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 for Curve of quickest descent
From The Collaborative International Dictionary of English v.0.48 :

  Curve \Curve\, n. [See Curve, a., Cirb.]
     1. A bending without angles; that which is bent; a flexure;
        as, a curve in a railway or canal.
        [1913 Webster]
     2. (Geom.) A line described according to some low, and having
        no finite portion of it a straight line.
        [1913 Webster]
     Axis of a curve. See under Axis.
     Curve of quickest descent. See Brachystochrone.
     Curve tracing (Math.), the process of determining the
        shape, location, singular points, and other peculiarities
        of a curve from its equation.
     Plane curve (Geom.), a curve such that when a plane passes
        through three points of the curve, it passes through all
        the other points of the curve. Any other curve is called a
        curve of double curvature, or a twisted curve.
        [1913 Webster]

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