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De Locis Solidis Secunda Divinatio Geometrica, fol. 163

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: 0.89.

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

The machine reads it as

  1. ORDINATTONVM COMTO. LIMITIBVS LIB. L.
  2. 163
  3. Nam ducta quacunque laterali FanSentC AH verticalem L F secante in
  4. HI, axem vero in C, X per A applicata A DI secante FIyperbolam DL
  5. in L. DicO DL. ipsi AHI aequalem esse.
  6. Per verticem B datae Parabolae adscribatur FTyperbola BL, quae sIE LI
  7. mes Ordinationis concingentium Parabolam, guarum vna est A C erit
  8. ergo a BE huius rectum lacus, d F.B cranluersum, quum sc subquadeu- 2 ex Br. hu-
  9. plum ipsius BF; ergo e rectangulum F DB, SiC quacrat DL in FAV- IuS.
  10. Perbola aequilatera, erir lubquadruplum quadrati DI, hoc estlinca DL. di-
  11. midium erit ipsuS DI, Sed etiam A FI dimidium CA FOTUS A GG, FOEX VerO
  12. DI, A C sune aequales, erso de dimidiae ipsarum, nempe DL, AHI
  13. aquales etUnE. OuaprOpter concauum huiulmodi Fyperbolae BL. est Limes
  14. Parabolam cansercium, quarum vna est AFL. Ouod erat _C.
  15. PROPOSTTIO LAXXNI.
  16. X Porabola. Limes Ordinationis normalium super
  17. Sectionem ductarum. C5 ad tancentem ex vertice or
  18. dinatarum; est ad Locum conuexum FIyperbola in
  19. vertice Parabola centrum habentis, (5 aequalium la-
  20. terum, vtrunque recto Parabola aequale.
  21. OVT Parabola A B, cuius axis B C, vertex B, de semirectum latus
  22. B D, Factoque centro B per verricem D sic circa cundem azem BDR
  23. Hyperbola aequilatera D F, de a quocunque Parabolae puncto A ducta
  24. normali AF super Sectionem A B, _ per A recta G AF axi B C paral-
  25. lela, quae producta, Hyperbolae occurrat in F. Dico normalem AF ip (I
  26. CF. ad cansentem BC Ordinatim ductae aequalem esse.
  27. Applicetur, in Parabola, ordinata
  28. AC, _e F R in TIyperbola, iungatue
  29. GD, de Tumatur BH in directum, ee
  30. aequalis ipA BD, iea ve HID sic erans
  31. versum Elyperbola DF.
  32. Tam, in ParabOla, GuU SIE A F nOFI
  33. malis ad punctum A, e AC ad axem
  34. Ordinata, eric C F aequalis B ips BD
  35. recti laceris dimidio: eltque AC equa
  36. lis G B, ergo in criangulis rectangulis
  37. A C F, G B D lubtenla A F, C
  38. aequales etunE.
  39. Praeterea, quum Eyperbola DF. (
  40. requilatera, erie quadratu F. IL, sive
  41. GB aequale reCtanguIO FLK D, e communi addito quadrato BD, crune
  42. quactrara simul CB, BD, line rnicum GD, vel AF aequale rectansulo
  43. HKD cum quadrato DB, hoc est vnico quadrato BH (nam HD secta
  44. B Prop. dc
  45. libri prii
  46. itiarE.
  47. 1

Cite

De Locis Solidis Secunda Divinatio Geometrica, fol. 163. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/898203430:0191?run=74