Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 317

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: 0.88.

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

The machine reads it as

  1. Accell
  2. erilim
  3. DOTCNU
  4. alsc
  5. quadea
  6. p0.
  7. M. P
  8. 10G
  9. an0q
  10. cubol
  11. 1B
  12. E S P O N S Y M.
  13. L Y X E R
  14. Si Fuerinc eriangula rectanoula quorcunque, et horum se cundi angulus
  15. acurus sc duplus ad acutum primi, cerri eriplus, quarri quadruplus, quinci
  16. quincuxlus, _ eo continuonaturaliprosreltu, primi aurem trianguliper-
  17. Pen diculum sacuatur prima proporrionalium, balis ejuldem secunda, ca-
  18. Que lcries continuetur.
  19. In secundo, crir balis ad perpendiculum, uccertia, minusprima ad se-
  20. cundam bis.
  21. Interrio, ut quarta, minus secunda ter, ad certiam cer, minus prima.
  22. LAquaEEO, uE quinta minuscertia sexies, plus prima, ad QuAFEAI QLLaFCF,
  23. minus secunda quater.
  24. Inquinto, u lexta,minus quarta decies, plus le cunda quinquies, ad quin-
  25. cam quinquies, minustertia decies, plus prima.
  26. Insexto, ut septima, minus quinta quindecies, plus terria quindecies,
  27. munus prima, ad sextam sexies, minus quarta ricies, plus secunda lexies.
  28. In seprimo, ut octara, minus lexta vicies lemel, plus quarta tricies quin-
  29. Guies, minus sccunda sepries, ad seprimam sepries, minus quinta trictes
  30. quinquies, plusterria vicies lemel, minus prima.
  31. Etica in infinitum, distributis suc cessire in duas partes proporcionalibus,
  32. Ccundum carum seriem, urrobique primum adtumatis deinde negatis, s
  33. lumpeis mulciplicibus, uc ordo gradtuum in arciticiola geneli porestatum,
  34. quibus ex addicuntur, exigit.
  35. T H E O R E M A IV.
  36. Si Fuerinceriangula rectangula aequalishrporenula, quorum primian-
  37. Culus acurus sir in submulcipla ratione ad an sulos acuros tucCCdentiUM OF-
  38. are criangulorum, ad acurum videlicet secundisic subduplus, cerriisuberi-
  39. elus, quarri subquadruplus, ex eo continuo ordine: construatur aurem se-
  40. Res lincarum recarum continuc proporcionalium, quarum prima litX qua-
  41. aS lemitiyporenulae, secunda bali criansuliprimi, incer succedentes conci-
  42. hlc proportionales ex succedentum criansulorum bales, hac erie xqua-
  43. litas.
  44. Fertia continue proportionalium, minus prima bis, erie aqualis bali
  45. criangulisecundi
  46. Duarta, minus secundater, bali triansulicertii.
  47. Duinta, minus certia quater, plus prima bis, bali crianguli quarri.
  48. Bexta, minus quarta quinquies, plus lecunda quinquies, balitriansuli
  49. Quinei
  50. Seprima, minus quinca lexies, plus certianories, minus primabis, bali
  51. criangulisexci
  52. Octara, minus sexta lepties, plus quarta quarerdecies, minus secunda
  53. epries, bali crianguli seprimi.
  54. Nona, minus seprima octies; plus quinca vicies, minus certia sedecies,
  55. Plusprima bis, Bau trianguli octavi.
  56. Occima, minus octara novies, plus sexravicies septies, minus quarta tri-
  57. cies, plus secundanories, bali criansulinoni.
  58. Ec ita in infinitum, ucper loca proporcionalium imparia nora adfectio
  59. TICCE.

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 317. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0323?run=74