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[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 119

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. Y, F C F. XVTI.
  2. AV. TV: : CV. CD; e consequentes subduplando, diridendo.
  3. QHC AR. RV:: RV. R D:: RV. CR. Vel AR. RHI:: RH. CR:
  4. hioc est HIN (RX). NC:: KH. CR; quare C R X K ~ = K H
  5. XN O, eA aNtCI XZ 9 = CZ 9 -- CX 9= X69.- CX9 =
  6. NC9 ). RH9 - 2 AC X RH: = RX9- CR 9. ]. 2CR
  7. XR X = N Cg.J. RHI9 - RX 9 - CR g. SuratuE K S = KX,
  8. discurtumque limilem aunibendo liquebit Fore EC = Z Z. _ ideo
  9. DZ = CZ. unde CE --DC (DZ - CZ) =C
  10. -CZ=
  11. Ey = XO = 2 KHI = TV. quare manitestum eAt cArVaS TI.
  12. VEesse Fyperbolas, quarum axis LV, Foci C, D.
  13. IV. Tertio demum, sic angulus C A F. semirectus (vel C A = Fig. 192
  14. CF) erit cum punctum Z ad parabolam; quae iridem ita determina-
  15. tur. Fiac angulus AC P Cenirectus, _ ab iplarum AF, C P in-
  16. tersectione R duCatUE R I ad C F Parattela; erit TVertex, atque C
  17. Focus Parabolae. id quod ex bene nota sectionis hujus proprietare con-
  18. sat; qua scilicet est I A = TR = TC (ob angulos. I AR,
  19. TC R RemirectOS) _ AX =XC = CZ.
  20. V. Manifectum est vero rectam A F sectionestas ad F contingere.
  21. quia nempe perpetuo major est CZ. (vel X(1) ordinata XZ; aderi-
  22. que puncta C exrra curras unagux que jacent hoc est tora AG exIra
  23. illas cadit.
  24. VI. Hilce peaestraris: Esto Circulare speculum MBND, cen F18. 193.
  25. trum habens C; cui exponatur recta quapiam LaC; e huic per-
  26. pendicularis sic recta Ca; quam ad partes avertas (umPEa C A, ad-
  27. aequer.. Sit etiam C F ad C A perpendicularis, ac requalis qua-
  28. dranci diametri BD: connexaque recta A F producatur utcunque.
  29. sumpto jam in recta Fa G puncto quolibetF, ConnectatuT F C, 8
  30. radiationis ab Pin ipla FC limes, seu focus, (it Z; ac per Z du-
  31. catur Z X ad A C. perpendicularis, ipsi A Foccurrensin HI, dico:
  32. fore X HIparem ip(ICL.
  33. Nam (e jam ante monstratis) est F C. CZ:: FMI. MIZ (hoc eA)
  34. : FC = CB. CB - - CZ. tinC exIE B C. CX (AC, CX)::
  35. FC CB. CB--CZ. quare (ducendo in se extrema, ac media)
  36. eric AC X CB - AC XCZ = CZ XFC -C ZX CB. hOC
  37. eA (ipsI C X X F C substimendo A C X CZ, PFOPter a C. CX::
  38. FC. CZ) erIt AC XCB - AC XCZ = ACXCZ -CXX
  39. C. B. transponendoque AC XC B + C L XC B = 2AC. XCZ.
  40. hoc.

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 119. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0191?run=74