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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 201

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: 0.87.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. III
  2. PRINOIPLA MATHEMATTCA.
  3. t
  4. vis qua planum quodris m II M cratiie punctum C eAt reciprOCC UE L. TVEM
  5. CFIn- 2. In PlanO m FYM capiatur longicudo FIM ipSI C FFn - 2 re PurmUS
  6. ciproce proportionalis, ee erie vis illa ut PI MI. Similiter in planis sin-
  7. sulistGLn LNI, OKO, ScC. capiantur lonsicudines EFL, TNI, K(O, ecc.
  8. IPsIS CCn- 29 C Tn2, C Rn-2, ecc. reciproce proportionales; ec vi-
  9. res planorum corundem crunt ue lonsicudines capexe, adeoque
  10. lumma virium uc summa longicudinum, hoc est, vis Solidi corius ut
  11. arC2 E L. O R in intinitum versus OR producta. Sed area illa (Per
  12. nocas quadraturarum methodos) eAt reciprOCCUt C. (Fn =3, eE PFOP-
  13. cerea vis Solidi torius cst reciprOCC UE C(7n = 3. d. F. D.
  14. Ca5. 2. Collocetur jam corpusculum C ex parre plani VGL. in-
  15. era Solidum, ec capiatur distantia C. R aequalis distantix CCr. RFS0-
  16. lidi parS L. G10KO, planis Parallelis LEF L, OKO terminata, cOr
  17. Dulculum C. in medio sicum nullam in partem crahet, contrariis op.
  18. Politorum punctorum actionibus se mutuo per aequalicatem tollenti
  19. bus. Proinde corpusculum C Sola vi Solidi ulera planum OR AIFi EF2-
  20. hitur. FlaeC autem vis (per C asum primum) CAreciprOCC UE CH n - 3
  21. hoc cA (ob aequales CG, CR) rECIPEOCC UE CCF n - 3. D. F. D.
  22. Corol. 1. TIinc si Solidum L CT. N planis duobus infinicis pa-
  23. rallelis L. C, INV utrinque terminetur; innotescit ejus vis attra-
  24. etiras subducendo de vi actractiva Solidi torius infiniti Y. C KC
  25. vim attractiram partis ulterioris NTCO, in infinitum vertus KC
  26. productae.
  27. Corol. 2. Si Solidi hujus infiniei pars ulterior, quando attractio e-
  28. jus collata cum aetractione partis citerioris nullius pene est momen-
  29. ei rejiciatur: attractio partis illius citerioris augendo distantiam de-
  30. crescet quam proxime in ratione potectatis C(n = 3
  31. Corol. 3. FF hinc s corpus quodris finitum ec ex una parte pla-
  32. num trahiac corpuiculum c regione medii illius plani, sc dictancia
  33. inter corpusculum ec planum collata cum dimensionibus corpo
  34. ris actratientis perexigua TC, Constet autem corpus actrahens ex
  35. Parciculis homogeneis, quarum vires actractire decrescunt in
  36. ratione potestatis cujusris plusquam quadruplicatae distantiarum;
  37. vis aetractira corporis totius decrescet quamproxime in ratione
  38. Potestatis, cujus lacus sc dictantia illa perexisua, ee Index terna-
  39. rio minor quam Index potestatis prioris. De corpore ex particulis
  40. constante, quarum rires acrractirae decrescune in ratione porestatis
  41. eriplicatae distantiarum, assertio non ralet; propterea quod, in hoc
  42. catus aecractio parris illius ulterioris corporis intiniti in Corollario
  43. lecundo, semper est intinire major quam auractio partis citerioris.
  44. Scholiumo
  45. PsIHIIII
  46. 1
  47. sIIIuIIsAIIIILIIIIIII
  48. Ns BIEHMN SIIIIII

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 201. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0235?run=74