LINES, SURFACES, AND VOLUMES.

MENSURATION is that branch of mathematical science which treats of the measurement of lines, surfaces, and volumes.

To measure a magnitude of any kind, is to find how often it contains another magnitude of the same kind called the unit; thus, to measure a surface, is to find how often it contains the unit of surface; similarly, to measure a volume, is to find how often it contains the unit of volume. In measuring such magnitudes, however, we do not do so by directly applying to the magnitude considered the unit magnitude; geometry affords us the means of deducing their measures, from the length of one or more lines connected with them.

The number which expresses how often a magnitude contains the unit, is called the numerical measure of that magnitude.