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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 237

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: 0.84.

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

The machine reads it as

  1. PRIMCIPTA MATHEMATICA.
  2. 2 3 09
  3. recta illa b, FC a. F d C, CFY e e CD o; rectangulum a F O LIBEI
  4. I c = a = 0 TCu aC = aa = 2a0 +c0 = 00 aequale CA rectanSWIO SECVRDOS.
  5. b in DF, adeoque DF aequale aC = a a, c = 2a
  6. bendus eset hujus seriei secundus terminus
  7. es
  8. Ob
  9. Jam Ccri-
  10. O PEO OO3 ter-
  11. eius icem terminus = PrO R0O. Cum vero plureS nOn HnE teF-
  12. minis debebic quarti coefticiens S cranelcere, et propterca quan-
  13. titas
  14. RVF +90
  15. cui Medii densitas proxortionalis est, nihil
  16. erit. Nulla igicur Medii densicate morebitur Projectile in Para-
  17. bola, uti olim demonstrarit Calileus. 9. F. I.
  18. Faempl. 3. Sic linea ACK FIyperbola, AErmpeocon habens
  19. NX plano horizontali AR perpendicularem; et guaratur Medii
  20. densitas quae Faciat ue Projectile moreatur in hac linca.
  21. Sic M X ACymptotos altoras ordinatim applicatae DG productx
  22. occurrens in V, ex ex natura IIyperbolae, rectangulum XV in VC
  23. dabitur. Datur aurem ratio D N ad V X, et propterea datur criam
  24. rectangulum D N in VC. Sit illud bb; e completo parallelogrammo
  25. D NXZ, dicatur BN an BD on NX c, de ratio data V L ad Z X
  26. vel D N ponatur eNe =. Et erit D NV aequalis a = o, V C aequalis
  27. = Y Z aequalis = a = 0, e GD Peu NX -VZ, -VC x-
  28. qualis c - a + m 0 - bb
  29. Resolvatur terminus- in seriem
  30. convergentem = + 0 + 00 + - 0 ec. de Hiet CD aequa-
  31. M
  32. lisc-
  33. bb
  34. a
  35. a
  36. aa
  37. m
  38. bb
  39. 2
  40. bb
  41. n aa a
  42. bb
  43. nus secundus mo -
  44. aa
  45. 0 -
  46. 40 c. Flujus seriei cermi-
  47. usurpandus est pro 90, tertius cum signo
  48. MuEatO == O PrORO, ee quartus cum sixnO etiam MuEatO , 0
  49. ProSo, corumque coeficientes - bb bb, bb
  50. e
  51. n aa a
  52. at
  53. Scribendxe TunE
  54. in Regula superiore, pro, R et S. Duo Facto prodit medii densitas
  55. uC

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 237. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0271?run=74