201 PREFACE. ALGEBRA, the logic of Arithmetic, or universal reasoning, is a science which far surpasses Arithmetic and Geometry in point of application, these two being chiefly fundamental sciences, whilst Algebra not only investigates rules and theorems of its own, but, by an admirable analysis, extends to every branch of mathematical learning, solving with accuracy, brevity, and elegance, the most abstruse and difficult problems. It was by the aid of this science, combined with Geometry, that Newton settled the whole system of the visible world. Hence it is one of the most im portant studies, at once useful and elegant, which can be pursued during the period of education, w Of these truths, every one acquainted with Algebra must be convinced. It is the most refined species of logic; an expert Algebraist cannot fail to be an acute reasoner, not only in the affairs common life, but in all pursuits of Literature and Philosophy. Style itself is characterised by an acquaintance with it. The certainty of its demonstrations allures the mind to a habit of clear and accurate reasoning, which is necessary, in order to keep the imagination in due subjection to the judgment, and prevents the understanding from becoming the dupe of our own weakness, or from being led captive by the wit and eloquence of others. If so important an art has been less taught than it deserves to be in the ordinary Education of British youth, the cause appears to be the want of a neat and compact Elementary Treatise, adapted to the practical use of the school-master, and also, to that economy of price which school-masters are obliged to respect, for the satisfaction of parents. Both these purposes will, it is presumed, be found to be effected by the present work; the Author is himself a school-master, and, a teacher of the mathematics of nearly twenty years experience; and having in his profession had the good fortune to acquire a fair reputation as a teacher, in one of the most populous towns in England, he may be presumed to be qualified for the task which he has undertaken None but school-masters can estimate a school master's difficulties, and few can have a chance of removing them but those who have felt them. It is this circumstance which emboldens the Author of this treatise to calculate on its success. He affects to have made no discoveries, but cherishes the useful ambition of rendering easy and practicable the acquirement of a useful and necessary branch of knowledge, side It need scarcely be remarked to intelligent teachers, that, before a youth commences this study, he ought to be moderately acquainted with the Elements of Arithmetic, and especially versed in the working of Fractions. These facilities may be acquired by y any system of Arithmetic which may be agreeable to the master, for Algebra is a science which grows out of the, general principles. of Arithmetic, and its study may follow any method by which those principles are taught. June, 18, 1829. Classical, Commercial, and Mathematical Academy, Trafalgar-Street, Leeds. |