BY JEREMIAH DAY, D.D. LL.D., LATE PRESIDENT OF YALE COLLEGE. A NEW EDITION.-FIFTEENTH THOUSAND. WITH ADDITIONS AND ALTERATIONS, BY THE AUTHOR, AND PROFESSOR STANLEY NEW HAVEN: PHILADELPHIA: H. C. PECK & T. BLISS. KE 12558 HARVAR Entered according to Act of Congress, in the year 1852, in the Clerk's Office of the District Court of Connecticut. PREFACE. THE following summary view of the first principles of algebra is intended to be accommodated to the method of instruction generally adopted in the American colleges. The books which have been published in Great Britain on mathematical subjects, are principally of two classes.-One consists of extended treatises, which enter into a thorough investigation of the particular departments which are the objects of their inquiry. Many of these are excellent in their kind; but they are too voluminous for the use of the body of students in a college. The other class are expressly intended for beginners; but many of them are written in so concise a manner, that important proofs and illustrations are excluded. They are mere text-books, containing only the outlines of subjects which are to be explained and enlarged upon, by the professor in his lecture room, or by the private tutor in his chamber. In the colleges in this country, there is generally put into the hands of a class, a book from which they are expected of themselves to acquire the principles of the science to which they are attending: receiving, however, from their instructor, any additional assistance which may be found necessary. An elementary work for such a purpose, ought evidently to contain the explanations which are requisite, to bring the subjects treated of within the comprehension of the body of the class. If the design of studying the mathematics were merely to obtain such a knowledge of the practical parts, as is required for transacting business; it might be sufficient to commit to memory some of the principal rules, and to make the operations familiar, by attending to the examples. In this mechanical way, the accountant, the navigator, and the land surveyor, may be qualified for their respective employments, with very little knowledge of the principles that lie at the foundation of the calculations which they are to make. But a higher object is proposed, in the case of those who are acquiring a liberal education. The main design should be to call into exercise, to discipline, and to invigorate the powers of the mind. It is the logic of the mathematics which |