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[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 53

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: 0.82.

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

The machine reads it as

  1. Lo R C F: VI.
  2. =_ GH = y. ergoBF =
  3. i OF = 8 y; Cr8O
  4. X
  5. C.7g: : b. r; HInC aute xequatio ry = y X = G X. unde DNH
  6. est hyperbola Tupra niox determinata.
  7. Ouod s punctum O sumatur infra DB; Het ae quatio y X - r y -
  8. ex. unde rurlus constat.
  9. ZXI. Ouinetiam, reliquis similiter posiris, recta F X non jam
  10. ipsiD B, sed alteri DII Feratur parallela; ita ut assumpto in B A
  11. puneto habeat semper B P. ad O F rationem altignatam (D B ad m) L18. 54.
  12. erunt intersectiones N icidem ad hyperbolam.
  13. Nam ducatur NVC ad AB Parallela; rocenturque DB = b; HIB
  14. =fa I1O = 8; DC = x; CN = y; eA ergo X. y: : b. -
  15. a
  16. = BF; X b. f: : x. - = OK; quarEN K (FH) =7.)
  17. _ O F - - y on)
  18. a
  19. - 5. Est er80. y - 8:: b. m.
  20. unde resulrat aequatio m y -) - g x - y ∞ = X x. vel Facto f. b::
  21. et
  22. m. r; est My) - ∞ X - 7 X = X a. COnSEaL iBitE lineam DHB
  23. esle hyperbolam; qualis superius trabetur determinata.
  24. Nocetur, Si compurario ab ipso puncto EI. inicium Cumat, (hoc est
  25. sIE P P. EIF:: DB. m) eranescente cune termino e; erie m y - y x
  26. x; unde quoque supra habetur alia determinatio simpli.
  27. n
  28. ciOr.
  29. ZZII. Estocrianoulum A DB, _ linea DY Y calis, ut duet a uE-
  30. cunque P M ad D B Barallela, SIE PexPCTIIO P Y = a : P M9 -
  31. DB9; erit linea D X P hyperbola; cujusurique Centrum eAt A, se
  32. midiameter AD, (vel asympeotos AB) semiparameter autem P; Faci- F1B. 55.
  33. endo AD. DB:: DB. P.
  34. Sit enim TD == 2 AD. EAqHe AD. P:: (AD9. DB9:: = 6. 2. Ftem.
  35. APG. PMg:: =TPFDP =) ADG. PMg:: TPXDP.
  36. PMg-DBG::) EPFDP. PY9. relFD, 2P; YPxDF.
  37. PYg. unde liquet Propositum.
  38. Corol.

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 53. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0269?run=74