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Definition: Spherical coordinates
1. A thing of the same rank with another thing; one two or
more persons or things of equal rank, authority, or
It has neither co["o]rdinate 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 co["o]rdinate axes and co["o]rdinate planes. See
Note: Co["o]rdinates are of several kinds, consisting in some
of the different cases, of the following elements,
(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
co["o]rdinate 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 co["o]rdinate axes, AX, AY, AZ, and measured
from the corresponding co["o]rdinate 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.
. See under Cartesian
, 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
, co["o]rdinates made up of a radius
vector and its angle of inclination to another line, or a
line and plane; as those defined in
, co["o]rdinates the axes of
which intersect at right angles.
, co["o]rdinates made up of right
lines. Those defined in
(c) above are called also Cartesian co["o]rdinates
or Spherical co["o]rdinates
, 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
, co["o]rdinates 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