Leibniz Legible

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[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 373

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. intet
  2. prina
  3. 1
  4. aED. G
  5. n
  6. MOTUC
  7. testas.
  8. Ietest
  9. id
  10. RESPONSORDM. LEBER VTTI.
  11. cubo = B quad. in D cub. 10. F B quadr. - quadr. in D 5. Perpendiculum B in D quad.-
  12. quad. 5. - B cubo in D quad. 10 F B quad. - cubo.
  13. Proponatur criangulum rectansulum cujus basis 10. perpendiculum r. es aneulus acurus eju sdem
  14. telligatur smpiao.
  15. Ad trianculum anculi criplis slatuerur basis 970. perpendiculum 299
  16. Aa trianeulum anculi quadrupit, stacuerur basis 9 401. perpendiculum 3960
  17. Ad erianculum anculi quintupli, Stacueeur basis 90050. perpendiculum 490Ot.
  18. Et cum angulus acucus primi crianguli deprehendetur esse.
  19. PART. SCRVD.SEC.
  20. erit angulus acurus secundi 2I 25
  21. teriii 17
  22. quarit 22 50
  23. 26
  24. 2
  25. quinei 28 33 10.
  26. Cum aurem factorum nequse fieri subtractio, argumemum est angulum mulciplum esse obeusum.
  27. eogue casus nihilominus excessus factorum adsignabitur lateri, es angulus subtensus intelligitur exte.
  28. tior mulcipl
  29. A L F F F R.
  30. SiFuerine erianoula rectangula quoccunque, et horum secundi anoulus
  31. acucuS SE duplus ad acutum primi, tertii eriplus, quarci quadruplus, quin-
  32. ei guincuxlus, e eo continuo nacurali progressu, primi aurem crianguli
  33. Perpendiculum stacuatur prima proporcionalium, balis ejuldem secunda,
  34. Caque Series COnFInUCtUE.
  35. In secundo, exit balis ad perpendiculum, ut cerria, minus prima, ad sc-
  36. cundam bis.
  37. In certio, aEguarta minus secunda ter, ad tertiam tex, minus prima.
  38. In quartO, uE quinca, minus tertia sexies, plus prima, ad quartam quater,
  39. minus secuncd Gllater.
  40. Inquinto, uc sexta, minus quarra decies, plus secunda quinquies, ad
  41. quintam quinquies, minus certia decies, plus pria.
  42. In sexto ut teptima, minus quinta quindecies, plus cerria quindecies,
  43. minusprima, ad sextam sexies, minus quarta vicies, plus secunda sexies.
  44. In seprimo, ut octara Minus sexta ricies semel, plus quarta tricies quin-
  45. quies, minus secunda septies, ad seprimam sepries, minus quinta cricies
  46. Quinquies, plus certia ricies semet, minus prima.
  47. ELIEAM MAICLI, Mriburis luccessire in duas partes proportionali
  48. bus secundum earum seriem, utrobigue primum adtrmaris deinde nesa-
  49. tis, _ lumptis mulciplicibus, ut ordo graduum in arriticiosa Seneli pOte.
  50. Carum, quibus ex addicuntur, exisit.
  51. F H E OR E M a II
  52. St L TerMInO diAMCEI SUMANEUE in CirCUIO CIFCIHHICLCMEX GUOECUI.
  53. que aequales, ee ab altera extremicare educantur linex rectae adlumpta
  54. rum circumferentiarum aequalium cerminos: cductae hunc bales criangu
  55. lorum rectangulorum, quorum communis hyporenula est diameter; ac
  56. balis quidem diameero proximior incelligitur balis ansuli simpli, succedens
  57. dupli, e eo continuo ordine. Constitmatur aurem leries lincarum recta-
  58. Cum continue proportionalium; quarum prima, lit ae qualis Lemidiameero;
  59. ecunda bali anguli simpli.
  60. ad trianculum anguli dupli, stacuecur basis 99. perpendiculum 20.

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 373. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0379?run=74