Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 153

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: 0.83.

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

The machine reads it as

  1. le fit 11
  2. Deir.
  3. lato
  4. ndun
  5. ratio
  6. quat
  7. Qua
  8. cob
  9. BCt
  10. A, 2
  11. 10b
  12. q
  13. euE
  14. 1XrI
  15. qua
  16. spid
  17. Oud
  18. AE OV A X +O N V M.
  19. Duoniam enim B est A de Gua quaerituE: erBO ex IIS QUX PFOPOHUITEEBCNDUS = BTR
  20. BGllad.. F D plano in B, aequtabirur B in D planum. quod quidem manitesto ira se habet.
  21. +Q FSN, aequatur 20. facto ex 4 in 5. ergo + N est 4.
  22. T H E O R E M A VI.
  23. TA cubis F B in A glad. = D quadr. in A, aquetur B in D quadeatuM.
  24. IPla D est A de qua quaTItIE.
  25. Ouoniam enim ipla D es A de qua quaxitIE, erBO CxiIS quX PEoPOnunEuE, D cubus
  26. F B in D quad. = D quadc. in D, xquabicur Bin D quadrarum. Ouod quidem mani-
  27. Fecto ira se haber.
  28. 2C + 52- 4 N, aequatur 20. facto ex 5 in 4. ergo XN fit V 4 vel 2.
  29. T H E OR P M A VII.
  30. FB in A quadr. F D quad. in A = A cubO, aquCtIF D quadratO in B.
  31. Ipta B rel D, est A de qua quaritur.
  32. Ouoniam enimipla B est A de qua quaeritur ergo ex iis quxe proponuneur B cubus
  33. + D quad. in B =B cubo, aequabitur B in D quadrarum. Ouod quidem ica manifesto
  34. sehrabet.
  35. Rurtus quoniam ip (a D est A de qua quaeritur, ergo ex iis quae proponuntur, Bit D
  36. quad. + D cubo =D cubo, aequabirur D quadraro in B. Ouod quidem ira quoquema-
  37. nifesto se haber.
  38. 68 Y 4N - 2 C, aquatur 24. fil L N 6 vel 2.
  39. F H E OR E N A VITI.
  40. GFD in A quad. - + B in D in A = A cubo, Xequetur B cubO: St D in A - A
  41. Quad. aequabitur B quadrato.
  42. Ex iis enim qux propOnuntur, manifestum sEper ancichesin. B cubum L A cub0;
  43. aequari D in A quad. + D in B in A. Veraque pars applicetur ad A Y B, erBo A quades
  44. B in A + B quad reguabitur D in A.
  45. EEPCFAnLitheGBD, Bin A= A quad, aquabituF B quadraTO.
  46. SiTOB, L ZON = ZC, aequecur 8. quia lacus cubicum ex 8 ductum in 10, facit 20. Jpitur 12
  47. N = +9, aequabieur 4. ex fit ZN 6 = V 32, vel 6 + N 32.
  48. T H E O R E M A IZ
  49. SFAcubuS =D in A quadr. + D in Bin A, Xguetur B cubo: D = B in A
  50. A quad. ae quabitur B quadrato.
  51. Ex iis enim quae proponuncur manifectum Arper ancichetin; quum A incelligitur ma-
  52. TOr quam B, A cubum -B cubo, aequari D in A quadr. = D in A in B. VIragUC PArS
  53. aequalicaris applicetur ad A = B. IBitur A quad. = B in A = B quad., aquabItUE D in As
  54. Ex perantichetinD = B in A - A quad., aequabirur B quadrato. AEqui quum B intelli-
  55. sicur major quam A, B cubus = A cubo, aequabitur D in A in B - D in A quad. Veraque
  56. pars aequalicaris applicetur ad B. - A, iraque B quad. F A quadr. + B in A, XquaBIEUIE
  57. D in A. UE anEC.
  58. SirC = 109 F 2ON, aquetur 8. quia V C. 8 ductumin 10, facit 20. I8ituT BN - 1 0.
  59. equabitur 4. 87 fit L N 4 = N 12, vel 4 = N 12.
  60. L E E O R F M A X.
  61. eas =DPL. MA, equetur VB plano- plano. Planiz, v vo3 + v D run.
  62. AE A de quaquariEE.
  63. Ouo.

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 153. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0159?run=74