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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 249

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.

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

The machine reads it as

  1. IIIHIII
  2. PRINCIPTA MATTTEMATICA.
  3. 243
  4. Nam relocitatis decrementum P Q, in data temporis particula LIven
  5. factum, est uc summa relictentix AP g F 2B A F e Gravitatis SECVNDUS.
  6. AB9 -B D9, id cAt, ut B F g - B D g. FA autem arCA D YV
  7. ad aream D F Q ut D Fg ad D Pg adeoque, si ad D F demitta-
  8. cur perpendiculum GT, ut GTg Teu GD g = D Fg ad B D9
  9. uEque GD g 2d B F q ec divisim uE D Fg ad B F g - BD9.
  10. Duare cum area D P G AE uE P 4 id eAt, uc B F g - B Dg; eric
  11. area D TV uc datum D Fg. DecreSCIE igIEUF arCA F, D F unifor-
  12. miter linsulis temporis parciculis aequalibus, per subductionem par-
  13. ticularum coridem datarum DTV, dt Propterea tempori propor.
  14. cionalis eAt. d. F. D.
  15. Cas. 3. Sit AF relocitas in descensu corporis, _t AF 9 + 2B AP
  16. resistentia, e BD g - ABg vis graritacis, existente anguio DB A
  17. recto. EF (I CentrO D, vertice
  18. principali B, describatur FTy.
  19. Derbola rectangula B F YY
  20. secans productas D A, D F et
  21. D Q in F; T e V; cxit HIy-
  22. Derbolae hujus (ectOE D F. T vE
  23. cempus deicentus.
  24. Nam velocitacis incremetum
  25. P 9 eique proportionalis arca
  26. DY
  27. eis supra relstentiam, id eAt, ut
  28. BDg -AB9 - 2B AF - AF
  29. (cu BD q =BF g. PC arca
  30. DTV eA ad aream D P Q uE
  31. DF9 ad D P9, adcoque uE
  32. 6T9 Icu GD 9 - B Dg 2d
  33. BF g ueque G Dg ad BDq
  34. ex dirisim ut B D q ad B D g - BF9.
  35. Ouare cum area D F0)
  36. sIE uE BD 9 - B F q. CrIE arC2 D TV uc darum BDg. Crescie
  37. IgieUE arC2 P DT unitormiter singulis temporis particulis equali-
  38. bus, per additionem tocidem datarum particularum D T V, ec prop.
  39. cerea cempori descensus proportionalis cAt. Q. F. D.
  40. Corol. Igitur velocitas AP est ad relocitarem quam corpus rem-
  41. DOrC P. DT, in spario non resistente, alcendendo amittere vel de-
  42. Ecendendo acquirere portets ut area crianguli D A F ad aream sC
  43. ctoris centro D, radio D A, angulo AD F descripei; ideoque ex
  44. dato cempore dacur. Nam relocitas, in Medio non resctentes tem-
  45. LK
  46. Pori
  47. LNEHHTNTISITHIHHHISTHNESBNIHIHHHNHEHHIIMIEBINIIMNII

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 249. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0283?run=74