employ a process, with the rationale of which he is not already The reference by Articles will always enable him acquainted. to trace any subject back to its first principles. The limits of a preface will not permit a statement of the peculiarities of the work, nor is it necessary, as those who are interested to know, will examine it for themselves. It is, however, proper to remark, that Equations of the Second Degree have received more than usual attention. The same may be said of Radicals, of the Binomial Theorem, and of Logarithms, all of which are so useful in other branches of mathematics. On some subjects it was necessary to be brief, to bring the work within suitable limits. For example, what is here given of the Theory of Equations, is to be regarded merely as an outline of the more practical and interesting parts of the subject, which alone is sufficient for a distinct treatise, as may be seen by referring to the works of Young or Hymers in English, or of DeFourcy or Reynaud in French. Some topics and exercises deemed both useful and interesting, will be found here, not hitherto presented to the notice of students. But these, as well as the general manner of treating the subject, are now submitted, with deference, to the intelligent educational public, to whom the author is already greatly indebted for the favor with which his previous works have been received. WOODWARD SCHOOL, May, 1852. NOTICE. A KEY to this work, containing solutions to the more difficult problems, with remarks and suggestions, intended principally for private students, will soon be published. The Key also embraces the DIOPHANTINE and INDETERMINATE ANALYSIS, with the NOTATION OF NUMBERS, &c., subjects not usually contained in the ordinary course of instruction in Higher Algebra THEOREMS-FACTORING-GREATEST COMMON ALGEBRAIC THEOREMS-Square of the sum of two quantities. What the reciprocal of a quantity is equal to. Any quantity whose exponent is 0 is =1.... a2m+1+b2m+1 is divisible by a-t-b 88 95 96-108 109-113 SUPPLEMENT TO EQUATIONS OF THE FIRST DEGREE. Generalization-Formation of Rules Examples .162-163 |