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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 73

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: 0.90.

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

The machine reads it as

  1. 1
  2. Nam in recta MN decur punctum Les ec ubi punctum mobile exiuvo
  3. M incidic in immotum N, incidac punctum mobile D in immo-
  4. cum P. JunscCNP, BNI,
  5. P, BF, ex a puncto
  6. P asC rectas FZ, PR
  7. Occurrentes ipss B D.
  8. CD in F _ R, e Fa-
  9. cientes angulum B F Y
  10. aequalem angulo dato
  11. B N M. ec angulum
  12. CP R aequalem angu-
  13. gulo datoCNM. Cur
  14. ergo (ex HIrpothesi
  15. aequales sine anguli
  16. MBD, NBF, ut dc
  17. anguli MCD, NC P
  18. auter communes NB D
  19. _ NC D, ee rectabune
  20. aequales NBMI _ PBT,
  21. NCMAF CR: adeoque criangula NB M, P BZ Similia UnE, UE
  22. ec triangula NOM, FCR. OUare PT eA ad NM uE P B ad
  23. NVB, _ F R ad NNNE FC ad NC. Sune autem puncta B, C, NV, Y
  24. immobilia. Rroo F T et F R datam habent racionem ad NMI, PFO-
  25. indeque datam rationem inter (C; atque adeo, peF L CMMa XX)
  26. punctum D (perpetuus rectarum mobilium BY et C R concurtus)
  27. contingit sectionem Conicam, per puncta B, C, P transcuntem.
  28. Q. F. D.
  29. Ec contra, si punctum mobile D contingat sectionem Conicam
  30. transcuntem per data puncta B, C, A, e Sc angulus D B M TemPCF
  31. aequalis angulo dato ABC, ex angulus DCM Temper aequalis ansu-
  32. lodato ACB, et ubi punctum D incidit successire in duo quaeris se-
  33. ctionis puncta immobiliap, P, punctum mobile M incidat successive
  34. in puncta duo immobilia n, NV: per cadem n, N agatur R oct a n N,
  35. e haec erit Locus perpetuus puncti illius mobilis M. Nam, A feri
  36. Potest, versetur punctum M in linca aliqua Curra. Tanset ergo
  37. punctum D sectionem Conicam per puncta quinque B, C A, p, F.
  38. cranscuntem, ubi punctum M perpetuo tangir lineam Curvam. Scd
  39. ec ex jam demonstratis tanset etiam punctum D sectionem Coni-
  40. Cam per eadem quinque puncta B, C, A, P, P cranscuntem, ubi pun-
  41. ctum
  42. RINCTPTA MATETEMATICA.

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 73. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0107?run=74