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Leibniz-Handschriften zur Mathematik LH 35, 10, 11, fol. 81r

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.

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. 82v); this page is its right half.

The machine reads it as

  1. LLC: () A. (A) si BC (B) et CL H
  2. LL )X CBI (BY
  3. C( L2 : L3:: A2: A3 si B2 = B3
  4. AA)) = (B)
  5. L4: L5:: B4:B5 Si Aa=A5
  6. Ergo L6: L7:: A6. B6: A7. B7. sit enim hoc falsum Ergo sumendo
  7. AC: B A6. aeg = A7 (alsum etiam erit L6: LZ:: B6: B1. rontin hypo
  8. sed hac non geludit, nisi u casu quo supponatur si semer cucyor sit ratio
  9. et fit L. L7 semper major quam quaerendus modus et conditio hoc
  10. demonstrandi generatiter
  11. d ovemie d oplis
  12. si curva sit rationalis integra, et elementam curor etiam latronile
  13. integrum, tnum momentum erit ravate integium; tales curvas
  14. quarm
  15. XC C Y = X et dy = e x dx. Ergo
  16. fiet dx + ly =, de e. x C X +)
  17. Y = X + X X M
  18. ax + du = d5.
  19. +
  20. dy = C X hX (m X ) et fier
  21. +2hm Xh+m - 2)
  22. L 2eh X A2em XP +m -2
  23. eth.r
  24. 2k. 25
  25. + th X
  26. 2m
  27. (+ nomi X
  28. fiat 1+2 eh X exhar = = 2eh X
  29. seu 4eh XCth - 2 = - 1 debet esse Xet hor = 1 (9. C+ h. 2 =0
  30. seu e +h = 2 et 4 e h = - 1. Ergo sit C + h + 2et = 4 et = 4 +1
  31. seu C - t = +15. Ergo e = 1 + s5 et h = 1 - 15 et siet
  32. (112 15) +
  33. L15)
  34. 62 15)
  35. et dy = 1F X E. + 1- s5
  36. et Sdx atu = S5X S + L s5 - 1 XCL s dato, ergo cirvo
  37. X
  38. Is +1 XC+ L5)
  39. 15+1
  40. vertice
  41. + x. 15 - 1 X (1 L: 15)
  42. 7(+ S
  43. summabile, quia est Q
  44. et momentum ex axe est
  45. (+ L55 - 1 X. + 215 +1. X) + L 15 - 1X
  46. - 15)
  47. x 15
  48. rendeu videnum an eadem methodo an plures literas assumendo
  49. X
  50. tk -C
  51. incidatur tande rationales, ut si ponatur 1 +. 2 eh X
  52. - = - 2 Ct NC +h - 1 - 2 era Z. C + m - 21
  53. etm - 2
  54. +2emX + 2hm XEam- 2
  55. 2hm Xhem. veum
  56. ub bi ebe ei. sed sic habentur quatuor aequades cum sint lantas tres titerae
  57. inteum suffererit nos curvam habere cujus dentur momenta et dimensio, sed
  58. . as
  59. Hanc curvam vere
  60. quae nisi suppositis logarihmis describi non possit.
  61. cun Mentono appelles Geometrice iphaavalem. Sid transcendente, ad huc sunt magis
  62. seque eum isto est trauscendens. Omres transcendentes sunt Geometri ce irraoates
  63. o contra firita esset quadratura circuli si esset rectacta ad Gpometrice
  64. irrationales non trausceidentes
  65. c possint alio rabates non intercae
  66. sumi, quae sempe etiam analusticesputtractabiles, quam scilicet
  67. mmnerator sit quadratur aut cubus smpli compositibes scilicet ex terminus
  68. quorum numeratores sint quadrat, ved cubi erc nunrorum simplicium
  69. ozbi gralia X + a X+ b erc., vg. y - X 1X + a FX+C erc
  70. X+b
  71. X +5
  72. ubi lantu cavendum ne h vel n sit unitas. Et pulo ope horum solorum erminoum
  73. infinitas haberi posse curvas ravales
  74. P+h -2
  75. quae quadrabiles quam areae quadrabiles
  76. et ipsae curro mersurabiles, pariters et curvae momenta, Haream momcnta

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 11, fol. 81r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068164:0161?run=74