Monday, March 15, 2010

The Complete Quadrilateral: The Mid-Diagonal Line

The next stop on our Complete Quadrilateral tour is the Mid-Diagonal line, or the Midline. This line goes by many names. Ripert called it the Axis of Mean Distances (which we will see why in the next stop on the tour). It is also known as the Newton-Guass line, or the Newtonian. Whatever it is called, it is one of the earliest known lines associated with the Complete Quadrilateral.

We begin by drawing the diagonals of the quadrilateral, and constructing their midpoints. Two of the diagonals will be familiar (for example, the A12 to A34 diagonal). One diagonal - from A13 to A24 - will seem a bit odd. Nevertheless, their midpoints are collinear, and this line is the Midline.

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