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Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 270

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: 0.92.

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The machine reads it as

  1. 270 DE VTRIBUS ET MIOZIBUS CORPORUM. L1B. II.
  2. PROPOSITIOLII. LPMMA.
  3. 468. Si recta AM positione datae alia AB magnitudine data perpen-
  4. diculariter insistat, per cujus terminum B rectae quaecunque BM, Bm
  5. ad alteram AMI ducantur, e per puncta M, m, SEC. in quibus huic
  6. occurrunt; perpendiculares MN, mn, eC. ipsis BM, Bm, eC. re-
  7. spective aequales, omnia puncta H, n, etc. in curva L. Nn hyperbolae
  8. aequilatera sita erunt, cujus centrum A, e semilatus transversum
  9. AL.
  10. Fi8. X18. Positisque punctis M, m indefinite vicinis, ac descripto centro B in-
  11. tervallo BM arculo Mu, junctisque ANT, An, rectanculum (ub radio
  12. BA e arculo Me dupbum erit trilinei AVn seu elementi sectoris hy-
  13. perbolici ANL.
  14. T. DuCatE NX parallela AM, ec quia (secundum hypothesin)
  15. MIN = BM, C AB = AL, CrIt AX =XNI2 + AL, vel XN2= AX
  16. ANV =rCC. IO BXL, ergo punctum N est in lrperbola aequila-
  17. tera LNY, cujus latus transversum cA BL. ex centrum A. C UEVa L N
  18. etiam hyperbola erit, (i M N ad BM fuerit in quacunque data ra-
  19. TiOne.
  20. TI. Per punctum N ducta sIC tangens hyperbolx Ng, cruntque
  21. ErES MIN vel BMI, AI vel BA e Ag in continua rationc, atque
  22. adeo BMI: BA = BA: Ag, atqui propter criangula similia ABM e
  23. A.Nm, est etiam BM: BA = Mm vel NO: MIp; ergO NO: MN =BA:
  24. A9, acque adeo BA. MIp = LIo. A9 (num. IV. 3. 464.) =2. AIn.
  25. Ouod crat demonstrandum.
  26. C OROL L A R L U _ I.
  27. 469. Adeoque, E tOta AMI infinitis composita sic particulis infi-
  28. nitesimis qualis NIm, ex per singularum terminos rectae BM ductxe
  29. intelligantur, erit factum ex omnibus arculis Mu, quos ricinae quae-
  30. que BM incercipiunt, ex radio BA aequale duplo omnium triangu-
  31. lorum AAm quae in sectore hyperbolico ANL. continentur, id est,
  32. duplo ipsius lectoris.
  33. C OR OL L A R FU N II.
  34. 470. Ducendo igitur per punctum interfectionis + rectae AN et
  35. tansentis hyperbola At in vertice, lineam isr parallelam AL, et
  36. USL.

Cite

Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 270. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1066518432:0298?run=74