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Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 12v

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 11r); this page is its left half.

The machine reads it as

  1. 26) = b = - 1, b signifiat b poni subtractive adhoc, seu multiplicam per numorum significantem unitatem subtraction
  2. ut scilicet b per hoc tollatur ex magnitudine cui ad ubi ponitur -b
  3. ponitu
  4. 26 diguam subtractionis, seu Minus, est
  5. contrarium signe + et quod fuit positum aufert
  6. (27) a a ∞0 seu pituto
  7. (28) ot a a seu 0 non auget
  8. (29) Et a - b significat vel b tolli ab a
  9. ex a, debere ex eo in quo ponitur Ra
  10. (27) b - b = 0
  11. ) sa bre si ab aequalibus auferas
  12. aequalia residua sunt aequalia. sit a = l
  13. et b = m erit a - b = l - m
  14. Nam a - b = a - b. _ in posteriore pro a
  15. ponatur l et pro b ponatur in Aaequalia ex hypothesi
  16. pro aequalibus (per 2) fiet a - b = l - m Q. E. d
  17. (29) si a = b+ e erit a -b = e.
  18. Nam a - b = + e - b (per CB) sa
  19. L b. b + C (per e+ B C b ( per 7)
  20. (29) eet si a = b + e erit a - b = e
  21. Nam a - b = B2BB brC = b (per 28)
  22. b +e - b = (per 7) e+b - b = (per 29) e+0
  23. = (per 10) e
  24. Q. E. d
  25. e t (30) ab ab 1b = = ab
  26. 30) is Minus in plus facit minus
  27. seu a, in + b facit - ab
  28. (28.2) Si a quantitatibus ducabus auferas
  29. iqualia et residua sint aequalia
  30. quantitates sunt aequales
  31. 31) plus in minus facitplus seu ta, in - b
  32. Nam +a in - b = (per 16) + a, B-1, +b
  33. = (per 20) 2t, ab = (per 26) = ab
  34. (( (32) Minus in CMinus facit
  35. plus seuag a b E
  36. 32)g
  37. Nam g Ergo Agug
  38. Nam 29-g = g-g
  39. (33)
  40. (2)
  41. si h= = g erit q- = h
  42. Nam h= = g (ex hyp.) Ergo FB (per 12)
  43. 9+h = g-. Ergo (per 27) 9th =0. Ergo
  44. )(pr (per 29) 9 = 0 -k
  45. per mete Eego(per 10) g= -h
  46. L. Eud
  47. _g= = - g
  48. Nam g = =h, posito h~ - g (per 33)
  49. Ergo in _ aequ. I =- h pro h. ponendo
  50. valorem -qfiet (per 2) fret.
  51. g= ∞- 9 9: E- D
  52. 34) Minus in Minus est plus
  53. seu s a in b = ab
  54. Nam = a = - 1, a et = b = -1, b, (per
  55. = C per 34) +1, ab = (1 per 21) ab
  56. n. addas aequalia (3) Axioma: a = a
  57. Nam si aequalibus ab e
  58. b et in fintt a - b + b et L = m + m seu (4) Si a = b sequitur b = a
  59. chagui
  60. per 27) a et l
  61. 9. E. d
  62. 28. 3) Si ab aequalius auforas duas quantitates
  63. Ergo L a; in b ( et ab, (per 20)
  64. 21, - 1, ab= (per 26) -i, ab
  65. et
  66. s a - b = l m et sit b = m
  67. erit d = l
  68. et residua euit aequalia erumt
  69. quantitates ablatae aquales sit a
  70. Nam =a in +b = - al in ab C per 26) - 1, a + b = (per 20)
  71. -1, ab ( ) = (per 26) = ab
  72. facit = ab
  73. Si et a - b = l-m
  74. erit b=m
  75. Nam ex a - b = l - in fiat (per 11)
  76. rando aequana ex ppesi) aet
  77. i a = b erit - a = -
  78. a + b be a - b + b + m = l - M rM X
  79. Id est (per 27) at =. l+ b ergo
  80. caper erunt C
  81. (32) = a - =a = 0 sit = a = n
  82. Nam sit = a = f erit - a- - a = f-5 per 20
  83. (per 18) M X b, (per 20) cuife
  84. (2) ge
  85. = - 9
  86. Nam - g Ergo (por v) qug
  87. Nam f ∞9 =0 (per 17) Ergo
  88. qug
  89. sed 2 -g 29 = 0
  90. g- g- -g = e.
  91. Ergo g = - - g
  92. Aliter a
  93. (∞9) = (g) = 0 (pr 32) = G9 (per 21
  94. g
  95. Aliter (8) (9) (p 31) = 0
  96. g 0 = (per 32) (=9) - (9
  97. seu -g - -g = (per 12) g - g. Ergo
  98. (per 28. 2) ag = 9. Z. E. d

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 12v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068010:0024?run=73