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[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 1081

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: 0.87.

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The machine reads it as

  1. GONOIDES HILLLRDOLLOrM
  2. 82
  3. Demonstratio.
  4. A FBCFTEDEXCCdentis proPOLICOIS ProBramma AEquE WXEa 17 J. = L alum-
  5. LLPEOTOS RLO hyxerbola, qCHin conoD F F. Ottensum est quod quadra
  6. tum ID excedit IFI quadeacum aeguali excessu, quo quadracum MO exocdic qua-
  7. drarum NCS. lcdquin X P est alympcoros hyperbola R M C, eriam quiadratum I L
  8. excedic aacum IO aquam excestu quo quadracum OP, excedie quadedeum
  9. OM cum quadrata lP X O P, excedanc quadeaca PC et OM, rectangulis sub YC
  10. dc duptâ YI; e (ub PM X dupla P O, guae per 18. hyperbola aequalia lunc. lgieur
  11. excellus quadrari IY luper quadraco IFI, aequalis est excestui quo quadracum OP
  12. excedis quadracum ONV. Sectioigicur BNII axi parallela, est hyperbola.
  13. Ouod auce similis sichyperbola B N FT, hyperbole A B C que per axem facta cA, p2
  14. tec ex eo, quod BNII hyperbola alimproris claudicur ijsdem, quibus claudicur hy-
  15. perbela KL C, ve ostensum es supra. Fre0 per 17 4. huiushyperbola B N E axi par al-
  16. lela similis est hyperbolx per axem. Ouod crac demonstrandum.
  17. Corollarium primum.
  18. Mnes sectiones conoidis quXe axi sune xouidistances angulum ast po CoM.
  19. Corollarium secundum.
  20. ine crtam manifectum est, omnium sectionum minimam ese ayperbea PL
  21. axCH, Comparetur cum Elavis hyperbola qua sic eidem sectioni parallela,
  22. cum enim ostentum sic omnes illas hyperbolas alrinprocisrei, qui sunc eiusdem an-
  23. suli. lsicur quo maiores cudent diametrieransuerta, co criam maiores cundenchy-
  24. perbolae: diamerer aurem cransuerla, minima illaCIt quA PCFAKCMM ETANEIE, VE PaECE
  25. curioluis has materias consideranci.
  26. eROTOSLTIOLLLXXX.
  27. prelciulum aquate ConinenC. Pacec ex 177. huius.
  28. DEcetur conoides plANO PEF AKCM ex-
  29. Dhibenshrperbolam: inuentis aurem
  30. huius sectionis alymprocis, hacsectio co-
  31. noidens alteri alzmprocon parallela.
  32. Dicoparaboraac scerione producis
  33. Demonstratio.
  34. Ec ABC platum per aAcM L B L conoidcos
  35. hyperbolici, exhribens sperbolam ABC.
  36. cuius cenerum F, a Pbci vero F C F FI. POL-
  37. es deinde recta BD que aequidistet alymproco
  38. FC. hac per eam lectio B l recta ad planum
  39. ABC VicotSTaBDF CHC ParabOla ad FBR
  40. axem comme conorucos a sectionis ABC
  41. constieuantur oramatm ICCl L MI, que produ-
  42. etx cuntalympeons d cum sectione concurrars
  43. ponancurq: B lalimptolo H aequidistans, et
  44. XBScansenssectionem AB C in B. Denique
  45. sectiones AanE L R V, que sinc rectx ad plamit
  46. per axem quarum commanes sectiones NR
  47. cum plano B R R, 19. vndec. _ detinic. 3. vndec.
  48. recte erune ad lineasF. D, BD. quoniamigieur
  49. FC, BD xquidictanE P N aquales exunt SB
  50. p e e es e uui s e e es qe es ee u e ee se ete s te site u e te r u p te u ( qu et 1 e e s 1. te e e e . at H 11 11

Cite

[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 1081. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1815201908:1138?run=74