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By the last Problem, with e, the giventension at the vertex, construct the inde-finite catenary ACB, having CD for itsaxis and EK for its directrix. From thevertex C on the axis CD, lay off CF equalthe other given quantity x, and throughF draw the ordinate FG, cutting the curveABC in G, then shall CGF be the catenaryrequired, as is evident from the foregoingarticles without any formal demonstration.

case ir.

When ct, c<|>, cz, xt, x<p, xz, t<p, tz, or <pz aregiven.

By means of the figure EIFC find c andx by article 20. and then proceed as inCase I. and the thing is done.

CASE III.

When c and y are the two given quan-tities.

On the directrix EK, of the indefinitecatenary ACB, constructed as directed inCase I. lay off EH equal to the given quan-

k 4