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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 131r

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. 130v); this page is its right half.

The machine reads it as

  1. enuntiari potest. Et quiliber modus habet tres radices. Unum tantum Nec
  2. video quid abiod dici passit contra possit.
  3. Porro ut valor ipsius
  4. M non nisi cubica aequatione habeatur, utitd ulile in aequatione data surdesolida
  5. effici praeparando ut sit e 70. seu ut absit terminus tertius; et ut ea prae paraoe
  6. facta maneant d, et h. eigoem signi. Quod semper fieri posse videtur.
  7. aequatio autem pro mostigando valore ipsius m, erit:
  8. =aeg - maf 4 ram Vdath eha + 2a h maus F ma t
  9. a
  10. 4 mah.
  11. Quam praeter grimionem video non esse nisi peanam et erit:
  12. rgugn 4n a Fh =gam h fdah Y ta (F2 a hmag + m ag
  13. Eno num si abest tenia
  14. Haec method,s si bona est poterimus eam etiam in quadrato quadraticis
  15. aequationibus experiri; sit aequatio X ax aY Bo: multiplicetur per A + m
  16. fiet.
  17. X A +ac X + dc B X + pX + aq X + ar X + as p0.
  18. scubamus: EdX +DX +ab H AX + pX + aq X +aer X ras
  19. + d2 . +2abd. + a b2517
  20. Axciletur quadatum ex latere: X + pX+ aes+ ab
  21. X + PX + 2 fastab X
  22. o + psasaeb X
  23. fiet:
  24. + as
  25. + ab2
  26. nas + a b ae Y + 2abd, + a9 + 4 d - p
  27. HI
  28. 4 paq +Ep A2 - p. L Y
  29. 16 ad
  30. + 8paque 4p d + 16p d2
  31. 2p3
  32. =16aY
  33. 4a d2.
  34. fictas
  35. ad eo
  36. et 62
  37. +16 p aq
  38. aopaq
  39. -64 pagar
  40. ribpar
  41. dga
  42. 16 a4 + 8aq 4d + 16d
  43. =8 aqp
  44. p
  45. Videndum ergo an sedi possit, ut fit 1bp aq 48) aqu oupagat p topat
  46. 1
  47. ita enitm aequatio reddi posset plana. Quem in finem cogiletur aequatio
  48. fiei:
  49. quadrato- quadratica facta ex cubica A X = X + Y. 0 ducta in X + mpo
  50. +cl X
  51. =ahm
  52. +2t m St
  53. Destruatur Y. ponendo M p C p.
  54. restabit aequatio: 1644) paq Lop.
  55. Ct
  56. 1C
  57. X+ X - bh. X
  58. substitutis hacoribus:
  59. +M X
  60. X
  61. +BW Ih + 10B1
  62. ak
  63. Unde radix. extrahi
  64. +ah
  65. et C0 1 D
  66. Quare
  67. necesse est i2 esse quantitatim negativam, seu Terminum penultimum aequationis cubreae
  68. 1
  69. ath2
  70. +1
  71. error. debet
  72. esse be
  73. 1h
  74. potest, et fiet
  75. Co
  76. datae esse affirmativum. Fiet autem bpi Ld et b 4p
  77. 16 p d qud - 49). et d7 49’ asa
  78. si es . 216, 4, hd s h0 siut ere sasit Ia 1 o
  79. Cum ergo K. sit grantitas negativa, debet esse Acolpt
  80. a
  81. e st
  82. 21
  83. 2
  84. C12
  85. as aedque scet:
  86. +hC
  87. A2H R - 1607
  88. co h = 16c

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 131r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0261?run=74