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THE various works of Dr. Hutton have ever been held in high estimation by a numerous class of instructors, and the intrinsic excellence of his Course of Mathematics has been universally acknowledged.
During the lapse of the last twenty or thirty years, the achievements in science have been varied and extensive. In the higher branches of Mathematics, several elegant and useful theoretical researches have added considerably to the previous stock of knowledge; while in the elementary branches many new and valuable arithmetical processes have been discovered, affording additional facilities to the practical computist. Were proof of this necessary, we have only to refer to the valuable discovery of M. Sturm for the separation of the real and imaginary roots of equations of all degrees—a subject on which energies of every order have been hitherto unavailingly exerted, but which has now yielded to the talents and industry of this ingenious and distinguished continental mathematician. Not less valuable and important have been the results of the researches of our countryman, the late W. G. Horner, of Bath, especially his beautiful, simple, and effective process for the evolution of the roots of numerical equations; which, combined with the theorem of Sturm, furnishes the student with ample means for the complete resolution of any numerical equation whatever.
The Editor of this edition of Hutton's Course has availed himself of these valuable discoveries; and, thinking that a work on elementary mathematics would now be considered incomplete without them, he has not scrupled to devote a sheet or two of this work to the important subject of Equations.
In this edition several alterations have been made, and, it is hoped, many improvements have been introduced. The whole of the work has been thoroughly revised; every example has been recomputed; and the matter has also been subjected to a somewhat different arrangement. The plane, solid, and spherical Geometry, and also the Geometry of the Conic Sections, have been placed continuously; and the Differential and Integral Calculus have been made to precede Mechanics. This arrangement has enabled the Editor to introduce into Mechanics the language of the Calculus, without which little or no progress can be made in Dynamics. To enumerate the various changes that have been made in the work would be altogether unnecessary. The more prominent of these are-a new rule for the extraction of the cube root; new and simple demonstrations of the binomial and exponential theorems; the complete analytical investigation of several important problems in trigonometrical surveying; the method of least squares; besides many other investigations and examples, which, it is hoped, will be highly acceptable and useful to the student.
The subject of Mechanics is now divided into Statics and Dynamics; and several additions have been made to this part as well as to the Integral Calculus; though, from the limits of the work, the Editor has not been able to introduce so much on these interesting and highly useful branches of study as he could have desired.
A new, correct, and improved edition of Hutton's Course has been a desideratum for several years; and while the present edition is intended to supply the deficiency, it has likewise been assimilated to the course of instruction now pursued in the Royal Military Academy, over which the Author so ably presided for many years; and, from the attention bestowed on the computations and investigations, and the exercise of a careful supervision of the work as it has emanated from the press, the Editor trusts that the present edition will be found to be the most correct of any extant.
Royal Military Academy, Woolwich,