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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 16r

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. 17v); this page is its right half.

The machine reads it as

  1. Si detur dya = X dx . t sit ds ambigua erit y etiam ambigua
  2. ejusdem gradus.. Nam quie libet ambignitatis ss casus habet suam propriam
  3. integralem, ergo integralis hrabet totidem casus. Idem est non tantum
  4. in du, sed etiam in ddys, vel in d y in genere, ut quot habet ambi-
  5. guitates tot etiam y habeat ambognitates.
  6. Sed quid si in valorem ipsius dus ingredititur y. Dico si g
  7. vit Dico si y ingreditur libera ab ambignitate valorem ipsius du ingre-
  8. aeuvation
  9. ditur, tunc Dico si y ingreditur valorem ipsius du rationalem u
  10. et y non est rationalis, sequitur formatum ex y ingrediens in
  11. Valorem ipsius du, non esse rationale; alioqui dus foret rationalis
  12. Et rursus si formatum ex y est rationale, etiam y esse rationale
  13. Et generiliter, si y ingreditur valorem ipsius dus rationalem, sequitur
  14. prout y est rationale vel irrationale etiam ex ipso formatum
  15. ingrediens valorem esse rationale vel irratinale
  16. veabusr verli guotia ds dy = X ey gy) + X, Dico tiay-gu
  17. st quantitos rationalis per X, etiam y tatum fore, nam si ay yus est
  18. cntonalis per X, etiam du est rationalis per X, ex per aequabionera
  19. hago etia in y est rationalis per X, ob regulam generatem
  20. si psolationalis fdgiy vaque est rationalis nec irrationalis per X.
  21. XY
  22. Si si sit aequatio 10 + yA = 0 sit differentando
  23. dio + dag + _ dus sit substituatuo valor ipsius y= . 1
  24. fiet dio dutro + ndu fiet d10 + du =0
  25. si sit aequatio 10 + 1y + u fiet duo + Duy + 2ydy + 11 dy =0
  26. et dy = - d10 - duy 3: 2y + 11 feree vel fiet
  27. V = = - 11 dy = dio: det +2du, adeoque
  28. 10 10 -
  29. 11. 11dy + 11d10 + 1. 11 dydy + 2 deodudy + dio dio
  30. du + 2dy
  31. etfiet 10 du +2 1otus
  32. =du du
  33. dudr + et duc dy + ex dydy
  34. 12. 12 yy +11. 12 ay +10. 12aa
  35. a 12. 129y + 11. 12 ay + 21a4 - 11 a - 10. 124
  36. y = a FCu-4. 1012) = 13 + 4
  37. 10da + 11 dy + 12yy =0 sit 12 constans
  38. 16 diau + 4. 10 dusdys + 4. 10 dydus ( + H. 11
  39. xcloulo
  40. =edyrydus) fit dio aa tdu ay + + IIa dy+ 2. 12ydy, = 0
  41. dio aa L 1 a du a, 1b = 4. 10.12) - 11
  42. E. 12
  43. seu 2410. 12 a (F 2. 11. 12_ay) = 11 d 11a(+ 2. 1 +2 dy - d11 L(... ) a = 2. 12dyil..)
  44. +2diodrdus fit y =
  45. a
  46. 2 dy 11 d90
  47. + 11 dydus
  48. du a + 2. 12 dy
  49. Eudio dua fiat 2. 1
  50. fial 2. 12 = 11 d1t = 2. 12 du seu 12 = LH d18,2 : xe, 90+ dio
  51. fiet denique dy =
  52. 2
  53. 00
  54. Et fiat du
  55. 2. 12 Y(152 4. 10. 12)
  56. = d1
  57. 00 +. 1d11) = 1. Ergo si 12- 4.1. 12 vocetur C
  58. le+ C SC W 00 F 11 dio - 10. 11 dir)
  59. ae
  60. ar
  61. dC)
  62. - du = dy Ergo
  63. du = d dio aa +dn ay = iL 9 sav (na n’av +4. 1aa + 4. 1r yy av = dio dio a + 2dueu ay t dnduay
  64. 4. 12 + (112 - 4. 10. 12
  65. seu
  66. 2. 12 1(1 - 4. 10. 12
  67. nihil hinc utile ducitur
  68. 1a + 2. 129
  69. fiet a1sc
  70. p +2 dudu+ modv a - av
  71. susu arta dudir aa - At aV
  72. =1flud1e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 16r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0031?run=74