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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 66

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: 0.91.

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The machine reads it as

  1. PTTILOSODHILA NATORALIS
  2. SE CTTC
  3. Inventio Orbium ubi umbilicus neuter datur.
  4. L E M NI A XVII.
  5. Si a datae Conicae Sectionis puncto quovis P, ad Trapezii alicujus
  6. ABDC, in Conica illa sectione inscripri, latera quatuor infinite
  7. producta AB, CD, AC, DB, totidem recta PO, PR, PS, P Y
  8. in datis anculis ducantur, sinculae ad singula: rectanculum due-
  9. tarum ad opposita duo latera P O Z PR, erit ad rectanculum duc-
  10. tarum ad alia duo latera opposita PS X P P in data ratione.
  11. Cas. F. Fonamus primo lineas ad e
  12. opposita latera ductas parallelaser-
  13. se alcerutri reliquorum lacerum,
  14. DuEa F Q_ F R lateri AC, ex FS
  15. 2c F Flateri AB. Sintque insuper
  16. latera duo ex opposcis, puta IC
  17. e B D. Abi invicem paealle.
  18. la. FC recta quae bisecat paralle-
  19. Ia illa lacera erit una ex diametris
  20. Conicae sectionis, et bisecabit eti
  21. am RD. Sit O punctum in quo
  22. R Q bileCaTuT, eE Crit P O ordinatim applicata ad diamerrutillam.
  23. Produc PO ad X UE SIC OK aequalis PO, e crit OK ordinatim
  24. applicata ad contrarias partes diametri. Cum isitur puncta , B,
  25. P _ K Enc ad Conieam sectionem, ec F _ sccet AB in daco an-
  26. sulo, erie (per Prop. 17 ec 18L ib. III Conicorum Apollonii) rectangu-
  27. lum P QR ad rectangulum QB in data rationc. Scd ) R e YR
  28. aequales TunE, uepote aequalium OK, O P, e O O R disterentiae,
  29. ec inde etiam rectanoula F OK eE F OX F R aequalia TUNE; 2C-
  30. que adeo rectangulum P Q X F R est ad rectangulum 1 B, hoc
  31. est ad rectangulum P SX P F in data ratione. Q. F. D.
  32. DE MIOTO
  33. POMPOROM
  34. C450

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 66. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0100?run=74