THE great Utility of a complete System of pure and mixed Mathematics, calculated to be put into the hands of a youth, as soon as he has become acquainted with the rules of Arithmetic, is too obvious to be insisted upon. Hitherto, no well-adapted volume for such general purpose has existed. A separate treatise of Algebra limits the energies of the Student to that science, and he appears to be pursuing it for its own sake; but all the branches of Mathematics are connected, and many advantages will result from the Books of Euclid being read at the same time that the student is engaged in Algebra. Again, the extension and application of these become apparent in the subsequent chapters, and an incentive is created to go through the course. The collected price of separate books in various branches of Mathematics far exceeds the cost of this volume; and distinct works on each subject are generally too full in their details, and too prolix, for the purposes of students. These, and many other reasons, will be apparent to all intelligent persons; and incalculable advantages must accrue to the rising generation from the power, thus possessed by every Tutor, of bringing the whole of these sciences at one view before his Pupils. Nor will the work be without its uses as a Text and Reference Book in our Universities, among whose Students it will serve, at least, as a chain connecting all the branches of mathematical study, and, in its several parts, will often assist in rendering obvious the sense of abstruse treatises in particular branches of these noble sciences. Every mathematician, of the present day, must be aware of the existence of a work, published upwards of a century ago, under the title of "WARD'S YOUNG MATHEMATICIAN'S GUIDE;" and many of them, particularly the self-taught, will readily acknowledge their obligations to it in the commencement of their studies. Nevertheless, Ward's book is an imperfect and limited series; and, since the great improvements in the principles of analysis, it has become altogether obsolete. It is a book which suggested the idea of the present volume; but it has by no means served as its model either in plan or execution. Ward's Guide commenced with the principles of Arithmetic; but the present system supposes that the Student has previously rendered himself familiar with that science. His book, also, was limited to practical Geometry, with little or no theory; whereas, the present work includes, not on the whole of Euclid, printed literally from Dr. Simscrr edition, but it also includes Conic Sections, and the entire doctrine of Curves, with their application to various branches of science and philosophy. The Algebra of Ward is, also, not only altogether obsolete, but did not extend beyond Quadratic Equations; while these Elements include the solution of all manner of Equations, together with Fluxions, and the Differential Calculus, according to the most approved theories and practices. As an introduction to Mathematics, for the use of Schools, and Students in general, the present volume possesses, therefore, original pretensions to the favour of the public. Other systems, of more recent date than Ward's, have appeared; but, on comparison, it will be found that no one is more comprehensive in its objects, or more compact in its details; while, in regard to the various improvements in Mathematics, which have been made by the great analists of France, England, and Germany, it will, as a general elementary book, be considered, by enlightened Mathemati cians, not inferior to any similar work in the English or any modern language. By means of economy in printing, the Author has been enabled to attempt more, within the same number of pages, than has previously been effected by works of greater magnitude, but printed in a larger type. He has thus been empowered to present to the public a complete body of Mathematics, at a price which accords with the often-limited resources of students. Of course, in such a work, it has been less the object of the Editor to invent, than to compile with discretion, and arrange with judgment. At the same time, he trusts it will be discovered, that, in every part where originality was required, he has supplied many deficiences, and corrected the errors of some of his predecessors. A few of the chapters have been adapted to the purposes of this publication from separate tracts of his own, and others have been originally compiled from materials which at present lie scattered in various expensive works. To confer every possible perfection on this work, a series of correct Logarithmic and Trigonometrical Tables have been subjoined; and a collection of upwards of two hundred Miscellaneous Questions have been introduced as exercises on the various subjects discussed through the volume. For the use of Tutors, a separate KEY has been printed, which contains Answers, worked at length, not only to the Questions alluded to, but also to all the oth Questions and Froblems scattered throughout the volume. Claremont-Place, Brunswick-Square. P. N. The Addition and Substraction of Surd Quantities The Multiplication and Division of Surd Quantities 89 On the Involution and Evolution of Surd Quantities 90 On the method of finding Multipliers which shall render Binomial Surd Quantities Rational Theory and Arithmetic of Sines Calculation of the Tables of Sines, by Series Solution of the Cases of Plane Triangles Triigonometry applied to Heights and Distances Miscellaneous Examples on Heights and Distances Application of the preceding Principles and Pro- Example of Right-Angled Spherical Triangles ble Quantities 496 Descriptions of Instruments useful in Projections ib. PROJECTION OF A SPHERE IN PLANO STEREOGRAPHIC PROJECTION OF A SPHERE DIALLING On the Integration of Fluxions containing several varia- 347 551 561 577 591 |