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[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 63

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: 0.75.

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

The machine reads it as

  1. 3l.
  2. Ee
  3. Ol.
  4. ale
  5. 1n.
  6. Ulo
  7. InE
  8. 1
  9. 1
  10. e
  11. 1.
  12. Dc
  13. OF-
  14. m.
  15. N.
  16. c0
  17. cA
  18. e
  19. B.
  20. 20
  21. B.
  22. B.
  23. F
  24. ne
  25. lis
  26. B
  27. ne
  28. B
  29. 5:
  30. B.
  31. 2.
  32. c
  33. B
  34. C
  35. GE OMET RIC A.
  36. PROPOSITIO XII.
  37. Eneur reslinex in concinua ratione AB, BC, CV, ad veBC sic
  38. Demonstratio.
  39. MI POnACL U COMEMU2 analoBia A B; BC, CD, iditur erie ve B Ca aa C D a L. Huin.
  40. Ita AC, hoc est ex constructione BF 2d B D. Frgo diuidendo nDD daDC.
  41. ita F D ad D B: _ inuerrendo vei CD ad BD, ita le habet BD ad D F. OuAFC
  42. BBD qUadrATM RQUATUE F. D C rectangulo; quadrarum autem cB F, aequale cA c q. Secuni
  43. 7. Sext
  44. quadratis BD; DB, ∞ rectansulo F. D B bis lumpro: acqui rectangulum ABP D
  45. Eequarur iisdem: nam rectangulum. A B F. D; EguaTuF F D C srectansulo(hoc est, ve dL. Secundi.
  46. octendi, quadrato BD) ex rectangulo F D AC (hoc es rectangulo BE D, id est
  47. rurtum e quadrato F D cum rectangulo F DB, _ rectan sulo inUPEF FDB, rC. c3. Sccundi.
  48. ctangulum icaquo AB F D, oum iildem e quale sic; sequabieur B P Guadrato: pacet
  49. sicur AB, EBB, BD eNelneoncinuaatulbsia. quoddehohsratidum Fuie: t l. lE17. Sexii.
  50. maior AC, _ hacrecta AC aequalis BF.
  51. Dico AB, B L, F. D esse proportionales.
  52. La
  53. DOnaneus AB, BC) C, lres linea in conrirsua propoitione; e Hac
  54. Dico AL, LC, C L Concinua analogia.
  55. Demonstrario.
  56. ondoquidem ponuneur este Con CmuX BLoporcionales linex AB, BC, CD, cC
  57. Liam erunc continuxe proporrionales RB, DEs C Di et B C. medixe equalis D L
  58. Crir quadrarum D E rect angulo AB C. D _ ualO, quadTALH AULEI SC P XGUAEUFCD, 5 +. Secun-
  59. BC aequalis DFC.
  60. DF quadraris, e rectangio C DR bis lumpio. Gurous ciam a quatuErectanoU-
  61. Ium AE CD. nam rectangulum AF CD aequacur F C D rectanoulo (hoc est qua-
  62. draton C D cum rectansulo CD F) ec rectansulo D C B, hoc CA (quia ex constru. h. 3. Secun-
  63. atione BC, D F aquantuT) icerum rectangulo C D P. ex rectangulo in uPeF AB CD,
  64. (id est, vemodo ostendimus, quadraco D E) quare rectangulum A P CD cum ijsdem
  65. equale GE, quadrato C P. aequarinecessc CA: ad eo que CD, C P, P. A esse in conci-
  66. noa analogia. Ouod erac demonstrandum; o
  67. INE AB, AC, AD, in continua analogia; ee hacve AB ad BC, it2
  68. eam ceADdaDe; HCB Mat 2aF.
  69. F lit
  70. DicOF _ F cNcinter le aquales.
  71. Demonstratio.
  72. Voniam supponuntur concinux AB, AC, AD, A Aac D G a qualis B C, CFUHE
  73. Lconcinux AB, BC, C C, ergo cum ex daris eriam sine in concua rarione, 13. Ruius.
  74. AB, BC.

Cite

[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 63. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1815201908:0120?run=74