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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 73r

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: 0.88.

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

The same scan as fol. 72v (00068195:0144), where its text is given.

The machine reads it as

  1. 1.1 = 1. Nam 1. A = 1 sit a t n = (per AX. 8) sit a = 1 fit 1. 1 = 1
  2. t
  3. E 1: 1 = 1. Nam sit a = 1 A aeqvalibent 1: 1 = a: a, sed aequiralet a: a = 1
  4. (per ax. 1) ergo 1: 1 = 1
  5. 0 =0. Nam O∞ t. 1 Ergo it Nam a 0-0 = 0 (per ax. 9) = 0+0 (per ax. 5)
  6. aequival:
  7. unde Ergo Epet ex 0-0 = 0+ 0. Ergo (per ax. 2) -0= +0
  8. -a =a e a a et a = d aequivalent. Nam aequiralent - a = a et +a - a, = 2a
  9. ∞1
  10. aqui (per ap. 2.) equia. o 2a aequival. 0. 2 = a aequival 1. 2 = a p10 l. 0 -a
  11. (11) 1: b, 1: d = 1: bl. Nam 1: b, 1: l, bl= 1: b, 1: l, b, l = (perl3) b, 1. b, l1. l =
  12. per 12) b: b, l: L = (per 11) 1, 1 = Cper 8) 1)b. Ergo jungendo
  13. prima ultimi 1: b, 1: l, bl = 1. Hinc forro (per th. 12) 1: b, 1: l, bl, : bl = 1:, bl.
  14. Ergo (per 11) 1: b, 1: l = 1: bl
  15. (12) a: b, l: m = al:, bm. Nam(per 12) a: b, l.m = a, 1: b, l, 1. m = (per th. 3)
  16. al, 1: b, 1: = (per th. 11) al, 1: bM = (per 12) al: bm
  17. ver 12
  18. (13) Ca: b) + (c: b) = atC : b Nam a: b = 600 a, 1: b et
  19. c: b = c, 1. b Et (a, 1. 6) + (C, 1.b) = (per 6) atc, 1. b = (per 12) ate, : b
  20. Aequivalent
  21. et
  22. (18) s a: b = l: m erit a + b, : b = l+ m, : m. Nam
  23. a: b = l: m aequivalet (per 2) (a: b) +1 = (L: m) + 1 A quod aequivalet
  24. (per 11) (a: b) + b: b = (l: m) + m: m quod aequivalet (per th. 13)
  25. a +b, : b = l + m,: m
  26. (7) a0 = 0. Nam a0 = (per 9) a, a - a = (perth. 4) aa + (a, - a) = (per 6)
  27. aa =aa = C per 9)0
  28. (8) - a, - b = t ab Nam - ab + (a, - b) = (per th. 5)
  29. + (-a, b) + (-a, - b) = = a, b - b = (per 9) a0 = (per th. 7.) Osr
  30. =(per 9) - ab + ab. Ergo prima novissimis aequando- ab + (a, - b):d
  31. = -ib + ab Ergo (per 2) -a, - b = ab. Hoc est quod vulgo
  32. dicunt, - in = facere +, seu = 1, -1 = 1, ita - 2, -3 =6
  33. (9) a : b, c = ac: b Nam a : b, c = teb, ac (per 12) 1: b, a, c
  34. =(pertZ) i ac 1:b
  35. = 1: b, ac (= (per 12) ac: b Ia 2:3, 4 = 2. 4:3 = 8:3
  36. a. C:C = (per
  37. = a. Nam ac: C = aC (per
  38. bm dt: 1: b, 1: t = p Nam 1.b, 1: l, bl = bs stib. :l, b, l = b, 1.b. l. iel a
  39. 10) aC: C
  40. 14) () a . Aequivalent a a = C et a: b = C :b. Nam
  41. e
  42. a: b = c: b aequivalet (per 12) ipsi a, l:b = c, 1: b qua
  43. per 3) aequivalet ipsi a = c sic si a = 2 erit a: 3 = 2: 3
  44. (15) (14) Aequivalent a: b = l: m et am = bl. Nam sper 3
  45. 16
  46. peri
  47. aequivalent a b a: b = l: m et abm: b = lbm: m
  48. id est (per th. 10) am = l b
  49. ) Aequivalent a: b = l: m et a: l = b: m. Nam (pe
  50. (por 3) aequivalent a: b, = l: m, et a. b, b.l= l. m, b il id est
  51. th. 15
  52. (per 10) aam = bl et (er itemque hoc et (per 11) a: l = b: n
  53. et (per th. 15
  54. 18) Aequiasi a: b = l: m eritt a: b = a + l:, b +m. Nam, quia
  55. (per dof. aequal.),
  56. a: b = l: m (ex hypothesi) erit qm b (per th. 14) am = bl. Ergo (per 2) a0 + a =
  57. ab + bl id est, a, b+m = b. 4+ Er (per th. 14) a: b = a + l,:, b +m
  58. 17) si a. b = d l. m erit a

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 73r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0145?run=74