ALGEBRA FOR 2529 bil HIGH SCHOOLS AND COLLEGES: CONTAINING A SYSTEMATIC EXPOSITION AND APPLICATION OF THE ELEMENTARY AND HIGHER PRINCIPLES OF THE SCIENCE. BY JAMES B. DODD, A. M., MORRISON PROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY IN NEW YORK: PRATT, WOODFORD, FARMER & BRACE, Entered, according to Act of Congress, in the year 1854, BY JAMES B. DODD, In the Clerks Office of the District Court of Kentucky PREFACE. THE following work is designed to meet the wants of the student at the commencement, and during the continuance, of his Algebraic studies. It aims at the most methodical arrangement, the clearest expositions, the best elementary exercises, the most varied and useful applications-in all these respects presenting some new features, which have been adopted as improvements in the method of teaching this science. It contains all that has been deemed appropriate to an Algebraic treatise, in a general course of mathematical studies, or necessary in preparation for the higher works of the course. To the latter purpose it is believed to be particularly well adapted. The appendage of a Table of Logarithms, and the introduction of logarithmic calculations, were considered necessary to a proper presentation of so important a subject; and will doubtless be generally regarded as enhancing the value of the work. REMARKS ON THE METHOD OF USING THIS WORK, AND CONDUCTING EXAMINATIONS IN ALGEBRA. The following remarks may be useful to the less experienced Teacher using this work, who would make it fully efficient for the purposes intended. 1. The definitions and propositions numbered (1), (2), (3), &c., and the Rules I, II, III, &c., should be accurately memorized and recited by the Student. 2. The accompanying examples, illustrations, or demonstrations, should be required of the Student, and discussed with him on the part of the Teacher, with reference to the principles involved in them. 3. The oral exercises in the earlier parts of the work, should be exacted; and the Student should often be examined on the exercises under the Rules, with his book 4. In the solution of Equations and Problems, he should explain each part of the operation, as exemplified in different parts of the work. 5. The Analysis of Contents (see the next page) will be convenient for reviews on the theory of the science; and such reviews should be frequent. The Student will thus become familiar with the phraseology, principles, and order of the science. 6. The Student's acquisitions will depend very much on the exactness, as well as on the frequency, with which he is examined. The requisitions made on him should |