CONCAVITY

, that side of a figure or body which is hollow.

An arch of a curve has its concavity turned all one way, when the right lines that join any two of its points are all on the same side of the arch.

Archimedes, intending to include in his definition such lines as have rectilinear parts, says, a line has its concavity turned one way, when the right lines that join any two of its points, are either all upon one side of it, or while some fall upon the line itself, none fall upon the opposite side. Archim. de Sphær. et Cyl. Def. 2, and Maclaurin's Fluxions, art. 180.

When two lines that have their concavity turned the same way, have the same extremes, and the one includes the other, or has its concavity towards it, the perimeter of that which includes, is greater than that which is included. Archim. ib. ax. 2.