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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 117

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. PRINOIPLA MATHEMATICA.
  2. PROPOSITIO ZLI. PROBLEMA XZVTII.
  3. Posita cujuscunque generis Vi centripeta s concessis Firurarum
  4. curvilinearum quadraturis, requiruntur tum Trajectoriae in qui-
  5. bus corpora movebuntur, tum Tempora motuum in Trajectoriis
  6. inventis.
  7. Tendat vis quaelibee ad centrum C et invenienda sit Trajectoria
  8. VTTRK. Detur CirculuS V XY centro C interrallo quovis CY
  9. delcriptus, centroque eodem describantur alii quiris circuli YD
  10. RF. Trajectoriam secantes in l ec R rectamque CV in D eE F.
  11. Rectum rectam C NTX sccantem circulOS IL F, VY in N Sc X,
  12. tum rectam CKY occurrentem circulo V XY in Y. Sint autem
  13. puncta Ie RE sibi invicem vicinissima, ec pergat corpus ab V per
  14. B3T_ K ad k; Scque punctum A locus ille de quo corpus aliud
  15. cadere debet ut in loco D relocitatem acquirat aequalem reloci-
  16. tati corporis prioris in P; ee Cantibus quae in PropOsitionC XXXIX,
  17. lincola TK, daco tempore quam minimo descripta, crit ut ve-
  18. locitas acque adeo ut lacus quadrarum arcae AB F D, ee triangu-
  19. lum TC R tempori proportionale dabitur, adeoque R N erit reci-
  20. Proce uc alcicudo TC, id est, si detur quantitas aliqua O de alci-
  21. cudo TC nOminetur A, uc =. Flanc quantitarem = nominemus Z
  22. ec ponamus cam esse magnicudinem ipsius ut sit in aliquo
  23. catu V ABF D ad Z AE CR P K ad X N, Se crit in omni caTu
  24. VABFD adZ UETK ad K NV, _E ABF D 1dZZ UE TK 9. 2dK Ng.
  25. ec dirisim ABF D - ZZ adZZ uE IN quad ad K N quad, 2d-
  26. eoque r ABFD = Z Z ad (Z (CU) = UE PN ad R N, _E PrODECrCA
  27. AXK N aequale
  28. CTW
  29. ABFD - Z7. Onde cUm YX X XC SIL ad
  30. A Z R N NE C X g 2d A A, erit rectangulum Y PX NC aequale
  31. DXINXC X quad.
  32. A A Y ABFD - L.T
  33. Temper Db, DC ip(IS
  34. Isitur si in perpendiculo D S CapIaNEUE
  35. X C X quad.
  36. 2VABFD - ZZ EAA YABL D -2. 2
  37. equales respectire, et describantur currae linex ab, cd quas
  38. DuACta
  39. L IBEK
  40. PRIMDS

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 117. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0151?run=74