into a science, which deals only with the abstract properties and relations of figured space. The term volume, has been introduced in its place, under the belief that it corresponds more exactly to the idea intended. Many other departures have been made from the original text, the value and utility of which have been made manifest in the practical tests to which the work has been sub jected. In the present Edition, numerous changes have been made, both in the Geometry and in the Trigonometry. The definitions have been carefully revised—the demonstrations have been harmonized, and, in many instances, abbreviated-the principal object being to simplify the subject as much as possible, without departing from the general plan. These changes are due to Professor Peck, of the Department of Pure Mathematics and Astronomy in Columbia College. For his aid, in giving to the work its present permanent form, I tender him my grateful acknowledgements. CHARLES DAVIES. COLUMBIA COLLBGA, New York, April, 1862. PAGE. limiting value of Circular Functions, Relations of Circular Functions, Particular values of Certain Functions, Formulas of Relation between Functions and Arcs,.. |