MEASURE, in geometry, any quantity assumed as one, to which the ratio of other homogeneous or similar quantities is expressed.
Measure of an angle, the length of an arch described from the vertex to any place between its legs: hence angles are distinguished by the ratio of the arches between the legs to the peripheries. See [Angle].
Measure of a figure, is a square, whose side is an inch, foot, yard, or other determinate measure. Hence square measures.
Among geometricians it is usually a square rod, called decempeda, divided into 10 square feet, and those into square digits, and those again into 10 lines, &c.
Measure of a line, any right line taken at pleasure, and considered as unity.
Measure of the mass or quantity of matter, in mechanics, is its weight: it being apparent that all the matter which coheres with a body, gravitates with it; and it being found by experiment, that the gravities of homogeneal bodies are in proportion to their bulks: hence while the mass continues the same, the absolute weight will be the same, whatever figure it puts on; for as to its specific weight, it varies as the quantity of its surface does.
Measure of a number, in arithmetic, such a number as divides another without leaving a fraction: thus 9 is a measure of 27.
Measure of a solid, is a cube, whose side is an inch, foot, yard, or other determinate length: in geometry, it is a cubic perch, divided into cubic feet, digits, &c. Hence cubic measure, or measures of capacity.
Measure of velocity, in projectiles, and mechanics, the space passed over by a moving body in any given time. The space therefore must be divided into as many equal parts, as the time is conceived to be divided into: the quantity of space answering to such portion of time, is the measure of the velocity.
Measures then are various, according to the different kinds and dimensions of things measured. Hence arise lineal and longitudinal measures for lines or lengths; for square areas; and solid or cubic, for bodies and their capacities: all which again are very different in different countries and ages, and even many of them for different commodities. Hence also arise other divisions, of domestic and foreign, ancient and modern, dry and wet (or liquid) measures, &c.