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[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 55

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. L B C Y VI.
  2. irem PO ad Y F. Parallela. F Aque F F 9 = F O g(C P9) )- OF9
  3. =1 2E OXOF (=L 2CPXOF). Verum obC P. C A:: OP.
  4. OF:: C F. OF; Cs C P XOF = C A X CF; ergO FF9=
  5. CP9-)n OFg.) 2C A X CF. item est AF9 = C Fg.)
  6. C A9 - = 2 C A X C F; quapropter est F F9.) AF 9 = C P9.).
  7. C A9 - ] OF9 C F g. hoc estE C9 == (AP9. 1- PF g =
  8. CV 9 ]. PF 4. vel ECg - PF4 = CV 4. Verum est CF.
  9. (PO). PF: : CP. AP:: C P. CV; unde FC9.
  10. CVC
  11. CPC
  12. CFg
  13. CV 9; adesque linea C V C est hyperbola, cujus centrum C; se-
  14. MIaXES CV, C P.
  15. Nor Ducta recta F O ad TH perpendiculari, sumptaque O R =
  16. AE; _E CONMEKa CR; exit C R hyperbola V GC perpendicularis,
  17. mihi praesta sistidem; aut ipse rem ad Calculum exise; co verba
  18. non protundam.
  19. XXVI. Positione dara SInE ReCEX A C, BD (se intersecantes in Z)
  20. quas decusset recta A B; cum ducta utcunque recti PRL ad A B FI8. 59.
  21. varallela, (quae rectas A C, BD seceE punCtiS P, R) SITP L aequa-
  22. lisipli BK; erit linea A L. L recta.
  23. Nam, (duCta Z O ad B A paralleli, est AO. AP:: (BZ.
  24. BR::) OX. P L: ersolinea AL. L est recta.
  25. XXVTI. Postione data sir recta A X, _C punctum D. Reque non
  26. linea DNN talis; ut per D ductâ quacunque recta MN (quare. F18. 60.
  27. ctam A X secet in M, _C lineam D N AI in N) sic perperim rectangu-
  28. lum ex D MI, DEI aequale dato (puca quadrato Cx Z); erie linea
  29. DN N circularis.
  30. Nam ducatur D B ad A X perpendicularis; sitque DB. Z:: L.
  31. DF; SE COnneCtATUE N F; LCt jaM D ML X D N = Z 9 =- DBX
  32. DE; quare D M. D B:: D E. D N. ergo triangula D B M, DN F
  33. similia sunc; quaproxter angulus D NI P rectus est; itaque linea DHIN
  34. est circularis: (ad circuluun perrinens, cnjus Diameter D F).
  35. Vides nedum rectam e hyperbolam; sed _ suo modo rectam ac
  36. circulum cibilineas esse reciprocas. Verum hic, ethi praeludiis no-
  37. Aris nondum absoluris, paulum subsiCtamuS.
  38. EC X. VL

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 55. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0271?run=74