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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 364v

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. 363r); this page is its left half.

The machine reads it as

  1. VX
  2. dy: AX = ax + yy,: aa
  3. du y = Saxex + Saxgy
  4. a
  5. dy -a ax dx + S la auxe + sexraxyys + fax y seu y = + fax yy
  6. Se
  7. +aa a
  8. aa
  9. aa
  10. fit y = XX + X (dx X + Sax X fax q + sex 1et sar gy
  11. y
  12. ra a 4ue
  13. L +K, + erc.
  14. Ea P20a
  15. d aady = axdx + Cyy dy
  16. sit y = _ 10 + u X + 1 X + 13X + 9 X erc
  17. est = 1 +2. 10. IIX +2. 10. 12X + 2. 10. 13X3 + 2. 10.4 X eu)
  18. 1. 11. 11 2. 1. 12 2. 11. 13
  19. =aadys. a1, 1. 11 +212. +3. 13 +4. 14
  20. + axx
  21. t a.
  22. r. 12. 12
  23. +5. 15
  24. st 10 20 et 1 = 1 fiet 12 = A. 2a et 13 = - 1. 3a et 14 = 1: 4a et
  25. ia
  26. si ponas 10 =0 sit etiam 11 = 0 et sed habetui 12, fit 13 = 0 et 14 =0 sed habetur 15.
  27. C redy 10 + vdy edy = 10 + uy + 12y
  28. O= 20 + 21y + 22 y + 23y et. d29 + y t t y d 20 + 21 y + d22. 7 + d23 y
  29. + 1. 21 dy + 2. 22 y dy + 3, 239 dy =0 seu Ody = d20 + d21. y + d22. 1 + d23. y
  30. seu fit ed21 + e d21 y + e d 22y + e d23 y
  31. 1. 10. 21 + 210. 22 + 3. 10.23 +4. 10. 24
  32. +, 1 21 + 2. 11. 22. + 3, 11. 23
  33. + 1. 12. 21
  34. + 2. 12. 22
  35. 1. 21 + 2. 22y +3. 231
  36. etc ) (4
  37. ell p=0
  38. MM
  39. ek
  40. Ponamus abesse 12 erunt tantum linees du in linea aequ. 9 quod est minimum
  41. si coincint it coincidant mulliplicemus per crucem, ultimo temino se mbsoluto
  42. ex
  43. fiet Eeldri + 1. 10. 21 = d21 + 2. 10282 + F fF 2 1. 1. 20. 21
  44. Si, faciamus 22 =0 23 =9, et fiet 1. 12. 20. 21 = 12C d21 + 1. 10. 12. 21, is 12 =0
  45. habetur d2+ ex ex 5 et 6 trabebitur aequ. sine 121, cujus ope dabum dabitu
  46. relatio inter 20, et 2) hanc differentiemus fiet nova aequad
  47. in qua 20, 21, dio, d21 po, ita tollendo tam 20 21, quam d21, habetur
  48. aequatio in qua sola incognitarum extal 2 et 20 et d2o. sed ita inci
  49. dirum in problema aeque difficile ac datum, nisi sciremus 20 et 21 et caetera omdi
  50. esse quantitates rationales per X. Hi calculi sunt imme usae difficultatis otlon-
  51. gitudine sed puto thecremam odi posse
  52. sane datae 10, 1t possunt ordine tolli, constat
  53. sed func descendet 20 ad multus aeferiores differentias adeoque apparebit
  54. tandem an tale quid sit possibile in rationalibus.
  55. si absit (2. sola superest aeg. 5. et habendo 2I pro costante
  56. piet 1. 10.21 = 2.02 C 1. 11. 20.21. seu 20 = 10. 21 : 11.
  57. e dy 10+ 11y O2 20 +21y 42o + du y + 21 dy = seu e2idy = = ed20 - edu1 y
  58. = 10. 21+ 11.219. ser +10. 21 + 11. 21 45)Confer cum aeq. 2. fiil 10. 2.LI e2tdro-
  59. 1 +C d20 + C d21
  60. 10, 21. 21 + C. 21d20 11. 20. 21 + 020 de1 si 21 esset gans fieret 10. 21 + C d 20 = 11. 20
  61. sed retenta L 21. diveilatur aeg. b in duas e(2) d20= 11. 20 (21 et 9 102
  62. et 10, 21. 21 = 2. 20d21, Ex ag. 7 fit (d20: 20 = (11: C. Et seu log 20 = S11:
  63. et ex aeq. g fit (10. C: 20 = - 1: 21 Habetur intur generaliter quando dys et y
  64. non assurgunt ultra gradum simplicem, nec ducuntur in se invirem, quicquid
  65. demum sit de habetur solutio per quadraturas. Et verum esse sum exsiertus

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 364v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0724?run=74