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[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 96

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. l. P C F. ZI.
  2. VI. FTyperbolam AF. B, cujus Centrum C, tansanE duae rectae
  3. BT, FS, _ reliqua ponantur ut in proxime praecedente; erit TD.
  4. AD SP. AP
  5. Nam est C A. CD:: CT. C A. unde C A - C T. CD.
  6. C A:: CT. C A3 hOc CA TA. AD:: CT. C A. suppare dis-
  7. CUxIU eAS A. AP:: CS. C A. Verum est C I. C A 2CS.
  8. C a. quare I A. AD = 3S A. AP; seu componendo TD. AI
  9. SF. AP.
  10. VII. Circuli A EB (cujuS Centrum C) ex paraboliformis A F B
  11. communes sint axis AD, e basISBD; CIE aurem paraboliformis ex-
  12. Donens ; d AD:
  13. C A (vel m =- n. M = 2n::
  14. C A. AD) circulum verotansar recta BT; haec quoque paraboli-
  15. formem A F B continget.
  16. Nam quia BP circulum tangic, est CT. CA :: C A. CD. unde TA.
  17. AD:: CACD. componendoque ID. AD:: C A. I CD. CD. lem, quo-
  18. uiam est (ex hypothesi) C A. AD:: m. n. m - 2 n; erit per ratio.
  19. nis convertionem C A. C D :: m -- n. n. ee componendo C A. )
  20. CD. CD:: m. n. HOC eATB. AD:: m. n. unde (a) palam FIL,
  21. quod B Eparaboliformem AF Btansit.
  22. VIII. Subnotetur, quod inverse, data ratione ipsius A D ad C A
  23. designabitur hinc paraboliformis; quae Circulum A P. B ad B contin-
  24. Bet. Nempe, A AD = -=, erir 2r --, dictx paraboliformis ex-
  25. Ponens. Nam polito Fore
  26. 5 - 1
  27. F - 5
  28. mi exirideo (juxta crucem
  29. mulciplicando) m F = m 5= 2 tn - -sn. _ transponendo mt
  30. 2nF = m s- n s. ac ideo (aqualicarem ad analogismum redisendo)
  31. m = - n. m = 2 n : : t. s:: C A. A D. itaque constat ex anteceden
  32. te Propolicu.
  33. IX. Manente quoad exrera sexrimx hypocheli, paraboliformis
  34. A F B extra circulum A F B tora cadet.
  35. Nam uccunque ducatur recta O F F ad D B parallela. quxe secet
  36. circulum ad F, parabolitormem in F; duetxque concipiantur rectx
  37. ES circulum, recta PR paraboliformem cominsentes; PAque
  38. versa praxima sequitur gy AC
  39. F18, 137.
  40. F18. 138.
  41. (4) 2 bajur a
  42. E18, 239.

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 96. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0324?run=74