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Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 5v

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: 0.94.

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. 6r); this page is its left half.

The machine reads it as

  1. explic. a
  2. (9) o+ a = a. seu 0
  3. est signum nihili, quod nihil addit.
  4. siunt aequalia. seu: si sit a = b, et b = m
  5. erit a+b = l + m
  6. Nam a + b = a + b (per 3). Itaque in alter
  7. postore a +b, pro a potrendo l (ex hyp. priore)
  8. et pro b ponendo in (ex hyp. posteriore.) quod
  9. licet (per 2) fiet utique ex atb = a +b fiet
  10. at b = l+ m Q. E. d
  11. SVB TRACTIO
  12. (11) Explic e
  13. + a -a = 0 seu signum, minus,
  14. seu signum significans minus vel subtractionem
  15. perinde esse ac si et actum esset nihil si quid aliud adest, residuum apperatur.
  16. significat id quod positum fuit rursus tollendo,
  17. (12) si ab aequalibus auferas aequalia,
  18. Dheor.
  19. residua sunt aequalla. Seu: si sit a- l
  20. et b = m erit a - b = l -m
  21. Nam a = b = a - b (per 3) in posterione
  22. pro a ponatur l (ex hyp. 1.) et pro ponatur l
  23. (ex hyp. 2) ergo ex a - b = a - b fiet a - b = (-m
  24. piss a quantitatibus duabus auferas
  25. aequalia et residua sint aequalia; ipsae
  26. quantitates sunttaequales seu: si
  27. sit a - b = l - m et erit b - m erit a = l
  28. Nam si aequalibus a - b = (ex hyp.1) l- m
  29. ddas equalia, b et ia (ex hyp. 2.) b et m, nempe
  30. priori posteriori m, fient (per 10) aequalia
  31. a = b + b = l - m + m, id est (per 11) a = l
  32. ss ab aqualibus auferas duas quan-
  33. titates, et residua sint aequalia; erunt
  34. 14)
  35. quantitates aequales: seu si sit etm
  36. et sit a = l. et a - b = l- m; erit
  37. Nam a - b = l - m (per hyp. 2). E qu addendo
  38. b = m.
  39. utrobique aequalia b+m et b+r fient per 10) aequalia
  40. a -b + b + m = l -m + b + m. Ergo (per 11R junct. 7)
  41. atm = l+b Ergo (per 11) A quibus
  42. aequalibus si anferantur aequalia a et l (per hyp. 1.) auferantur
  43. fient (per 12) residua aequalia, m = b. Q. E. d
  44. (15) si a = b + e erit a - b = e
  45. tea
  46. Nam uab utroque aequalium auferendo b
  47. fient fient aequalia, a - b = b + e - b id est
  48. (per u) a - b = e
  49. Q. E. d.
  50. (16) d a - - b erit b = - a
  51. Nam a = -b (ex hyp.)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 5v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068010:0010?run=73