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Leibniz-Handschriften zur Mathematik LH 35, 5, 15, fol. 5v

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: 0.85.

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. 4r); this page is its left half.

The machine reads it as

  1. ab + b - a
  2. aeque
  3. 2a
  4. b +b a
  5. + bb - 2ba +aa
  6. 4 aa b6
  7. aab b + 2abb - 2a ab + bb - 2ba + aa a b + b - a
  8. ergo a aequ
  9. L aequ
  10. 2 ab
  11. 4a a bb
  12. abbrab 2 ab + bb -2ba +aa - 2aab = Xabl
  13. +aabb
  14. -a bb + bb = 2baH + aa aequ 4 abb + a a bb
  15. seu b - a aequ b s2a +aa. seu b aequ
  16. a aequ
  17. 2XX - X
  18. asrax tgx+8 -x 2 seu baqu
  19. l’aequ.
  20. 1- Vrataa
  21. 2XX +7X + 6
  22. 15 225
  23. 2XXa = Xa aequ. 1. Eugo a XX aequ 1 = Xa ( aequ = X. Rarsus 1XXb + 7Xb + 6b aqu. d
  24. Ergo 2X∞ aequ. 4(- b - 7X sErgo L (x) aequ - 6 - (dX. Ergo X aequa - L + 1
  25. seu x aequ. b - 4 +6 ab. Ergo a aequ.-
  26. seu
  27. 6 ab.
  28. 3b a abb
  29. bb -2b a + 12 abb + aa + 12 a ab + 36 a a bb 1b.
  30. 36aabb.
  31. bb - 2ba + (2) abb taa (12) aab 36 aa bB 6 abb _ b aat 2qbaabb)
  32. s
  33. sub
  34. seu bb =2b a + ag aequ36 a bb= 6a bb - 6aab aequ 30 abb-6a ab
  35. ergo necesse est a tb - 6aab cric sempen esse quantitatem
  36. ratio nalem a. b erc. sunt. 4. 3 he 2 etc.
  37. Ergo sia est 1. et b est 2 erit 2a bb ∞6d ab ∞qu.. 30 - 6
  38. aego
  39. baequ IXXHEFB = X1 2XX+ZKHI
  40. CXK. X
  41. per erit 2XX aequ. 1+ xa
  42. peraqu. 2. erit 2XX aequ. 1 - 3xb - b. per 3 et 4. erit: b + ab X aequ a = 3b= ab. seu erit
  43. er
  44. X aequa - b - ab
  45. 4 ab et pur3. A etrC
  46. 2ab.
  47. 29b +34 abX aequ afx - Abx (d gb∞. seu 3 X aequ. 2a
  48. aequanda duos valores ipsius X, ontic 6 e: 8. fiet.
  49. 21
  50. ENCL L
  51. aa ab -ab a - b - 3ab 45
  52. Ergo 4abg +4a ab-3aabb semper
  53. (8) a bb aequ. aa - 2ab + bb, ( aab t abb) (3aab (+ 3 abb) + 3aa bb iit quadulu
  54. a et B sint dut
  55. proqessionishujus E. B.
  56. X seu _ 2 ab + 4 abb + 4a ab aequ aa + bb + 3a ct bl.. Et ordinando bb - 4aa. 2a b aqu - aa
  57. G3
  58. aequ (1) + GC + 72
  59. seu bl gaa ora BCs bb - 4aa +2a b. + 9a1+ 4a + aa
  60. 1thaa 4a
  61. 1+ 3aa-4a
  62. Ergo b aequ 2aa +2 + a + 8a
  63. 1- 4a +3aa.
  64. 1-8a +6a a - 24a + 9at
  65. aequ.
  66. +16aa
  67. 1+3aa- +a 1+haa +a
  68. aa +44- 32, 14 ar quta
  69. 1- 8a en.
  70. si a sit L. func a + 8a erit = + 8sa
  71. Ergo a + 8a. debet semper esse quadratus posito esse
  72. a terminum seriei. si a sit 1. tunc a +8a erit 9.
  73. seu 1 + 48. seu 49. quod unde patet rem succedere
  74. sed nullum inde video usum nisi ad varia theoremata 3Condenda. 36 possunt quidem hoc modo etiam
  75. occurrere problemata, sed quae raro occurrere solent, ut si quaerat aliquis a me regula
  76. inveniondi infinitor numeros numororum paria, ita ut uno nominato a, altero b sit
  77. 4abb + 4 a4b - 3 a abb quaedratus, et A abb - a a + 2 ab - bb + aa bb etiam quadratus
  78. quod alias difficile, quia dua tantum
  79. salie sacient bin quolibet proximi seriei proposilae, a
  80. incognitae et totudem postulata,
  81. X aoqu
  82. seu XX aequ aabb fa bb 2aab

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 15, fol. 5v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068033:0010?run=73