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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 40v

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: 0.77.

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The machine reads it as

  1. _, _ X + bXX +aCX, ae quari debet quadrato. Itaque patet
  2. seu X, Xx + bx + ac = agy si ergo sit X = Ergo
  3. a
  4. L
  5. debebit abZF ac. ae quari quadratovo Atque adeo
  6. quadato
  7. etiam AbD+ bb aequabitur qeaet B vi + +bb - ac ad
  8. vel bb + ac vocemae fi debet uta tandem ess
  9. +4bZZ+ hadb n ap
  10. 94
  11. Adhibeamus irrationales, et.
  12. sit Z= 1(o P ti a) + DRoV+2I, a) + ((30H + 31, a) = O + D +
  13. fiet 2Z = 00 + DD + 2E + 2(OD+ 02+ D8) G5 O: p E + bBODHEBD, WDB,ADDq
  14. 10al + nb +2, dD + OE+ 2 19
  15. 200
  16. 10 1
  17. 3a
  18. 2t
  19. 10. 20 P (P. ( on ad 1ua
  20. 2030.
  21. 182
  22. 0.
  23. uad u
  24. 30.21
  25. 21.50. n.
  26. 2.1. H..
  27. .
  28. 31.
  29. 2131..
  30. c
  31. e
  32. 1. 11 a
  33. 4 4 +
  34. 1400O
  35. sit a = 12OD F 13OQ+ 23DE7
  36. et fiet aav
  37. = VV = aa OC (12OV +2. 132390) + 2. 12. 2310 n
  38. 1390 +2. 17 ar 2. 13 ar
  39. sit nDD+ 13C 238 seu
  40. 2. 131
  41. 2 21.
  42. 1210. 20 aa PIBF 15. B 21 ~ I p. 12 a + 2. 1B. 3P9D + 2. n 3) 99, 3035
  43. 13, 10. 30
  44. 231 20. 30
  45. 11. 20
  46. 132. 10 31
  47. 23, 20 31
  48. 110 5.. +
  49. 13. 11.31 X2. 1 ar.. +2. B3ar. +2. 2har.
  50. 25, 213)
  51. aarr
  52. itaque Coincitentiati ante omnia Rationate, rrationales primaria
  53. 2.3
  54. 30..
  55. 30.31... 31
  56. in irrationalibus tentanda. Ubi paulo arctius res restricta est
  57. +aC
  58. Hic seideo e forc 13, 23 = 8. 12 33 = 12. 1 = 2 deni
  59. dende fore. (2 1. 25 4) 31a = 2ab, sed hoc non licel, quia 212 23. 4 =0
  60. 48 +(Z. 1 ( 13 ( 1. 23(4 2. 13. 24 4 -
  61. video 1 12, 13, 14 debere aequari ipter se
  62. esse (2) 12 ar = (2). Bar = 3, 23ar = (2) ab Unde
  63. Rursus 2. 13. 23 = 2. 12. 23 = 2. 12. 13 = 4
  64. nam debet
  65. 12 = 13=23
  66. sequ 12. 12 = 2 seu ent
  67. 12 - t2 12 = 13 = 23 = V2. Ergo Y = b: 12
  68. supersunt 10, 11, 20, 21, 30, 31, pro cointidentiandis
  69. Per y quaeratur, et
  70. per 20 quaeratur 21; utrunque rationaliter si commode licet
  71. 1p.
  72. sed quiq tandem in sydzue prodiret prodit ODD ider oprt ut hoc evitetur oportat facere
  73. et comparando VV, fint 1010+30. 30 + B,. 10. 30 = 4. 10. 30
  74. vel +a ar3 30.30 +4. 10. 30 Y 4. 10. 10 = 4. 10. 1B - 10. 10
  75. porro coincidentiando Y, fiat
  76. terminis WR,
  77. aliquuam t)) constantem seu 20 20.
  78. seu 30 = -2.10 +, V3 seu 30 = (2 + 13)10
  79. (0 +30)5 b Lsi l 1 121) (+ 2 (10: 114303)) = 2 21 (10 + 30) (4 2 (10. 31 + 11. 30) a)
  80. sin 10430 = V- , 10.30
  81. Aofioroo)ia desonun seu (10 + 30) (b + 421 a) + 2. 10 (1 + 2.31) = 2.30 (21(431) =
  82. 32
  83. = 80 +20) Z= 6 + 6000 + 4 67 + 120078

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 40v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0080?run=74