Newton line should not be confused with Newton-Gauss line.
In Euclidean geometry the Newton line is the line that connects the midpoints of the two diagonals in a convex quadrilateral with at most two parallel sides.
The line segments and that connect the midpoints of opposite sides (the bimedians) of a convex quadrilateral intersect in a point that lies on the Newton line. This point bisects the line segment that connects the diagonal midpoints.
By Anne's theorem and its converse, any interior point P on the Newton line of a quadrilateral has the property that
[\triangleABP]+[\triangleCDP]=[\triangleADP]+[\triangleBCP],
If the quadrilateral is a tangential quadrilateral, then its incenter also lies on this line.