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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 54

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. 54
  2. PTTTLOSODMLSE NAIDRALIS
  3. DEMOrD Corol. Hinc Fllipseos area toras eique proportionale rectanou-
  4. Conronon lum sub axibus, est in ratione compolica ex lubduplicata ratione
  5. laceris recti ex ratione temporis periodici. Namque arca tota eAt
  6. uE area QI X SP ducta in tempus periodicum.
  7. PROPOSITIO ZV. PHEOREMA VII.
  8. Tisdem positis, dico quod Tempora periodica in P. lixsibus sunt in ratione
  9. sesquiplicat a majorum axium.
  10. Namque axis minor est medius proportionalis inter axem majo-
  11. rem ex latus rectum, acque adeo rectangulum sub axibus eAt in ra-
  12. tione composita ex subduplicata ratione lateris recti et selquiplicata
  13. ratione axis majoris. Sed hoc rectangulum, per C orollarium Prov.
  14. XTV. est in ratione composita ex lubduplicata ratione laceris recti
  15. et ratione periodici temporis. Dematur uerobique subduplicata
  16. ratio laceris rectis e manebit selquiplicata ratio majoris axis aequa-
  17. lis rationi periodici temporis. 9. F. D.
  18. Corol. Sune igitur cempora periodica in Ellipsibus eadem ac in
  19. Circulis, quorum diametri aequantur majoribus azibus FIliplcon.
  20. PROPOSITIO XVI TMEOREMA VIII.
  21. Tisdem positis, es actis ad corpora lineis rectis, quae ibidem tangant Or-
  22. bitas, demissisque ab umbilico communi ad hastangentes perpendi-
  23. cularibus: dico quod Velocitates corporum sunt in ratione composi
  24. ta ex ratione perpendiculorum inverse es sub duplicata ratione la-
  25. terum rectorum principalium directe.
  26. Ab umbilico sad tansentem P R demitte perpendiculum SY
  27. ec relocitas corporis P crit reciproce in subduplicata ratione quan-
  28. citaris -2. Nam relocitas illa cA ut arcus quam minimus P B
  29. in data cemporis particula descriptus, hoc CA (per LC. VTL.) ut
  30. tansens P R, id est (ob proportionales P R ad _ F e S = ad SY) ur
  31. X
  32. =, EIVC VE SY RCCIPTOCE et SPX GF directe; eAque
  33. S~ X∞+
  34. MINII

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 54. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0088?run=74