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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 197

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: 0.87.

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

The machine reads it as

  1. PRINCIPTA MATHEMATICA.
  2. 197
  3. cerrallo AD describitur, trahiunt corpus P versus A, eA uE arCa LIVen
  4. TOta ATTTKL ducta in AF. Q. F. D
  5. Corol. 1. Elinc si vires punctorum decrescunt in duplicata di
  6. ctanciarum ratione, hoC CA, SI SIE F R ut P fi quad. 2EquC ad eo a-
  7. rea ATIZK L. UE p A Y F; erit accractio corpusculi P in Circu
  8. Ium UE F -
  9. P F id eAt, uc P
  10. Te
  11. I
  12. Corol. 2. Fx universalicer, E vires punctorum ad distantias D sInC.
  13. reciproce ur distantiarum dienitas quaelibet Dn, hoc eAt, si SIC FR
  14. UE
  15. dn adCOquC area AFY YK L. UE ∞ An-1 D Hn - = exIE AEETA
  16. A
  17. ctio corpusculi P in Circulum uE.p An - 2 P Fn - 1
  18. Corol 3. F. F s diameter Circuli auseatur in intinitum, de nume
  19. rus B Sic unitare major; aetractio corpusculi F in planum torum
  20. intinicum crie reciproce uE P An -2, proprerea quod terminus al.
  21. per VHn- eranelcet.
  22. PROPOSITIO XCI PROBLEMA XLV.
  23. Invenire attractionem corpusculi siti in axe Solidi rotundi, ad cujus
  24. puncta sincula tendunt vires aequales centripetae in quacunque
  25. distantiarum ratione decrescentes.
  26. In Solidum A D F F G Era-
  27. hatur corpusculum F, Sicum in
  28. ejus aXC AB. Circulo quoli-
  29. DEE R F S ad hune aZem per-
  30. Pendiculari secetur hoc Solidum
  31. ec in ejus diametro AS, in pla-
  32. no aliquo P AL, K B per axem
  33. cranscunte, capiatur (pEr PrOP.
  34. XC) lonsicudo FR vi qua cOr-
  35. pusculum F in circulum illum
  36. accrahitur proxortionalis. Fangat autem punctum K curvam line-
  37. am P RI Planis extimorum circulorum AI. B P OcCurrentem i
  38. ec T; e erit actractio corpusculi P in Solidum ut area L. AB l.
  39. C. L.
  40. P. RI MVS.
  41. Corob.

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 197. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0231?run=74