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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 14r

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: 0.83.

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The machine reads it as

  1. sit aequatio differentialis data scrimi gradus: dus: dx = 50 + 51y,:, 60 +61y. Assumatur
  2. alia quadraturabilis dae: dx= 20 posito 20 dari utcunque ex sola X. sit = 30 + 31 Y + 3241: 40 41
  3. per compendium (4t) = C: D Ergo d0 = 5dB - 0 +,: 5D. Est autem d0 = (t) dx 40 + dy d dx assec. X) + du alccu)
  4. et similitur d9. Et fint du (7mo) = dx D sec. X) O + ay D d (ser. y) C) = dx O d ec. X) D - dy O sec. 9) 5, : 37
  5. Et d (sec. X) D = (8V0) 430 + d31. y + d32. gy Et d ec. y) 0 = (9no). 1. 31 + 2. 32y. E+ similiter
  6. (sec. X) y = som) d40 + 4 41y
  7. Et 4 (sec. y) D = (imo) 1. 41. Uend tandem explicando tg. 7. fiet
  8. jam ex 2 est du ax 20. Ergo hunc valorem aequando valori in aeq.7. explicat fret
  9. amo
  10. dx, 2057 = 8 d (ec. X)D + C ( sec. X) D dy, D d (sec. y) C = C d (fec. 7) D. quae explicendo per 3. 4, 8, 9, 10, 11
  11. fiet 4 20. 40+ 2. 20. 40. 41y + 20. 41. 41 9y
  12. -, 430. 40 + d31. 40 y (+ d32.907y
  13. + 430. 41 + d31. 41. + 452. 41y
  14. +, 30 d 40 + 31. 440 y + 32. 44o yy
  15. + 30. 4411. + 31. d41 .. + 32. 441 y3
  16. (4, 1. 31: 40 + 2. 32. 40y
  17. (+1. 31. 41 . + (232. 419y
  18. =, 30. 1. 91 + 31. 1. 91) y (F 32. 1. 41) 9y
  19. jam aequation data 1, multiplicetur, per 10 + 81y tam numerator quam nominator et fint
  20. 50. 80 + 51. 80y
  21. (14+0) dy
  22. 1B. 20 est dimensionis nullius, n est dimensionis, uno minus quam nulius it 2n sit conti 4)
  23. (60. 80 + 61. 80y
  24. dx
  25. (15to)
  26. dy
  27. +60. 81.. + 61. 81yy dx
  28. +50. 81. = 51. 819y Xy
  29. qui duo valores ipsius dy: dx ex aegg. 14 et 15 sunt comparandi inter se, et per y numeratorisfint (16to) 41d32 = 32441
  30. seu 432: 32 = 441: 41 seu log. 32 = log. 41 = 5 seu 41 = (17mo) 32n. posito n esse numelum constantem
  31. Nunc incipiamus a nominatore, quia ille caret differentiis, et quaeramus 80 et 81, fintque (18B0) 80 = 1. 31. 40 - 30. 1. 8 6b, et
  32. (19no) 81 = (2) 32. 32n(= 32. 1. 321,: 61. vatores Htini ratores ex 18 ot 19 substituendo in coefficiente ad y nominatoris fiet
  33. 69. 61. 3. 32. 32n - 67. 61, 52. 1. 5en 61. 61. 1. 31. 40 -61. 61. 30, 1. 32n 4 60. 60(2732. 32n(60. 60. 32. 1. 321- (20mo)
  34. 60,61, 2. 32. 40 +60 61 1. 31. 32 60. 61 2 n. unde (21 mo) fit 40 = (60. 61. 31. 1. 32n - 60. 61. 1. 31. 321--6, 61. 30. 1. 32p
  35. 460. 60. (4) 32. 32n (60. 60. 32. 1. 327, : 60. 61. 2. 32.90 = 61. 61. 1. 31. sture veniamus ad numeratorem
  36. ibi per y est 2d (22d0) 20 = 50. 1. 31. 40 = 50. 30. 1. 32n + 60. d 30. 40 - 60. 30d40, : 60,40.40. Unde
  37. per y. fit 61. 2. Y. 50. 1. 31. 40 ~2F. 50. 30. 1. 32n +2. 41. 60. d 30. 40 - 2. 4r. 60. 30. dq0 + 60. 40. d39. 40 - 60. 70d304
  38. 150. 40. 31 d40 +60. 40. 30 d 32 51. 61. 1. 31. 40. - 40. 51 61. 30. 1. 32n + 40. f6050. 2.32. 32n - 49. 60. 5032. 1. 32n
  39. si esst semo firet 20 LL, 30r+0. Et ex 5 fl. 61. 41. 41. 50. 1. 31.90 - 61. 4 fJ. 50. 30. 1. 32n +61. 41. 47. 60 430. 40
  40. =61. 41. 41. 60. 30840 - 6+ 6 61. 60. 40. 40. d32. 40 - 61. 60. 40. 40 L 31. 3, n +69. 60. 40. 40. 31440 +6,7. 60. 0. 103 pd 3
  41. 60. 40. 40. 51. 2. 32. 32n = 50. 40. 40.51. 32. l. 32n. super sunt exg0, aegy. 2. 23. 24
  42. si in datis ponamus esse 50 = 0. fiet ex 22, 20= , 30:40 quodsi etiam 31 simul esset, 0. fieret
  43. Et ex y in numeralore fieret;
  44. eitu
  45. q0= - 61. 61. SE30. n + 60. 60. P. 32n ,:2. 60. 61.
  46. fcee nbdus
  47. 2. d (30:40) 40. 32n 30 32n 30n d32- 51. 39. 32n: 60, et ex yy in numeratore
  48. fieret: (30: 40) 35 n d32. 40, +32d40 =51. P. 32.32n : 61 + 2 n 6o (432)
  49. d2o: 402 40d30 - 30440: 40 40= 6e n 32 = L S1 n 30, 440 = +n d6e X32 - = n + b 20
  50. Ergo d (30: 40) = 40430 - d = 30 460 3 n 30 + a 30 :130 s8, ap + 1 n 306 d3: 40
  51. (30:40) = 2n 60 32 d, 8 - Ln 51 30 d 30 - Ln 30 d 32 + Ln 30 d 6, o, - = n 3060 432 + L n306 d3
  52. 4
  53. compendii causa, sit sit seu oin) In Ce, 3at3o 3od3r

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 14r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0027?run=74