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[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 233

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: 0.89.

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

The machine reads it as

  1. extrema
  2. extret
  3. 1II.
  4. ec
  5. H
  6. C A N ON PC A AF CF N SFO.
  7. CONSECT A R LVM AD MIEC H ANICFA EVADRKII
  8. adfecti mulia plani sub larere.
  9. uaque cum proponetur Aquadratum, minus B in A aequari D quadrato: intelli-
  10. setur Dmedia inter extremas, B differentia earum dem. Ft ex media es differen-
  11. lia extremarum quarentur extrema, quarum major erit A, de qua quaritur.
  12. Vehic ex daris GF, F D ConAruentur proporrionales BF, FD, FC. FFeriE BFmajoF
  13. quaelica. Vc ex Zecerieis porerat arpui, et jam tixura Geomerrica per synchelin de-
  14. monstrat.
  15. PROP OSF= FO XI.
  16. Si Fuerinc eres linex rectae proporrionales: rectangulum lub compolita
  17. ex excremis ex harum alcera majore minorere, mulcarum ejuldem alterius
  18. quadraro, a quarur medixe quadrato.
  19. Exponacur canonicum diagramma
  20. erium proportionalium. Dicorectan-
  21. sulum lab BC, FC, minus quadEaTO CX
  22. C, aequari quadratOexDF.
  23. Ex rurtus rectangulum sub BC, BF,
  24. minus quadrato ex BF, aquari quadea-
  25. EDCEDF.
  26. Duoniam enim BC est compolica
  27. Ex BF, FC, ideo factum ex BC in FC
  28. Valec FaCtUI Cx BF IN FC, _LFC in FC,
  29. hocekquadeatum ex FC. Cum itaque
  30. ex Facto BC in FC auterecur quadta.
  31. TUM exFC, relinquetur factum ex BF
  32. in FC. Cui facto sub exrremis conse-
  33. uencer aequale est quadratum ex DF
  34. media inter extremas. Acque id esto
  35. Primum.
  36. AEque quoniam BC composira est ex CF, FB, ideo Factum ex BC in BF valer Factum
  37. ex C F in BF, X BF in BF, hoc est quadracum ex BF. Cum icaque ex Facto BC in BF aute-
  38. retur quadratum ex BF, relinquetur factum ex C. F in BF. Cuifacto sub extremis conse-
  39. qencer aequale eA quadrarum ex DF mediaincer excremas. Ve lecundo loco tuic demon-
  40. Arandum.
  41. C ONSECF A R YVH A D M E CA AAIUEN PEA HF
  42. sublatere necari de quadrato.
  43. Teaque cum preponetur D in A, minus A quadrato aequari D quadrato: intela
  44. igetur D media inter extremas, B aderecarum earumdem. Ft ex media ex ad-
  45. crecato extremarum quaerentur extrema, quarum alterutraerit A, de qua quae-
  46. ritur.
  47. Ic ex Zecericis pocerarargui, de jam figura Geometrica per synchelin demonstrat.
  48. PR OPOSFFTO XTI.
  49. Dacamedia rrium proportionalium ee differencia extremarum, inveni-
  50. C exETCMAS.
  51. Meshanibe

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 233. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0239?run=74