Spherical coordinates
(gcide) | Coordinate \Co*["o]r"di*nate\, n.
1. A thing of the same rank with another thing; one two or
more persons or things of equal rank, authority, or
importance.
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It has neither coordinate nor analogon; it is
absolutely one. --Coleridge.
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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 coordinate axes and coordinate planes. See
Abscissa.
Note: Coordinates 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
coordinate axes AY and AX.
(b) Any radius vector PA (Fig. 1), 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 coordinate axes, AX, AY, AZ, and measured from
the corresponding coordinate 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.
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Cartesian coordinates. See under Cartesian.
Geographical coordinates, 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 coordinate.
Polar coordinates, coordinates 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 coordinates, coordinates the axes of which
intersect at right angles.
Rectilinear coordinates, coordinates made up of right
lines. Those defined in
(a) and
(c) above are called also Cartesian coordinates.
Trigonometrical coordinates or Spherical coordinates,
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 coordinates, coordinates 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.
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