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things in the following pages, and am ready to acknowledge, that I have used an unreserved freedom in selecting from their works, wherever I found them to answer my purpose. To Dr. Hutton I am particularly obliged, and am so far from desiring to supersede the use of his performance by this publication, that I only wish it to be thought a useful introduction to it. His treatise is excellent in its kind; and had it been as well calculated for the use of the uninformed Artist as it is for the Mathematician, the following compendium had certainly never been published.

The method I have observed in composing this work, is that which was used in the “ Scholar's Guide to Arithmetic ;” and, as my object has been to facilitate the acquirement of the same kind of useful knowledge, I am not without hopes of its being received with equal candor and approbation.

In school-books, and those designed for the use of learners, it has always appeared to me, that plain and concise rules, with proper exercises, are entirely sufficient for the purpose. In science, as well as in morals, example will ever enforce and illustrate precept; for this reason, an operation, wrought out at length, will be found of more service to beginners than all the tedious directions and observations that can possibly be given them. From constant experience I have been confirmed in this idea, and it is in pursuance of it that I have formed the plan of this publication. I have not been ambitious of adding much new matter to the subject: but only to arrange and methodize it in a manner more easy and rational than had been done before.

The text part of the work contains the rules in words at length, with examples to exercise them; and, in order that the learner may not be perplexed and interrupted in his progress, the remarks and demonstrations are confined to the notes, and may be consulted or not, as shall be thought necessary. To those who would

wish not to take things upon trust, but to be acquainted with the grounds and rationale of the operations they perform, they will be found extremely serviceable: and for this purpose I have endeavored to make them as easy as the nature of the subject would admit. But they can be consulted only by such as have made a previous acquaintance with several other branches of mathematical learning.

Some of the most difficult rules relating to the surfaces of solids, &c. could not be conveniently given, but by means of algebraical theorems; and as this was foreign to my purpose, I have not scrupled to omit them; being well persuaded that what is done upon that head will be fully sufficient to answer most practical purposes. In the Practical Geometry, likewise, which is prefixed to this treatise, such problems only are introduced as were known to be most intimately connected with the subject. And as this part of the work is a

proper

and
necessary

introduction to the rest, I have spared no pains in making it as clear and intelligible as possible.

Upon the whole, I have endeavored to consult the wants of the learner, more than those of the man of science. And if I have succeeded in this respect, my purpose is answered. I have not sought for reputation as a mathematician, but only to be useful as a tutor.

N. B. The favorable reception this work has met with, has induced me in this edition to make such alterations and additions as have since occurred to me, and which are such as I hope will render it still more acceptable to the public. Royal Academy, Woolwich,

July 14, 1807.

ADVERTISEMENT.

The favourable reception and great demand for BONNYCASTLE's MENSURATION and PRACTICAL GEOMETRY, since its first publication in this country, induced me to publish the present edition, which contains not only the whole of that valuable work, but all that is most useful in Hutton, Hawney, Ingram, and other modern works on the same subject.

To this edition is also added an article on MECHANICS and Dynamics, containing the principal problems in Brunton's Mechanics :—that is, Falling Bodies; the Pendulum ; the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge, and the Screw, which are usually called the six Mechanical Powers ; Velocity of Wheels ; Steam Engine ; Water Wheels ; and Pumps.

JAMES RYAN. New York, Oct. 1st, 1833.

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