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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 175

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. PRTHCIDTA MATHEMATIOA.
  2. arcus TFI convolutione semicirculi R B circa diametrum AB LIDEY
  3. delcribet, ad superticiem circularem, quam arcus ih conrolutione etuos.
  4. semicirculi ak b circa diametrum ab deseribet. It vires, quibus
  5. hae superficies secundum lineas ad se tendentes attrahune corpuseu.
  6. la P ec p, sunE (per IIy Pochetin) ut iplae superticies applicata
  7. ad quadraca distanciarum fuarum a corporibus, hoc est, uc p FXPS
  8. ad P F X P5. Suneque hae rires ad iplarum partes obliquas
  9. quae (Facta per Leoum Corol. 2. resolutione virium) secundum
  10. lincas FS, p5 ad centra tendunt, ut F L ad F Q e pi 2d pg; id
  11. CA (ob similia criangula D F~ ec P S F, piq e p5F) uE FS ad
  12. PL ec p5 ad pf. Ondes ex aequo, tic accractio corpusculi hujus F
  13. vertus s ad ducractionem corputeuli e vertus s, u P F Xp sXpS 2d
  14. DFXD EXDS
  15. B5 = hoc ost, uc p 5 quad. 2d PS quad. FF simili argu-
  16. mento vires, quibus suxerficies convolurione arcuum RL, Rl de-
  17. Teriptae trahune corpuseula, crunt ue ps quad. ad PS quad; inque
  18. eadem ratione erunt rires superficierum omnium circularium in quas
  19. utraque superticies Sphaerica, capiendo semper sd aequalem S D et
  20. se aequalem SF, distingui porest. Er, per compotitionem, rires
  21. cotarum Cuperticierum Spharicarum in corpulcula exCTCITA CrUINE
  22. in eadem ratione. 8. L. D.
  23. PROPOSITIO LXXII. THEOREMA ZKXII
  24. Si ad Sphaerae cujusvis puncta singula tendant vires aequales cen-
  25. tripetae decrescentes in duplicata ratione distantiarum a punctis,
  26. ac detur tum Sphaerae densitas, tum ratio diametri Sphaerae ad
  27. distantiam corpusculi a centro ejus; dico quod vis qua corpus-
  28. culum attrahitur proportionalis erit semidiametro Sphaerae.
  29. tam concipe corpuscula duo scorsim a Sphaeris duabus acrrahi,
  30. unum ab una ec alterum ab altera, ec dictantias eorum a Sphaera-
  31. rum ceneris proxortionales esse diametris Sphaerarum respective,
  32. Sphaeras autem resolvi in particulas similes de similiter positas ad
  33. corpuscula. RE accractiones corpusculi unius, Factae versus singulas
  34. particulas Sphaerae unius, crunt ad actractiones alterius versus ana-
  35. logas tocidem parriculas Sphaerae alterius, in ratione composita ex
  36. cacione particularum directe ee ratione duplicata distanciarum in-
  37. verlCo.

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 175. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0209?run=74