FIRST BOOK OF EUCLID'S ELEMENTS, SIMPLIFIED, EXPLAINED, AND ILLUSTRATED, FOR THE USE OF BEGINNERS; WITH ΑΝ APPENDIX, CONTAINING A FEW PROPOSITIONS, OF WHICH THE SOLUTION THE FIRST BOOK OF EUCLID'S ELEMENTS. INTRODUCTORY NOTE. MATHEMATICS, from the Greek μálnμa, signifies science; and it is so called, as it were par excellence, because it is the only branch of knowledge which admits of a rigorous demonstration. It treats of whatsoever has relation to number or magnitude; and GEOMETRY is that particular division of it which investigates the mensuration and properties of lines and angles, of surfaces and solids. Geometry is said to have originated with the Egyptians in the necessity of remeasuring the lands of which the periodical inundations of the Nile continually effaced the boundaries. Hence the science derived its name from the Greek words γῆν and μετρεῖν, or γεωμετρεῖν. Thales of Miletus carried it into Greece, where, from the rude state in which it first existed, it was gradually enriched by the discoveries and demonstrations of Pythagoras, Anaxagoras, Plato, Leodamas, and others, who extended its application to astronomical and other philosophical purposes. Among these, the most celebrated was EUCLID, a native of Alexandria, who flourished in the reign of Ptolemy Lagus, about B. c. 280. He was, in fact, the first who reduced Geometry into the form of a science, by arranging the discoveries of preceding mathematicians, and the results of his own labours, with systematic regularity and order. Some writers have improperly confounded him with Euclid of Megara, who lived more than a century before him. B |