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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 187

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: 0.83.

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The machine reads it as

  1. PRINOTPTA MATHEMATICA.
  2. Exempl. T. Si vis centripeca ad singulas Sphaerae particulaS Cen- PRIAVS
  3. dens sic reciproce ur dictantia; pro V Ccribe dictanciam P F; dein
  4. 2FSXL D PrO PFg, _ ACE D N uE SF - EY 7
  5. Ponc D N equalem duplo ejus 25F -F D - AF B
  6. ED
  7. LB
  8. : ordinate
  9. pars data 2 SF. ducta in longitudinem B describet aream rectan-
  10. Sulam 2SL. X AB; ec pars indetinita L. D ducta normaliter in
  11. eandem lonsitudinem per motum continuum, ca lese ut inter mo-
  12. vendum crescendo vel decrescendo aequetur semper lonsitudini
  13. E. D, deleribet arcam L. B9 - L a9
  14. t
  15. L IdCC, aream SL X AB; Oux
  16. subducta de area priore 2SL. X AB relinquit arcam SI. X AB.
  17. Pars aurem certia L
  18. licer in eandem longitudinem, describet
  19. arcam Hyperbolicam; quae subducta de
  20. area SL. X AB relinquet aream quaesitam
  21. ABNA. Onde talis emergie Proble-
  22. matis constructio. Ad puncta L A, B
  23. erise pervendicula L I, Aa, Bb, quorum
  24. Aa ipS L. B, _ Bb ipA L. aequetuT.
  25. ACMPEOtIS L. B,L. B, per puncta a b de-
  26. scribatur IIpperbola ab. Et acta chor.
  27. da ba claudet aream ab a arex quaelIEX
  28. ABN A aequalem.
  29. i.
  30. ENempl. 2. Si ris centripeta ad lingulas Sphoerae particulas ten-
  31. dens sic reciproce ut cubus distantia, vel (quod perinde cst) ut cubus
  32. ille applicatus ad planum quodvis datum; seribe L. cub
  33. 2 ASq PrOV.
  34. dein 2F SX L D DrO P F g; _E ACE D N uSL X ASq AS 9
  35. AL BX ASg
  36. 2PSXL. D
  37. S
  38. SXF
  39. 2et
  40. id eAt (ob continue proportionales PS, S, SF)
  41. D = = SI -AL BXSI
  42. 2L. Dg. Si ducaneur hujus partes ereS
  43. in lonsitudinem AB, prima
  44. 3b
  45. 5I
  46. D Generabie arcam IIyPCr-
  47. 2
  48. bolicam;
  49. LTBEL
  50. e+

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 187. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0221?run=74