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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 112

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: 0.87.

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

The machine reads it as

  1. 1II
  2. PHITLOSOPMLA NATURALIS
  3. PROPOSITIO XXXIH. PROBLEMA XXVII.
  4. eosita cujuscunque reneris vi centripeta, es concessis figurarum
  5. curvilinearum quadraturis, requiritur corporis recta a(cenden-
  6. eis vel descendentis tum Velocitas in locis sinculis, tum Tempus
  7. quo corpus ad locum quemvis perveniet: Et contra.
  8. De loco quoris A in recta AD F C cadat corpus l3 aeque oc
  9. ejus P crigatur semper perpendicularis P. C, vi centripetx in loco
  10. illo ad centrum C cendenti provortio.
  11. nalis: Sitque B FC linea curra quam
  12. punctum C perpecuo tangit. Coinci
  13. dat autem LC ipso mocus initio cum
  14. perpendiculari AB, e crit corporis V c
  15. locitas in loco quovis L. UE arCK CUr-
  16. vilincae ABG F. latus quadratum.
  17. Q. F. T.
  18. In E G CaPIREUE F. M laceri quadr2
  19. Eo arex ABG F reciproce proportio-
  20. nalis, _C AE AL. M linea curra quam
  21. punctum Mperpetuocangit, _c erit Pem-
  22. pus quo corpus cadendo describie li-
  23. neam A F. uE area curvilinca AL. MF.
  24. . F. I.
  25. Fcenim in recta AF capiatur linca
  26. quam minima D P datae longitudinis,
  27. SIEqUC D L F lOcuS linea F MC ubi
  28. corpus verlabatur in D; et si ca sic ris centripeta, uE arCX ABCF F.
  29. latus quadratum sic ut descendentis velocitas, erie arca ipla in du-
  30. plicata ratione relocitatis, id est, s pro velociratibus in D et F
  31. Seribantur V dc V fI, Crit arCa ABF D UEVV, _ arC2 ABC F. ut
  32. YV + 2VI F II, dc dirisim area D FG F. uc 2VL F II, adeoque
  33. DFGF
  34. DF.
  35. 2VI. F I
  36. DF.
  37. id cst, si primae quantiracum nascencium
  38. V
  39. rationes sumancur, longitudo D F ut quaneitas F adeoque c.
  40. CY
  41. cium ve quancitatis hujus dimidium F. PA autem tempus quo
  42. COrDUS
  43. DE MOTV
  44. EDAFORVH

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 112. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0146?run=74