It is a part of the history of man, which, like that of his domestic habits and daily occupations, has been too seldom the subject of research; having been thrust aside by the more dazzling topics of war and political revolutions. We are not often conducted by historians within the houses or huts of our ancestors, as they were centuries ago, and made acquainted with their domestic utensils and domestic arrangements. We see too little both of the conveniences and inconveniences of their daily and ordinary life. There are, indeed, rich materials for interesting details on these particulars to be collected from the labors of Goguet and Beckmann, Henry and Turner; but still, a thorough and well-written history of those inventions in the mechanic arts which are now commonly known is a _desideratum_ in literature. Human sagacity, stimulated by human wants, seizes first on the nearest natural assistant. The power of his own arm is an early lesson among the studies of primitive man. This is animal strength; and from this he rises to the conception of employing, for his own use, the strength of other animals. A stone, impelled by the power of his arm, he finds will produce a greater effect than the arm itself; this is a species of mechanical power. The effect results from a combination of the moving force with the gravity of a heavy body. The limb of a tree is a rude, but powerful instrument; it is a lever. And the mechanical powers being all discovered, like other natural qualities, by induction (I use the word as Bacon used it) or experience, and not by any reasoning _a priori_, their progress has kept pace with the general civilization and education of nations. The history of mechanical philosophy, while it strongly illustrates in its general results the force of the human mind, exhibits in its details most interesting pictures of ingenuity struggling with the conception of new combinations, and of deep, intense, and powerful thought, stretched to its utmost to find out or deduce the general principle from the indications of particular facts. We are now so far advanced beyond the age when the principal leading, important mathematical discoveries were made, and they have become so much matter of common knowledge, that it is not easy to feel their importance, or be justly sensible what an epoch in the history of science each constituted. The half-frantic exultation of Archimedes, when he had solved the problem respecting the crown of Hiero, was on an occasion and for a cause certainly well allowing very high joy. And so also was the duplication of the cube.