Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 44

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: 0.84.

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

The machine reads it as

  1. +4
  2. PHILOSOPMLE NATDRALIS
  3. GORFONON I CA, Ut SP X R P g 2C
  4. SF cub. X PV cub.
  5. PT Cub.
  6. trianoula FSG, T PV) ad SC cub.
  7. sive (ob similia
  8. Corol. 3. Vis, qua corpus P in Orbe quocunque circum virium
  9. centrum Srevolritur, est ad rim qua corpus idem P in eodem
  10. orbe codemque tempore periodico circum aliud quodvis ririum
  11. centrum R revolri porest, ut SP X R P g contentum utique sub di-
  12. stancia corporis a primo virium centro s’ec quadrato distantix ejus
  13. a secundo ririum centro R ad cubum rectae SEF quae 2 primo vi-
  14. rium centro Sad orbis tangentem PC ducitur, e corporis a (c-
  15. cundo ririum centro distantia RF parallela est. Nam vires in
  16. hoc Orbe, ad ejus punctum quodris P, eadem tunt ac in C irculo
  17. ejusdem curratura.
  18. PRODOSTTTO. VIII. PROBLEMA. III.
  19. Moveatur corpus in Circulo P C A: ad hunc effectum requiritur L ex
  20. vis centripetae tendentis ad punctum adeo loncinquum S, ut linea
  21. omnes PS, RS ad id ductae, pro parallelis haberi possint.
  22. A Circuli centrO C agatur semidiameter C A parallelas iltas
  23. verpendiculariter secans in MI e
  24. N. ec jungatur CP. Ob similia
  25. crianoula CF MI, PZT _E RZ
  26. eAt CF 9 2d F MG UE F R9 2c
  27. Fge ex natura Circuli P R9
  28. equale est rectangulO ORXRN F ON
  29. sive cocuntibus punctis P, O) rect.
  30. angulo 4RX2F M. ErgO CA
  31. CP g2d F MIquad. Ut B R X 2TMI
  32. ad 97 quad. adeoque quad.
  33. aequale
  34. 2FMCub.
  35. C+
  36. QR
  37. DE quad. XSF quad.
  38. QR
  39. 2qualc
  40. MCub. XSFqu.
  41. CF quad.
  42. FR erGO (PEF COrOL. Z _E S PrOP. VT.) viS CenTrIPETA ReCIpROCE Ux
  43. PMcub. XSF quad. noc est (neglecta ratione determinata 25P quad.
  44. CF quad.
  45. reCIPEOCC UE P MI Cub. 9. F. I.
  46. C
  47. e
  48. Idem tacile colligitur etiam ex Proposirione prxecedente.
  49. denon
  50. DE MOTO

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 44. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0078?run=74