Excerpt from Famous Problems of Elementary Geometry: The Duplication of the Cube, the Trisection of an Angle, the Quadrature of the Circle

The more precise definitions and more rigorous methods of demonstration developed by modern mathematics are looked upon by the mass of gymnasium professors as abstruse and excessively abstract, and accordingly as of importance only for the small circle of specialists. With a view to counteracting this tendency it gave me pleasure to set forth last summer in a brief course of lectures before a larger audience than usual what modern science has to say regarding the possibility of elementary geometric constructions. Some time before, I had had occasion to present a sketch of these lectures in an Easter vacation course at Gottingen. The audience seemed to take great interest in them, and this impression has been confirmed by the experience of the summer semester. I venture therefore to present a short exposition of my lectures to the Association for the Advancement of the Teaching of Mathematics and the Natural Sciences, for the meeting to be held at Gottingen. This exposition has been prepared by Oberlehrer Tagert, of Ems, who attended the vacation course just mentioned. He also had at his disposal the lecture notes written out under my supervision by several of my summer semester students. I hope that this unpretending little book may contribute to promote the useful work of the association.

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