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Geometry of the Isosceles Trapezium and the Contra-parallelogram, with applications to the geometry of the Ellipse

Published online by Cambridge University Press:  20 January 2009

R. F. Muirhead
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In Figure 11 let ABCD be a contraparallelogram having AB = CD, AD = BC.

Let O, P, Q, R be the midpoints of AB, BC, AD, DC respectively. They obviously lie in the line parallel to AC and to BD, and equidistant from them.

Let U be the mid-point of AC and V that of BD.

OURV is a rhombus each of whose sides is half of AD or BC, and parallel to AD or BC. PUQV is a rhombus each of whose sides is half of AB or CD, and parallel to AB or CD.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , February 1901 , pp. 70 - 72
Copyright
Copyright © Edinburgh Mathematical Society 1901