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Radical axis of two circles

Radical Rad"i*cal, 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. 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. The most determined exertions of that authority, against them, only showed their radical independence. --Burke. 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. 4. (Philol.) Relating, or belonging, to the root, or ultimate source of derivation; as, a radical verbal form. 5. (Math.) Of or pertaining to a radix or root; as, a radical quantity; a radical sign. See below. 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. Syn: Primitive; original; natural; underived; fundamental; entire. Usage: Radical, Entire. These words are frequently employed as interchangeable in describing some marked alternation 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 a 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.

Radical Rad"i*cal, 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. 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. The most determined exertions of that authority, against them, only showed their radical independence. --Burke. 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. 4. (Philol.) Relating, or belonging, to the root, or ultimate source of derivation; as, a radical verbal form. 5. (Math.) Of or pertaining to a radix or root; as, a radical quantity; a radical sign. See below. 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. Syn: Primitive; original; natural; underived; fundamental; entire. Usage: Radical, Entire. These words are frequently employed as interchangeable in describing some marked alternation 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 a 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.

Radical axis of two circles

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. 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. 3. (Bot.) The stem; the central part, or longitudinal support, on which organs or parts are arranged; the central line of any body. --Gray. 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. 5. (Crystallog.) One of several imaginary lines, assumed in describing the position of the planes by which a crystal is bounded. 6. (Fine Arts) The primary or secondary central line of any design. 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 telescope or microscope, 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.

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. 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. 3. (Bot.) The stem; the central part, or longitudinal support, on which organs or parts are arranged; the central line of any body. --Gray. 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. 5. (Crystallog.) One of several imaginary lines, assumed in describing the position of the planes by which a crystal is bounded. 6. (Fine Arts) The primary or secondary central line of any design. 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 telescope or microscope, 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.

- the circles. If the circles cross, their radical axis is the line through their two crossing points, and if they are tangent, it is their line of tangency...

- of the given circle (solid black in Figure 2). This construction of an orthogonal circle is useful in understanding the radical axis of two circles,...

- Apollonian circles are two families of circles such that every circle in the first family intersects every circle in the second family orthogonally, and...

- the two given circles. Therefore, the point G also lies on the radical axis of the two given circles. For each pair of antihomologous points of two circles...

- lies outside of all three circles, then it is the center of the unique circle (the radical circle) that intersects the three given circles orthogonally;...

- connecting the two poles may be called the axis of rotation. Circles on the sphere that are parallel (i.e. not great circles) to the equator are lines of latitude...

- The circles of Apollonius are any of several sets of circles ****ociated with Apollonius of Perga, a renowned Gr**** geometer. Most of these circles are...

- The radical axis of two circles is the set of points of equal tangents, or more generally, equal power. Circles may be inverted into lines and circles into...

- power of P. In the case n = 2, the power diagram consists of two halfplanes, separated by a line called the radical axis or chordale of the two circles. Along...

- Radical Axis, Inc. (stylized as radicalaxis) is an American animation studio headquartered in Atlanta, Georgia known for its diverse work in both episodic...

- of the given circle (solid black in Figure 2). This construction of an orthogonal circle is useful in understanding the radical axis of two circles,...

- Apollonian circles are two families of circles such that every circle in the first family intersects every circle in the second family orthogonally, and...

- the two given circles. Therefore, the point G also lies on the radical axis of the two given circles. For each pair of antihomologous points of two circles...

- lies outside of all three circles, then it is the center of the unique circle (the radical circle) that intersects the three given circles orthogonally;...

- connecting the two poles may be called the axis of rotation. Circles on the sphere that are parallel (i.e. not great circles) to the equator are lines of latitude...

- The circles of Apollonius are any of several sets of circles ****ociated with Apollonius of Perga, a renowned Gr**** geometer. Most of these circles are...

- The radical axis of two circles is the set of points of equal tangents, or more generally, equal power. Circles may be inverted into lines and circles into...

- power of P. In the case n = 2, the power diagram consists of two halfplanes, separated by a line called the radical axis or chordale of the two circles. Along...

- Radical Axis, Inc. (stylized as radicalaxis) is an American animation studio headquartered in Atlanta, Georgia known for its diverse work in both episodic...

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