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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 145

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: 0.93.

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

The machine reads it as

  1. PRINCIPLA MATHEMATICA
  2. partium illarum aliqua. Cenero C, interrallis C D, C a actCHBAH- L. THF. H
  3. cur circuli DF, dt, linex curvae SF+ R occurrentes in Y d t. FF enimon
  4. ex data tum lege vis centripeta, tum
  5. alticudine CS de qua corpus cecidit;
  6. dabitur velocicas corporis in alia qua-
  7. vis alcitudine CT, Per PEOD. XXXIX.
  8. lempus aurem, quo corpus describit
  9. lincolam TF, est ut lineolx hujus lon-
  10. sicudo (id cM ut secans anguli +TC
  11. directe, et velociras inverse. Tempori
  12. huic proportionalis sic ordinatim appli-
  13. Cata D N ad rectam C S per punctum
  14. D perpendicularis, ec ob datam D d
  15. erit rectangulum D d XD N, hoc CA
  16. area D Nn d, cidem tempori proxor-
  17. tionalc. RrgO A SNn sE curra illa li-
  18. nea quam punctum N Perpetuo cangit,
  19. erit arca S ND Sproportionalis tem
  20. Pori quo corpus descendendo descrip-
  21. Sc lineam SF; proindeque ex inventa illa area dabitur Tempus.
  22. 2. F. I.
  23. DROPOSITIO LV. THEOREMA ZIX.
  24. Si corpus movetur in superficie quacunque curva, cujus axis per
  25. centrum Virium transit, e a corpore in axem demittatur per-
  26. pendicularis, eique parallela e aequalis ab axis puncto quovis
  27. dato ducatur: dico quod parallela illa aream tempori proportio-
  28. nalem describet.
  29. Sic BSHL L Suxerkcies curra, F CorpuS in ea revolvens, STY R
  30. Prajectoria quam corpus in eadem describit, Sinitium Trajecto-
  31. rix, OM NK axis supericiei curra, T N recta a corpore in axem
  32. perpendicularis, O P huic Parallela ec aequalis a puncto O quod in
  33. axe datur educta, AP restisium Trajcetorix a puncto P in lincae
  34. volubilis O P plano 1O P descriptum, A veltisii inicium puncto s
  35. respondens, TC recta a corpore ad centrum ducta; TG pars ejus
  36. vi centripeta qua cOrpuS urgetur in centrum C proxortionalis:
  37. M recta ad superticiem curvam perpendicularis, P L Pars ejus vi
  38. Crectionis, qua corpusurs ec super liciem ricissimque ursecur versus I

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 145. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0179?run=74