Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 4, 13, 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: 0.87.

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. (6) Theor. si a = - b erit b = -a
  2. Nam quia a = - b (ex hyp). Ergo
  3. (per 10) addendo aequalibus istisque aequalia b et
  4. b (per 3) fietit (per 10) aequalia:
  5. a + b = - b + b. Ergo (per ((ic) a + b = 0
  6. seu (per 15) a = 0 - b, seu
  7. (per 9) a = b. nu
  8. 17 pheotadi
  9. a -a =0
  10. Nam -a sit f. Ergo ex hypothesi
  11. -a = La opsiot 5- f a 14
  12. Nam a sit =f jam (per 3)5.f0
  13. Er Nam -a designetur per f. seu sit
  14. =a = f jam l f - f = 0 (per 3.) Ergo
  15. pro f ponendo aequale ipsi (ex hyp) - a fiet
  16. =a = -a = 0
  17. sheoro)
  18. Q. E. d
  19. 18-- a = + a
  20. Nam = a = = a = 0 (per 17) et 0 =
  21. =a + a (per 11). Ergo (per 5) - a - - a = a + a
  22. Etg Unde utrobique addendo a fient (per 10)
  23. aequalia +ara 2- a = -d + a + a.
  24. Unde (per 11) cecaaC QED
  25. 0- - a = 0 + a seu (per 9) - - a = +a
  26. E
  27. (18 Addenda ascibuntur signis.
  28. retentis. sit f cui addi debet
  29. a - b fiet f+ a - b
  30. sit a - b = e. ergo si f addi debet es
  31. efit f+C (per 6) Ergo pro e substituendo mimorum abjicere ab una parte
  32. tuendo valorem (per 2) qui est a- b
  33. +(ex byp.) fiet f+ a = b Q. E. d
  34. 19) Adde Subtrahenda asribuntur
  35. signis mutatis + in d vel - in +
  36. At F cui detrahi debet a- b fiet
  37. = a
  38. - a-b = f + a - b
  39. Nam f- a b - f - a b et
  40. mo (21(18) Qua Explic. Quod de S toto sub
  41. formula sub vinculo comprehensa
  42. significatur, intelligendum est de
  43. singulis membris vinculo conclusis
  44. ut a ut - (a = b) aignificatur a
  45. vel a - b significat - a - - b
  46. (22)Addenda ascribuntum signis
  47. (per per
  48. retentis. seu sit f + (a - b) = f +a
  49. mant
  50. Nam f, (a -b) = 4 +a + b = Mperto (per 19
  51. Sran b
  52. 19) Theor. - ta = -a aut + - a = -a
  53. (19)C
  54. +da
  55. e-
  56. Aa t
  57. patet ex 8
  58. patet 8.
  59. n
  60. (20) in omni aequatione licet
  61. et signo contrario affectum ponere
  62. in altera
  63. sit a f+ a - b = h. dico
  64. fore f = h - a + b. Nam in
  65. aequatione (ex hypothes vera) f+ a - b -
  66. addatur utrobique -a + b, fiet indes
  67. futa - b - a +b = h = a + b, id
  68. est (per 11) f= h - a + b
  69. G. E. d

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 6r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068010:0011?run=73