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[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 43

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: 0.80.

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

The machine reads it as

  1. ex
  2. 2c
  3. 1
  4. M.
  5. 1.
  6. 2
  7. m
  8. B.
  9. O-
  10. id
  11. n
  12. e
  13. NE
  14. 5
  15. M.
  16. ut
  17. n
  18. POTFNLLL.
  19. P R O P OSTYIO LAVTI.
  20. AB, AC, AD linea Fuerinc continux, quibus aegltales tanE AF,
  21. AL, HO, in direCFUM;
  22. Dico DCC rectangulum, ad C B F rectangulum, elle ve D A ad B A.
  23. Demonstratic
  24. Enero A, inceruallis AC., AD, semicirculi
  25. deseribanEur DFILC, CR F; crectaque ex C
  26. normali C FI, ducatur recta AF, occuerenS Cir-
  27. culO CKF in K, WUNSANEIEquC BR, vE AC ad
  28. AD, HC AR ad ATI, sed vE AC ad AD SIC AB
  29. estad AC per constructionem; igitur ve AB ad
  30. AC, AC AK ad AFI: adeoque BK, FC linex
  31. sune parallela, d BR recta, normalis ad lincam
  32. AC: quare DCC rectangulum, est ad rectangulum CBF, DE TTC quadratum,
  33. ad quadrarum KB, id est in duplicaca ratione linex IIC ad KB, id eA AC ad AB,
  34. id estre AD, linea ad lineam A B. Ouod crac demonstrandum.
  35. P R OPOSITIO LXVTTL
  36. SI Fuerint quoreunque linex concinux proportionales AB, C B, DB.
  37. DEB, FB, CB
  38. Dico rectancula ABDE, CBDE, CBEF, DBEF, DBFC,
  39. FBF C in concinua cscanalogia; e quidem inratione AB ad C B.
  40. Demonstratio.
  41. Eaangulum enim AB D E. ad rectangulum CB D P, est RE A B 2 linea, ad lineam LL. Sexti.
  42. CB; _ CBD E rectangulum ad rectangulum CBF F, est ve b DF 2d F F, b Ibid.
  43. id cst, ve AB ad CB; Rurlum rectangulum CBF F, ad rectangulum DBF F,
  44. estve CB ad DB, id est AB ad C B. (qiia AB, CB, DB, SC. ponuneur conti-
  45. nUX, e DBF F rectangulum, ad rectangulum DBF G, est vER I: 2d F G, id est
  46. icerum AB ad CB; d lic de cereris. Pgitur rectangula ABDE, CBD B, CBBF,
  47. ecc. in concinualunm analosia, es quidem in racione AB 2d C B. Ouod erat de-
  48. monstrandum.
  49. lFuerinteres ordines continue proporrionalium A, B, C, D. L, F, C,
  50. DtI. L,K, L, M. _e AF rectangulo aquale hac quadracum N: e R
  51. quadrarumxquale rectangulo FH; sir aurem ee lF. rectangulo, aequale
  52. quadrarum O, _ E. B rectangulo, quadrarum S. dein e rectanguloC FI,
  53. xquale quadracum P; ex T quadrarum, aequale rectangulo CM; denique
  54. rectangulo L H, aequale quadrarum 1, e OD rectangulo, quadea-
  55. cum V;
  56. Dico quadratum N ese ad quadrarum P, ve cA quadrarum 5, 2d qua-
  57. dracum V: e R quadrarum, ad quadrarum F, ve O quadracum 3d qua-
  58. deacum
  59. A OABSITIO LXIX.
  60. Detrot

Cite

[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 43. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1815201908:0100?run=74