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The design of the present work is to supply beginners with a cheap and easy edition of the first Book of Euclid. The object of the Author in preparing these pages, has been to make the demonstrations as strict and concise as possible, and at the same time to reduce them to the most simple form. In order to afford every facility to the Learner, each demonstration is begun and completed on the same page with the figure to which it refers; so that the inconvenience arising from having the demonstration on one page, and the figure to which it refers very often on another, is completely removed.
Prefixed to the work is an historical Introduction, showing the rise and progress of this science, with the explanations of the principal terms; and at the end is a selection of useful Problems and Theorems as Exercises for Pupils.
GEOMETRY is a science which teaches and demonstrates the properties of lines, angles, surfaces, and solids. The word is from the Greek, and signifies "to measure the earth," it being the necessity of measuring the earth, or portions of land, that first led to the invention of the principles and rules of this art, which has since been extended and applied to magnitudes of all kinds of extension. It is generally believed that the Egyptians have been the inventors of Geometry, and that the annual inundations of the Nile have occasioned the invention. For as that river overflowed its banks, and covered the whole face of the country, it destroyed all landmarks, and confounded the boundaries of men's estates; so that the people were laid under the necessity of inventing certain methods and measures, to enable them to distinguish and adjust the limits of their respective lands, when the waters were withdrawn.
And so highly valued was this science among the Egyptians, that as soon as youths could read, they were taught Geometry and Arithmetic with the greatest possible care. Plato held this science in such high esteem, that on the door of his Academy was read this inscription, "Let none ignorant of Geometry enter here." Another instance which proves how highly it was valued by men of former ages, is, that when a certain person, who was ignorant of Geometry, was desirous to be Xenocrates' auditor, he said, "Go thy way, for thou wantest the very handle to Philosophy."
The writer who has contributed most to the improvement and refinement of this science, is the celebrated Euclid, professor in the Academy at Alexandria, whose Elements will be admired as long as a taste for true science remains. Euclid flourished about 290 years before the Christian era, and of his Elements we have abundance of editions and comments at the present day.