Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 6r

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: 0.80.

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. 5v); this page is its right half.

The machine reads it as

  1. Et primum ope
  2. es aelups
  3. aequationum 6 et 7 tollamus y. Et quidem ecribendo explicatius aequationes
  4. bex fier (yy+ 3by612by + ∞ bb aequ9bb +3bv + vV
  5. +l
  6. b
  7. +=VY + 8 b0
  8. +
  9. ex VD
  10. 1b
  11. 16
  12. Lbb. =bV
  13. ina
  14. +1 bb - E bV + vo - 2b- +v
  15. aa
  16. 16
  17. b
  18. seu yaqo -aa + quad +v + b - vb qui valor
  19. 4
  20. potest substitui in aeq 6. et ita restabunt solum V et
  21. Sed videmur breviori calculo aed idem pervenire posse.
  22. Nempe quaeramus differentiales aequationum 3 et 5 tam y. X et Y.
  23. quam v. Z. S. considerando ut duplices.
  24. Ex aqu. 3 fiet:
  25. 9
  26. ZdZ - Zdx- xd xdx aqu sas
  27. i
  28. Et aequ. 4 fiet: adque. Et punctu quia du aequ t ex aeque
  29. vdv + vdy +ydvrydu
  30. adque = adx aequ vdy + ydv +2y dy + bdy + b dv sbaequ. 2
  31. 1o
  32. Et ex in his aequ. G et co. pro dy ponendo yib ax: a sex 9 et co fcet
  33. (11)
  34. vdvt vydx: a + vb dxia + ydo + yy dx. a F rb dx. a FZ dz Zdx xZ xdae
  35. adZ = +t ego vYdr: a + vbdc. a t ydv 1 2yy drra + 2yb dx:a
  36. Et in aequ. 9 et 10 pro dx ponendo ex aequ. 2.) dya: g+b fiet
  37. (11)
  38. sas
  39. var +vdy +ydv +ydy +ZdZ - Z dya: 7tb - xdz +Xdya: 7 + b aegu sas
  40. adze- aa du: ytb aequ ady + y dx +2y dy + bdy + bdv. quas
  41. 12).
  42. quationes jungendo fiet: ex aequ. 1c. dus aego sds- vav tyav +Zd2 + XaZ: v +y
  43. (13
  44. a+Z+X a: y+b. et ex aequ. 12 fiet dy aequ. adz. ydv - b dv: aa: y +b 1v t2y +b
  45. on
  46. (141L
  47. qui duo valores ipsius dypossunt inter se aequari, sed dividantur prius per d do
  48. et pro d dz: do ponatur per 8 et 9 valor y+ b:a. et pro gs ds: do
  49. e
  50. lz
  51. dz: du + i seu quad ytb +aa: a et
  52. ita ex junctis aegu. 13. 14. fiet:
  53. Quia differentiae
  54. Seu y aequ
  55. differentialis.
  56. de
  57. qutat C4, Si quad ytbraa: ∞- v + y B
  58. d stem
  59. + Z+X y+b: a,:
  60. v+y - Ztxa: gtb aequ (V +b - y - b): aa: y rb +v + 2y + b.
  61. 65
  62. e
  63. L
  64. c
  65. (15
  66. seu fiet O: D aequ 80: Q seu fiet: O0 aequ 0D. unde
  67. 1G
  68. sequitur vel O vel 8 vel D esse o. et si est o vel po tanr rarsus
  69. vel poteunte verum aliunde constat jam l ex aeque.7. quo f aequ.o

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 6r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0011?run=74