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Leibniz-Handschriften zur Mathematik LH 35, 3 A 32, fol. 4r

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: 0.84.

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. da
  2. b+dX b
  3. Nequa autem dubitatio restet ca - E o a ita probor probo:
  4. Eb
  5. DE a - c a. ca. est auteum hoc loco tignum
  6. multiplicationis
  7. Pars - a s. def. 3.) a = Minus def: 3. )
  8. quater
  9. Duarto aequimultiplicia esseat simpla, vg. ut sunt trca ad A. itabistria adbis
  10. quater. Cg = e Nam ca e e
  11. a
  12. C
  13. Ouinto si proportionalibus addantur demanturue proportionalia producta esse
  14. proportionalia, Ut, cum ita sint 4 ad s. ut 3. ad 6. eliam 4 +3 seu 7
  15. ad P+6. seu it eodem modo erit seusi Ergo = arc
  16. autem praedemonetro hoc lemma . bc = ad. Nam quia a
  17. utrumque per d. erit ad-
  18. H consequentia patet: (
  19. jam pergo si a+c Y a
  20. eudit
  21. 6+d = 1 erit a+C a H S
  22. Cergornultiplicando
  23. a +6
  24. antecedens probo b+dX batb
  25. (quiaha jam bc = a d per lemma praemissum. Ergo ba 4bc batbc
  26. a +
  27. cb
  28. ab + ad ab +bc U
  29. Dab t ad
  30. ca-avi Intelligitur ex ultimo isto exemplo, propositionem hara quintam inter
  31. b+ d
  32. atc. D
  33. Axiomata positam non facilioris esse de mon strationis quam alias nonnullas.
  34. b+o a qua theorematis accensentur. Crempli causa: tleorema est, si duae rationes sint
  35. atc t.
  36. b+d 2 a
  37. aequales, etiem carum inversas esse aequales; id ita demonstratur facillime
  38. a
  39. = ajo - Namsi a X = - 1. erit 6 -d: Andecedens probob
  40. d
  41. 6c
  42. da
  43. =bc - 1. Nam per temma dictum da - bc. Atque ista quidem sufficere
  44. arbitror in exemplum observationis parum creditae, necessariae tamen. ad
  45. stabiliendam contra Pyrrhonios, scientiarum severitatem
  46. a+8 b
  47. +o

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 32, fol. 4r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068245:0007?run=74