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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 177

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: 0.93.

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The machine reads it as

  1. DRINCIPTA MATHEMATICA.
  2. nihili sic; nimirum Orbes eranescentes ex quibus Sphaera uleimo LrVKn
  3. constat, ubi Orbium illorum numerus augetur ee crassitudo minui- Pxiuve
  4. cur in intinitum. Similiter per Puncta, ex quibus lineae, superticies
  5. ec Colida componi dicuneur, intelligendae sune particula sequales
  6. magnitudinis contemnendae.
  7. EROPOSITIO LXXIV. THEOREMA XXXIV.
  8. Tisdem positis, dico quod corpusculum extra Sphaeram constitutum
  9. attrabitur vi reciproce proportionali quadrato distantia suae ab
  10. Epsius centro.
  11. Nam distinguatur Sphaera in superficies Sphaericas innumeras
  12. concentricas, et actractiones corpusculi a lingulis superticiebus
  13. oriunda crunt reciproce proportionales quadrato dictantix cor-
  14. Dusculi a CeNErO, PeF PFOD. LXXI. Et componendo, hicc Cum-
  15. maattractionum, hoc est accractio corpusculi in Sphaeram totam, in
  16. eadem rarionc. 9. F. D
  17. Corol. 2. Tlinc in xequalibus distantiis a centris homogenearum
  18. Sphaerarum, aetractiones Pune ut SphXER. NTaM PET PFOD. LXXIL,
  19. si distantiae lune proxortionales diametris Sphaerarum, vires crune
  20. uc diametri. Mlinuatur distantia major in illa ratione; ec, dittan-
  21. tiis jam Factis aequalibus, ausebitur accractio in duplicaca illa ratio-
  22. ne, adeoque erit ad actractionem alteram in criplicata illa rationen
  23. hoc est, in ratione Sphaerarum.
  24. Corol. 2. In dictanciis quibusvis aEcraCtiOneS TUNE UE SphXrX LD-
  25. plicacae ad quadraca distantiarum.
  26. Corol. 3. Si corpusculum, extra Sphaeram homogencam policum,
  27. trahicur vi reciproce proportionali quadraco distantix luae ab iplius
  28. centro, conster autem Sphaera ex particulis aetractiris; decrelcet vio
  29. partieulae cujusque in duplicara ratione distantix a particula.
  30. PROPOSITIO LXXV. THEOREMA XXXV.
  31. Si ad Sphaerae datae puncta sinsula tendant vires aequales centripe-
  32. cae decrescentes in duplicata ratione distantiarum a punctis; dico
  33. quod Sphaera quaevis alia similaris ab eadem attrabitur vi reci-
  34. proce proportionali quadrato distantiae centrorum.
  35. Nam particulae cujulris aetractio est reciproce ut quadratum di-
  36. Cancixe suxe a cenero Sphaerae trahentis, (DEF PFOP. LXXIV) dc prOP
  37. TCrCa

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 177. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0211?run=74