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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 255

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: 0.81.

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

The machine reads it as

  1. PRINOIDTA MATHEMATICA.
  2. duplicata ratione ipsius S Q reciprOCC. Sunt autem arcus illi F Q LIDEK
  3. ec QR ut relocitates descriperices ad invicem, id est in subdupli- SEcvnDD.
  4. Cata rationC SG ad S P, Sve uE SG ad V SP ZSB; e ob aequa-
  5. les angulos SF
  6. Se
  7. r et aequales areas PS _ QSr, eAt ar-
  8. cus P Q ad arcum Qr ut S) ad SP. Sumantur proportionalium
  9. consequentium diferentix, _ HCF arcUS P Q ad arcum Rr uE SL
  10. ad SF = VSPXSC
  11. seu
  12. EYe
  13. nam punctis P ec Q) cocunti-
  14. bus, ratio ultima SP = V SF XS ad =V SC aequalitatis.
  15. Ouoniam decrementum arcus F9, ex relictentia oriundum, live
  16. hujus duplum Ar, eA ut relistentia ec quadratum temporis con-
  17. junctim; crit resistentia ut p
  18. ut S Q ad :V Q. et inde
  19. Ut
  20. 05
  21. Q9Z5Z. Frat autem P Q ad RP,
  22. + _4X S. F EC VE Z
  23. IVG
  24. sre
  25. OFX5F9. Namque punctis P de Qcocuntibus, SF de S
  26. coincidunt, et angulus FV Et rectus; ec ob similia criangula
  27. PV 9, FSO, AC F Q ad EV a ut OF ad EOS. FR igitUE
  28. OP X SPqut relstentia, id cst,. in ratione densitaris Medii in Z
  29. ex ratione duplicata relocitatis conjunctim. Ruferatur duplicata
  30. ratio relocitaris, nempe racio, et manebie Medii densicas in
  31. D ut.
  32. D.
  33. O∞X 5. F. Decur Spiraliss e ob datam rationem OS ad
  34. OF, densitas Medii in P erit ue . In Medio isitur cujus
  35. densitas eAt reciproce ur distantia 2 CenErO SP, corpus syrari PO-
  36. rest in hac Spirali. Q. F. D.
  37. Corol. 1. Velocitas in loco quovis P ea semper est quacum cor-
  38. Dus in Medio non relstente srrari porest in Circulo, ad candem a
  39. centro distantiam SP.
  40. ∞3. Et
  41. distancia illa non daturs ut D. F X S.F. Et inde Spiralis ad quam.
  42. dibet Medii densicarem aptari potest.
  43. Corol. 3. Vis relistentia in loco quovis P, est ad vim ceneripe.
  44. Far
  45. 235

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 255. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0289?run=74