Publisher's Synopsis
From the INTRODUCTION.
MENSURATION is that branch of mathematics which has for its object the measurement of geometrical magnitudes. It has been called, that branch of applied geometry which gives rules for finding the length of lines, the area of surfaces, and the volume of solids, from certain data of lines and angles.
A Magnitude is anything which can be conceived of as added to itself, or of which we can form multiples.
The measurement of a magnitude consists in finding how many times it contains another magnitude of the same kind, taken as a unit of measure. Measurement, then, is the process of ascertaining the ratio which one magnitude bears to some other chosen as the standard; and the measure of a magnitude is this ratio expressed in numbers. Hence, we must refer to some concrete standard, some actual object, to give our measures their absolute meaning.
The concrete standard is arbitrary in point of theory, and its selection a question of practical convenience. A discrete aggregate, such as a pile of cannon-balls, or a number, has a natural unit, -- "one of them." But in the continuous quantity, space, with which we chiefly have to deal, the fundamental unit, a length, is defined by fixing upon a physical object, such as a bar of platinum, and agreeing to refer to its length as our standard. That is, we assume some arbitrary length in terms of which all space measurements are to be expressed.
The one actually adopted is the Meter, which is the length of a special bar deposited in the French archives. This we choose because of the advantages of the metric system, which applies only a decimal arithmetic, and has a uniform and significant terminology to indicate the multiples and submultiples of a unit.
