THE ELEMENTS OF ALGEBRA DESIGNED FOR THE USE OF SCHOOLS, BY THE REV. J. W. COLEN SO, M.A., RECTOR OF FORNCETT ST. MARY, NORFOLK, AND LATE FELLOW OF ST. JOHN'S COLLEGE, CAMBRIDGE. PART I. Sixth Edition, REVISED AND CORRECTED. LONGMAN AND CO., LONDON. MDCCCXLVIII. [Fourteenth Thousand.] ADVERTISEMENT. In this Edition (which is stereotyped, and so will be secured from further change) the Simpler Parts, those, namely, suited for general School purposes and required for the attainment of an ordinary B. A. degree in the University of Cambridge, are printed separately as Part I.; to which is appended a large collection of easy Miscellaneous Examples, specially adapted to the contents of this Part, and supplying means of complete Examination in them. It will be seen that the easiest kinds of Simple Equations and Equation Problems are in this Edition introduced much earlier than is usual in Treatises on Algebra: but there can be no reason why this branch of the subject, which is so interesting to most Students, and gives them some idea of the practical applications of the Science, should not be brought forward as soon as possible. Part II. is in the Press, and will contain the higher parts of the Subject, with such additional remarks on the earlier portions as will suit the wants of more advanced and promising Students. This Part may be begun as soon as the Student, having thoroughly mastered Part I., has entered upon the Miscellaneous Examples. The errata given below should be corrected at once, before using the book. They will not appear in future impressions. A Key to Part I. is in the Press and will be ready after Christmas. 23, Ex. 16, 2, for x2+x-15 read x2 + 2x - 15. 36, line 13, for vaa read a1. 62, Ex. 36, 12, for 5a in numerator read 5a3. 85, Ex. 47, 16, for two thirds read one third. 86, Ex. 47, 22, for 72 read 42; for twice read also; for 18 read 27 13 13 91, Ex. 49, 3, for 1V{xy' &c. read 1V/{x3y2 &c. Misc. Ex. 73, for 6x read 2x ̄1. 66 3 73, for 96, 6x read 96 x, 2x. 194, for |