radical axis of two circles

from The Collaborative International Dictionary of English v.0.48
Radical \Rad"i*cal\ (r[a^]d"[i^]*kal), a. [F., fr. L. radicalis
   having roots, fr. radix, -icis, a root. See {Radix}.]
   1. Of or pertaining to the root; proceeding directly from the
      root.
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   2. Hence: Of or pertaining to the root or origin; reaching to
      the center, to the foundation, to the ultimate sources, to
      the principles, or the like; original; fundamental;
      thorough-going; unsparing; extreme; as, radical evils;
      radical reform; a radical party.
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            The most determined exertions of that authority,
            against them, only showed their radical
            independence.                         --Burke.
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   3. (Bot.)
      (a) Belonging to, or proceeding from, the root of a plant;
          as, radical tubers or hairs.
      (b) Proceeding from a rootlike stem, or one which does not
          rise above the ground; as, the radical leaves of the
          dandelion and the sidesaddle flower.
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   4. (Philol.) Relating, or belonging, to the root, or ultimate
      source of derivation; as, a radical verbal form.
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   5. (Math.) Of or pertaining to a radix or root; as, a radical
      quantity; a radical sign. See below.
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   {Radical axis of two circles}. (Geom.) See under {Axis}.

   {Radical pitch}, the pitch or tone with which the utterance
      of a syllable begins. --Rush.

   {Radical quantity} (Alg.), a quantity to which the radical
      sign is prefixed; specifically, a quantity which is not a
      perfect power of the degree indicated by the radical sign;
      a surd.

   {Radical sign} (Math.), the sign [root] (originally the
      letter r, the initial of radix, root), placed before any
      quantity, denoting that its root is to be extracted; thus,
      [root]a, or [root](a + b). To indicate any other than the
      square root, a corresponding figure is placed over the
      sign; thus, [cuberoot]a, indicates the third or cube root
      of a.

   {Radical stress} (Elocution), force of utterance falling on
      the initial part of a syllable or sound.

   {Radical vessels} (Anat.), minute vessels which originate in
      the substance of the tissues.
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   Syn: Primitive; original; natural; underived; fundamental;
        entire.

   Usage: {Radical}, {Entire}. These words are frequently
          employed as interchangeable in describing some marked
          alteration in the condition of things. There is,
          however, an obvious difference between them. A radical
          cure, reform, etc., is one which goes to the root of
          the thing in question; and it is entire, in the sense
          that, by affecting the root, it affects in an
          appropriate degree the entire body nourished by the
          root; but it may not be entire in the sense of making
          a change complete in its nature, as well as in its
          extent. Hence, we speak of a radical change; a radical
          improvement; radical differences of opinion; while an
          entire change, an entire improvement, an entire
          difference of opinion, might indicate more than was
          actually intended. A certain change may be both
          radical and entire, in every sense.
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from The Collaborative International Dictionary of English v.0.48
Axis \Ax"is\, n.; pl. {Axes}. [L. axis axis, axle. See {Axle}.]
   A straight line, real or imaginary, passing through a body,
   on which it revolves, or may be supposed to revolve; a line
   passing through a body or system around which the parts are
   symmetrically arranged.
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   2. (Math.) A straight line with respect to which the
      different parts of a magnitude are symmetrically arranged;
      as, the axis of a cylinder, i. e., the axis of a cone,
      that is, the straight line joining the vertex and the
      center of the base; the axis of a circle, any straight
      line passing through the center.
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   3. (Bot.) The stem; the central part, or longitudinal
      support, on which organs or parts are arranged; the
      central line of any body. --Gray.
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   4. (Anat.)
      (a) The second vertebra of the neck, or {vertebra
          dentata}.
      (b) Also used of the body only of the vertebra, which is
          prolonged anteriorly within the foramen of the first
          vertebra or atlas, so as to form the odontoid process
          or peg which serves as a pivot for the atlas and head
          to turn upon.
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   5. (Crystallog.) One of several imaginary lines, assumed in
      describing the position of the planes by which a crystal
      is bounded.
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   6. (Fine Arts) The primary or secondary central line of any
      design.
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   {Anticlinal axis} (Geol.), a line or ridge from which the
      strata slope downward on the two opposite sides.

   {Synclinal axis}, a line from which the strata slope upward
      in opposite directions, so as to form a valley.

   {Axis cylinder} (Anat.), the neuraxis or essential, central
      substance of a nerve fiber; -- called also {axis band},
      {axial fiber}, and {cylinder axis}.

   {Axis in peritrochio}, the wheel and axle, one of the
      mechanical powers.

   {Axis of a curve} (Geom.), a straight line which bisects a
      system of parallel chords of a curve; called a {principal
      axis}, when cutting them at right angles, in which case it
      divides the curve into two symmetrical portions, as in the
      parabola, which has one such axis, the ellipse, which has
      two, or the circle, which has an infinite number. The two
      axes of the ellipse are the {major axis} and the {minor
      axis}, and the two axes of the hyperbola are the
      {transverse axis} and the {conjugate axis}.

   {Axis of a lens}, the straight line passing through its
      center and perpendicular to its surfaces.

   {Axis of a microscope} or {Axis of a telescope}, the straight
      line with which coincide the axes of the several lenses
      which compose it.

   {Axes of co["o]rdinates in a plane}, two straight lines
      intersecting each other, to which points are referred for
      the purpose of determining their relative position: they
      are either rectangular or oblique.

   {Axes of co["o]rdinates in space}, the three straight lines
      in which the co["o]rdinate planes intersect each other.

   {Axis of a balance}, that line about which it turns.

   {Axis of oscillation}, of a pendulum, a right line passing
      through the center about which it vibrates, and
      perpendicular to the plane of vibration.

   {Axis of polarization}, the central line around which the
      prismatic rings or curves are arranged. --Brewster.

   {Axis of revolution} (Descriptive Geom.), a straight line
      about which some line or plane is revolved, so that the
      several points of the line or plane shall describe circles
      with their centers in the fixed line, and their planes
      perpendicular to it, the line describing a surface of
      revolution, and the plane a solid of revolution.

   {Axis of symmetry} (Geom.), any line in a plane figure which
      divides the figure into two such parts that one part, when
      folded over along the axis, shall coincide with the other
      part.

   {Axis of the} {equator, ecliptic, horizon} (or other circle
      considered with reference to the sphere on which it lies),
      the diameter of the sphere which is perpendicular to the
      plane of the circle. --Hutton.

   {Axis of the Ionic capital} (Arch.), a line passing
      perpendicularly through the middle of the eye of the
      volute.

   {Neutral axis} (Mech.), the line of demarcation between the
      horizontal elastic forces of tension and compression,
      exerted by the fibers in any cross section of a girder.

   {Optic axis of a crystal}, the direction in which a ray of
      transmitted light suffers no double refraction. All
      crystals, not of the isometric system, are either uniaxial
      or biaxial.

   {Optic axis}, {Visual axis} (Opt.), the straight line passing
      through the center of the pupil, and perpendicular to the
      surface of the eye.

   {Radical axis of two circles} (Geom.), the straight line
      perpendicular to the line joining their centers and such
      that the tangents from any point of it to the two circles
      shall be equal to each other.

   {Spiral axis} (Arch.), the axis of a twisted column drawn
      spirally in order to trace the circumvolutions without.

   {Axis of abscissas} and {Axis of ordinates}. See {Abscissa}.
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