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[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 1023

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: 0.86.

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

The machine reads it as

  1. Y N CYL A P A HC ABOLIC A.
  2. Demonstratio:
  3. Vcatur recta PD, et sume in axC F B.
  4. quoduis punctum I. a quo ducta ordinacim
  5. TFT, que proindle parallela eric ad AF, CZ TI in
  6. cxlindri superticie ponatur recta FIC, quam
  7. quia axi FS aequidistat, pacec eriam recte AF
  8. requidictare. Ouoniam isitur TFI, FTG aequidi-
  9. REANE P A, AF, crunc plana 2 ITTG, F AF P2
  10. rallela: quae quoniam sccat planum F. AD, C.
  11. runcbcommunes sectiones AF, R C parallela.
  12. sane aurem _ TII, AF parallelae. ergo criam
  13. CiK. FTI parallele. Demde quoniam parallela
  14. PlanA F AF, S,ITIOK secac planum BF SD.
  15. erune communes sectiones TR, F. S Parallele:
  16. led eciam FTG ad axem F S, est paralIela. eF
  17. SOTR, ITO ParallelX. Ergo OFI, IK paralle.
  18. logrammum est. erso HII, CR aequales. ITis dc
  19. monstraris huncin modum concludemus pro-
  20. Policu. ducatur in exlindri superticie recta BD
  21. cric haec parallela axi F S, acproinde eriam ad
  22. TK eric Parallela. Igieur F. D est ad RD, vE
  23. FB, ad IB, hoc eA, cvE quadratum A F ad qua-
  24. C d. parabi
  25. deacum TTT, hoc est ve quadratum A P, ad quadeatum CR. ergo d AC.D parabo- dibid.
  26. la est. Quod crac demonttrandum.
  27. P R OP OSITIO LX X X V1
  28. ixlindrus parabolicus rectus ABCD (cuius balIS ABD, e balCOS
  29. LaxIs E B, ordinatim verO pOsITa A P. D) Secerur primo sectione per
  30. AD exhribence parabolicam vngulam F AOCBD, e alcera sectione
  31. GFMI qua aequidisterbaM ABD.
  32. Dico rngulam eoram AOCBD ad
  33. partem rescistam G F. C. M, quincuplica-
  34. iam eius habere racionem quam habet
  35. AD, ad C NI.
  36. Demonstratio.
  37. DTuidaMCML PIOBOTCIOHALIEEK FECLE AV.
  38. CM in quibuluis punctis I e L, de cri-
  39. Sancur diametri TK, L N) de sectiones hane (e.
  40. cundum lincas EB, TK, XTIF, L N exhiben.
  41. ces in superficie cylindrica rectas lineas BC,
  42. KO, _ FC, NP. lunsantur denique P C, 1O
  43. ex FTC, L P. Ouoniam plana TRO, F BC
  44. parallela secar planum A C D, crune commu-
  45. hesfectiones IO, F C parallela. pari argumen-
  46. EOpaFaHIClX sunE FTC, L P; X similia exunE
  47. criangula F BC, TKO _HIEC, L. NP cum
  48. tam anguli BF C, RIO quam anguli FBC,
  49. TKO. icem eam anguli FTTC, NLD quam
  50. FIFC, LNP aequales sinc. Deinde quia re-
  51. Etx AD, CM Smilicer ex Constr. sunc diuilx,
  52. eric rectangulum AID ad rectangulu AF. D,
  53. ida
  54. 13
  55. b.
  56. 5. Vndoc
  57. Au e t ut pes e e te e e e ete e et e u te e e t t ps e s t tt s e te t 1 e e s 1 .

Cite

[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 1023. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1815201908:1080?run=74