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An Obvious Demonstration of the 47th Proposition of Euclid

Abstract

SOME years ago in trying for a simpler demonstration of this theorem I worked out the following. Its extreme simplicity suggested that it could scarcely be original; but as some years have elapsed, and as none of my friends have seen it elsewhere, I send it to you as possibly of interest to some and perhaps of use where practical geometry is being taught. It is evident that the two larger squares are equal, the side of each being equal to the sum of the sides AB, AC of the triangle ABC. It is also clear that the four triangles marked “a” are equal to one another. Again, the four triangles marked “b” are equal to one another, and to the four triangles marked “a.”

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BICKERTON, A. An Obvious Demonstration of the 47th Proposition of Euclid. Nature 46, 315–316 (1892). https://doi.org/10.1038/046315d0

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