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[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 52

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: 0.88.

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

The machine reads it as

  1. 18.
  2. 218. 53
  3. L. E C Y. VI.
  4. :: b. r. unde talis emerser aequatio: y a -) - B X y-
  5. X a x; hoc est (BosiTO = = m) y X ) B~ - my = X X; FA
  6. isicur curra B HI NI hyperbola, qualem superius exhibuimus determi-
  7. MaLaM.
  8. ZVTII. Dacx posirione sint rectae DB, B A; (_ in DB detiene
  9. cux punctum D) Cirque linea D N N calis, ne duct a utcunque CH
  10. ad B A parallela; Sumpris vero determinaris e, r, vocatisque DC)
  11. = ∞; dC OH = y, CiEr y - y x = 8 x; erir linea DNN hy-
  12. perbola, lic determinanda.
  13. CapiatuED F = r, _ BO = 8. _ per F duCatuF recta F R ad
  14. BA, 2c per O recta O S ad BD parallelx; erunE ZR, ZS asym-
  15. PFOtI.
  16. Nam ducta N P ad D B parallela, esEZ P = 5 -- y; _PH =
  17. r - X; quare L. Px P ( = Cr - C x = ry = Y X. VerUT CX
  18. typocheli eA - ∞ . ) -. x y - y X = 0. erBOZ PXPN = Gr =
  19. LF X F. D. unde liquido constat Provolicum.
  20. Ouod Si fuerit aequatio x y = r y = C x; sumenda eAt D F = Y
  21. e BO= (intra rectam DB) ductisque, ceu prius, parallelis
  22. SZR; eric hyperbola NVN N ansuloSZ R comprehenla; quod co-
  23. dem facile comprobatur modo.
  24. Z1Z. Datae positione sint recte D B, B A; ac ita serantur rectx
  25. EZ ad DB parallela, ac D Y per punctum delignatum D transiens,
  26. ut sic semper ratio iplius B P. ad ipsam BF aequalis altionatae D B ad
  27. R; crunt rectarum DY, PX incerlectiones ad lineam rectam.
  28. etam per N ducatur CR ad B A parallela; est que DB. DC::
  29. B B. GH:: BF. BF:: BD. R. itaque semper est DC =R. Pa-
  30. tet igitur Facta DC = R, _ ductâ C R ad B A parallela, incersecti-
  31. ones omnes ad hanc exictere.
  32. ZX. Ouod Sireliquis similiter posiris; sumpro aurem alio in B A
  33. puncto O: ab hoc lumatur compurandi inicium; ut nimirin CIE
  34. perpetuo BF, O F:: DB. R; crune intersectiones H ad hyper-
  35. bolam.
  36. Nam duct a N C, ad AB paralleta, si D B = b; OB = 5; DC

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 52. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0264?run=74