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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 250v

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: 0.81.

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. 251r); this page is its left half.

The machine reads it as

  1. Generaliter (2) = 4 = (8) - 8, 1Z sin fiet. () + - 2 (2 4 - (2) 8, + Y (9 4 8
  2. seu (D qu ((7) - 4) = 8, 1 - RY) sid qu (2) - 4) L biqut (2) 7), quia qul(2) - 2) est 1orlo,
  3. ideo hinc biqu. (124) -4) = ∞ qu (1 - 24) id se sed Au (1 - 27)) = 1 et biqu (27) - 2) = qul x). 4)
  4. Ergo fit qua (2) -2) = 4 seu (7) + 2 - 2(2) 4 =8 seu 12), 1- 24 = 2- 4, et quadrando
  5. utrique (2) = 8 + 2 - 244 seu (2) - 4 8, 1- 24 atque adeo et ()- d = 8;1 e D
  6. (L unde quadrando utrobique rediret qu ((2) - 4) = X Retineamus jam aequationem
  7. 1) - 2 = 8, 1- 4, quia ita incognitae foefficientes non assurgunt ad potentiam. Et applicemus
  8. ad d et C, fietque (D) = D = C, - D videamusque quomodo id se verum ostendat
  9. explicando: D = p ab + q abe + r abed + 8 abides + erc. Et (D) -D = l, pa + q abetr abe + 8 abed
  10. C = a - 2 ab + 4 abc - 8 abed + esc. Nunc opus est ut investigemus OD,
  11. a. a = 1 a + 2 ab a. ab = 2. ab A 3 abc a. abe = habe + gabed a. abid = 4 abid +G, abede
  12. ab. ab - 1 ab 5abe t Gabed ab) abc = 3abe t Dabed L le abede ab. alid - 6abud + 10 abde + 1G abedes
  13. abe. abe - laver qabed + 19, abidet 20, abidef abc. abed = T abcd + 1 abide + 2a abides F 3 3abidesg.
  14. Et ita porro,
  15. a C - 2ab + 4abc
  16. 2. 25 ab 23 abc
  17. hinc OD = 2D0 ent
  18. - 8 abed + 16 abi de - 32 abcdef
  19. 511
  20. 2. 5,5
  21. l.bid
  22. (5) -0 = l - 210
  23. 4) =
  24. 1.
  25. Ery
  26. nota
  27. Et eodem modo (D) + D - 2(B) D = g- ) C3, 1- (9)
  28. -21()
  29. -210
  30. 6) ((C))
  31. (4) - 4 = 10062 1-27
  32. 4) - = 1016,
  33. 24
  34. 1-24
  35. Utique 1096 est vel l, vel 0, sissit 1. adeoque
  36. si omnes nota praecedentes sint 1, manifesta.
  37. est consiquentia, sed si l, vel una aliqua ex
  38. notis praecedentibus sit 0, tunc
  39. 2) - 2 = 0, 1- 24, adeoque (24) - 2 = 0, et similiter (8) -4 - 0 et hoc
  40. a notis rem revocando ad res, signiticat, si vel nota addenda nova, vel una aliqua
  41. eu notis p prioribus praecedentium columnarum sit o, notas omnes
  42. sigu
  43. sequentium columnarum post has manere, quod utique manifestum est.
  44. - 22
  45. sed hinc non licet facere
  46. 2
  47. 1-
  48. Et quia posito 2 = 2a + 22 ab +23 dbc + et Et (4) - 27 = _ l, 21 + 22a + 23 ab VabC
  49. Sed hine jam fieret 0 = 8 -, - 2
  50. seu non licet facere 8 = 1 neculicet etiam furere ex
  51. similiter posito E = 1t a + r. b + 2 abc + eted et es() - Y - l, 1 + na + 13 ab + 14 abc et
  52. ita
  53. 1, 21+22a + 23 ab +h non licet tollere l, si l =0
  54. Noluta diguum est formutam L, 2a+ l, 81a + 82 ab + 83 abc + e4 alio, + et divisilem
  55. , 1F 12a + 13 ab + etc
  56. 15) - D = 10, 1 -2 (6) =6 = 10D, 1- 28
  57. Hinc. (2)
  58. (4) - 7
  59. (27) = 4 = 1096G. et quia quadiutum ab 1- 24 est 1. fial qu (2, 4 = 3 4, divisile per
  60. esse per omnes praecedentes.
  61. Et (2) - 4 seu l, 81 + 82 a +83 abc +84 abcd. divisibile est per
  62. sumnas
  63. l’et omne
  64. 1- 2
  65. per l, 8a +8 ab 483. be tec, et per omnes provitules
  66. columnas
  67. U)
  68. 3)
  69. Ha ergo
  70. 4
  71. 4) +4 -2(4) 4 8 et (2 + 4 - 2(22 =
  72. (
  73. + 8 - 288 - 8- 2(8)
  74. (15) + P- 1+ seu (2 ) +2+ - 2(2) 2 = 4, 1-14 quadritum
  75. seu differentia duarum
  76. notarum proximatum cocumnae, est puuctum ex priore in ofpititam novae solu oppositar columnae propime prris
  77. ∞)- D =
  78. 1 - 27

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 250v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0500?run=74