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[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 282

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.

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The machine reads it as

  1. ELL IPSTS
  2. PROPOSITIO LXXIIF
  3. sencibus aequale cM parallelogramito concenco lineis exrrema qua-
  4. rumuis Matecto Comuhalau Comungeneibus.
  5. Demonstratio.
  6. InE ABC ellipseos AXeS ABCD, ex alia quauls
  7. diametrorum comiusacio P F G FI Tungancurquetam
  8. 2xium, quam diamecrorum exerema: dico C AD B Pa-
  9. rallelogrammum aequari parallelogrammo P, IT F C. rC-
  10. ctangulum ex A B _ D I duplum est crianguli AD B:
  11. de rectangulum ck AB _ CI, duplum est crianguli
  12. ACB. ergorectangulum ex AB, CD, duplum est p2-
  13. rallelogrammi ACBD, Sinc A C B D parallelograM.
  14. mum, dimidium est rectanguli super AB, CD. limili-
  15. cer octendam patallelosrammum F. C F. II dimidiun
  16. esse parallelogrammi (uper F F, CFI in angulo FIFI:
  17. sed parallelogrannum super RL, CFT. xquale cst pa-
  18. rallelorrammo supet A B CD; igitur _E AC B D paral-
  19. leloprammum aequale est parallelosrammo P. C FH.
  20. Demonstratio.
  21. Vm exhyporhek DE sic ad E. B vE A F ad F C, exie
  22. permurando DH ad AF, VE BF 2d FC. quare
  23. SEFOTA DB, ad EOFAM AC, VE DF ad AF, _E F B, 2d
  24. FC. ioicurrationes BC, ad F C, _E DF ad AF, simul
  25. sumpre duplicaex sure racionis D B ad A C. AEqui ra-
  26. tio rectanguli BF D del rectangulum AFC, compo-
  27. nitur exracionibus BL 2d F C, _ DF ad AF. CrgO
  28. rarto rectanguli BF. D dd rectangulum A F C duplica
  29. ea estracionis BD, ad A C, hoc est rationis BI ad AL
  30. ergo lectanguluI DL. D est ad rectangulum A F C, ve
  31. quadracum BI ad quadracum AI. Ccd idem quoquere-
  32. atangulum BF. D est ad quadracum CE, ve rectangulu
  33. N ellipsi paralleloerammum quod hc à lineis excrema axium coniun-
  34. Dubature demonstrandum.
  35. ROPOSITTO LZZIV
  36. VInE ABC ellipleos axes vel dianerri coniugatae, AC, BD. diuise
  37. que BD vccunque in L, diuidatur AC in F proporrionalicer, de per
  38. F. _ F ordinarim ducantur linex L. (1, F II:
  39. quadrato HIF, e liguaatacum CF. lic aequale rectansulo AF C. dico
  40. Dicorectangulum A F C aequari quadrato C F, et B F. D rectangulum
  41. BD, AC proporcionalicer esse dinilas in F. _ F.
  42. EIL xqualia csc.
  43. Sineiam aequalia quadrarum C+F. _ rCclaHOIum AF C: dico BD, AC pFOPOr.
  44. cionalirer esse sectaS: Nam si non eA ve B F 2d E D, sIC AF ad F C, SICVE BK, 2d
  45. BFD, hoc est, quadratum B I, ad quadratum A I; Xquancur igitur quadracum C L
  46. de lectangulum H C. nmus rectangulum BF. D, _ quadrarum
  47. 172. huiuso
  48. Iam
  49. ED, GC AR dl LC. L C a L de rectansulo AK C per pri

Cite

[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 282. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1815201908:0339?run=74