Definitions
from The Century Dictionary.
 noun In geometry, the curve of intersection of any surface with a plane indefinitely near and parallel to the tangentplane at any point.
 noun In the theory of equations, a curve which exhibits the joint effect of the two middle criteria of Newton's rule, in the case of an equation of the fifth degree having all its roots imaginary.
 noun In crystallography, a surface, in general (for a biaxial crystal) an ellipsoid having axes proportional to the principal refractive indexes, whose geometrical characters serve to exhibit the optical relations of the crystal: for a uniaxial crystal the surface becomes a spheroid and for an isotropic crystal a sphere.
from the GNU version of the Collaborative International Dictionary of English.
 noun (Geom. of Three Dimensions) A certain conic section supposed to be drawn in the tangent plane to any surface, and used to determine the accidents of curvature of the surface at the point of contact. The curve is similar to the intersection of the surface with a parallel to the tangent plane and indefinitely near it. It is an ellipse when the curvature is synclastic, and an hyperbola when the curvature is anticlastic.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun mathematics, crystallography An
ellipsoid whose threeaxes represent therefractive indices of ananisotropic crystal forlight following different directions with respect to the crystal axes
Etymologies
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Examples

Quality of a surface such that  by specular reflection or an acute reflection indicatrix  it shows bright reflected lights or the reflected pictures of bright things.
2. Elements Frank Ponemunski 1991

In 1813 he published a pamphlet, "Développement de géométrie pour faire suite à la géométrie pratique de Monge" (Paris, 1813, containing many new and brilliant theories, the most important of which were one relating to the indicatrix of curved surfaces and another on orthogonal surfaces.
The Catholic Encyclopedia, Volume 5: DioceseFathers of Mercy 18401916 1913
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