Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 1, 9, fol. -

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: 0.86.

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

The machine reads it as

  1. si a = l et b - m erit a - b
  2. si a = l et bem erit a - b = l- m. si aequalibus detrahas aequalia restant aequalia
  3. num a - b = a - b. (per ident.) et in posterione
  4. pro a substituendo l, et pro b substituendo m
  5. aequalia (ex hyp. 1. 2) quod licat (per ..) fiet
  6. a - b = l- m
  7. Z. E. D
  8. coroll. si a = l fiat a - b = l - b
  9. constat ex propiiupro M ponendo b
  10. si a = l et a+ b = l + m fiet b = m
  11. Nam b +a = M + l, (per transpos. add)
  12. Er ergo (per praeced.) b+ a - a = m + l- C
  13. Ergo b = m Q. E. D
  14. Ca corulli si a - l et a rb = leb erit
  15. coroll si, a + b = a + m erit b = m
  16. constat ex prop. pro l ponendo a
  17. si a = l et a - b = l- m erit b = m
  18. A - b = =b a Nam
  19. si a - b = l - m et b = m erit a = l
  20. Nam adtibs aequalibus fit a - b. + b = l - m + M
  21. id est a = L. E. D
  22. si a = b = l - m et sit a = l erit b = M
  23. adt detructis aequalibus fiet - a + a - b =
  24. -l+ l- m idest - b = - m. Unde per ...
  25. est b = m
  26. -a - b = -b - a. seu transpositio
  27. Nam si = a - b = c et - b - a = d fiet
  28. + a - a - b + b = a + C + b et 1b b a +a
  29. = b a d+ a Ergo a+ c+b =0. Et similiter
  30. + b = b = a + a = b + d + a = 0.
  31. Ergo a +c+ b = b+d + a Ergo c = d, Q. E.d
  32. 0 - a - a seu e non su
  33. Nam 0 a = b
  34. Nam o a = _ 06+0 - a
  35. sit 0- a = C Ergo 0- a ta = c+ a.
  36. 0= a = c. Ergo + b +0 - a = b + c. Sed
  37. Ergo 0 = c+ a
  38. ma = - a
  39. b+0 = b (ex def. Nihili) Ergo b - a = b + c. seu
  40. per.. 1) C = -a Z. E. d
  41. +9= 20, vam 40+0 =0 -0 sd +0
  42. urobique ablici et fit
  43. ea a b irit na-
  44. hoc demonstrari non pt, nisi porendo anc
  45. o- a = -a. li ona=c sit oaram cta
  46. fit s eta Nar
  47. pa ergo e 10+0a = 0+C
  48. non sit b aa - a +Y
  49. ona = - a +b b- a
  50. b1o A= a
  51. on a C fit b40C
  52. 4+0 a = a+C. sd b +0=b
  53. ergo a-a =a+C
  54. ast
  55. rb
  56. a + b = +b -a
  57. Assumatur pro vero fC. ta atb b+a+ a + b
  58. Ergo b+b = b1 at a+b- bebrara =ata
  59. +a b = xb a - a + b + a = + b - a + a seu
  60. Ergo bab= Ba
  61. =a 1a +b = b - a + a seu b = b quod est verum
  62. Inde cotinere converso L b a+ at b = b - a +q
  63. b2b e B b = b et Ergo 0+ b = b+0.
  64. ergo
  65. 2a+ a + b = b - a + a. Ergo- a + b + a = b - a + a
  66. a b- c erit c- 1 a + b
  67. et u si C = a + b erit -c = - a - b
  68. si C= a +b erit - C = = (a+b) ex lege substitationis
  69. sed (a+ b) = - a ub (ex significaoe vinculi)
  70. Ergo si c= atb erit - c = - a b
  71. di - a - b eut = - b - a
  72. Nam sit nab =c fit a.
  73. sit a+b = C sit = a - b = = C (per..) erit et b+a =C
  74. aeb auaub esit ea
  75. ergo -ba a = =C Ergo - a -b = - b - a q. E. d.
  76. 0 - a = = a Nam a +0 - a = + a = a = 0. Ergo
  77. a+0-a = 0 2 = a= 0 quod est verum jum
  78. invertomus incipiendo a finelli a-a = 0 Ergo a +0-a = - a2 a
  79. Ergo a + - a = a - a. Ergo at
  80. hic nod haec consequontu ut demonstretur st praesusponi
  81. a+0
  82. videlu a oua=a
  83. ergo = a +b = b-a
  84. s
  85. t0-d - 8-a

Cite

Leibniz-Handschriften zur Mathematik LH 35, 1, 9, fol. - . Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 39). https://leibnizlegible.com/page/00067968:0040?run=39