Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 988

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.

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

The machine reads it as

  1. N OVLAACYCLNDRICA
  2. 210. Vndec.
  3. b15. naec.
  4. C16. Vndcc.
  5. dL. Sexti
  6. Demonstratio.
  7. Ctciragueongula AB C, à eylindro recto ab-
  8. scisa habens alcicydinem O B diametro
  9. bascos A C parem: eius basi inlcripea sIC AguT2
  10. regularis ADF FOC, de ducta lic AC ad
  11. terminum vicimi laceris CC. Denique plana
  12. Ponantur per latera polysoni quae requidistene
  13. axi cylindei exhibeneia communes incertectio.
  14. nes cum ellipsi ABC rectas AM, M N, NO
  15. Dicoplana haec omnia Bmul Cumpea, nimi-
  16. TUM ADM, DENM, E. FON, LOPO8
  17. CCP, aequarirectanguloC AO.
  18. Duod sic ostendo: PX CCMETO AUCATUE SO
  19. normalis diametro, de à puncto O ducacur in
  20. superticie crlindrica recta O B, que crie rnou-
  21. la alcicudo, et ex hypochesi xqualis diamecro
  22. AC, iungatur deinde SB, ductis insuper D II,
  23. E I, FK, CE normalibus ad A C, iunsCTINI.
  24. INRO, T. F. Ouoniam OS, DFT LinE p2.
  25. rallele, icemque BY, ND, anguli BOS.
  26. ND FT aequales acrune. Rursum quia OS, Q B
  27. aequidistanE DII, DMI, plana SOB, IIDM
  28. suncbparallela. ergo carum sectiones commu-
  29. nes cum plano elliprico CB A, rectenimirum
  30. BS,MTT, Sunccparallela. Cum isieur OS,
  31. BS xequidiltent DH, MFI, crunc ansuli
  32. OSB, D LTM xquales. crianoulaivieur BSO.MHD Sumilia tunE, erBOVE BO ad
  33. O.5, ita HD ad D HI. Sed BO ex hrpocheli por Cst diametro AC, adeoque du-
  34. plasemidiamerri S. Ergo ex MD dupla eA D FI. Pari modo octendam rectas
  35. NF. OF, P C duplaS esse rectarum F L, F R, C F. Precerea quoniam exlindeus ex
  36. Ayporhiea rectus est, a quo decusaTUE VnGULA, CTUNE M D, NE, OFs P Crectae pla-
  37. nobaleos AO C, adeoque per definitionem 3. vndecimi angulosrectos Faciune cum
  38. lineis AD, D F, EF, F G, GC. TrIanGUIA ErSO ADM, COP rectangula LIIME, d
  39. PIANADMNE, P NO F, FOPO, crapezia rectansula. Ouoniam isitur MID, crian-
  40. suli ADM es alcicudo, eaque dupla est octensa iplius D HI, criceriangulum ADM
  41. rectangulo sub AD _ D II aequale. Jam vero rectis P D, NM bilectis in Y ec V.
  42. iunctaque TV, rectam TV dimidiam eAe (IIIIX rECtATUM MD, N F; de rectan-
  43. Gulum ED TV, aequari crapezio rectanguIO MNR D in sequenEI, FGUTX OpPOTEI
  44. nicarersi, demonstrabimus. Ouare cum rectansulum lub F D _ MI D. N P canquam
  45. vni guae duplae suncrecte T. V, rectanouli E D TV duplum asic, cric quoque rectan-
  46. gutum sub E D, XNTD, N F. canquam vn2; duplum plani MNE D. Ouin aurem
  47. rectae MD. NVF, octenlae lunc duple rectarum DIT, FI, rectangulum (ub PD; 8
  48. MD, NP Simul Cumpris duplum etiam est rectanguli sub F. D, _ D HI P I simul
  49. Cumpeis. planum igIEUE MNY F D aequacur rect angulo (ub D R, SINC AD _ED IT. BF
  50. simul sumpris. Pari argumeneo octendam planum P. NOF, aequarirectangulo sub
  51. EF id eA AD, _ B I, FR; planum veroF O. P C rectangulo sub F C, hoc est
  52. AD _ FK, C E,criansulum denique CP, C ostendam rectangulo lub eC, id est
  53. AD, d C:T aequari, veoltendi supra criansulum AD M aequari rectansulO AD II.
  54. omnia igicur plana vngula inseripea Cmul sumpea xequancur omnibus rectangulis il
  55. lis simul sumpris, hoc est per Corollarium praecedentis rectangulo quod rectis C A.
  56. AC ContinCTT. Quod erac demontlrandum.
  57. Corol-

Cite

[Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli, fol. 988. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1815201908:1045?run=74