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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 246

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.

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

The machine reads it as

  1. 2.46
  2. PHTLOSOPHLE NATDRALIS
  3. Conronon velocitas, altera ue quadratum relociratis: et iplus decremen-
  4. cum est ue summa quanciratum de
  5. CG
  6. CC
  7. CD g. Quarum prior CA
  8. ipta de polerior G. D q est ut CD q Proinde . Ob an.
  9. alosum decrementum, est ut velocitas. PF (i quantitas EFD, ipA=
  10. reciproce proxortionalis, quantitare data C G augeatUE; Tumma C D,
  11. cempore ABE. D unitormirer crelcentes crelcet in progressione
  12. Ecometrica. d. F. D.
  13. Corol. 1. Igitur si datis punctis A, C exPOnatuE tempuS PCF
  14. aream typerbolicam ABF. D, exponi potest velocitas per iplius
  15. ED reciprOCAM
  16. Corol. 2. Sumendo autem C A ad C D ue relocitatis reciproca Tub
  17. initio, ad relocitatis reciprocam in finc temporis cujulris AB P. D,
  18. invenietur punctum C. Fo autem invento, relocitas ex dato quo.
  19. vis alio tempore inveniri potest.
  20. PROPOSITIO XII. THEOREMA IZ:
  21. isdem positis, dico quod si spatia descripta sumantur in progressio
  22. ne drithmetica, velocitates data quadam quantitate auetae e-
  23. runt in prooressione Ceometrica.
  24. In ASMPEOEO C D detur pUn- F
  25. ctum R, et crecto perpendiculo RS,
  26. quod occurrat IIyperbolae in S, Cx-
  27. Donatur delcriptum spacium per a-
  28. ream IIpperbolicam RS F D; e
  29. velocitas erie ut longitudo GD
  30. qua cum data C C componit longi.
  31. cudinem C D, in progressione Cco-
  32. metrica decrescentem, interea dum
  33. spacium RSF. D augetur in Arith.
  34. metica.
  35. tenim ob datum spacii incrementum P. D de, lincola D a, quae
  36. DE AOTV
  37. eocite

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 246. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0280?run=74