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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 201r

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: 0.83.

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. 200v); this page is its right half.

The machine reads it as

  1. 3XX + aq =0 et in aequatione x raqu +aar =o substituendo valorem ipsius
  2. X inventum sut S- La4 fiet aqV. aq aq . aq + aar =0
  3. seu 341-Ea9 + ar =0 seu aj Hinc si aq est quantitas affirmativa
  4. limes est impossibilis, omnesque adeo radices sunt possibiles. Sed si sit aq quantitas
  5. negativa = =ap siet - 2DY ap + ar =0 seu p 27 p = rr
  6. qui elites radicu ei possibeleam itaque arY - 2, p3 = 0 est lines
  7. possibilium q radicum binarum, ut aliu dudum constat
  8. Sit aequatio X x apKX + aeqX + ar = 0 multi plicando per 0, 1,2, 3, 4, frit
  9. 2a pXX + 3 aa qX + 4 aY ~ vel 3X+ ap + aaq 3X t 2apX _ + aaq = 0
  10. Harum prio trium aequationum priga multiplicetur per e, secunda W0XX + YX + 1
  11. tertia per 22X + 23 addendoque in hinum duas primae posteriores ce primae aequa
  12. ix secunda--3a+ 4aar,. E
  13. iud
  14. diet
  15. eX+ X +CapXX + CaaGX + Car
  16. identificanda cum
  17. 102a pX + 103acIX10. 4ar +
  18. +IaBX7 + II. 3augX = 4 11. 4aY X
  19. + 122 ap XX + 12. 3aagX +12. 4 eY
  20. 2d3X+ hap 22. 2a p +22 aagr
  21. 1. 3X3 +23 2 123mq
  22. 23. 2a pX + 23xa9
  23. +23137
  24. ex htia - - X3 = 2a pX + aaq, : 3
  25. fiet XX = +4 pp X + 2ap9, : 39
  26. 1 aV X
  27. = = Z agx - 2aaY
  28. seu X = +2ap : (4 ar.
  29. seu Y U 4 appqi traarq,i 2 arp Bp9ag9
  30. X
  31. F2aa2
  32. ha
  33. l 3ag
  34. quem valorem ipsins X sub itnendo in aequ. 2P∞X +367X + 4aar - 0.
  35. habebitur aequato dans liniitem. videamus
  36. Examinatu operae pretium foret, an haec liminum investigsatio non servial
  37. ad radices irrationales aequationum inveniendas. In secundo certe
  38. et tertio gradu manifeste id contingit videndum et in quarto, qui
  39. et ipse jam dudum in potestate est

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 201r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0401?run=74