will understand perfectly what he is about, and he will thereby be enabled to encounter those, which are difficult. When the learner is directed to turn back and do in a new way, something he has done before, let him not fail to do it, for it will be necessary to his future progress; and it will be much better to trace the new principle in what he has done before, than to have a new example for it. The author has heard it objected to his arithmetics by some, that they are too easy. Perhaps the same objection will be made to this treatise on algebra. But in both cases, if they are too easy, it is the fault of the subject, and not of the book. For in the First Lessons, there is no explanation; and in the Sequel there is probably less than in any other books, which explain at all. As easy however as they are, the author believes that whoever undertakes to teach them, will find the intellects of his scholars more exercised in studying them, than in studying the most difficult treatise he can put into their hands. When the learner feels, that the subject is above his capacity, he dares not attempt any thing himself, but trusts implicitly to the author; but when he finds it level with his capacity, he readily engages in it. But here there is something more. The learner is required to perform a part himself He finds a regular part assigned to him, and if the teacher does his duty, the learner must give a great many explanations which he does not find in the book. TABLE OF CONTENTS. Introduction. Containing a brief explanation of the purpose of algebra, and of some of the signs Coefficients, what II. Questions producing simple equations, in which the unknown quantity is divided by known quan- III. Questions producing simple equations, in which the unknown quantity is added to known quan- IV. Questions producing simple equations, in which V. Questions producing simple equations, in which quantities consisting of two or more terms are to VI. Questions producing simple equations, in which PAGE. them having the sign before them, are to be sub- Case of fractions to be subtracted, when some of the terms in the numerator have the sign XXI. A few abstract examples in equations XXII. Miscellaneous Questions producing simple XXIII. Questions producing simple equations involv- ing more than two unknown quantities XXIV. Negative quantities, explanation of them XXV. Explanation of negative exponents XXVI. Examination of general formulas, to see what values the unknown quantities will take for par- ticular suppositions made upon the known quan- XXVII. Questions producing equations of the second XXVIII. Extraction of the second root |