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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 109

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: 0.89.

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The machine reads it as

  1. PRINOIPIA MATHIEMATICA.
  2. Cas. 2. Jam E Figura D F. SC irculus eAt rel Hxperbola, bisece.
  3. cur ejus transversa diameter AS in O, dc CriE
  4. S0 dimidium laceris recti. EE quoniam cA
  5. TC 2d TD ut C c 2d D d _ TD ad FS uE
  6. CD ad ST; CFIE CX aequo F C ad Y S ut
  7. CDXCC ad SPZ D d. Scdper Corol. T. ProP.
  8. XXXIXI CA TC ad FS ut AC 2d AO, DUTa SI
  9. in coitu punctorum D, a capianeur lincarum
  10. rationesultimae. Freo AC cA 2d (AO PCu) SR
  11. UE CD X CC ad S Y X D d. POTTO COrPOTIS
  12. descendentis velocitas in C est ad velocitarem
  13. corporis Circulum intervallo SC circa cen-
  14. trum S describentis in subduplicata rationc
  15. AC ad (AO vel) SR (pEF PFOD. ZXXILI.) RF
  16. haec relocitas ad velocitatem corporis descri.
  17. bentis Circulum OFk in subduplicata ratione
  18. SK ad SC Per COr. 6. Prop. 1V, ec Cx aequo velo.
  19. citas prima ad ulcimam, hoc est lincola Cc 2d
  20. arcum Xk in subduplicata rarione AC ad SC
  21. id est in ratione AC adC D. Onare CAC D XCC
  22. aequale AC X KK, dE PrOpterca AC ad SR uE
  23. ACZ RR2dSYY D d, indeq; SR XRh aequa-
  24. IC SYZD du _ ZSRX KK aequalC = SYX D d
  25. id est area KSk aqualis arexe SD d. Singulis
  26. isitur temporis particulis generantur arearum
  27. duarum particulae RSs, ec SD d, quae, si mag-
  28. nitudo carum minuatur ex numerus auseatur in infinitum, racio-
  29. nem obcinene aequalitatis, et proprerea (per Corollarium Lem.
  30. atis IV) areae coca simul genicae sunt semper aequales. . F.. D.
  31. Cas. 2. Ouod si Figura D F S ParabOla (E, invenietur eNC UE s
  32. PTa C D XCC 2dSYX D a uE FC ad ZS, hoc est ut 2 ad r, 2d-
  33. eoque = CD X Cc aequale ese : SPX Dd. Sed corporis caden-
  34. eis velocitas in C aequalis est velocitati qua C irculus interrallo ZSC
  35. umtormiter deseribi posit (per Prop. XXXLV) LFhaec velocitas ad ve-
  36. locitatem qua Circulus radio SR describi poMic, hoc elt, lincola
  37. Cc adarcum RLR (per C orOI. 6. PFOD. LV) eAt in subduplicata ratione
  38. SRad 2SC, id est, in ratione SR ad = C. D. Duare clt ZSR X KK
  39. aequale +C D XC∞, adcoque aequale 2SPX D dhoc est, arca R Se
  40. aequalis areae S D d, UE TUPrA. d. Li. D.
  41. 109
  42. eROL e
  43. L TBEK
  44. EuInDE

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 109. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0143?run=74