loguethmicu
  2. AX, X
  3. es
  4. XY, y
  5. X P subriormalis
  6. X+ ctar su ttangentialis
  7. A1 X+
  8. - y =
  9. AH, a, ubi XE0 AB, b cujus - uius log. est 0.
  10. AB, D cujus leg sit 1 = BF = AH BF, b cuius log. AB sit 1.
  11. y = bx seu qua y:a = b. a X.a 10g9 = X. a
  12. _ (i -x) + VF= minim
  13. ly: dx = CCCy: + seu tdy = gax sen dg. y = ax: t. sit Y = (O+ IIX + 127X + 13X et
  14. AB = WV
  15. a
  16. ergo dy. HX dy: dx = 1. 11 + 2. 12 X 3. 13 ~ + 4. 14X = y: t. Ergo fiet
  17. 1F. 11 + 2t. 12X + 3l. 13XX + 4t. 14X + ek ∞ 10 + 11X + 12XX + 13X + eec
  18. ib 11 = 16 ex 10. et 12 = 11 = 10, et 13 = 12 = 10. et 19 - 10
  19. Et 1E
  20. tandem g. a = yea = 1Y
  21. Et fiet
  22. 0
  23. qu (W
  24. Sioa
  25. 3+ 1. 24
  26. 1. 2. 3. 4+
  27. 4
  28. L X + 1 XX + 1 X + erc
  29. 1.2 H 1.2.3 13
  30. C) + 14 = + = X + L XX +1
  31. aa
  32. + 1. 2 H 1.2.3 13
  33. et differentiando ( 1 + 81 X +
  34. in qu (1 +
  35. XX
  36. +
  37. L X
  38. et
  39. 1 It 1. 2 +3 1. 2.3 (+
  40. (W-X
  41. +en)
  42. = (min-qu a
  43. + 70 W0 -x. 2 Y(.
  44. + 20- X
  45. XK + L X
  46. id- X - Z
  47. sed ita aequatio prodit quam jam hatermus interim
  48. +
  49. 10
  50. a
  51. 12 It 1.3.3
  52. eat tali aequatione ex dato W daretur X se A X.
  53. X) = _ t
  54. et hhoc reperto
  55. AX
  56. + W. X = 1 e b. (2x: a). ita ex dato W habetur X X adboque et p
  57. sed dissimules
  58. ponumus binastonantimus lors asytn ptotae seu axis se langere, quod utique
  59. y
  60. habebitur et fier ioqoaa
  61. 10 a
  62. 1010) a
  63. fieri potest, cum una sursum deosumve moveri possit donec tota infra vel supra
  64. uxa
  65. alteram cadere inciprat fiet qu oX) +
  66. us.
  67. esumendo aequationem
  68. i
  69. (0+ (2)) b
  70. + 1 x + L xr + et.) minim - e qu
  71. 10
  72. 1. 2 H
  73. si esset solum serces utque ad eet+ IX Ci, 1 + 2X + XX = minim-
  74. Y +
  75. H
  76. Lu = LX
  77. 1 100 +
  78. (610aa
  79. seu x = _ W - totaa. 10aa + H
  80. idub
  81. a
  82. 10aa 10aa
  83. alitr 4 10 aH + 2. 10aatx + I0CaXX = m 10a aH m -iv1o + 2WHX = Et XX
  84. t
  85. XX (+B2. 10aat X + 10a aH (- m) + H Woo
  86. s2W H
  87. 1va_ +F
  88. 2 WX -X7
  89. 10 aa gaa
  90. x = - . 10 aa + 2t + S1ona - W0t) - 10aa (. n 7 ptoa
  91. e
  92. 10na + EF
  93. tous
  94. ergo X incipil esse impostibilis, cum qu (10aa -20L) = (100a (1- m) + 1010) (10aa + H)
  95. Eodem modo sine consideratione radicum aequalium

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 41r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0081?run=74