Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 58

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: 0.91.

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

The machine reads it as

  1. 58 DE V ERIBDS EF MIOTIBVS CORPOROM. L. IB. L.
  2. qualiter distantibus eadem solicitatione centrali BF urcentur, erit ubi-
  3. que momentum solicitationis centralis seu rectaneulum BEC aequale Bo-
  4. moloeo rectane ulo XTn. SF. vel NTn. NB, quod exponit momentum solici-
  5. rationis tangentialis in curvae puncto quolibet N.
  6. Aecus circuli epn centro D deleripti locet rectam DI, in pun-
  7. eto p, ex triangulum Anp tanquam rectilincum ob suam infinitam
  8. parricatem spectari porest rectangulum ad p, atque adeo simile trian-
  9. sulo NaB. Idcirco erit Na vel BF: NB (SF) = Nn: BC (NP), e
  10. BF. Fe = NTB. FC =SF. NTn = NTB. NTn. Ouod erat demonstrandum.
  11. C OR OL L A R E U M I.
  12. 234. FTinc si scalae celeritatum AVF ad punctum F perpendicu-
  13. laris FI ducatur axi occurrens in T, Tubnormalis PP dequalis ubi-
  14. que erit respectirae BF, quae solicitationem centralem exponit in
  15. distantiis ED, ND a centro D aequalibus; nam quia TFF rectus
  16. est, triangula FTP ex Ffa similia erunt, atque adco FF: FI = P a
  17. FC): af. ErGO PF. af = TB. Ce; atqui (5. 133.) SF. Nn =BF. PC
  18. ec (5. 132.) SE. Nn =M. PF. aF, aut Cumta M instar unicatis, = LF.
  19. af, erit TP. De = BF. Fe atque adeo TF =BF.
  20. C O R OL L A R Y U M II.
  21. 135. In quibuslibet punctorum F, N distantiis aequalibus F. D
  22. et NVI a CCnErO D, momenta celeritatum cadendo acquisitarum
  23. erunc aequalia. NNam Sicut (5. 132.) ACr vel CHI celeritatem acqui-
  24. litam mobilis M in curra MON descendentis, ec rectangulum IIg
  25. triansulo IIAC inscriptum celeritatis momentum in N exponunt.
  26. ita etiam 2A2C e rectangulum 2FI28 triangulo 2FI2A26 inscri-
  27. Deum, exponent celeritatem ex descentu mobilis A per spatium
  28. AE in puncto P. acquisitam, ejusque momentum. Verum (9. 132.)
  29. CASF. NVn =MI. FF. af =MI. TICE, item BF. F C = A. 21T2C528. atque
  30. (5. 233.) SF. Nn =BF. FC; PrOpFerCa Het MI. TIOB =A. 2L126128,
  31. vel quia (secundum hrpothelim) iplae M et A aequales IIC8 =
  32. 21126528.
  33. PROPOSTTTOZTZ. PHEOREMA.
  34. 15. 32. 736. Si mobilia M e A ex punctis M ex A in cur Da MOH e
  35. recta AD a quiete cadere incipiant, celeritates ipsorum in punctis N

Cite

Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 58. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1066518432:0086?run=74