RAY'S ALGEBRA, FIRST BOOK. • PRIMARY ELEMENTS OF ALGEBRA, FOR COMMON SCHOOLS AND ACADEMIES. BY JOSEPH RAY, M. D., LATE PROFESSOR OF MATHEMATICS IN WOODWARD COLLEGE. REVISED ELECTROTYPE EDITION. CINCINNATI: WILSON, HINKLE & Co. PHIL'A: CLAXTON, REMSEN & HAFFELFINGER. NEW YORK: CLARK & MAYNARD. RAY'S 14 Je1426 LIBRARY. Peters R.Peters MATHEMATICAL COURSE. EACH BOOK COMPLETE IN ITSELF, AND SOLD SEPARATELY. PRIMARY ARITHMETIC, OR FIRST BOOK: Simple Mental Lessons and Tables. For little learners. INTELLECTUAL ARITHMETIC, OR SECOND BOOK: the most interesting and valuable Intellectual Arithmetic extant. PRACTICAL ARITHMETIC, OR THIRD BOOK: a full and practical treatise on the inductive and analytic methods of instruction. For Schools and Academies. HIGHER ARITHMETIC, OR FOURTH BOOK: the principles of Arith- ELEMENTARY ALGEBRA, OR FIRST BOOK: a simple, thorough, and ELEMENTS OF GEOMETRY: a comprehensive work on Plane and TRIGONOMETRY AND MENSURATION: Plane and Spherical Trigo- SURVEYING AND NAVIGATION: Surveying and Leveling, Navigation, Barometric Heights, etc. (Preparing.) To be followed by others, forming a complete Mathematical Course for Schools and Colleges. Entered according to Act of Congress, in the year 1866, by SARGENT, WILSON & HINKLE, In the Clerk's Office of the District Court of the United States, for the Southern ELECTROTYPED AT TINKLIN TYPE FOUNDRY CINCINNATI. LIBRARY PREFACE. THE object of the study of Mathematics is two fold-the acquisition of useful knowledge, and the cultivation and discipline of the mental powers. A parent often inquires, "Why should my son study Mathematics? I do not expect him to be a surveyor, an engineer, or an astronomer." Yet, the parent is very desirous that his son should be able to reason correctly, and to exercise, in all his relations in life, the energies of a cultivated and disciplined mind. This is, indeed, of more value than the mere attainment of any branch of knowledge. The science of Algebra, properly taught, stands among the first of those studies essential to both the great objects of education. In a course of instruction properly arranged, it naturally follows Arithmetic, and should be taught immediately after it. In the following work, the object has been to furnish an elementary treatise, commencing with the first principles, and leading the pupil, by gradual and easy steps, to a knowledge of the elements of the science. The design has been, to present these in a brief, clear, and scientific manner, so that the pupil should not be taught merely to perform a certain routine of exercises mechanically, but to understand the why and the wherefore of every step. For this purpose, every rule is demonstrated, and every principle analyzed, in order that the mind of the pupil may be disciplined and strengthened so as to prepare him, either for pursuing the study of Mathematics intelligently, or more successfully attending to any pursuit in life. Some teachers may object, that this work is too simple, and too easily understood. A leading object has been, to make the pupil feel, that he is not operating on unmeaning symbols, by means of arbitrary rules; that Algebra is both a rational and a practical subject, and that he can rely upon his reasoning, and the results |