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Leibniz-Handschriften zur Mathematik LH 35, 11, 9, fol. 1v

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: 0.88.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. lecare rectam in extrema et media ratione
  2. Analysis indeque deductae tam constructio Linearis
  3. sit recta ule canda
  4. quam appropinquatio numerica
  5. A quaeritur punctum sectionis B, ita ut sit
  6. m
  7. AC ad majorem BC, ut BC ad minus AB
  8. BC erit a - b et fint ab = aa + bb -2ab
  9. seu bb - 3 ab + 3 aa = 2 aa - aa = 5 aa, seu b - 3 a = s5 eritque
  10. AC sit a
  11. AB sit b
  12. b = 2a - 4 15 seu b = (1+ 2) a - a H1 + 4) Hinc constructio
  13. erit talis AB Rectada data AC addantur tres dimidiae cd, ab eadem
  14. detrahatur quarta pars AE ad datul dimidia CD, et rursus tota DE asqualis AC
  15. et ab eadem AC detrahatur quarta pars AF, Tum super FE descri.
  16. BA. AC = CBqu
  17. bame seuncirculus
  18. FGE cui ex D educta perpendicularis occurrat in G
  19. ex jam ex D ad partes A sumatur DB aequa
  20. lis ipsi DG, eritque erectem B
  21. B punctum quaesitum demonstratur ita:
  22. Nam si AC sit a erit AD ex constructione
  23. AD. (1+ 2) a, a qua si detrahas AF a
  24. restat Fd (1+ ) a currus dE est a
  25. ergo DG med. prop. inter Fd et dE, erit
  26. a ((1+ 2), cui si aequalis sumatur dB
  27. tunc erit AB, _ seu AD - DB, erit (+ 2) a - a (+ 4)
  28. jam quia AB seu b est (1+ ) a = a (1+ 4)
  29. =a + a ( = 4 comprobationes duas
  30. 1
  31. utique fiet
  32. Hini comprobationes AB = a + = a - a V1+ 4
  33. Cen
  34. Ninc
  35. prima
  36. BC = - a + a. 11+ Z
  37. Ergo AB + BC = a X
  38. segunda AB in B AC =
  39. aa (1+ =) = aa (1+
  40. secun B C quadrat = 4 aa + 1+ ) ac s- aa Y(1+
  41. da
  42. seu
  43. aa (it L)= aa Y (1
  44. Ergo AB in AC = BC quadrat
  45. 15 = 24
  46. 236062 + etc
  47. 1000000
  48. Ergo AB = L a = 118033; + et
  49. a-
  50. 1000000
  51. 481966 + et
  52. 1000000
  53. seu AB ad AC ut 481966 + ek ad 1000000
  54. 2
  55. 500000
  56. 118034
  57. 481906
  58. Figura paginae
  59. versae Huc transferatur
  60. tre
  61. e
  62. 14) = 2 1

Cite

Leibniz-Handschriften zur Mathematik LH 35, 11, 9, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068182:0002?run=74