THE FIRST THREE BOOKS OF EUCLID'S ELEMENTS OF GEOMETRY, FROM THE TEXT OF DR. ROBERT SIMSON, TOGETHER WITH VARIOUS USEFUL THEOREMS AND PROBLEMS, AS GEOMETRICAL EXERCISES ON EACH BOOK. BY THOMAS TATE, MATHEMATICAL MASTER OF THE NATIONAL SOCIETY'S AUTHOR OF "THE PRINCIPLES OF THE DIFFERENTIAL AND INTEGRAL CA∙BO LONDON: PRINTED FOR LONGMAN, BROWN, GREEN, AND LONGMANS, PATERNOSTER-ROW. ADVERTISEMENT. THIS edition of Euclid has been published in a cheap form, with the hope that it may tend to advance the mathematical education of this country, and with an especial reference to the instruction of Schoolmasters who may be desirous of obtaining a Government certificate. EUCLID'S ELEMENTS OF GEOMETRY. BOOK I. DEFINITIONS. I. A POINT is that which hath no parts, or which hath no magnitude. A straight line is that which lies evenly between its extreme points. V. A superficies is that which hath only length and breadth. VI. The extremities of a superficies are lines. VII. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. B |