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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 190

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. 190
  2. PHTLOSOPMILL NATDRALIS
  3. Dy. MOrO Cem uE SP quad ad S A quad: Si in quadruplicata, ut SF cub ad
  4. Corronvi A cub. Onde cum accractio in P, in hoc ultimo casu, inventa
  5. fuiE reciprOCC UE F Scub X P F actractio in I crit reciproce ut
  6. S Acub Z P I, id eA (ob datum S A cub) reciproce ut PY. EF
  7. similis est progressus in infinitum. Theorema vero sic demon-
  8. AratUr.
  9. Scancibus jam ante constructis, e existente corpore in loco
  10. quoris P, Ordinatim appliCaTA D N inVeNEA FUIE UE F. 9X FS
  11. PFX
  12. FrGO A agatuF PF, ordinata illa ad alium quemris locum B, mu-
  13. ratis mutandis, evadet ut FgX Id
  14. FXV. PONC VirES CentrIDCTAS, C
  15. Sphaerae puncto quoris P manances, ese ad invicem in distantiis
  16. TF P L UE PP ad YF, (ubi numerus n designet indicem
  17. DF 9XES
  18. porestatum PF ec PF.) ec ordinatae illae AEnE UE P F Z P F n de
  19. DFgX7S
  20. TF X TFn quarum ratio ad inricem es UE PSXTF XIF ad
  21. TSXPF. XP Fn. Ouoniam ob similia triangula SF F, SF. I, AE
  22. TF ad F F. uE IS ad SF vel S A; PrO rationC PF ad P F. IcribC
  23. rationem IS ad S A; ex ordinatarum ratio eradet PSXIFn 2d
  24. SAXF Fn. Sed FS ad SA subduplicata est ratio distantiarum
  25. DS, SF; ec TFn ad F Fn Subduplicata est ratio virium in distan-
  26. tiis FS, YS. Eroo ordinatae, et propterca arcae quas ordinata
  27. describune, hisque proportionales actractiones, lune in rarione com-
  28. Posica ex subduplicatis illis rationibus. Q. F. D.
  29. PROPOSITIOLXZXIII. PROBLEMA XLII.
  30. Invenire vim qua corpusculum in centro Sphaerae locatum ad ejus
  31. Sermentum quodcunque attrahitur.
  32. Sit P COrpUS in CCNErO SpHrX, _E RBSD Sermentum ejus
  33. plano R DS e CaperEcie SpHXrICa RBS CONTENTUM. SUPCrE-
  34. eie Sphaerica P F G centro P descripta seCCtUE D B in F, ac di-
  35. stinguatur Seomentum in partes BR F F CS, F F D G. Sit
  36. aurem superticies illa non pure Machematica, Sed Phrsica, PrO-
  37. funditarem habens quam minimam. Nominetur icta protundi-
  38. TaSO

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 190. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0224?run=74