Definition of osculating circle
: a circle which is tangent to a curve at a given point, which lies in the limiting plane determined by the tangent to the curve and a point moving along the curve to the point of tangency, which has its center situated on the normal to the curve at the given point and, also, on the concave side of the projection of the curve onto the limiting plane, and which has a radius equal to the radius of curvature
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First Known Use of osculating circle
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