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Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 2r

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. 1v); this page is its right half.

The machine reads it as

  1. auteras aeqnalia, et teridua sint ae-
  2. qualia, qpsae quantitates sunt aequa-
  3. les. Seu: si sit a - b = l = m Et
  4. b = m erit a = l
  5. Nam Si aequalibus a - b = (ex hyp. D)
  6. l- m addas aequalia (ex hgc. 2) b et m,
  7. nempe priori b posteriori m, fient
  8. (per 10) aeqnalia a - b + b = l - m + m
  9. id est (per 11) a = l. _. ED.
  10. 14) Theor. Si ab aequalibus auteras
  11. duac quantitates, et residua sint a
  12. qualia; erunt quantitates, aequales:
  13. seu si sit a = l et a - b = l - m; erit
  14. b = m.
  15. Nam a - b - l. m (per lyp. 2) Ergo
  16. addendo utrobique aqualia V+ m
  17. et b + m fient (per 10) aequalia
  18. a - b + b + m = l - m + b + m. E190
  19. sper V. punet 7.) a + m = l+ b a quibus
  20. aequalibus si aqualia a et L
  21. (perhyo. 1) auterantur fient (per 12)
  22. reridua aequalia, m = b. . ED.
  23. (15) Deor. Si a = b + e erit a - b = e.
  24. Nam ab utroque aqualium
  25. auferendo b fient aegnalia, a - b = b + e - b,
  26. id eet (per 1) a - b = e _. E. D
  27. (16) 7seor. Si a = - b erit b = - a
  28. Nam qui a a = - b (ex hyp) C9.
  29. addendo aequalibus irtis aequalia a e
  30. b et b (per 3) fient (per 10) aequa-
  31. lia: a + b = - b + b. Ergo (per 11)
  32. a + b = 0 seu (per 15) B = 0 -a, seu
  33. (per 9) a -- b
  34. . E. D,
  35. 17) Teor. - a - = a = 0
  36. Nam- a designetur per f. seu
  37. sit - a = f
  38. in omni aequatione alijiere licei quod est ntratia
  39. ostendendum et si a = b esse - a = - b
  40. equitur ex 1
  41. sed si - a = - b sequitur a = b

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 2r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068010:0003?run=73