Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 291

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: 0.87.

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

The machine reads it as

  1. icium late
  2. subject
  3. gi1Bj
  4. 11b.
  5. 3cub. 1184
  6. Din B
  7. pd a1
  8. diaeo
  9. 115
  10. unce
  11. Inquarto, ut guinta minus cercia lexies, plus prima, ad guartam quater,
  12. minus sccunda quater.
  13. In quinto, uc lexta, minus quarta decies, plus lecunda quinquies, ad
  14. quintam quinquies, minus cercia decies, plus prima.
  15. In sexco, ucsepcima, minus quinea quindecies, plus tertia quindecies,
  16. inus prima, ad sextam (exies, minus quarca vicies, plus secunda lexies.
  17. In sexrimo, ut octaraminus sexta vicies semel, plus quarta tricies quin-
  18. Guies, minus secunda sepries, ad seprimam sepries, minus quinca tricies
  19. quinquies, pluscerria vicies lemet, minus prima.
  20. Ecita in infinicum, distriburis cuccesire in duas parces proportionalibus,
  21. lecundum carum lexiem, urrobique primum adtrmatis deinde nesaris, et
  22. C lumprismuleplicibus, uc ordo graduum in arriticiola geneli porestatum,
  23. gubus ex addicuntur exigit.
  24. Ouxe quidem omnia, superius expolicam cabellam in spicienti, clara (unE.
  25. E H E O R E M A IV.
  26. Si a puncto in peripheria circuli, SuIAHEUE SESIENEA GUOTCUNGUC XQUa-
  27. da et ab eodem ad lingula sectionum punctarecta educantur: exit urmi-
  28. nuna ab libi proximam, ita reliquarum quaevis a minima deinceps, ad sum-
  29. Enam duaruI SIBI VEFINGUC PTOXIIAFUIM.
  30. Sic circuli circumferentia quantalibet AE, secta in parces quorcunque aequales, quibus
  31. abrendancur rectae AB, BC, CD, DE, e educanur recta AC, AD, AF: ducancurque
  32. rectae CF, DC ip (ISC A, D A aequales.
  33. ExicigitUEUE ABad AC, ita AC ad
  34. AE, _ AD ad AG, ob similicudinem
  35. eriangulorum iloscelium ABC, ACF,
  36. ADC. CA aurem recta AF aequalis
  37. iplis AD, AB: nam in eriangulo aequi-
  38. CTUTE ACF, est angulus C FA aqualis
  39. angulo CAF, id est anguloBAC, an-
  40. sulus vero CDA anguti BAC duplus
  41. A
  42. (Equidem dupIx circumterencia
  43. insic.) est isicur CD A angulus du-
  44. plus anguli CFD, acqui aequalis est
  45. duobuSCFD, FCD. Cunc icaque an-
  46. suli CFD, FCD aequales, latetaque
  47. D, DF aqualia: aE latuS CD aqua-
  48. le ost ipk AB, erBO_ FD ipH AB~-
  49. qualis eric; _ recta AF aequalis com-
  50. POTIIX ex AD AB. Similicer in erian
  51. blloisosceli ADC, suncanguli DAC, DCA ad basin aquales, est icaque angulusDCA,
  52. auasis angulo CAD, de angulaS DEA externus criangulIDCF, aequaliscriplo ejuldem
  53. meuli C AD vel DCE: liquidem eriplae circum terencia in Cltic, qualium igicur parrium
  54. angulus DCE unius, calium est angulaSFD C duarum. est ica que criang ulum F.DC
  55. aquiangulum ccrangulo ACD, et lacus D E aequale lateri CD; exirigicur et laruS L. C. aequa-
  56. Claceri C. A, re ctaque AC aequalis compOlIIX ex AC, AE. Ecigicur AB ad AC, ica AC
  57. Compolitam ex AB, AD; ec ica AD ad ComBOlIcam ex AC, AF, acque ira deinceps l
  58. lura Tuerine legmenra. Quo derac demonstrandum. acque hine
  59. AD ANOVE A R ES SECFTONES.
  60. 29)

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 291. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0297?run=74