Principal axes of a quadric


Principal axes 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. [1913 Webster]

Wisdom is the principal thing. --Prov. iv. 7. [1913 Webster]

2. Of or pertaining to a prince; princely. [A Latinism] [Obs.] --Spenser. [1913 Webster]

{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. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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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… …   The Collaborative International Dictionary of English

  • 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… …   The Collaborative International Dictionary of English

  • Principal axis — 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… …   The Collaborative International Dictionary of English

  • Principal challenge — 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… …   The Collaborative International Dictionary of English

  • Principal plane — 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… …   The Collaborative International Dictionary of English

  • Principal point — 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… …   The Collaborative International Dictionary of English

  • Principal ray — 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… …   The Collaborative International Dictionary of English

  • Principal section — 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… …   The Collaborative International Dictionary of English

  • Eigenvalues and eigenvectors — For more specific information regarding the eigenvalues and eigenvectors of matrices, see Eigendecomposition of a matrix. In this shear mapping the red arrow changes direction but the blue arrow does not. Therefore the blue arrow is an… …   Wikipedia

  • Eigenvalue, eigenvector and eigenspace — In mathematics, given a linear transformation, an Audio|De eigenvector.ogg|eigenvector of that linear transformation is a nonzero vector which, when that transformation is applied to it, changes in length, but not direction. For each eigenvector… …   Wikipedia