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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 68

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.

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The machine reads it as

  1. 68
  2. PHTLOSOPMILLE NATDRALIS
  3. Per puncta , B, C, D ec aliquod infinitorum punctorum P, p1-
  4. Copronon ed p. concipe Conicam sectionem describi: dico punctum P hanc
  5. Tempertangere. Si negas,
  6. junse Cecantem hanc
  7. Conicam sectionem alibi
  8. quam in F, S Acri PocCA,
  9. puta in b. Ergo ( ab his
  10. punctis p ee b ducantur in
  11. dacisangulis ad latera Tra-
  12. Perii rect_ P9, pF, P5, pF
  13. e bk, bF, bs, b d; eric
  14. uE bk X bF ad bfX b d ita
  15. (Der LCm. XVIL) p9XpY
  16. 2d p5 X pF, d ita (per
  17. FIypOch.) P QX P R ad
  18. FSX P T. F.H _C DFOD.
  19. ter similicudinem Traperiorum bk As, P _ A5, ut bk ad bs ita
  20. P
  21. terminos correspondentes hujus, erit br ad b d ut F R ad FT. RF-
  22. 80 Trapezia requiangula Drb a D R F T Cimilia PunE, S corum
  23. diaronales Db, D F proxeeren coincidunt. Incidic itaque b in
  24. intersectionem rectarum AP, D P adeoque coincidit cum puncto
  25. P. Ouare punctum P, ubicunque Cumatur, incidic in assignacam
  26. Conicam sectionem. 9. F. D.
  27. Corol. HIinc A rectae ErCS P Q F R, PSa puncto communi F
  28. ad alias rocidem posicione datas rectas AB, CD, AC, singulx ad
  29. singulas, in datis angulis ducantur, Aieque rectangulum sub duabus
  30. ductis P _X P R ad quadratum tertis P S quad. in daca racione:
  31. punctum F, 2 quibus rectae ducuntur, locabitur in sectione Conica
  32. quae tansit lincas AB, CD in A e C; e contra. Nam cocac linca
  33. B D cum linca AC manente positione crium AB, C D, AC; de-
  34. in cocac etiam linca F F cum linea F S: sc rectangulum FSX P Y
  35. erader PS quad. rectae que AB, C D quae curvam in punctis A_B,
  36. C_ D secabane, jam Curram in punctis illis cocuntibus non am-
  37. plius secare PoNune sed tancum tangenE.
  38. Scholium.
  39. Nomen Conieae sectionis in hoc Lemmate late sumieur, ita ve
  40. sectio tam Rectilinca per verricem Coni cransiens, quam Circutaris
  41. basi parallela includatur. Nam s punctum p incidie in rectam, qua
  42. quaeris ex punctis quatuor A, B, C, D junsuntur, Conica sectio
  43. VertE.
  44. DE MOZV

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 68. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0102?run=74