Co-ordinates, System of.
A system for indicating the position of points in space by reference to
fixed lines, intersecting at a determined and arbitrary point 0, termed
the origin of co-ordinates. In plane rectangular co-ordinates two lines
are drawn through the origin, one horizontal, termed the axis of
abscissas, or axis of X. All distances measured parallel to it, if
unknown, are indicated by x, and are termed abscissas. The other axis is
vertical, and is termed the axis of ordinates, or axis of Y. All
distances measured parallel to it, if unknown, are indicated by y and
are termed ordinates. Thus by naming its abscissa and ordinate a point
has its position with reference to the axes determined, and by
indicating the relation between a point, line or curve, and a system of
abscissas and ordinates, the properties of a line or curve can be
expressed algebraically. Co-ordinates may also be inclined to each other
at any other angles, forming oblique co-ordinates; relations may be
expressed partly in angles referred to the origin as a centre, giving
polar co-ordinates. For solid geometry or calculations in three
dimensions, a third axis, or axis of Z, is used, distances parallel to
which if unknown are indicated by z.
Fig. 112. AXES OF CO-ORDINATES.