CALCULATED FOR THE USE OF SCHOOLS, ACADEMIES, BY TOBIAS OSTRANDER, TEACHER OF MATHEMATICS, AND AUTHOR OF THE ELEMENTS OF NUMBERS," "PLANETARIUM," Edy T 198.32,660 HARVARD COLLEGE LIBRARY GIFT OF GEORGE ARTHUR PLIMPTON Entered according to the Act of Congress, August, 1833, by In the Clerk's Office of the District Court of the Southern District of New York. PREFACE. THE mensuration of superficies and solids, is so important a branch of the mathematical science, that no apology is necessary for presenting this work to the public. It is generally known, that that useful branch of education has been too long neglected, and that no production of the kind, well calculated for the use of common schools, has before this, made its appearance. Those who have written on the subject, have calculated their works more particularly for the use of colleges than other seminaries of learning; and consequently the great mass of the people have not had an opportunity of extending their researches beyond the common limits of plain arithmetic; and the farmer and mechanic, who are immediately concerned, have not had the privilege of becoming acquainted with that branch of education which their daily avocations demand. The design of the author is, to remove the evil, and present to the public a production necessary to be understood by every class of citizens, and to aid both teachers and students in acquiring a knowledge of this pleasing, useful, and entertaining branch of science. I have commenced with the work in such a manner, that the student is led along with problems easy and simple, to those of more complicated results, and such as are calculated to exercise his reasoning faculties, and give him an accurate conception of the relation that one figure bears towards another. In the miscellaneous matter will be found some problems, where the student will have ample scope to exercise his ingenuity and improve his understanding. The Key is given to aid such teachers as are not sufficiently acquainted with the science to demonstrate the nature and propriety of |