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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 258r

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: 0.83.

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. 259v); this page is its right half.

The machine reads it as

  1. Esto aequatio ad Circulum,
  2. by - y (X +dX. + ea.
  3. et salia aequatio ad circulum, fy - y ) X + gX + ha proy posterioris ponendo
  4. ejus valorem ex priore fa: nembe X + dX + ea - b9. fier:
  5. srecta X + ha, ideoque yp +d X - ea
  6. fy - by + X + dX + ea
  7. nd quae aequario est ad Triangu
  8. duobus cinculis solui potest id etiam uno cinculo et linea
  9. recta solvi posse.
  10. +9 + haseu XyYC + C
  11. sed aliter veniamus ad radices attollendae aequationis causa.
  12. faciamusque bus ga ea + d ( N X + d vel 7 + (M+ d. Imo
  13. et pro y substituamus V+D fet 5 bV + bst - v - 2V1 AV ea + d et
  14. brevius by - y + ca 1) X + d. et alia aequalio eya Y + fa p X
  15. fiet Abg- y t ca Sey- y + fa + d, ei quadrando utrobiqu
  16. onsyttetur vel
  17. bys - y + ca 1 ey -Y + fa + d + 2d... Multiplicetur atraque aequationis
  18. pars per y + Ergo antequam huc procedatur multipli
  19. aequations pars per Y + g. 0, fiet,
  20. fier. NbV +269V + qby - y- 29V3
  21. per y+g.
  22. u
  23. fiet
  24. Multglicetur utraque
  25. seu radices per fy4agy+
  26. et multiplicetur utraque aequationis pars
  27. y + cay, + gby -91 +gea p ey 17 etc. male
  28. non ita assurgemus ad cubum, ergo sic potius
  29. una aequationum datarum
  30. by - yt LX, + dx + ea multiplicetur per y +G fiet:
  31. by - y2 - yX + dXY + ea Y + bpy - ∞Y + X + ad X. + ea ) 0. pro X substi.
  32. Auatur ejus valor ejus ex aequatione ad lineam rectam, nempe XM C + Cd
  33. fiet: - . V
  34. ..
  35. =2 nto 1
  36. + b .
  37. + da.
  38. +cad
  39. = c. ut
  40. =co V
  41. +dd...
  42. +2ndc..
  43. +ea..
  44. + bc
  45. +eda..
  46. Ergo, b p 2 (n C∞ - d = c m2
  47. + Cd
  48. + cdcd
  49. fiet postrema equatio haec: - c to
  50. Esto jam aequatio (ubica pura:
  51. conferenda cujus factitia plana ad cubicam
  52. quo valore ipsi in tertio termino cedente inserto
  53. adeoque d e - + n ad C + ea + 2 - cV n
  54. sed notandum est ipsam
  55. _X Y + 2(C, +Cd
  56. 2 X X
  57. 13. p0.
  58. sublata: fiet c +cd arx2
  59. =a (+ eC - ema)
  60. substituendo valorem ipsius d in
  61. 170
  62. caelera erunt p0.
  63. nondum haberi,
  64. arx
  65. uy
  66. + C
  67. +cdp, Ho
  68. eoque valore in ultimo termino
  69. inserto, sit.
  70. isus valor in termino ultimo
  71. niserendo
  72. e
  73. mno possumus pergere ut ante
  74. 00 + do ejgslocum in aequatione ultima
  75. -C∞ + 4 MDC + ea C = c n+ c3p, +
  76. + M2 a2∞
  77. Unde sequeetur ex tot incognitis super c. . M. e omnes demta una sumi posse
  78. pro arbitrio. Quod videtur absurdum sane C non potest sumi pro arbitrio, alioqui
  79. posset cabus ax habere radicem quam libet. Unde sequi An forte tunc sequitur
  80. ipsam C esse radicem imaginariam, et sequeretur in omni aequatione subica simplice
  81. unam esse radicem imaginastiam, sed nihil referret tamen, nam et ope radicum
  82. incpparicnum postent deprsui aequatires ,si coqurisserentu
  83. u

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 258r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0515?run=74