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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 129

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: 0.86.

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The machine reads it as

  1. PRINOTPTA MATHEMATTOA.
  2. 129
  3. ec collatis numeratorum cerminis, ACE R C C = RFF + T F F LIBEK
  4. 2d b F + CT, UE = FF ad = m B F m = .
  5. + Mm- M, n - 2, nB - n
  6. LXY
  7. n
  8. NC Xn = , PRIXVS
  9. _C. EF sumendo rationes ulti-
  10. mas quae prodeune ubi Orbes ad Formam circularem accedune, tc
  11. CC 2d B F m.
  12. F cFn.
  13. vicistim C C+ ad F F UF B F m. 2 L C 7 n. 1
  14. ad mb F m. 1 = nc F n. 2
  15. Oux proxortio, exxonendo altitudinem maximam CV seu Y Arich-
  16. meticeper Onitatem, scC C 2d F F ut b = c ad m b = nc, adeoque VF
  17. T 20mb + nC
  18. hs Onde cA C ad F, id est angulus VCP ad angulum
  19. VCF, UE F 2d mb +nc
  20. hLc. EF propterea cum angulus VCP inter
  21. Apsidem summam et Apsidem imam in F llipsi immobili sIC X8O er
  22. erie angulus VCD inter caIdem APSides, in Orbe quem corpuS vi
  23. Centripeta quantitati Am F C A2
  24. Acub. proportionali describit, aequa-
  25. lis angulo graduum 160 V +
  26. ErIDCTA SIEUL A = CA
  27. 180V
  28. mb = nC
  29. Et eodem argumento si viscen-
  30. A cub. angulus inter APSides invenietur gractUUM
  31. mb =ne NeC SecuS resolvetur Problema in casibus diffi-
  32. cilioribus. Ouantitas cui vis centripeta proportionalis est, re-
  33. Solvi semper debet in Scries convergentes denominatorem ha-
  34. bentes A cub. Dein pars data numeratoris qui ex illa opcratione
  35. provenic ad ipsius partem alteram non dacam, ec pars data nu-
  36. meratoris Bujus R C+ C -R E F F T E E = E F Z ad ipSIUS PaFFCM
  37. alteram non datam in eadem ratione ponendae TUnE: EE GuantitaLes
  38. cupertuas delendo, cribendoque Vnitatem Pro T, obrinebitur
  39. provortio (r ad F.
  40. Corol. L. Tlinc s vis centripeta sit ue aliqua alcicudinis digni-
  41. tas, inveniri potest dignitas illa ex motu Aplidum; ee COntra.
  42. Nimirum s mocus totus angularis, quo corpus redit ad Apsidem
  43. eandem, sic ad motum angularem revolutionis unius, Peu graduum
  44. 360, ut numcrus aliquis n ad numerum alium n, e alcirudo no-
  45. minetur A: erie vis uc alcicudinis dignitas illa Amm 3, cujus In.
  46. dex

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 129. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0163?run=74