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Machine transcription of the Leibniz Nachlass

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[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 157

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: 0.82.

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

The machine reads it as

  1. tis parie
  2. TUF qud
  3. unegt
  4. quabi
  5. est
  6. Tene
  7. ecta i
  8. duP.
  9. OTULa
  10. secd
  11. seCUI
  12. in A
  13. C0
  14. sec
  15. eI
  16. uad.
  17. FDL
  18. FCH
  19. 1aFIII
  20. HFC
  21. A. OV a L LO A V M.
  22. T H E O R P M A FI.
  23. EtA cubus -F B in A quad. = B quad. in A, xquetur B quad. i1 Z: est D
  24. prima in serie quatuor CoMnue proportionaliumi ageresatum reroxeli-
  25. Quarum erium eAt L, _ A Asecua.
  26. EA EOR EM A ITI.
  27. SF Aquact. Guad. + B i A cubum -+ B quad. in A quad. + B cubo in A
  28. aequetur B cubo inZ: est Bprima in seric quinque ContinuE pFOPOKHO-
  29. nalium; asrresatum reroreliquarum quatuor est Z, _ Ac A sccunda.
  30. TH E OR E M A IV.
  31. SF A quad. -enbus = Bin A quad. quad. + B quad. in R cubum + B cu-
  32. b0 i Aquad. -+ B quad. quad. in A, aequetur B quad. quad. in Z: eAB
  33. Prima in seric sex continue proportionalium; aggregatum veroreliquarum
  34. quingue estZ, e tc Alccunda.
  35. E A E O R E M A V.
  36. SFAcubO. cubuS : +. B in A quad. -cubum -+ B quad. in A quad. quad. t B
  37. cubo in Acubum-+ Bquad. quad. in A quad. - + B quad. - cubo in A, X-
  38. quecur B quadrato. cubo in Z: est Bprima in sexic LepteM CONFIHUC PFOPOE-
  39. cionalium; aggregacum vero reliquarum sex est Z, e Ac A secunda.
  40. C A P V F ZTTT.
  41. Farundem collectio terria.
  42. T H E OR E Mt A +.
  43. TBIn A = A quad., Xquetur B in Z: CAB pFIIA MaIOFINEEF EXECMAS in
  44. lererium proporciohalium; differentia vero duarum reliquarum est L,
  45. _EAE A Secunda. Porest aurem ese duplex, nam est eciam disterentia inteK
  46. Primam a secundam.
  47. Sed AA quad. =BI A, ZGuetUEB in Z: estB pFIMAMINOF INFEF exETE
  48. mas; difterentia vero duarum reliquarum est Z, _ Ar A similirer se cunda.
  49. Suncoproportionales 4. 6. 9.
  50. 1O 4 N, aequetar 12. fit 1N 6.
  51. 9N 1 9, aequarur 18. ft LN 6, atque eriam 3. Sed s
  52. EO R B M A II
  53. EFA cubus = B in A quad. F B quad. in A, aequetur B quad. in Z: est B
  54. prima in serie guatuor continue proportionatium; differentia rero crium
  55. reliquarum alterne sumprarum est Z, _ tc A sccunda.
  56. Sumo proporcionales continue 1. 2. 4. 8. 1C = 89 64 H, aquatur 192. fit L N 4.
  57. Vel 2C - 1D . F YN, aequatur 6. fit L N 2
  58. A E OR E M A ITI.
  59. FB cubus in A = B quad. in A quad. - = B in A cubum = A quad. quad.,
  60. xquetur B cubo in Z: eAt B prima major in serie quinque continué pro-
  61. Portionalium; differentia vero quatuor reliquarum alcerne lumpearum cAt
  62. _E HE A sccunda major inter medias. Porest aurem eAc duplex.
  63. Sed (A quad. quad. = B in A clbuim F. B quad. in A quad. = B cubo in A,
  64. aequetur B cubo in Z: est Bprima inox inter extremas; difterentia vero
  65. Guatuor reliquarum sumpearum alcerne est Z. _e fc A Se cundaminorinter
  66. Medias:
  67. Suio proportionales continue 1. 2. 4. 8. 16. 4096d - 2560 + 16C - 18. 2
  68. equatur 20480. fir 1N 8. Vet 19D - 1C + 19.- 1N, aquat ur 10. fit 1N 2.
  69. T H E 0

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 157. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0163?run=74