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Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 49

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. DE VIRTEDS ETMOTTBOS CORPORVH. L. IB. L. 43
  2. eROPOSITIO XIV. THEOREMA.
  3. 112. Recta AD curva P. R A perpendicularis, mediae directioni BD Fi8. 31.
  4. potentiarum curva perpendiculariter applicatarum, occurret in punctoD
  5. lineae mediarum directionum CVD.
  6. Sit Ad CurrX Clementum, eE ab TanOOnS CVEVX in a, _ bD linca
  7. bisccans anculum, abF crit media directio potentiarum arcui curre
  8. FRa applicatarum: unde cum b ipsi B infinite ricinum sE, sequi-
  9. tur unam bD alteram BD secare in puncto D currae quaesitx. Igi-
  10. cur probandum tantum reltat, perpendicularem currae AD trantire
  11. per punctum illud intersectionis D, duarum infinite ricinarum BD,
  12. bD. Centro quolibet P in tangente BF aNumto, e radio EP de
  13. scripto lemicirculo LCHI, agantur radii FCs tangenti AB, ec fip
  14. tangenti ab paralleli, junctisque FC, Fg, agatur Cm radio FF
  15. Parallela, recte Fe productx occurrens in h, et radio Fg prolon-
  16. sato in m: denique ductxe sint semicirculi tangens OIE in puncto
  17. C, _ F.M eidem tansenti parallela, quae proinde radio LC Dei-
  18. Dendicularis exit. Jam quia FC tangenti AB Parallela cA, crit an-
  19. suluS ABTI = FFO, _ duO FFC X FOF limul aquales angulo
  20. ABE, seu duplo anguli DBF, quandoquidem BD angulum ABF
  21. bifariam dividit, isitur FFO = DBK, unde rectae BD e OF. sunt
  22. Parallela. Pari argumento probatur, parallelas esse bD et eF. Igi-
  23. tur dueta mL. Parallela ipsi BE, vel sE, ABuTa ABBD _ FOML.
  24. erunt similes, cum compostae sint ex triangulis similibus ABB, BDb,
  25. ex FCm, Cm. Hlisce pesitis, parallelx FK ex Cim a media FB
  26. provortionaliter diridentur, atque adeo Cm: Ch = FK: F. H (vel
  27. propter parallelas MF ex CIE) = FO: MCr. Friangula vero similia
  28. GEB, ∞ CIm (nam per conAr. PB e Im parallelx TunE) PEX-
  29. DenE, Cm: Ch = CL: CF. TOIEUT FO: MG =CT: GF; atque adco
  30. FF junsens puncta F, L. Parallela est rectae ME, ac proinde LFC
  31. es rectus, cum P. MI perpendicularis sit ipsi FC. Vnde propter (i-
  32. milicudinem AGuTAruM ABBD, e FCm L, erit AB: BD = FC: CL,
  33. hinc, quia angulus LFCr rectus eAt, angulus D AB itidem rectus crit,
  34. aeque adeo AD currX E. R A perpendicularis in A. Quod erat de
  35. monstrandum.
  36. R OL K k L a M.
  37. et3. Aceosle etiam criansula ADB ex ML. C similia TunC, ex
  38. quo

Cite

Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 49. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1066518432:0077?run=74