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1. QUANTITY is anything that can be increased, diminished, and measured.
To measure a thing is to find how many times it contains some other thing of the same kind, taken as a standard. assumed standard is called the unit of measure.
2. Since the unit of measure is of the same kind as the thing measured, there are as many kinds of units as there are species of quantity. In Geometry, there are four species of quantity, called GEOMETRICAL MAGNITUDES, viz., LINES, SURFACES, VOLUMES, and ANGLES: hence, there are four kinds of units of measure, viz., Units of Length, Units of Surface, Units of Volume, and Units of Angular Measure.
3. GEOMETRY is that branch of Mathematics which treats of the properties and relations of Geometrical Magnitudes.
4. In Geometry, the quantities considered are generally represented by pictorial symbols. The operations to be performed upon them, and the relations between them, are indicated by signs, as in Analysis.
The following are the principal signs employed:
The Sign of Addition, +,
Thus, A+ B, indicates that B is to be added to A.
Thus,, A — B, indicates that B is to be subtracted
Thus, Ax B, indicates that A is to be multiplied by B.
Thus, 43, indicates that A is to be taken three times as a factor, or raised to the third power.
The Radical Sign, √:
Thus, A, B, indicate that the square root of A, and the cube root of B, are to be taken.
When a compound quantity is to be operated upon as a single quantity, its parts are connected by a vinculum or by a parenthesis:
Thus, A+B x C, indicates that the sum of A and B is to be multiplied by C; and (A + B) ÷ C, indicates that the sum of A and B is to be divided by C. A number written before a quantity, shows how many times it is to be taken.
Thus, 3(A+B), indicates that the sum of A and B is to be taken three times.
The Sign of Equality, =:
Thus, A = B+ C, indicates that A is equal to the sum of B and C.