Page:A History of Mathematics (1893).djvu/62

 By the word 'conoid,' in his book on Conoids and Spheroids, is meant the solid produced by the revolution of a parabola or a hyperbola about its axis. Spheroids are produced by the revolution of an ellipse, and are long or flat, according as the ellipse revolves around the major or minor axis. The book leads up to the cubature of these solids.

We have now reviewed briefly all his extant works on geometry. His arithmetical treatise and problems will be considered later. We shall now notice his works on mechanics. Archimedes is the author of the first sound knowledge on this subject. Archytas, Aristotle, and others attempted to form the known mechanical truths into a science, but failed. Aristotle knew the property of the lever, but could not establish its true mathematical theory. The radical and fatal defect in the speculations of the Greeks, says Whewell, was "that though they had in their possession facts and ideas, the ideas were not distinct and appropriate to the facts." For instance, Aristotle asserted that when a body at the end of a lever is moving, it may be considered as having two motions; one in the direction of the tangent and one in the direction of the radius; the former motion is, he says, according to nature, the latter contrary to nature. These inappropriate notions of 'natural' and 'unnatural' motions, together with the habits of thought which dictated these speculations, made the perception of the true grounds of mechanical properties impossible.[11] It seems strange that even after Archimedes had entered upon the right path, this science should have remained absolutely stationary till the time of Galileo—a period of nearly two thousand years.

The proof of the property of the lever, given in his Equiponderance of Planes, holds its place in text-books to this day. His estimate of the efficiency of the lever is expressed in the