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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 202

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: 0.85.

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

The machine reads it as

  1. II
  2. PHILOSOPHLSE NATORALIS
  3. Scholium.
  4. Si corpus aliquod perpendiculariter versus planum datum era-
  5. hatUT, ex ex data lege attractionis guaeratur motus corporis: Sol-
  6. recur Problema quaerendo (per PFOP. ZXXIX) motum corporis recta
  7. descendentis ad hoc planum, et (per L egum Corol. 2.) Componen-
  8. do mocum iltum cum uniformi motu, secundum lincas eidem plano
  9. parallelas Facto. EE COntrA, Si quaeratur L ex accractionis in planum
  10. secundum lincas perpendiculares Factae, ca conditione uF COrDuS aF-
  11. eractum in data quacunque curra linea moreatur, Solvetur Proble-
  12. ma operando ad exemplum Problemaris terrii.
  13. Operationes aurem contrahi solene resolvendo ordinatim appli-
  14. catas in Scries convergentes. VF si ad basem A in angulo quoris
  15. dato ordinatim applicetur lonsitudo B, quae sic ut basis dignitas
  16. quaelibee An; ec quaeratur vis qua corpus, secundum positionem
  17. ordinatim axplicatae, vel in balem actractum vel a baS Fugatum,
  18. moveri postit in curra linea quam ordinatim axplicata termi-
  19. no suo suveriore semper actinsit: Suppono balem augeri Parte
  20. quam minima O, ec ordinatim applicatam a F On resolvo in
  21. m -n
  22. Seriem infinitam An + = OA + mm-mn
  23. et
  24. 2nn
  25. m - 2n
  26. OOA eC. aC.
  27. que hujus cermino in quo O duarum est dimentionum, id est, cer-
  28. Mm-mM
  29. mino
  30. m - 21
  31. 2nn OOa n rim provortionalem eNe suDDOnO. P. A
  32. isitur vis guXesiTa uE
  33. M
  34. 2
  35. mm-mn
  36. nn
  37. m - 2n
  38. vel quod perince cAt, ve
  39. mm-m B m. OE s ordinacim axplicata Parabolam acringat,
  40. nn
  41. existente m = 2, _ n = F: Het vis uE data 2B, adeoque dabi-
  42. Tur. Daca isieur ri corpus morebieur in Parabola, quemad-
  43. modum Galilans demonstrarit. Duod si ordinatim applicaca
  44. HIyperbolam attingat, existente m =O -T, eE n = L; ECL vis uE
  45. 2A=3 Seu 2B3: adeoque ris quxe sic ue cubus ordinatim applicata,
  46. corpus movebitur in FIrperbola. Scd mistis hujusmodi Propoliti-
  47. onibus, pergo ad alias quasdam de Motu, quas nondum attisi.
  48. DE MOTD
  49. PORPORVM

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 202. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0236?run=74