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[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 46

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: 0.90.

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

The machine reads it as

  1. l E C Y. VI.
  2. DH. L. N -- HIO:: L H. LB::) LHI. HIR. CritDH X HR =
  3. HOXLH; hOC CADL. XHIK = L HKHIR = ROXFHI . IIR
  4. XL IL. UndC CTIED L XHIR = ROXL HI, vel ZIXF D = ZK
  5. XX O. ergo constat lincam ODO esse PTyporbolen, cujus ASYmpTOIr
  6. 7. A, ZS. Breriuis hoc ostendi posset, producendo rectam NI LS.
  7. NNam est DS =D M -=D O FOM =N M F OM =ON. Simi-
  8. tex quartam ec nonam brerius demonstres licer.
  9. Ouinimo siM N ad D C quamris eandem perpetuo rationem Dona-
  10. cur habere (pura datam R ad S) etiam linea ODO Fsyperbola exic;
  11. Elempe (2 cumm Hat R. S:: L B. LZ; _R. S:: DL. DF; _ per
  12. Z ducatur Z S ad BC; ac per F cransear R P adZ A parallela, cum
  13. ZS conreniens in Y; Crune PR, ZS dictae FTyperbola asymptoti
  14. quod jam sufticerir innuisse.
  15. Flinc intranscursunoro facile contici Problema (quo problematum
  16. confectionesista Archimedea, as Vietea ope primae Conchoidis peracta,
  17. ad Sectiones conicas rediguntur) Pex darum punctum D rectam lincam
  18. ducere, sic ue anguli dati AB C lateribus intercepta ductae rectxe pars
  19. aequetur datxe T. Nam descripta hyperbola OBO; centroD, in-
  20. terrallo datam T xquante describatur circulus POO hyperbolam in-
  21. cersecans in O; e producatur DON; Herq; M H ==BO =T.
  22. Modus aurem hic generalior est, e concinnior eo, quem in Opticis
  23. eradidimus.
  24. IV. Sic angulus A BC, et punctum datum D, sic etiam linea O
  25. BO calis, uc per D ducta quapiam recti DN, sic anguli lare-
  26. ribus intercepra MH ad recta BC currique OBO interceptam
  27. MO in eadem semper ratione (pura Z ad Y; ) erir linea OBO
  28. hyperbola.
  29. Ducatur enim recta DL ad CB parallela, ipsi A B OcCurrenS
  30. in L; secenturque DL, BL punctis F, F, ut lEDL. DF:: X.
  31. Y:: BL. BF; tum per F ducatue recta FR, ad B A. SC per
  32. F recta FS ad BC Parallela; concurrancque rectae PR, FS pun-
  33. etoZ; denuo per punctum O ducatur OHI ad A B parallela. Jam
  34. ob DL. DH:: LN. 1O:: LB + BN. HIO:: DE X LB
  35. . DF X BN. DF X HIO. ItEM DLXRO = DF X BNI
  36. (namDL. DF:: MN. MO:: BN.KO) _DEKLB =DL
  37. X BF (obDF. DL :: BF. LB;) exItDL. DH:: DL X BF
  38. = DL X RO. DE X HO; hoc eADL X BF L DL X
  39. RO. DHx BF. V DH x HO:: DL X BF + DL X K O.
  40. 218. 38.
  41. Ei8. 39.
  42. E18. 39.

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 46. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0258?run=74