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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 37r

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: 0.78.

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. 38v); this page is its right half.

The machine reads it as

  1. de extractionibus Radicum ex Aequat.
  2. X aequ. a + b + Ce M. L aoqu. ab +act be dc. L. aequ. ab
  3. 2
  4. X’aqu. a + rab.. Ergo ab aequ. X _ ab aqu. X- 2a X + a t 146)
  5. et
  6. 5
  7. 4
  8. 4
  9. et a b aeq. X- 4a X + 2a X + 4 a X
  10. qua
  11. e
  12. iga
  13. +a8bX
  14. 16
  15. vel quia X aequ. a erab.
  16. + 28
  17. 4 aX +2ae b+)
  18. Faab
  19. +4
  20. fet X aequ. a + + 4 a b + 4abc + 4 ab +8 abc
  21. seu X aequ. a + 4ab + +6 a b + abc. ut alionde
  22. Ergo possumus statum scula X8
  23. est autem ab aequ. a b + 4 a bc + abC + 1 a b2
  24. 4
  25. Inde aequatio 14b aqu. X 4a X +6a t - 4a, ∞
  26. X aequ a + b + c.
  27. a + b+ Ct aequ. 54.
  28. +gab 12aY2
  29. a+ C+
  30. c4
  31. + a
  32. +4aV
  33. 1E 24 at bCX = 4a bC
  34. idu
  35. - 24467
  36. =12(1bC
  37. X aequ . qX + rX + (+.
  38. abc aqu. 93
  39. quaeritur quantitas a+ ex datis q. r3 54
  40. ro X subslituatur esu intr in aequ. 2. ejus valor ex aequ. 1.
  41. (0) Y12 ex aequ. 4
  42. utique a aqu. s4 b ex aeq. 3 aequ et a aequ.
  43. Ergo 5+ b
  44. + b C8 + r 12
  45. 144
  46. locum In aequatione 2 substituatur valor ipsius X fiet.
  47. (a + + ab +6 a b + (12 abe 2 a aqu. 9a + 24 ab (. at s+)
  48. ubi pro a substituatur ejus valor, ex aequ. 4. fiet:
  49. 42 r92b +ab b +6 n 16L
  50. 2
  51. Aqu. 9
  52. 12 Y
  53. e
  54. bc
  55. b c + 6b
  56. 4, 12, Y, + 4b b +6, 1 Y, bc by +6bc aequ.
  57. o2
  58. aequ. r2, qr bc +2, 12, 972b 2b + 29b=
  59. X X + lae X + n _ X + pa
  60. Aursus:
  61. d
  62. c
  63. +
  64. +mab + p aeb
  65. + A abc
  66. in X
  67. +
  68. a
  69. 3X3 +7qX HIa X + 1 a
  70. 43 ab + 1g ab in X2 - a
  71. ab
  72. + 23 abc
  73. Sed posterius inutile esse puto quae cujus posterioris multiplicationis productum addi posset priori;
  74. sed jam re recta expensa, puto nos nihil lucrari per posteriorem multplicationem, nam
  75. multiplicare C in Ft -a, est multiplicare C, x- a in A -g. jum O,X-q potest
  76. considerari ut species formulae D perinde ergo foret ac si ac si loco D aliam formulam
  77. suntem fiigeremus, mutatis tantum literis (. l. m. etc. et productum puori producto
  78. adderemus ita enim, nihil lucrabimus, nam si quid lucraremur, nimium mcraremur, possumq
  79. enim similes alias formutas fingere infinitas (N. eae notabilesi ratiocinandi in tabib,
  80. exemplum 3). Et perinde esset si ponamus loco in secunda formula loco D sumta) nos
  81. sumsisse I. utique poterit C+ A assumi pro una cnuantitate. Sed aagendi
  82. tamen arbitrarias uno succurrit pulcherrima gatio si ducamus in X- g. et
  83. productum addamm ad productum ex D in X-a. Et nusus aliam fingamue formulaque
  84. 39X +29 4X + B0 e in X - et denique 41X + 43a in x- aHis omnibus simil
  85. aditis a habebinus utue ad 23 inbinarias idest multo plures quam sit opus e
  86. 20 fals 1678
  87. 2
  88. abab
  89. aequ.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 37r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0073?run=74