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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 137

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.

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The machine reads it as

  1. PRTNCIPLA MATHEMATICA.
  2. is
  3. id est, rario mutationum momentanearum curvae AP, rectxe LIbe
  4. CF, arcus circularis BF, ac rectae VP, eadem erit quae linca-
  5. rum PV, PF. FC, PY respectire. Cum autem V. F ad C F et
  6. II ad CV perpendiculares sunc, angulique AIVO, VCF prop.
  7. terea aequales; ex angulus VHIO (ob angulos quadrilateri YIV F F
  8. ad V ec P rectos) angulo CF. P aequalis eAt, limilia CruINE FrI
  9. angula VIIO, CF. P; _ inde ACE UE F. P ad C F. ica NIC ad YIB
  10. seu TYP ec ita R Y ad R P, de composire vel divisim ut CB ad
  11. CF Ita P Y ad P K, e duplicatis consequentibus uc C B ad 2 C F
  12. ita P I ad P V, atque ita adco P g adt P m. F. s isitur decremen-
  13. cum lincae V P, id CA, incrementum lincae BV = V P ad incremen-
  14. tum lincae currae AF in data ratione C B ad 2 CF, _E PTOP.
  15. cerea (per Corol. Lem. IV.) lonsitudines BV - V P de AF, in-
  16. crementis illis genitae, sunt in eadem ratione. Scd, existence BV r2-
  17. dio, eAtV P co sinus anguli BV P Pcu = BF. P, adcoque BV -V Y
  18. sinus versus ejusdem anguli; e propterea in hac Rota, cujus radius
  19. CA = BV, Crit BV =V P duplus linus versus arcus = B F. PrgO
  20. AF cA ad duplum sinum versum arcus = BP Ut 2C F. ad CB.
  21. 2. F. D.
  22. Lineam autem AP in Proxostione priore Ccloidem extra
  23. Globum, alteram in posteriore Cycloidem intra Clobum distincti.
  24. onis gracia nominabius.
  25. Corol. 2. Flinc A describatur Crclois inceora ASP _E BISCCCTUE
  26. ea in S, erit longieudo partis P S’ad lonsicudinem V P (quae du-
  27. plus est sinus anguli VB P, existente P B radiO) uE 2C F ad C B,
  28. acque adeo in ratione data.
  29. Corol. 2. Uc longitudo semiperimeeri Crcloidis AS equabitur
  30. lineae rectae quae eA ad ROI_ diametrum BV, UT 2 C F. 2d CB.
  31. eROPOSITIOL. PROBLEMA ZZXIII.
  32. Facere ut Corpus pendulum oscilletur in Cycloide data.
  33. Intra Globum QVS, cenerO C descriprum, detur Cyclois QRS
  34. bilecta in R ex punctis luis extremis e S superticiei Clobi hinc
  35. indC OCCUErENS. RGatuF C R bisecanS arcum QS in O, ec produca
  36. cux ea 2d A, uC sIC C A 2d C O uc C0 ad C R. Centro C in
  37. terrallo
  38. P et hev

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 137. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0171?run=74