Definition of Conjugate diameters. Meaning of Conjugate diameters. Synonyms of Conjugate diameters

Here you will find one or more explanations in English for the word Conjugate diameters. Also in the bottom left of the page several parts of wikipedia pages related to the word Conjugate diameters and, of course, Conjugate diameters synonyms and on the right images related to the word Conjugate diameters.

Definition of Conjugate diameters

Conjugate diameters
Diameter Di*am"e*ter, n. [F. diam[`e]tre, L. diametros, fr. Gr. ?; dia` through + ? measure. See Meter.] 1. (Geom.) (a) Any right line passing through the center of a figure or body, as a circle, conic section, sphere, cube, etc., and terminated by the opposite boundaries; a straight line which bisects a system of parallel chords drawn in a curve. (b) A diametral plane. 2. The length of a straight line through the center of an object from side to side; width; thickness; as, the diameter of a tree or rock. Note: In an elongated object the diameter is usually taken at right angles to the longer axis. 3. (Arch.) The distance through the lower part of the shaft of a column, used as a standard measure for all parts of the order. See Module. Conjugate diameters. See under Conjugate.
Conjugate diameters
Conjugate Con"ju*gate, a. [L. conjugatus, p. p. or conjugare to unite; con- + jugare to join, yoke, marry, jugum yoke; akin to jungere to join. See Join.] 1. United in pairs; yoked together; coupled. 2. (Bot.) In single pairs; coupled. 3. (Chem.) Containing two or more radicals supposed to act the part of a single one. [R.] 4. (Gram.) Agreeing in derivation and radical signification; -- said of words. 5. (Math.) Presenting themselves simultaneously and having reciprocal properties; -- frequently used in pure and applied mathematics with reference to two quantities, points, lines, axes, curves, etc. Conjugate axis of a hyperbola (Math.), the line through the center of the curve, perpendicular to the line through the two foci. Conjugate diameters (Conic Sections), two diameters of an ellipse or hyperbola such that each bisects all chords drawn parallel to the other. Conjugate focus (Opt.) See under Focus. Conjugate mirrors (Optics), two mirrors so placed that rays from the focus of one are received at the focus of the other, especially two concave mirrors so placed that rays proceeding from the principal focus of one and reflected in a parallel beam are received upon the other and brought to the principal focus. Conjugate point (Geom.), an acnode. See Acnode, and Double point. Self-conjugate triangle (Conic Sections), a triangle each of whose vertices is the pole of the opposite side with reference to a conic.

Meaning of Conjugate diameters from wikipedia

- geometry, two diameters of a conic section are said to be conjugate if each chord parallel to one diameter is bisected by the other diameter. For example...
- {\displaystyle {\overline {P_{2}Q_{2}}}} . Conjugate diameters in an ellipse generalize orthogonal diameters in a circle. In the parametric equation for...
- major axis. Conjugate diameters are a pair of diameters where one is parallel to a tangent to the ellipse at the endpoint of the other diameter. Several...
- hyperbola conjugate to the first." The following property was described by Apollonius: let PP', DD' be conjugate diameters of two conjugate hyperbolas...
- follows: The diameters or conjugates of the pelvis are measured at the pelvic inlet and outlet and as oblique diameters. Two diameters may be measured...
- two diameters are said to be conjugate if and only if the tangent line to the ellipse at an endpoint of one diameter is parallel to the other diameter. Each...
- pair of conjugate diameters are taken as new axes, and a new unit of length is taken proportional to the length of either of these diameters." On this...
- (1801–1868). Conjugate diameters appear always if a circle or an ellipse is projected parallelly (the rays are parallel) as images of orthogonal diameters of a...
- diameter. A conjugate diameter bisects the chords, being placed between the centroid and the tangent point. Moreover, both diameters are conjugate to each...
- Osgood and Graustein used the rectangular hyperbola, its conjugate hyperbola, and conjugate diameters to rationalize tie rods at 15 degree radial spacing,...