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Machine transcription of the Leibniz Nachlass

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[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 125

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: 0.80.

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

The machine reads it as

  1. 2. 01
  2. OFCO1
  3. lidum
  4. CI
  5. nadi
  6. aesisL
  7. 10
  8. ImPI
  9. 1e2P
  10. Elceriu
  11. 1xli5
  12. OTCC
  13. eliqua
  14. rCI
  15. Am P
  16. N3
  17. (0
  18. solid
  19. M C
  20. Winq
  21. inqu
  22. rellib
  23. BPIa
  24. ldCI
  25. IIC
  26. IL. OV A F F O N VY M.
  27. AlFerne sumpra diferunEP eF DPLU. FiC aucem Z. Solidum, ductu alcerius
  28. extremae in ditterentiam quadratorum a reliquis. e est A prima minor in-
  29. cer extremas, Pterria.
  30. Sunco proporcionales 2. V2. 2. 3N = ZC, aquabitur 2. e7 fit L N L. FF NUr Sus 2 C. - 3 N,
  31. aequabitur 2. 8 fit LN 2.
  32. F H E OR EM A TI.
  33. SFB plano. planum in A - A quadraco cubo. aequetur Z. plano. Colido.
  34. X TurUS E quadrato- cubus =B plano plano in A, Requetur Z planO. Soli-
  35. do: lunequinque continue proportionales lonsicudines, a quibus quadr2-
  36. co. guadraca alterne lumpra differunt per B plano-planum. Pic autem Z. pl2-
  37. no-lolidum ductualterius extrema in differentiam quadraco-quadrrto-
  38. rum areliguis alterne lumpris: ex Ac A prima minor inter exercinas, F.
  39. guinta.
  40. Sine concinue proporcionales L. W 2. WV 4. W 8. 2. TLN = 1 DC, aquatuT 1O. 8 fit LN 1.
  41. EF rursus 1QC = LIN, aquatur 10. e fit LN 2.
  42. P H E OR EM A III.
  43. CTB in A quad. + A cubO, XguetuE Z Colido, S rurtuS B in L quad. - F
  44. cubo, aequetur Z. Solido: sunt eres proportionales, quarum alterne sump.
  45. carum differentia eA B. Fit aucem Z. Tolidum ductu alterutrius extrema in
  46. quadratum differentie reliquarum alterne sumpearum: dx dum incelligitur
  47. Primaminorinter exeremas, est A differentia alterne Cumpra duarum pri-
  48. marum, E disterentia duarum poAtremarum.
  49. II. III.
  50. Sunto proportionales l.
  51. 2C, aequatur 4. 8 fiTL N 2.
  52. 2. 4. 38 = 1C, aquatur 4. et sic X N 1. FI rursuo 3 Q
  53. T H EOR F NE A TV.
  54. B in A quad. quad. r A quadrato cubo, xquetur Z plano- Colido, e
  55. ructus B in E quad. quad. = P quadraco cubo, aequetur Z plano. Colido:
  56. sunc gunque proxotales, quarum alterne sumpearum difterentia est B.
  57. Fic aucem Z Blano Lolaum ductu alterutrius extreme in guadeato. quad.
  58. difterencie reliquarum alcerne Cumpearum: _ dum intelligitue primâ mi-
  59. NOE InteF extremas, est A difterencia alterne sumpea quatuor primarum, L.
  60. differentia quatuor poltremarum.
  61. II. TIL. IV. V
  62. 4. 8. 16. 119O - + + QC, aequaTUr 10000.
  63. fit IN f. ETrursuS LLQ =+OG, aequatur 10000, Cx fit L N 10.
  64. A E O R E M A V.
  65. EB planum in A cubum =F A quadrato. cubo, XguetuIT L plano. 1OH
  66. ae curlus B planum in L CuBHM F quadr. cubo, aguetur Z plano. Coli-
  67. do: lunclex proportionales continue, quarum extreme ducte in difteren-
  68. tiam quarre _ prime, Faciune Bplanum. Fit aurem Z plano.- Colidum ex
  69. cubo disterentie quarre de prime in B planum plus ejuldem difterentix qua-
  70. deaco. cubo; vel ex cubo differentie quinte de secunde in B planum mulea-
  71. cum illius disterentix inter quintam _ secundam quadrato. cubo: _ quum
  72. Prima incellisitur minor inter exeremas, tic A differentia quartxe de primx,
  73. e P disterencia quinrae ex lecunda.
  74. 1.
  75. SAnd
  76. Sunco proporiionales

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 125. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0131?run=74