REVISED BY FREDERICK H. SOMERVILLE, B.S. HEADMASTER, HILLMAN ACADEMY, WILKES-BARRE, PA. FORMERLY OF LAWRENCEVILLE SCHOOL HARVARD COLLEGE LIBRARY GIFT OF COPYRIGHT, 1908, 1913, BY ENTERED AT STATIONERS' HALL, LONDON. EL, ALG. REV. W. P. II PREFACE In arrangement this text follows the plan of the older standard works, supplementing their strong points by the addition of the newer features demanded by modern conditions. A teachable algebra must provide a practical and well-graded general course, and, in addition, must meet the varied requirements of the college entrance standards. In recognition of these needs this text provides certain features, among which may be mentioned the following: 1. Negative numbers are introduced as a direct and natural extension of the arithmetical numbers already familiar. 2. New definitions and symbols are introduced slowly, so that the beginner may not be confused at the outset by a inass of new and strange terms. 3. The difficulties of the beginner are kept constantly in mind, and his progress is assisted by frequent illustrations that are sound and free from technicalities. 4. Oral drills, which form an important part of the early practice, occur wherever practicable. 5. Easy and well-graded exercises, provided in abundance, give constant opportunity for drill work on all important topics. 6. The drill work, which begins with simple exercises, increases in difficulty by gradual steps until it adequately meets the average college requirements. 7. Review exercises, covering both elementary practice and college preparation, are frequent and comprehensive. Special attention is directed to the thorough treatment of the graph, and to the exercises applying the more common formulas used in physics. In both of these subjects the treatment is non-technical, and is easily within the grasp of the young student. In several of the subjects where more than one good method might be given, it has been thought best to suggest a single practical process. One practical method thoroughly mastered is usually best for the young student, who has no need for comparative discussions that interest only the mature mind. In response to the suggestions of several prominent teachers, the drill-work of the text has been increased by more than fourteen hundred new examples. For further practice of an elementary character there has been included an exercise consisting of nine hundred examples so classified as to supple. ment those of the earlier chapters; and for classes whose aim is college preparation a large group based upon recent examination questions has been provided. With these additional drill features, the five thousand examples in the text include more than twelve hundred equations and problems. The author gratefully acknowledges his indebtedness to those friends whose suggestions and encouragment have been of material aid in the preparation of this text. Particular acknowledgment is made to those who have so generously responded with suggestions for the present revision. FREDERICK H. SOMERVILLE. THE WILLIAM PENN CHARTER School, PHILADELPHIA. CONTENTS PAGE 9 Multiplication of a Monoinial by a Monomial . Multiplication of a Polynomial by a Monomial 42 Division of a Monomial by a Monomial Division of a Polynomial by a Monomial. 95 |