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

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: 0.82.

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

The machine reads it as

  1. nadrat
  2. Duo numeru aequales
  3. quatrato numero datr Dato in numeris AC vel AD, radio circuli DC. contro
  4. A descripti, vig. 15. invenire in numeris ipsas
  5. AB et BC
  6. Manifestum est si in numeris irveniantur DB et BC
  7. etiam haberi AB et BC quia DB auferendo a radio
  8. in numeris dato, restat AB.
  9. jam appellemus DB, X
  10. fier aequatu 2a X - X B y.
  11. pro y sub stituamus X7
  12. fiet aequatio reformata.
  13. B2
  14. et BC, y. et AD, a.
  15. eptolt
  16. ponendo bp, 1.
  17. 2aX = X s X
  18. et divisis omnibus per X, fiet 2a - X p XZ2
  19. l
  20. 2
  21. sive 2ab ,, bX + X. sive 2ab
  22. et erit AB,, a - X, +
  23. et BC
  24. Z ay
  25. b +7
  26. posita AC a.
  27. ab + ay - 2 ab b2+ 72 H
  28. e
  29. 2+Z2 1 sive B
  30. X
  31. itaque in rumeris, ponendo a 15
  32. x
  33. e
  34. 2
  35. D
  36. ay2 ab2
  37. b2 + Za
  38. et sumta Z. pro arbitrio
  39. b
  40. 1
  41. 1. -
  42. 2
  43. fier b + Z2 15. adeoque a dividi poterit per b +7. ac proinde
  44. L
  45. etiam in numeris integris habebuntur, et fiet: X p 6. et AB, +9.
  46. et BC AV ⊓ 24. Nempe 24 - 9 e 15.
  47. Ratio cum pr summa quodratorum exierit differentia, haec est, quod
  48. det debet fieri X minor quam a.
  49. Erit ergo a 24b
  50. et
  51. 9 + 24 1
  52. seu b+
  53. 62+ Z2
  54. 152
  55. a
  56. P 2b
  57. sed si quastio nec sit dato in numeris quadrato radii, non ipso
  58. operatio ese. Nec semper exitus habet
  59. radio, inveniie AB, BC, in numeris, alia difficiliorque quaestio est
  60. videamus. Estr AC, 1ab. ponendo a B 1.
  61. ponendo AB e C, et BC,y. fiet: co + y r ab.
  62. et ponendo M DB, X fiet: 2 fab X - X H V. et X, sab = co
  63. erit
  64. earde
  65. Cd1 tab = X. et ponendo X Y + sab
  66. 2)b (= 2 sab co) et b + 2 sab 1) = Co ny
  67. L
  68. sit aequatio yx Y + v + er + dv + ac 0.
  69. Unic ordinando auterantur ut auferatur ter minus ex, ponet pro Y, s- =C, fiet:
  70. n S C, 1 (F
  71. + +2 - = c2
  72. a c
  73. C)
  74. et ex e (Cs)- () c. item DH T- Ld, et fier:
  75. v. pone +C+
  76. +ab ne
  77. L4 25, 12, 2
  78. B p. 10
  79. BC
  80. ax
  81. 100
  82. aX
  83. a + X

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 2r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0003?run=74