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From: Webster's Revised Unabridged Dictionary (1913)

 Ho·mol·o·gous a.  Having the same relative position, proportion, value, or structure. Especially: (a) Geom. Corresponding in relative position and proportion.
    In similar polygons, the corresponding sides, angles, diagonals, etc., are homologous.   --Davies & Peck (Math. Dict.).
 (b) Alg. Having the same relative proportion or value, as the two antecedents or the two consequents of a proportion. (c) Chem. Characterized by homology; belonging to the same type or series; corresponding in composition and properties. See Homology, 3. (d) Biol. Being of the same typical structure; having like relations to a fundamental type to structure; as, those bones in the hand of man and the fore foot of a horse are homologous that correspond in their structural relations, that is, in their relations to the type structure of the fore limb in vertebrates.
 Homologous stimulus. Physiol. See under Stimulus.