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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 435

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: 0.88.

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The machine reads it as

  1. PRINCTPTA MATHIEMATICA.
  2. 435
  3. NMXmC: de harum disterentia L. NX Mm-- NNIX MC L mC,
  4. est vis particularum ambarum simul sumpearum ad Perram
  5. rotandam. Pujus differentix pars affirmatira L NVX Mm seu
  6. 2L. NVX NX, est ad parcicularum duarum ejusdem magnitudi-
  7. nis in s consistentium vim 2 AAIX EC, UE LX9 ad ACg.
  8. FE pAES nEGAEIVA NMX MC F mC ICU 2XYXCY, ad parti
  9. cularum carundem in A consittencium vim 2 AHIXHIC, ut
  10. Cxg ad ACg. Ac proinde partium disterentia, id cA, par-
  11. ticularum duarum L ec Eimul Cumpearum vis ad Terram FOtan-
  12. dam, est ad vim parcicularum duarum iisdem aequalium ec in loco
  13. A consistentium, ad Terram icidem rorandam, ut L Zg =C X9
  14. ad ACg. Sed E circuli PK circumterentia PR dividatur in DaF-
  15. ticulas innumeras aequales L crune omnes L. Xg ad coridem lX 9
  16. UE F 2d 2, (per Lem. I.) acque ad toridem AC 9, ut IX9 ad
  17. 2 ACg; e tocidem C Xg ad cotidem ACg uE 2C X9 2d 2 AC 9.
  18. Ouare vires conjunctae particularum omnium in circuitu circuli
  19. TK, sune ad vires conjunctas particularum coridem in loco A, ut
  20. TX9 = 2CX9 2d 2 ACg: _E pFOPEErCa (per L CMI. I.) ad vires
  21. conjunctas parcicularum toridem in circuitu circuli AF, uE
  22. TX9 = 2C X9 2d AC9.
  23. Jam vero si Sphaera diameter Pp dividatur in partes innume-
  24. ras aequales, quibus insistane circuli cocidem PK; materia in peri-
  25. metro circuli cujusque PK erir ut lPg: ideoque ris materix
  26. illius ad Terram rocandam, crit ut IXg in IXg = 2C Xg. EF
  27. vis materix ejusdem, si in circuli AF. perimetro consisteret, esset
  28. uc IN9 in ACg. EC Propterca vis particularum omnium ma-
  29. cerix totius, exera globum in perimetris circulorum omnium con-
  30. Sictentis, eA ad vim particularum toridem in perimeero circuli
  31. maximi AF. consistentis, uc omnia IXg in IXg = 2C X9 2d
  32. cocidem IXg in ACg, hoc eA, ut omma AC9-C Xg in
  33. AC9 = 3C Xg 2d cocidem AC g -C X9 in ACg, id cA, ut
  34. omnia ACgg = 4 ACgZCXg + 3C X99 ad cocidem AC. g9
  35. ACgX C X9, hoc eAt, uE tota quancitas Auens cujus Auxio
  36. est ACgg - 4 ACGXC X9 + 3C X9q ad totam quantitatem AU-
  37. entem cujus Auxio eA AC gg AC gX C Xg; ac proinde per NC-
  38. thodum Fluxionum, ut ACggZCX- Z ACgZC X cub + = C XgC
  39. ad AC99ZCX = = AC 9X C Lcub, id eAt, A PEO C Z CCrIbAEUE
  40. tota Cp vel AC, uE 5 C96 2d 3 C96, hoc cAt, ut duo 2d
  41. quinque. Q. E. D.
  42. IKK L
  43. L1oL
  44. FCRFIVS.
  45. l LLaL L_

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 435. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0469?run=74