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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 107r

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: 0.76.

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. 108v); this page is its right half.

The machine reads it as

  1. X 10 arb + (3 b
  2. XB +b + 3b X. adeoque X arb X - b e sb. et quadrando utrobique; fiet.
  3. N - 6b X - 2b X, +9b2 X + 6( X +b Y est autem b. quantitas
  4. affirmativa:
  5. Haec aequatio duas minimum habet radices reales, ob sb Sed matum in eo consistit
  6. quod non nisi una habetur arbitiaria b.
  7. An c An rectius ita C
  8. XN 1O. LY + Sir + 4 + 10 + 1r + sirrus
  9. XH ZS r + q 4q X sed adit determinatio cipionis Ferrei. Aliter.
  10. X N 3 r
  11. X r
  12. : rq t
  13. ult +......
  14. X +ZY (- =r + 90
  15. + r + t...
  16. 221 L 6 7 13
  17. 7
  18. 0.
  19. i
  20. 4Sr 14, 2tir
  21. 1li 19
  22. summae Ergo bE HC
  23. Eoce notabilem formam duarum radicum d
  24. quadatranum, quarum quadratum est numerus
  25. Pro 24. compendi causo ponanus v. fiet aequatio
  26. X2 - Y A0
  27. Rectius ab initio ponemus: X + v B ..... et fiet X + 2XV +V A..
  28. Serve adhuo rectius faciemus X ponenda, sed malum in eo praevideo quod ita duae radices fiunt
  29. aequalis. Vi d eamus tamen pro V. = Y ponamus f. fiet aequatio: X - f 1.
  30. Cx pro _ X ponendo Y + n. fier: _ + 2n y + nt B0
  31. comparetur haec aequatio cum
  32. aliqua cubica data,
  33. + m
  34. + ings + n y
  35. m. rmm. m
  36. mas
  37. y + p y + aqy 4 aer pjo. fiet 2n +m pP unde paras aq. sue np P n
  38. sed manifestum est eam comparationem esse impossibilem, nisi alteretur datu, et ejus loco
  39. scribatur: y + 3d72 + 3Y
  40. +d3
  41. +apd. =pA2 B unde comparando:
  42. Sed haec inutilia arbitror.
  43. m 3d +p - 2n.
  44. tar afp n + hdu + 2pn = 4n - 3d-2pd - ag.
  45. as 3du +pu - in - d - p d - aqd - ar
  46. 3d + p - in
  47. Sed si abinitio posuissemus X +G Y3.... + Y6)...
  48. habuissemus aequationem X 4 2g X + s f. sive: X + 2gX + g ppo.
  49. si a Ergo aequatio inter duos ipsius af valores,
  50. Notanda haec
  51. comprehensio
  52. forma:
  53. (343 ut 43
  54. d
  55. +
  56. malliplicetur per X +m
  57. = pd XE + eg N +g X
  58. - aqd (
  59. er
  60. Am..
  61. fa.
  62. id - 3d 3d = 2 pd 3d - aq 3d, + 9d 6 pu p (n 3d +. d
  63. n)
  64. Lin
  65. -2n
  66. in
  67. sed ita ascenditur ad aequationem Culicam
  68. in 9
  69. +4
  70. non minus difficilem quam est datu olsi mas habeat in specrem
  71. abitrarias:
  72. videndum quid fiat si radix superior culetur: tiet: Quad retur potus X - 3g X . L Y +96. fet
  73. 12F
  74. + r
  75. + 29
  76. +13
  77. 14fr
  78. -39
  79. compre
  80. X = 6gX + 9g X2 - p Y Corparetur cum X 4. 3n X 4 + 3u V X - 3
  81. -Eg data
  82. = p . + 2p - pn2
  83. fiet. q 7 3nat pa. et 27+ Epa 2n + 2pn +aq et fer n + : pn + Ap e taque agu
  84. et fiet n et n -
  85. post 5.4 uta q _ na Pa + npae n
  86. dug
  87. 216
  88. + et
  89. + 33
  90. H
  91. + C- ag
  92. 21.
  93. e
  94. 73a.
  95. =ar
  96. 72 - 2pa (7a) (2p a) + L pa
  97. +9a +ga aq
  98. 16
  99. 14
  100. ai gueltis qudi sa raa guanus 5. si ete pe s. e age us pui a e , ver 1 n i1
  101. scilicet: , + 3d 2 - 3d
  102. d
  103. +ag. +aqd
  104. 3d
  105. 4bc H 4
  106. 6dp
  107. -12 dn,
  108. C2n) ragd
  109. en
  110. -Fu

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 107r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0213?run=74