Abstract
THE great geometrician Euclid, before demonstrating to us the various propositions contained in his “Elements of Geometry” requires that we should be able to effect certain processes. These Postulates, as the requirements are termed, may roughly be said to demand that we should be able to describe straight lines and circles. And so great is the veneration that is paid to this master-geometrician, that there are many who would refuse the designation of “geometrical” to a demonstration which requires any other construction than can be effected by straight lines and circles. Hence many problems—such as, for example, the trisection of an angle—which can readily be effected by employing other simple means, are said to have no geometrical solution, since they cannot be solved by straight lines and circles only.
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