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Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 1v

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: 0.90.

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. 2r); this page is its left half.

The machine reads it as

  1. (8) Explic. Signum + omni notae magni-
  2. tudinis sine siono sumtae pretigi potert
  3. aut pratixum intelligi. Sed initio
  4. sape omitti solet, ita que a = + a et
  5. a + b = + a + b. Hinc et + + a = + a
  6. U ripenatur f= + a, fiet a- + a f
  7. (ex hypoth.) = + f = + + a
  8. 9). Explic. +0 + a = a. Seu 0 est signum
  9. nitili, quad nisil andit.
  10. 10) Teor. Si aqualibus addac a-
  11. qualia, tiunt aequalia. Seu: si sit
  12. a = B, et b = m erit a + b = l + m
  13. Nam a + b = a + b (per 3) eitaque
  14. in altero a + b, pro a ponendo
  15. l(ex hyp. priore) et pro b ponea-
  16. do m (1x hyp. posteriore) quod licet
  17. (per 2 utique em a + b = a + b fiet
  18. a + b = C+ m _. E. D.
  19. (1) Ab a Subtritne B. Significat in magntudne inqua ponitur a, suncte aequalem ipsi b, eamque tolleri. Hnc si in
  20. ( Expbiont an a =0. eu
  21. (signum denotans minus vel sub-
  22. tractionem) significat id quod
  23. quoad qu sui
  24. positum fuit urus
  25. terroiam, etru
  26. otam
  27. u et
  28. nitil. Ci quid aliua ad est resi.
  29. duum appebatur.
  30. 12) Theor. Si ab aequalibus ante.
  31. rar aqualia, residua sunt aequa-
  32. lia. Seu: si sit a = l et b = m
  33. eret a - b = l - m
  34. Nam a - b = a - b (per 3) in
  35. posteriore pro a ponatur l (et hyp. 1)
  36. et p bponatur C (ex hyst. 2)
  37. Ergo ex a- b = a - b fiet a - b = l - m
  38. Q. E. D
  39. (13) Thor. Si a quantitatibus duabus
  40. anteras
  41. dus indicatur
  42. s scribendo: a - b vel + a - b.
  43. magnitudine, in quo est a, nihil pliud esse ponatur
  44. intelligatur quam restat nihil
  45. adeoque e ne
  46. CO
  47. Et
  48. aa b R- b seid ab = 26. Erro per 15 a =b
  49. = vel ei aequale, seu uno verbo
  50. q ejus quantitatem positam,

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068010:0002?run=73