1. A thing of the same rank with another thing; one two or more persons or things of equal rank, authority,
or importance.
It has neither coördinate nor analogon; it is absolutely one.
Coleridge.
2. pl. (Math.) Lines, or other elements of reference, by means of which the position of any point, as
of a curve, is defined with respect to certain fixed lines, or planes, called coördinate axes and coördinate
planes. See Abscissa. Coördinates are of several kinds, consisting in some of the different cases, of
the following elements, namely: (a) (Geom. of Two Dimensions) The abscissa and ordinate of any
point, taken together; as the abscissa PY and ordinate PX of the point P (Fig. 2, referred to the coördinate
axes AY and AX. (b) Any radius vector PA together with its angle of inclination to a fixed line, APX, by
which any point A in the same plane is referred to that fixed line, and a fixed point in it, called the pole,
P. (c) (Geom. of Three Dimensions) Any three lines, or distances, PB, PC, PD (Fig. 3), taken parallel
to three coördinate axes, AX, AY, AZ, and measured from the corresponding coördinate fixed planes, YAZ,
XAZ, XAY, to any point in space, P, whose position is thereby determined with respect to these planes
and axes. (d) A radius vector, the angle which it makes with a fixed plane, and the angle which its
projection on the plane makes with a fixed line line in the plane, by which means any point in space at
the free extremity of the radius vector is referred to that fixed plane and fixed line, and a fixed point in
that line, the pole of the radius vector.
Cartesian coördinates. See under Cartesian. — Geographical coördinates, the latitude and longitude
of a place, by which its relative situation on the globe is known. The height of the above the sea level
constitutes a third coördinate. — Polar coördinates, coördinates made up of a radius vector and its angle
of inclination to another line, or a line and plane; as those defined in (b) and (d) above. — Rectangular
coördinates, coördinates the axes of which intersect at right angles. — Rectilinear coördinates, coördinates
made up of right lines. Those defined in (a) and (c) above are called also Cartesian coördinates. —
Trigonometrical or Spherical coördinates, elements of reference, by means of which the position of
a point on the surface of a sphere may be determined with respect to two great circles of the sphere.
— Trilinear coördinates, coördinates of a point in a plane, consisting of the three ratios which the three
distances of the point from three fixed lines have one to another.
