Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 86r

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: 0.80.

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. 87v); this page is its right half.

The machine reads it as

  1. Si aquana hsfe- ageraaac sobb
  2. 111I. 11 1, 110. 110 ad
  3. o 4. 1ono
  4. 2a)n+ qu (n (+ 1o a)
  5. 4. 10
  6. 2. 111 10al 4. 120. 120I = 4. 190.120 al - 4. 100. 120 a a
  7. a eve
  8. seu n + 111b + 10a =
  9. 2. 120
  10. ((1 = 4. n0 20) + 2. 1o( D - 4. 120) al + (110. 110-4. 100. 129 au)
  11. 2. 120
  12. 1. 2 120 . (16 -4. 100. (20) aa (115- 4 12d
  13. Ergo C.2 qu 1o. 1 10 10a a lu 11. 2 25
  14. qu. 111- 4. 128
  15. 118. s qu (at - 2. 120) = (118 - 9. 100. 120) (115- 4. 120)
  16. seu 110. (111- 2. 120) = (110- 4. 10. 129) 111 + 2. 120
  17. (110. 111) -, 110. 120 = (110.111) 5, 118. 120 = 4. 100. 129. 111 = 8. 100. 128. 120
  18. et divisis oumbus per 120 fint (L118 = 4. 100. 1 4. 100. 120 1 seu 110. 10 = 100. 11 4
  19. ae bb - 2 bb (9. 2a) - 4 bb a = 0 se bb - 2bb + 2a bb - 4 a lb = 0 - 1 - 2 - 0
  20. seu 2bb = 2 a bb su g = - 2a = B- qua,: a firet l = 2aa seu f - a V2
  21. nn + 1M + naa =0 fiet nn + nan + unaa = Y (11. 1 - 4. 12) aa: 4
  22. et fiet nec n = - na + YC11. 11 - 4. 12) a, : 2
  23. sit c 120l + 11In + 1ca + 100R a fiet nn + (nl + 10a) n + I + Weal 2100 ac
  24. et fiet W na = 111 I + 10 a et 12aa = H1 + 110 al + 100 aa
  25. 120
  26. Ergo fet n = = 11L = 10a + Y(nI. m 2.m. 11042 + 110. 10aa) : 2. 120
  27. C4. 20 1oll 4 4. 10. 10 al - 4. 100. 1204a
  28. I + 211 (1 = 2 120) al = 10. 10 = 9. 100. 120 au, debet reddi extrahibilis
  29. 2ca
  30. 120
  31. 1II. 11I - 4, 120. 10.
  32. III. 11I - 4. 120. 120
  33. hoc fet si qu (=. (11 - 2. 120) ) = 110. 110- 4. 100. 120
  34. hoc liet si ubuu1
  35. 111. 11I - 4. 120. 120
  36. 1II. 11I = 4. 120. 120
  37. ce + aY seu g+ 112 C = 1(. M 4 1o nocC + 3 1 10a p) - (9geC. dage C HaB) e11. 0 C 1M M1 seu seu 11- 242
  38. 11L. = 4. 120. 120 (11+ 2. 120
  39. Ergo fiet 1o. 10 qu C11 - 2. 12o) = 10. 110 = 4. 100. 120, 1, 11 = 4. 120. 120
  40. siu 110. 110 (111 - 2. 120) = 110. 110 - 4, 100. 120, 111 +. 2. 120
  41. aitoque (110. 110. 119 - 2. 10, 10 120 =(110. 10. 11, 4. 100. 120. 111 - L 2. 10 n0. 120 - 8. l0v. 10. 120
  42. destructisque destruendis et divisis omnibus per 2120 fiet
  43. . 100. B. 111 + 2. 100. 120 = 110. 110. aquatio generalis pro solvenda
  44. aequatione 120 l + 1i ln +110dl + 100 aa = 0, ita ut FCeten
  45. ino l’et n habeantur inter se ratione relatione rationali simplice egr
  46. jam in casu praesenti ubi est al + quln + abt + aabl. = 0 fier
  47. un 2a,
  48. 100 = ) Ac- abl - q
  49. 120 = a et 111 = q 2a, et 110 = b et 100 = bb : q fiet
  50. 150.10
  51. 2. 106. 120l
  52. 119. 110
  53. bb- 2abb + E abb = bb
  54. quae est aequatio identica, adeoque
  55. itaque calculum exequamur in ipsa aequatione
  56. (h +42a in + b5 + abb =0 firt nn + (2 2a( + b) n + U + bl + abb = 0
  57. ris succedit:
  58. nn + (4 2 al + b) n + 4 (99 - 4 a4+ 4 aa H+ 2b 4 2al + bb) ceq.
  59. (x ef 14 - 4 a q aa)) U + Cab (4 a) 2ab 11 + aa bb
  60. seu
  61. 40a
  62. 4aab
  63. -44bb :9): 4aa
  64. seu aeq. (94- 4aq H + +2 ab4)) + aabb (1- 4a) reden: qua videatur an
  65. pars dextra aequationis habeat numera torem extrahibilem, fiet dividendo eum
  66. e aab
  67. per 47. 4aq fiet H 4 qui I + 2a 4a 1 + aa bb
  68. seu
  69. 9. 9. 4a
  70. I + rab 1 + aa bb quod est extrabibile. Itaque fient
  71. + Cg 2a) l taab
  72. seu
  73. 2aa
  74. + ab a1(q 2ai) aq. = f - 4aa et fiet
  75. H- baq
  76. 2aa
  77. tandemque n(-
  78. sud trta malius sint
  79. 2aa Hq ai)
  80. ∞ seu n
  81. 4.49. 2a
  82. n + s= 40a - 2aad l + aab
  83. raa
  84. (H - 6ac) l + aab + l +
  85. H- 2aa
  86. raass i
  87. 2aa guassu iud 2A Ganssrbu
  88. (ff. 6aa) l + aab l ,eat
  89. s
  90. 1auf +164
  91. 16a
  92. abiS 1ac + 324)
  93. 8. s.t- 8aaf+ 28a -0
  94. 4 aas + 16a = 0 non. i pli s, et (5 naats + 324) aut = 4, 5f- 2aa
  95. raa
  96. ita enim abjiciendo
  97. 2laus
  98. 2 -3
  99. s 1
  100. (... )
  101. 1oaass uca aa
  102. f. 4aa falia mq
  103. mculet A. 2aa - 3a
  104. ada
  105. Vs
  106. seu f f- a1L
  107. iligamus ergo f - Z aa

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 86r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0171?run=74