FOR HIGH SCHOOLS: CONTAINING THE ELEMENTARY AND THE HIGHER PRINCIPLES A NEW AND IMPROVED EDITION, WITH AN APPENDIX ON BY JAMES B. DODD, A. M., MORRISON PROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY IN TRANSYLVANIA UNIVERSITY. NEW YORK: PRATT, OAKLEY & COMPANY, HARVARD Entered, according to Act of Congress, in the year 1856, In the Clerk's Office of the District Court of Kentucky. Stereotyped by JONES & DENYSE, 183 William-Street, New York. PREFACE. THE first ten Chapters of this work, with an Appendix containing Geometrical Definitions and Practical Mensuration, constitute the author's revised Elementary and Practical Arithmetic. With the additional Chapters, the work will be found to contain a very complete arrangement of principles and exercises, adapted alike to elementary and to higher education in this Science. The concluding Chapter, on mathematical Probabilities and their applications to Life Annuities and Life Insurance, has not been given on account of its practical utility to the business man, though it is manifestly not without such utility; but because its expositions must be matters of interest to the liberal scholar, in a merely theoretical point of view. These subjects have probably not been treated, in a demonstrative manner, in any other educational work known in this country. In the author's elementary work, which, as abovementioned, consists of the first ten Chapters of this, with an Appendix, the Teacher will find all that is essential to a preparatory or a business education in Arithmetic. When the pupil is to be put on a more |