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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 71

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: 0.85.

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The machine reads it as

  1. PRINCIPLA MATHIEMATICA.
  2. L E MI M A XX.
  3. Si Parallelorrammum quodvis ASP D’anculis duobus opposiris A
  4. Prancit sectionem quam vis Conicam in punctis A e P; e lateri
  5. bus unius angulorum illorum infinite productis A Q AS, occurrit
  6. eidem sectioni Conicae in B e C; a punctis autem occur suum B e
  7. C ad quintum quodvis sectionis Conice punctum D acantur rec-
  8. tae duae BD. CD occurrentes alteris duobus infinite productis pa-
  9. ralleloerammi lateribus PS, P O in T ( R: erunt semper abscissa
  10. laterum partes PR es PT ad invicem in data ratione. Et contra, si
  11. partes illa abscissae sunt ad invicem in data ratione, punctum D tan:
  12. set Sectionem Conicam per puncta quatuor A, B, C P transeuntem.
  13. Ca5. T. TUnganEuE BF, C F ec 2 puncto D agantur rectxe dux
  14. DO, DF, quarum prior,
  15. DG ipA B Parallela (IE d
  16. OCCUTTAE PB, P Q.
  17. e
  18. A
  19. II, L, G; altCTa D F paral.
  20. lcla sIE ipA AC _E OCCUEraL
  21. FC, FS. AB in F, L, F:
  22. ec crit (per Lemma ZVTL.) re-
  23. etangulum D F. X D S ad re
  24. etangulum DGX D NTin ra-
  25. tione data. Sed est F C) ad
  26. DF (CCu TO) uc P B ad HIB,
  27. adeoquevc F F ad D HI; dc
  28. vicissim P _ ad ~ T UE D F ad D HI. EA _C P R ad D F UE RC
  29. ad D C, adcoquenE (TC vel) PS ad DG, ee vicissim F R 2d S
  30. UE D F ad D G; ex conjunetisrationibus sic rectangulum P Q X F se
  31. ad rectanoulum F SX F F uc rectangulum D F X D F ad rectan.
  32. sulum DGX DEI, acque adeo in data rationc. Scd daneur P d
  33. ec FS e propterea ratio P R ad PT datur. Q. P. D.
  34. Ca5. 2. Ouod A P R ec P T ponantur in data ratione ad invi-
  35. cem, cum simili ratiocinio reprediendo, sequetur esse rectangulum
  36. DEX D F ad rectangulum D GX D H in ratione data, adeoque
  37. punctum D (Per LemIA XVTTL.) concingere Conicam sectionem
  38. cranscuntem per puncta , B, C, P. d. Ls. D.
  39. Corot.
  40. LIBEK
  41. P R1MVS.

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 71. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0105?run=74