Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 227 · Eckhard, A., fol. 74r

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: 0.80.

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. 73v); this page is its right half.

The machine reads it as

  1. Ntoc, quorum differentia sit numerus retus. Pono
  2. itaque pro radice majorit numeri uti Xty, pro radice
  3. minoris x -y. Atum minoris xx-2xy tyy subtractum
  4. a to majoris ex+rxy +yy relinquit axy numerum
  5. Htum ex hypot. Esto rada exics. 4. fiatu uti qx
  6. .Unde si proma
  7. jore numero ponatur x+ , pro minore autlem e- et
  8. ritunque minoris x- 2+ subtrahatur a
  9. C4
  10. clai
  11. majoris xet = EF relinguetur (2 numerus sHtus
  12. cbxc
  13. Vel contra si pro majore numero sumatur x+
  14. b
  15. et prominore 2. Latumqe minoris Et subtratatur
  16. a bo majorci X∞+ 2, residurem XC - 2Y
  17. Exe
  18. ia
  19. . Later
  20. autem numerum 2X majierem este detere nimero f,
  21. HLX
  22. Es
  23. quia alioqui x seul nullus esset. Cportes
  24. enim tum et subdtere a to 2x. Ex. 92. sit
  25. X X4 et E∞, eritque
  26. e
  27. ∞3. Unde si la Ato ex 5 iempe 25 ausoate
  28. Titum ex 3 nempe 9, rclinquetur ttum ex 4 nempej.
  29. Vel etiam si a to 25 auferatur Ntum 9, relinquefus
  30. 2itum 1, cujus rarlix est 4. Eodem modo si statuae
  31. e
  32. A de 13
  33. etx- ∞5. Unde lh a Fito ex 13 pempe 1b9 aus
  34. ratur tum ex 5 nempe 25, relinquetur Atum ex
  35. 12 nempe 144. Vel etiam ( a teto ileus auferatur
  36. Atum 144, relinquetur iutrem 25. et sic de ceter;
  37. Uf itage in Alo rectanoulo, ABC latera omnia
  38. sint numeri rationales, hypotenusa H(sempet debet
  39. reliquorum autem laterum;
  40. esse aequalis X+
  41. circa rectum anoulum AD, BC alterum aquale
  42. ∞.
  43. +x alterum vero aequale f.
  44. Corollarium 2
  45. jicung numerus exprimitur per F, ille etiam exu
  46. mi potest per x. et contra, quicunque numetur

Cite

LBr. 227 · Eckhard, A., fol. 74r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 103). https://leibnizlegible.com/page/DE-611-HS-960119:0147?run=103