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Principal of a quadric

Principal Prin"ci*pal, a. [F., from L. principalis. See Prince.] 1. Highest in rank, authority, character, importance, or degree; most considerable or important; chief; main; as, the principal officers of a Government; the principal men of a state; the principal productions of a country; the principal arguments in a case. Wisdom is the principal thing. --Prov. iv. 7. 2. Of or pertaining to a prince; princely. [A Latinism] [Obs.] --Spenser. Principal axis. See Axis of a curve, under Axis. Principal axes of a quadric (Geom.), three lines in which the principal planes of the solid intersect two and two, as in an ellipsoid. Principal challenge. (Law) See under Challenge. Principal plane. See Plane of projection (a), under Plane. Principal of a quadric (Geom.), three planes each of which is at right angles to the other two, and bisects all chords of the quadric perpendicular to the plane, as in an ellipsoid. Principal point (Persp.), the projection of the point of sight upon the plane of projection. Principal ray (Persp.), the line drawn through the point of sight perpendicular to the perspective plane. Principal section (Crystallog.), a plane passing through the optical axis of a crystal.

Principal Prin"ci*pal, a. [F., from L. principalis. See Prince.] 1. Highest in rank, authority, character, importance, or degree; most considerable or important; chief; main; as, the principal officers of a Government; the principal men of a state; the principal productions of a country; the principal arguments in a case. Wisdom is the principal thing. --Prov. iv. 7. 2. Of or pertaining to a prince; princely. [A Latinism] [Obs.] --Spenser. Principal axis. See Axis of a curve, under Axis. Principal axes of a quadric (Geom.), three lines in which the principal planes of the solid intersect two and two, as in an ellipsoid. Principal challenge. (Law) See under Challenge. Principal plane. See Plane of projection (a), under Plane. Principal of a quadric (Geom.), three planes each of which is at right angles to the other two, and bisects all chords of the quadric perpendicular to the plane, as in an ellipsoid. Principal point (Persp.), the projection of the point of sight upon the plane of projection. Principal ray (Persp.), the line drawn through the point of sight perpendicular to the perspective plane. Principal section (Crystallog.), a plane passing through the optical axis of a crystal.

- In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and...

- ellipsoid is a quadric surface; that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces...

- degenerate quadric surfaces. When the prin****l axes of a quadric are aligned with the reference frame (always possible for a quadric), a general equation of the...

- methods for the representation of the stress state at a point include the Lamé's stress ellipsoid and Cauchy's stress quadric. The Mohr circle can be applied...

- Quadric geometric algebra (QGA) is a geometrical application of the G 6 , 3 {\displaystyle {\mathcal {G}}_{6,3}} geometric algebra. This algebra is also...

- is a central goal of algebraic number theory. Let X be the quadric cone of dimension 2, defined by the equation xy = z2 in affine 3-space over a field...

- Augustin-Louis Cauchy saw how their work could be used to cl****ify the quadric surfaces, and generalized it to arbitrary dimensions. Cauchy also coined...

- transformation. A hyperboloid is a quadric surface, that is, a surface defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces...

- certain quadric surfaces. The prin****l tool in this process is "completing the square." Use a translation of coordinates to identify the quadric surface...

- stress quadric are two-dimensional graphical representations of the state of stress at a point. They allow for the graphical determination of the magnitude...

- ellipsoid is a quadric surface; that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces...

- degenerate quadric surfaces. When the prin****l axes of a quadric are aligned with the reference frame (always possible for a quadric), a general equation of the...

- methods for the representation of the stress state at a point include the Lamé's stress ellipsoid and Cauchy's stress quadric. The Mohr circle can be applied...

- Quadric geometric algebra (QGA) is a geometrical application of the G 6 , 3 {\displaystyle {\mathcal {G}}_{6,3}} geometric algebra. This algebra is also...

- is a central goal of algebraic number theory. Let X be the quadric cone of dimension 2, defined by the equation xy = z2 in affine 3-space over a field...

- Augustin-Louis Cauchy saw how their work could be used to cl****ify the quadric surfaces, and generalized it to arbitrary dimensions. Cauchy also coined...

- transformation. A hyperboloid is a quadric surface, that is, a surface defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces...

- certain quadric surfaces. The prin****l tool in this process is "completing the square." Use a translation of coordinates to identify the quadric surface...

- stress quadric are two-dimensional graphical representations of the state of stress at a point. They allow for the graphical determination of the magnitude...

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