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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 125

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: 0.89.

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

The machine reads it as

  1. PDINCIPLA MATTIEMATICA.
  2. F25
  3. qua corpus in Ellipsi mobili u p h iildem temporibus revolvi LIvex
  4. DONIE.
  5. Corol. 3. Ad cundem modum colligetur quod, si Orbis immo-
  6. bilis VL X Fllipsis sic centrum habens in virium CCNErO C; ei
  7. que similis, aequalis e concentrica ponatur Rllipsis mobilis W p R5
  8. sitque 2 R Ellipseos hujus lacus rectum principale, et 2Y latuS
  9. transversum sire axis major, acque angulus V C p semper sit ad
  10. angulum VC P uc G ad F; vires quibus corpora in Lllips im
  11. mobili ec mobili temporibus aequalibus revolvi pONUNE, CrUnE VE
  12. A F A
  13. E Cub.
  14. EE A RGG = R F P
  15. PCub.
  16. Acub. respective.
  17. Corol. 4. EF universaliter, A corporis alcieudo maxima CV no-
  18. minetur V, e radius curraturae quam Orbis V P R habet in V, id
  19. est radius Circuli aequaliter curris nominetur R, ex vis centripera
  20. qua corpus in Trajectoria quacunque immobili V P R revolvi po-
  21. test, in loco V dicatur satque aliis in locis P indetinite dica-
  22. cur Z, altieudinc C P nOminatA A, ex capiatuE C ad F in data
  23. ratione anguli VCp ad angulum VCP: crit vis centripeta qua
  24. corpus idem eoldem motus in eadem Prajcccoria u p e circula-
  25. riter mora remporibus iildem peragere potest, ut summa virium
  26. X L VRC G-V RFF
  27. A CMb.
  28. Corol. 5. Dato igitur motu corporis in Orbe quocunque immo-
  29. bilis augeri vel minui porest ejus mocus angularis circa centrum
  30. virium in ratione data, ex inde inveniri novi Orbes immobiles in
  31. quibus corpora novis viribus cencripetis orrentur.
  32. Corol. 6. Isitur ( ad rectam CV PO.
  33. sitione dacam erisatur perpendiculum
  34. P lonsicudinis indererminata, jun-
  35. Sacurque C P, ex ipA aequalis agaEur
  36. C.P. constituens angulum VC p, qui (IE
  37. ad ansulum VC P in data ratione;
  38. vis qua corpus srrari potest in Curra
  39. illa VPk quam punctum p DerpCEHIO
  40. tansir, erit reciproce ur cubus altitu-
  41. dinis C p. Nam corpus P, per rim inertix, nulla alia vi urgente,
  42. unitormiter progredi porest in recta VP. Addacur vis in cenrrum
  43. cubo alcicudinis C F vel Cp reciproce proporrionalis, _ (PeF
  44. jam demonstraca) decorquebitur mocus ille rectilineus in lincam
  45. PRLMDS.
  46. CVEVAM

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 125. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0159?run=74