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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 242v

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: 0.79.

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. 241r); this page is its left half.

The machine reads it as

  1. Juterm hac acterRabue ver si quae sunt in nuneris extrahi possunt u stampioe
  2. et possicunt a Sichotenio prasciplum est; ad literales verd aequationes non serviunt, nisi
  3. literae ad numeros rationales irrationalesque reducantur un
  4. Si sinel habetur nethodu
  5. LH
  6. Methodus
  7. 3 aet 7 ps an 4. () at = l. an p Bp a Y
  8. fier ay p dal (+ a S -an) +31 à V- a l s- an, + 2a (5 a
  9. et( à Lan
  10. (ab + an J-an
  11. +35() à 13+ a l S-an, - 2a ls an a ln
  12. a y - 2al 25) Al( VS an) Al. Laan) 3aIn + ams au
  13. Xqu
  14. a lp). ant an
  15. ja l S. an) J an talm alque
  16. B sa vocemus 13- 3aln H94, et 17 anssfa
  17. si Et quodrm Do cubando a -GXa ) Yquit agstuns on ga t atlanasn
  18. .71) il Lan) ( 8i) alu = 27 an S an
  19. fas-an
  20. YA(7 d (271 1 an) + 27 aln = 27 an Juam
  21. Jiii 54 (a = X2a - 54 a n appellemus Va 5+ a
  22. et ga + fas- an appellemus
  23. =9X + 27X 3 ea
  24. brevius X Aph + K. Unde
  25. ta X - hp K. Ergo X - 3Xh + 3X h - W K3
  26. Ex puire Xp KY va l + axte
  27. et mnehijolicatis omnibus per , fit: 3X b3 - 3 X t H 2 ati
  28. hep K x + h + 3X h, exquem valorem inserendo
  29. 1d1X
  30. in posteriore, fier:
  31. + 3X - 2 X h (3 Xt to) p. 3K ht BXTh) + h+ X eritque
  32. sie tam Ergounk X - 6xhid - 3X3 4 3X
  33. 6Xth - 3 xta p3 + 3X C 3 H 3)
  34. 3MX + het ada
  35. 125 X H etc
  36. 1: cub a 3K3+h3
  37. tier a L-an X F axb- la Fta brb
  38. et avaetae eta
  39. 4.54 an
  40. fiei: -9ua D ea +. 27p D Ca va, fier.
  41. S0 eae
  42. Ergo 3X h = 3X h. K3 - x3+ h
  43. 3XK3
  44. Lvoce
  45. a vat -2va + l’at explicet
  46. 2per cubum ab ∞ +b, separanda tandem
  47. 3X3 + hi
  48. sie H, (3NX) (C XH) ( H DXK) x
  49. 3K3 + H3
  50. 3.Xha + 17X ta vaer 1 quin et -9Xi + 27xh iuah
  51. Ergo h vah - 27X h3
  52. inseratur in prioue, fier: - 9 ha - 31 (a 81 aX H3 va X
  53. rt
  54. hi AvaX +or axh
  55. in duas, ita ut si fieri potest, valor ipsarum xerb sine
  56. +9+a+ 3a
  57. is Eetracionibus imaginaris obtineatur, tai enin =ani p Xb( X +6X b (42X9Xb2+ (18 Xb 64b (t bD ab
  58. - 2X3a 2l - 6 X bael - 6xb a l = 2b a l = l at. Vrdendum q
  59. I X + b noundo y esse rudicem cubicam, et et a esse quadraticam,
  60. X + 3x d 2Xt + B pro y ponamus ar, et pro X ponamus ea
  61. aequatio dissui possi
  62. in duas, ut liceat et
  63. fier: aV Ea X + 3Fab. = 3Xb + b3 sive a 6 - 3Eab - b X. Ergo purum tractabilem
  64. Ea H a = 6aVXb 2 a vb rgs al a 5a + 32
  65. 2 a + 68 ab + 9bZ
  66. unde
  67. (+65 ab + b.
  68. 5a +68ab 96 aa a b a ab
  69. et ordinando a ua 3bac + 3Eab = b5-
  70. av- 6 a 2b- 2ab, V.
  71. sive as- b+ y 1 a - 6a xb 2ab3 Explicetur jam b ita, ut ex radice porit
  72. extrahe radix cubica, quod non difficile ope aequationis planas indeterminatione
  73. ponendo b expercando b per duas quantitates, atque inde destructiones comminiscendo) 3t ab - b
  74. aequatio carens radice cubica, si pro y substituatur ejus valor nempe b ac 3F ab - b3
  75. potndo at -b 10. fit aequatio ejusdem cum eodent Z a +li
  76. Za + 36
  77. opem ita) inti provemientem licebit
  78. de fal1362
  79. sejungere in
  80. mas, sive altentiam arbitrariam
  81. tandum aeq. 8 dividi posse per x + b) et fieri: x- b 1Va = a b 263 explicare quam licet commodissime, ut valor
  82. 2a- 0a5l. (3b3 Ea (346) + 3 xb (- b)
  83. ie val a 1o npt- l X L 1 Xb sanibu laratr at
  84. quasitus habeatur ipsius V. aequatione vel planam
  85. les alora quo, su Mnoris geomretire Hoactabiti
  86. sive X
  87. b, vel ipsius x, et
  88. tandem per ipsas ipsio

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 242v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0484?run=74