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Note on a Theorem connected with the area of a 2n-sided polygon

Published online by Cambridge University Press:  20 January 2009

Thomas Muir
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The theorem is:—Ifa1, a2, a3, …, a22be the middle points of the sides of any convex polygon A1A2A3…A2nthen as regards areas

The following proof depends only on the theorem that the line joining the points of bisection of two sides of a triangle cuts off a triangle equal in area to a quarter of the original triangle.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 2 , February 1883 , pp. 8
Copyright
Copyright © Edinburgh Mathematical Society 1883