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From The Collaborative International Dictionary of English v.0.48:
Osculatrix \Os`cu*la"trix\, n.; pl. Osculatrixes. [NL.] (Geom.) A curve whose contact with a given curve, at a given point, is of a higher order (or involves the equality of a greater number of successive differential coefficients of the ordinates of the curves taken at that point) than that of any other curve of the same kind. [1913 Webster]