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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 75v

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: 0.75.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. ex AB delapsum
  2. curvam quaerens in qua descendens grave aequabiliter recedit a certo
  3. quodam puuncto, hanc tandem aequationem differentialem inveni:
  4. 8 bt AC = X. Bd = v dv: ax = 8
  5. Des
  6. c
  7. ()L(C)
  8. fore b V - 2b VX G + Vet = 0 quae aquatio resolvenda
  9. e2d
  10. + ax
  11. Quod quia in ordinariis difficile est, tentetur per seriem infinitam:
  12. sit V Lx 1 mX + ux px a qu etC et V l’et retme
  13. v - 1X + 2 X + 3X+ 4x + 5X +6X esc et v = 11 X + (2)1. 2X + () 13X (2) 14X L (2) 15X esc
  14. = (1). +() 2X + (3)3X + (4) 4 X + (5) 5X + (6) 6 X ds C
  15. Y 2.2 +(2) 23 ()24 ese
  16. 3.3 est
  17. 492 = (16) 1. 1 + (2))(16) 1. 2X + (2( 1(2) 1. 3 (2, 19(4) 1 4X + (2)(1)5)1. 5. X +(2)16) 16. X =I, 611,B
  18. SuB (1) Cx CeX. )1 X Neges 125 ) ( 1
  19. 1(2). 2.2 +(()) (3) 23 +() 4 + (9 (2(5). 2.5 Xe D (2)(6) 1.6.
  20. 2.
  21. jam d = 2 v d 28. Ergo v = d vi
  22. seu V8s = (1)1. 1 X + B) 1. 2 X + (4) 1. 3X3 + () 1. 4 X= +b)1. 5XE esc
  23. + (2) 2.8R (5)2.3, (6) 24 esc
  24. (3) 3.3 ec
  25. et m vB () i x +
  26. + (9(44. 4
  27. bvg1)Xn 1B) ∞X + (4) 1. 5X 2 F(2Y (5) B aX +() (16) B35 Wx 1 = b5 g2
  28. D (1.2) 12. (2) (15) (2. 23 (2) (16) 1. 24
  29. (2) (1.3) 1. 3.3,
  30. +(3.3) 5.5 Y(eD B+) 1. E3. (2∞65) 124
  31. (2) (3.5) 1. 23 (2) (35) 1. 2.3
  32. dunibus ergo in unum additis, fiet: +(44) 1.5 dC e
  33. (27) (4. 2) 12. 3
  34. arv: - ) CaX - (e C3) i2a X CxCealisaL entes) it aX -- axves
  35. (4
  36. -(21 (. 2) Cta. =(2) (1.5) 12. 23a Al
  37. =(3.3) 1. 2 a. -(2) (. 4) 5. 2. 3a
  38. 1)’ax HAB) I2aX + () B)13 ax
  39. (D Ge Vx IB)LLVX (HCt B X
  40. -() (1) e2 BX- ( 1 2bX (3) ( 1. N X (es e l14B X
  41. 1+ b X + (2)1 2b X + (2) 1.36 st F + () 14b X
  42. () 23V
  43. Extermino x fit 11) (2)41) = 0 quod verum. ut allatur a X
  44. tollatur. I x3 fit
  45. =(2) (3. 2) 1. 2 a
  46. +(N I X = ax g2
  47. +(4) 2.2 a + 6211 (6) 2.3 a.
  48. =(2B) eb
  49. ) 21. 7211 () 23b1c
  50. 2at
  51. 4(2) 1. 5. bX e
  52. (2) 2.4. V.
  53. 26(2) = 6(2) +) -0 Ergo
  54. bv
  55. m a et conesit) set (401 - 9b)+ etrao, ax sesi tubia
  56. 4
  57. Et ut tobtabus s quod
  58. uobse lati
  59. xl
  60. =()10) 1. 5. b X (s = - 26∞1
  61. (2) (5) 24V Al
  62. (2) B) 33V

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 75v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0150?run=74