TREATISE ON THE ELEMENTS OF ALGEBRA. BY JAMES BRYCE JUN., M.A. F.G.S. CORRESPONDING MEMBER OF THE ROYAL GEOLOGICAL SOCIETY OF CORNWALL; MEMBER OF THE GEOLOGICAL SOCIETY OF DUBLIN, ETC.; AND MASTER OF THE MATHEMATICAL SCHOOL IN THE BELFAST ACADEMY. EDINBURGH, ADAM AND CHARLES BLACK; LONGMAN AND CO. LONDON; JOHN CUMMING, DUBLIN; J. BRASH AND CO. GLASGOW. 1837. PREFACE. THIS Work was originally undertaken at the suggestion of Dr. JAMES THOMSON, who, in common with other persons interested in mathematical education, had long wished for an elementary treatise on Algebra, better adapted to the purposes of instruction than any which had appeared. When it was first announced as preparing for publication, a near relative of the Author's was to have been associated with him in its execution; but circumstances having occurred which withdrew that gentleman from mathematical pursuits, the only portions of the Work composed by him, are-the Definitions, the explanatory parts of Addition and Subtraction, and Note B at the end, which contains a defence of the views on which the Definitions are founded. Great pains have been taken to express the Definitions and Rules in the most simple and accurate manner, so that their meaning should be at once apparent, and that the student should from the first be accustomed to the most rigid mathematical exactness. As the theory of every operation is fully given, and a copious collection of examples subjoined to each Rule, this Treatise combines more theory and practice than any hitherto published: and it has therefore been necessary, in order that the Work might sell at a moderate price, to omit several subjects usually embraced in books on Algebra. These will be treated of in a separate Work, which will form a supplement to this Volume. The intelligent teacher will perceive that it is of great importance to introduce Equations, and questions producing Equations, at an early period of the student's progress. The examples of Simple Equations are so arranged, that a few of them may be used after the student is acquainted with Addition and Subtraction; a few more after he has learned Division; the rest will require a knowledge of Fractions and Surds. If Equations be taught in this way, the examples which can be solved without Fractions and Surds will not be found sufficiently numerous; but others may easily be constructed upon the same plan. regular treatise, it is necessary to bring together all that relates to the same subject, in whatever order the subjects themselves may be taken up; but in the practice of teaching, it is not desirable to adhere strictly to this arrangement. In a The Author cannot conclude without stating, that he is indebted to the two gentlemen already mentioned for advice and assistance on various subjects contained in this Work. Belfast Academy, Oct. 21, 1837. |