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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 373r

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. L2
  2. () 2
  3. Aye = dx aa + bXx:, aa + exx est aequatio in qua du est element
  4. curvae Elliptuae vel Hyperbolicae. fiet aa du + exxdus aad x - bx de
  5. sit y = 10 + 1X + 2 X + 13 X +14X et C et dy = 11 + 2 12X + 3. 13X + 4. 14X etC
  6. fiet audy = aa, + 1. 1. 1. II + 21. 2. 11. 12 X + 2. 1. 3, 11. 13X 4 2. 1. 4. 1. 14+ X f 2. 1. 5. 11. 15X
  7. 12. 2.12.12 2123. 12. 13 2.2.4. 12. 14
  8. 3, 3. 13
  9. 2. 1. 3. 1
  10. J. 1. 11. 11
  11. 2. 1. 2. 11. 12
  12. Cxxdu = C,
  13. da
  14. +BXX s
  15. naa
  16. Et inquirendo in destractitias, fit 12L _ 1H - f+.
  17. 1. 11. 11 aa = aa =0 seu 11 = +1, et 2, 1. 2. 11. 12=0 seu 12 =0 Et fit
  18. B3 (7) - b - C, : 6
  19. et 1920 ex termino X. videndum an non
  20. et ex termino X fiat 16 =0 nam is ita stabil 2. 1. 6. 11. 16 + 2. 2.5. 12. 15 + 2. 3. 4. 13. 14
  21. ndios
  22. + 2. 1. 4. 11. 14 +. 2. 2.3. 12.13b ubi patet omnia ubique esse teni
  23. (11)
  24. pares, alioqui omnibus reliquis destructis destrui et 16 seu esse 16 = 0. Rem
  25. ergo reassumamus: dy = 1. 11 + 3.13X + 5. 15X + 7. 17 X etC. Et fiet
  26. +aa dis = a4, 5H. H. 1. + 3. 1. 3. 11. 13 X + 2. 1. 5. 11. 15X 4 2. 1. 7. 11. 17X + 2. 1.9. 11.19Y
  27. ca
  28. + 3. 3. 13. B3 2.3.7. 13.15 2. 3.8.13. 17
  29. .... ..... ......-..
  30. .-.-
  31. -- - - DH. II. 11
  32. ..-. -. 5: 5. 15 15
  33. 2. 1. 3. I1. 13
  34. 2. 1. 5, I1. 15
  35. 3rai ............... 3. 3. 13.13
  36. AbX EX = (1qua + EaV Lo maatiCL thaathaC2 = 31 + BX +3AX ere
  37. 0
  38. u
  39. =a
  40. .
  41. ana
  42. ygRX
  43. 114) ti n 34+ 3 19+C94 130
  44. Est bitu Hinc quia y = uut 13X + 15X + 17X ete. ideo incipiendo
  45. at X quia a 15 X, quia in aequationis 13 termino 15 continente nempe x incipiunt
  46. omnia procedere uniformiter, fiat 15X3 + 17X + 19X etc = v. Et ex
  47. Et fiet y = 11X + 13X + v seu v = y = 11X = 13X3
  48. Assimatur jam alia
  49. aequatio aa dco + Cxx deo- aa dx0 quae nihil differt a priore, nisi quod b = 0
  50. et fial cd = 21X + 23X3 + 25X + 27 X etc. Constat Dari relationem
  51. inter x et co ex suppositis quad quadraturis Conicis. sit autem
  52. 118)
  53. (181)
  54. 25 X + 27X + 29X C = e fietque eo = 21X + 23 X + e seu e = c0 - 21X - 23X
  55. 6
  56. ob datas auteri quadraturas Conicas, datur ex c ex X ergo datur et e ex x.
  57. porro 21 = 1 et25 et 23E0, si absit b. fiet C = co - x et notandum
  58. etia 13, 17, 21, 25 ete. fore = 0 seu debere evanescere, si absit b. quia
  59. quia abest b. Ex his quidem patet e eodem modo deficiri ex a invenim
  60. ex X, a, et 0, ut V invenitur ex X, a, et b. sed ita ex data e per X eto
  61. non deo indeniri v, quia non apparet quomodo pssit o ingrediatur calculum, id
  62. enim fieri ab infinitis modis, neque adeo apparet quod proo substitui debeat . b.
  63. illud interim si contra data fuisset V ex x, a, b habita fuisset potius e ex
  64. X et a; pro b substituendo 0. nisi forte contingat, ut ora tunc evanescant
  65. illud si sit b = 0. proditum evanescere etiam 23, 27, etc. et fore
  66. Et
  67. W = WKX +25 X + 29X etc
  68. uXX
  69. Cd = 21 X 4 25 X + 29 X etc.
  70. ut yx = et ut Y Axt = F ut y - 1X = 13X + 15 X et c. videamus an constans
  71. quaedam lex haberi possit, secundum quam 13 15, etc eodem modo habeantur, quam 25, 29 et
  72. ac
  73. hoc posito haberetur semsi veluti si 13, 15, etc eodem modo haberentur ex a et b
  74. quo 25, 29 etc. haberentur ex a, et 3a. Jane 13 = b:, 2. 1. 30, 11 (15 = 3C. 1. 1. 11. 1.- 3.3,
  75. 3: 2.1. 5. 11a4 et 17 = et et 19 e.
  76. . 1.g. Ina sed video id uta ecedere
  77. sed 25 = fC, 8. =C. 1.t. 11. 11,., 2. 1. 5. 1 au 2 29 = 2E 1. 3 b Bu S l sis
  78. 2. 2.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 373r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0741?run=74