RAY'S ALGEBRA, PART FIRST: ON THE ANALYTIC AND INDUCTIVE METHODS OF INSTRUCTION: WITH NUMEROUS PRACTICAL EXERCISES. DESIGNED FOR COMMON SCHOOLS AND ACADEMIES. BY JOSEPH RAY, M. D. PROFESSOR OF MATHEMATICS IN WOODWARD COLLEGE VAN ANTWERP, BRAGG & CO., 28 BOND STREET, 137 WALNUT STREET, CINCINNATI, NEW YORK. KDH 490 BCL ECLECTIC EDUCATIONAL SERIES. RAY'S MATHEMATICS. EMBRACING A Thorough, Progressive, and Complete Course in Arithmetic, Algebra, and the Higher Mathematics. Ray's Primary Arithmetio. Ray's Higher Arithmetio. Ray's Plane and Solid Geometry. By Eli T. TAPPAN, A. M., Pres't Kenyon College. 12mo., cloth, 276 pp. Ray's Geometry and Trigonometry. By ELIT. TAPPAN, A. M., Pres't Kenyon College. 8vo., sheep, 420 rp. Ray's Analytic Geometry. By Geo. H. HOWISON, A. M., Prof. in Mass. Institute of Technology, Treatise on Analytic Geometry, especially as applied to the prop. erties of Conics: including the Modern Methods of Abridged Notation. 8vo., sheep, 574 pp. Ray's Elements of Astronomy. By S. H. PEABODY, A. M., Prof. in the Chicago High School. Handsomely and profusely illustrated. 8vo., sheep, 336 pp. Ray's Surveying and Navigation. With a Preliminary Treatise on Trigonometry and Mensuration. By A. SCHUYLER, Prof. of Applied Mathematics and Logic in Bald win University. 8vo., sheep, 403 pp. Ray's Differential and Integral Calculus. Elements of the Infinitesimal Calculus, with numerous examples and applications to Analysis and Geometry. By Jas. G. CLARK, A. M., Prof. in William Jewell College. 8vo., sheep, 440 pr. Entered according to Act of Congress, in the year 1848, by WINTHROP B. SMITH, in the Clerk's Office of the District Court of the United Staces for the District of Phio. HARVARD 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 |