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PREFACE.

THE design of the present work is to afford an elementary text-book of a practical character, adapted to the wants of a community, where every day new demands arise for the applications of science to the useful arts. There is little to be done, in such an undertaking, except to collect, arrange, and simplify, and to adapt the work, in all its parts, to the precise place which it is intended to fill.

The introduction into our schools, within the last few years, of the subjects of Natural Philosophy, Astronomy, Mineralogy, and Chemistry, has given rise to a higher grade of elementary studies; and the extended applications of the mechanic arts call for additional information among practical men.

To understand the most elementary treatise on Natural Philosophy, or the simplest work on the Mechanic Arts, some knowledge of the principles of Geometry is indispensable; and yet, those in whose hands such works are generally placed, feel that they have hardly time to go through with a full course of exact demon

stration.

The system of Geometry is a connected chain of rigorous logic. Every attempt to compress the reasoning, by abridging it at the expense of accuracy, has been uniformly and strongly condemned.

It is the object of the present work to present all the important truths of Geometry in such a way as to render them accessible to the general reader, without departing from the exactness of the geometrical methods. This, it was thought, could be done only by omitting the demonstrations altogether, and relying for the impression of each particular truth on the accuracy of the enunciation and the illustrations of the diagram. In this way, it is believed that all the properties of the geometrical figures may be learned in a few weeks; and after these properties are carried out in their practical applications, the mind receives a conviction of their truth little short of what is afforded by rigorous demonstration.

The work is divided into five parts. Part I. Explains the properties of the geometrical figures. It is, indeed, a complete course of Geometry, (if the term is admissible,) with the difference only that the demonstrations are omitted.

Part II., entitled "Practical Geometry," explains the construction of the Geometrical figures, the construction of scales, and the various uses to which they are applied.

Part III. contains the application of the principles of Geometry to the mensuration of surfaces and solids. A separate rule is given for each case, and the whole is il lustrated by numerous and appropriate examples.

Part IV. is the application of the preceding parts to Artificers' Work. It contains full explanations of all the scales and measures used by mechanics-the construc

tion of these scales-the uses to which they are applied -and specific rules for the calculations and computations which are necessary in practical operations.

Part V. explains the nature and properties of matter, the laws of motion and equilibrium, and the principles of all the simple machines.

From the above explanations, it will be seen that the work is entirely practical in its objects and character. Many of the examples have been selected from a small work somewhat similar in its object, recently published in Dublin, by the Commissioners of National Education. Some examples have also been taken from Bonnycastle's Mensuration, and the Library of Useful Knowledge was freely consulted in the preparation of Part V.

The author has indulged the hope that the Arithmetic, First Lessons in Algebra, and First Lessons in Geometry, will form a practical course of mathematical instruction adapted to the wants of Academies and the higher grade of schools.

Hartford, July, 1839.

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