Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Ps. 1], fol. 140

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: 0.81.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. F L. OR TM O HDE DE BE AMNL
  2. BIna PTOPONUNEuE: exhibenda tantum restat demonstratio radi-
  3. cum, qua ex ipsis, secundum Cardani regulas, quas superhac re
  4. in medium aftert Capite secundo libri ejus, quem de Arre Masna
  5. Seu Regulis Algebraicis inlcripsIc, educuntur. Cum hoc iplum
  6. difficulcarem Force non exisuam parere polseriis, qui in eundem
  7. locum aliquando inciderent, quippe qui a Speciola AISCbFX, e
  8. mucux incer Arichmeticam e Ceometriam relationis atque con-
  9. renientix ignaris, non facile percipiatui. Quocirca ut veritas
  10. exrractionis harum radicum expendatur, demonstrabimus pri-
  11. mun sequens
  12. 14
  13. ascendune, reduei posse ad aliquam formam carum, quae hac pa-
  14. L E M M A
  15. CFctâuteunque linea AC
  16. Din B, Ostendendum Css
  17. Cubum linca AB, una cum
  18. cubo lineae BC, _ triplo
  19. producto lincarum AC.
  20. BC, AB, Cumul aquari cubo linex AC.
  21. Sit AB ∞ a, B C ∞ b, erieque A C ∞ a F b. Productum li-
  22. nEaTUI AC, BC, AB, eric ba a F bb a, cujus triplum 3 b a a
  23. +3 bb a. FIuic C addantur cubi lincarum AB, BC, FCE a3 L 3b a a
  24. .3 bb a- L b3. Ec manifectum est, Cummam hanc aqualem esse
  25. cubolinea AC.
  26. Demonstrato itaque hoc Lemmate, habebitur primo Loco
  27. VC. 1 :9ut V = 49. ] :, P - V C. - 29. V +94 + 1, P3.
  28. Ilinc in tigura adjecta supponendo binomium
  29. VC. + :q. V 294 . + , p3 aequale lineae AC, _ residuum
  30. Y C. - = g Y V = 99-L, p3 aqualelinca BC, erit corum
  31. ditterentia V C. + : q ) V = 99- L ,, P
  32. VC. =qu V +99. , P3 aqualis linea AB. Tam vero
  33. Ctacuendo A B ∞ Z crit difterentia Cuborum ex lis radicibus
  34. nimirum ditterentia inter cubum L = g. V = 99 - ] 2 P3, et
  35. cubum - = 4- = V = 49. P3, Causerendo hunc ab ill0) aqua-
  36. lis g. Oux propterca aqualis eric differentix inter cubum li-
  37. DCa
  38. uin L
  39. id
  40. n
  41. earu
  42. MIUM
  43. Per A
  44. linea
  45. 199+
  46. ned
  47. smmul a
  48. eranelci
  49. PrOd
  50. tietp
  51. conter
  52. Monltiu
  53. Siti
  54. Z0YC.
  55. de ippona
  56. ell) aqual
  57. aequdie
  58. ejuldemen
  59. reliquent
  60. ipsiglun
  61. quodtre
  62. mulipien
  63. radice en
  64. Catur uII
  65. + 1, P
  66. ctaeranel
  67. IC Cum pE
  68. rentu (I
  69. YC
  70. qua
  71. pracelente

Cite

[Ps. 1], fol. 140. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175905688X:0162?run=74