MENSURATION (Lat. mcnsuratio, from anensurair, to measure, from measure, from nu to measure). A braneh of applied mathematics dealing with the calculation of lines, angles, surfaces, and volumes from measured that the volume of a rectangular parallelepiped or prism is found by multiplying together the length, breadth, and thickness; and of the oblique parallelepiped, prism, or cylinder. by multiply ing the area of the base by the height.
As in case of the circle, so in the mensuration of the cylinder. cone, and sphere, the theory of limits (see LIMITS, THEORY or) is applied in connection with the circumscribed and inscribed figures. The following formulas of mensuration will be found convenient: data. The metrical relations between lines and angles are computed chiefly by the principles of trigonometry (q.v.). The mensuration of com mon surfaces and volumes, however, can gen erally be effected by the principles of geometry. For the purposes of either direct measurement or computation a unit is necessary. The straight line is measured by direct comparisons with some linear unit, as the inch, foot, or yard. Ilut in measuring a surface or a volume it is unneces sary to apply an actual square or cubic unit, or even to divide the magnitudes into such squares or cubes. It is only necessary to measure certain of its boundary lines or dimensions, and from these measurements to calculate the contents in terms of the appropriate unit; e.g. if II inches
and b inches are the lengths of the adjacent sides of a rectangle, its area is a •b• 1 square inch = ab square inch; i.e. the number of square units of area in a rectangle is equal to the product of two numbers which represent its base and altitude, measured by the same linear unit. The areas of other figures are found from this by the aid of certain relations or properties of those figures; for instance. the area of a parallelo gram is the same as the area of a rectangle hav ing the same base and altitude. and is therefore equal to the base multiplied by the altitude. As a triangle is half of a parallelogram of the same base and the same altitude. its area is one ha 1 f the product of its base and altitude. Cert a in quadrilatt.rals and polygons are measured by dividing them into triangles. the area of each of which is separately calculated. (for the area of the circle, CIRCLE.) lly reasoning similar to that employed in the ea-e of areas, it is slomn For the mensuration of geometric Solids. con sult Holzmiiller. Element(' dcr ,`?tcreoinairic (2 vols., Leipzig. 19001.