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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 52

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: 0.85.

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

The machine reads it as

  1. 21
  2. PFTLOSOPEILLE NATDRALIS
  3. DEMOTD CorOl. 3. EF concursus tangentis cujuris P MI cum recta SN.
  4. Conronvu quae ab umbilico in iplam perpendicularis est, incidit in rectam AN,
  5. quae Parabolam tansi in vertice principali.
  6. PROPOSITTO. ZIII. PROBLEMA VTII.
  7. Moveatur corpus in perimetro Parabola: requiritur L ex vis centri-
  8. petae tendentis ad umbilicum hujus ficurae.
  9. incac constructio Lemmatis, ltque F corpus in perimerro P
  10. rabolae, ex a loco in quem cOrpuS Proxime OveTUT, asC ipAISF
  11. parallelam R ec perpendicularem I, necnon QV tangenti pa-
  12. rallelam ex occurrentem tum diametro YF G in v, cum dictancia
  13. SF in x. Jam ob similia triangula P ∞ V, SP M et aequalia unius
  14. latera SM, SP, aequalia sune alterius latera P a (eu R ec F V.
  15. Sed, ex Conicis, quadratum ordinata dV aequale cAt rectangulo sub
  16. lacere recto ex seomento diametri PV, id cAt (per L em. Z III.) rectangu.
  17. 10 4 F SX P V, Cen 4 F SZ OR; Et punctis P ec O) cocuntibUS, ra-
  18. eio V 2d 8 x per (Per Corol. 2 L Cm. VII.) Sic ratio aequalitatis. Rr-
  19. ∞0Daquad. eo
  20. in catu, aequale
  21. eA rectangu.
  22. 104 FSXOR.
  23. F. A autem (0b
  24. similia crian-
  25. outa x 7,
  26. SPN) Q∞g.
  27. ad dY g. uE
  28. P59. ad5N
  29. hoc eA (per Z M
  30. Corol. I. LCM. XEV.) UE PS ad S A, id cAt ut 4 F S X R
  31. ad 4.S AX QR, de indc (DEF PFOD. LX. Lib. V. F. lem.) GF9. d
  32. ex
  33. 45 AX QR aequantur. Ducantur haec aequalia in
  34. QR de Aet
  35. S Pg. X Q=4. aequale S P g. X 4. S A: _ Propterea (per C OrOl. L ex 5
  36. R
  37. PrOD. VI.) ris centripeta es reciprOCO UF S F g. X4 S A, id cst, ob da-
  38. tam 4.S A, reciproce in duplicata ratione distantiae 5F. 8. F. l.
  39. Coret.

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 52. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0086?run=74