Cartesian coordinates

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.
      [1913 Webster]

            It has neither coordinate nor analogon; it is
            absolutely one.                       --Coleridge.
      [1913 Webster]

   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.
          [1913 Webster]

   {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.
      [1913 Webster]
    

Cartesian \Car*te"sian\, a. [From Renatus Cartesius, Latinized
   from of Ren['e] Descartes: cf. F. cart['e]sien.]
   Of or pertaining to the French philosopher Ren['e] Descartes,
   or his philosophy.
   [1913 Webster]

         The Cartesion argument for reality of matter. --Sir W.
                                                  Hamilton.
   [1913 Webster]

   {Cartesian coordinates} (Geom), distance of a point from
      lines or planes; -- used in a system of representing
      geometric quantities, invented by Descartes.

   {Cartesian devil}, a small hollow glass figure, used in
      connection with a jar of water having an elastic top, to
      illustrate the effect of the compression or expansion of
      air in changing the specific gravity of bodies.

   {Cartesion oval} (Geom.), a curve such that, for any point of
      the curve mr + m'r' = c, where r and r' are the distances
      of the point from the two foci and m, m' and c are
      constant; -- used by Descartes.
      [1913 Webster]
    

Cartesian coordinates

   <mathematics, graphics> (After Renee Descartes, French
   philosopher and mathematician) A pair of numbers, (x, y),
   defining the position of a point in a two-dimensional space by
   its perpendicular projection onto two axes which are at right
   angles to each other.  x and y are also known as the
   {abscissa} and {ordinate}.

   The idea can be generalised to any number of independent axes.

   Compare {polar coordinates}.

   (1997-07-08)