MATHEMATICAL TEXTS Edited by PERCEY F. SMITH, PH.D. Professor of Mathematics in the Sheffield Scientific School of ADVANCED ALGEBRA BY HERBERT E. HAWKES, PH.D. ASSISTANT PROFESSOR OF MATHEMATICS IN YALE UNIVERSITY GINN & COMPANY BOSTON NEW YORK CHICAGO LONDON ✓ HARVARD COLLUSE LIBRARY CIFT CF FROF. WILLIAM FOGG C28000 COPYRIGHT, 1905, BY H. E. HAWKES ALL RIGHTS RESERVED 55.10 The Athenæum Press PREFACE This book is designed for use in secondary schools and in short college courses. It aims to present in concise but clear form the portions of algebra that are required for entrance to the most exacting colleges and technical schools. The chapters on algebra to quadratics are intended for a review of the subject, and contain many points of view that should be presented to a student after he has taken a first course on those topics. Throughout the book the attention is concentrated on subjects that are most vital, pedagogically and practically, while topics that demand a knowledge of the calculus for their complete comprehension (as multiple roots, and Sturm's theorem) or are more closely related to other portions of mathematics (as theory of numbers, and series) have been omitted. The chapter on graphical representation has been introduced early, in the belief that the illumination which it affords greatly enlivens the entire presentation of algebra. The discussion of the relation between pairs of linear equations and pairs of straight lines is particularly suggestive. In each chapter the discussion is directed toward a definite result. The chapter on theory of equations aims to give a simple and clear treatment of the method of obtaining the real roots of an equation and the theorems that lead to that |