Elementary Algebra for Schools: With Answers PDF
Preview Elementary Algebra for Schools: With Answers
This is a reproduction of a library book that was digitized by Google as part of an ongoing effort to preserve the information in books and make it universally accessible. https://books.google.com NEDL TRANSFER KD 46052 HN SFDZ M ا ز ر Geb. E.Crosby. (E Ch. S.L.S.S apr.1.1890 ELEMENTARY ALGEBRA FOR SCHOOLS WITH ANSWERS BY H. S. HALL, M.A., FORMERLY SCHOLAR OF CHRIST'S COLLEGE, CAMBRIDGE, MASTER OF THE MILITARY AND ENGINEERING SIDE, CLIFTON COLLEGE. AND S. R. KNIGHT, B.A., FORMERLY SCHOLAR OF TRINITY COLLEGE, CAMBRIDGE, LATE ASSISTANT MASTER AT MARLBOROUGH COLLEGE. FOURTH EDITION. REVISED AND ENLARGED. London: MACMILLAN AND CO. AND NEW YORK. 1887 [TheRightofTranslationisreserved.] KD 46052 HARVARD UNIVERSITY LIBRARY 50*72 PrintedbyC. 7. CLAYand SON, 1885. SecondEdition 1886. ThirdEditionFeb. 1887. FourthEdition, Revised and Enlarged, Oct. 1887. PREFACE. THE present work is an attempt to supply a want which we have long felt ourselves, and which we believe to be shared bymany experienced teachers. In setting before a beginner the real and perplexing difficulties of elementary Algebra, there is some fear lest first lessons should degenerate into a mere mechanical manipulation of symbols, uninteresting and uninstructive, because little understood. This well known danger led us to devote special thought to the question of order; to consider, in short, what succession of the various parts of the subject would best illustrate its bearings at an early stage; and we have finally adopted an arrangement, which if it varies somewhat from the common use of elementarytext-books-is atleastbasedupon theexperience of many years, and embodies the result of frequent con sultation with our colleagues and other teachers. As regards the earlier chapters, our order has been determined mainly by two considerations: first, a desire to introduce as early as possible the practical side of the subject and some of its most interesting applications, such as easy equations and problems; and secondly, the strong opinion that all reference to compound expressions and their resolution into factors should be postponed until the usual operations of Algebra have been exemplified in the vi PREFACE. case of simple expressions. By this course the beginner soonbecomesacquainted with the ordinary algebraical pro cesses without encountering too many of their difficulties; and he is learning at the same time something of the moreattractive parts ofthe subject. Again, bypostponing Resolution into Factorsuntil thestudenthas acquired some freedomand readiness inthe useofsymbols, weareenabled to treat this important section, and all the processes to which it gives rise, more adequately than is possible where factors are introduced and disposed of in one short early chapter. We had originally intended to arrange the chapters in an order that might be followed without deviatio.n from beginning to end; but in the course of the work this was found impossible without very extensive sub division in some parts, and needless repetition in others. Wehavetherefore marked withan asterisk all articles and examples which may conveniently be omitted byastudent whois reading the subject for the first time, and we have occasionally added a note suggesting the most suitableplace fora section whichmayhavetobepostponed. To one feature of the book we wish to draw special attention. After Quadratics we have introduced two re capitulatory chapters in which are discussed certain classes of questions requiring for their solution a very ready and skilful use of factors. Such questions are undoubtedly hard, and wholly out of place at an earlier stage; yet in existing text-books their importance is hardly recognised, and they are generally introduced at a point where the ordinary student cannot use or appreciatethe best methods ofsolvingthem. To theseharder applications ofearlyrules in Chapters XXVIII and XXIX, we have added severaluseful PREFACE. vii miscellaneous theorems illustrated by carefully selected examples. These chapters are the outcome of our own experience in preparing boys for Army and University Examinations during the last twelve years; they will be found very valuable for revision, though they also contain some new and interesting matter. The examples are very numerous, and have been com piled withgreat care. They arefor the mostpart original, though some have been selected from recent Examination Papers. In the early chapters we have given an unusual number of very easy questions, many of which will be found well suited for viva voce work. In each chapter several examples are fully worked out to illustrate the most useful applications of important rules. Also, under the belief that prevalent mistakes are not sufficiently guarded against, we have given occasional notes to caution thereaderagainst the blunders which experience shews to be almost universal among beginners. We have to acknowledge our indebtedness to many kind friends for their valuable help and advice. In the arrangement of the early chapters we have been largely influenced by the opinion of the Rev. J. M. Wilson, Head Master of Clifton College; and practical suggestions re ceived from him have been frequently worked into the text and examples throughout the book. Wehavealsoto express our thanks for the assistance and encouragement freely given by many of our Mathematical colleagues : to the Rev. H. C. Watson and Mr F. H. Stevens of Clifton College we are especially indebted for their practical hints and able criticism; while in revising the manuscript and correctingtheproof sheetstheiraidhas been most generous anduntiring.
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