102

line (CD) drawn through the vertex per-pendicular to the horizon, is termed theaxis. A horizontal line (HF) drawn fromany point (FI) in the axis to meet the curve,is called an ordinate, and the distance (CH)between the vertex and the ordinate iscalled abscissa, or. absciss.

4. Theorem. If any point F in thechain ACB be supported in the positionit has taken by the formation of the cate-nary ACB, the part BF, above that point,may be removed without altering either theposition or the tension of any point in theremaining part ACF.

For it is manifest that B F has no othereffect upon ACF than by cohesion to sup-port the point F in the position which ithas assumed in the formation of the cate-nary ; and if that point be supported inthe same position by any other power, itfollows that no alteration can take placeeither in the position or tension of anypoint in ACF, by the exchanging of similarand equivalent powers.

5. Corollary. From this theorem it ismanifest that if the position of the support-