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[[File:Newton-Gauss Line Default Figure.png|thumb|The line created by connecting the midpoints of all diagonals (''L'', ''M'', and ''N'') is the Newton–Gauss Line.]]
In [[geometry]], the '''Newton–Gauss line''' (or '''Gauss–Newton line''') is the [[Line (geometry)|line]] joining the [[midpoint]]s of the three [[diagonal]]s of a [[complete
The midpoints of the two diagonals of a [[Convex set|convex]] [[quadrilateral]] with at most two parallel sides are distinct and thus determine a line, the [[Newton line]]. If the sides of such a quadrilateral are extended to form a complete quadrangle, the diagonals of the quadrilateral remain diagonals of the complete quadrangle and the Newton line of the quadrilateral is the Newton–Gauss line of the complete quadrangle.
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