EUCLID'S ELEMENTS OF PLANE GEOMETRY. WITH EXPLANATORY APPENDIX, AND SUPPLEMENTARY PROPOSITIONS. ADAPTED FOR THE USE OF SCHOOLS, OR FOR SELF-INSTRUCTION. BY W. D. COOLEY, A.B. LONDON: WHITTAKER AND CO., AVE MARIA LANE. PRINTED BY JAMES HOLMES, TOOK'S COURT, CHANCERY LANE. 1840. 503. PREFACE. EUCLID'S volume on the Elements of Geometry has been regarded for more than two thousand years as the ground-work of Mathematical Science. It has been translated into the language of almost every nation pretending to the least degree of intellectual refinement; and in the more civilized countries of Europe, where mathematical studies have been prosecuted with so much success, and where so many rival treatises have been composed, the work of the Greek Geometrician still retains its pre-eminence, and is generally adopted as the Introduction to the Scientific Course. Such universal and steadfast approbation can be ascribed only to the intrinsic value of the work which is the object of it; and, indeed, such is the excellence of Euclid's Elements, that if all the merit of that work belonged to a single author, he might be deservedly ranked not only as the greatest man of antiquity, but even as one who, in fertility of genius, and in extent of conquest over the domains of demonstration, has far outdone the NEWTONS, EULERS, LAGRANGES, and LAPLACES of modern times. Euclid was not, however, so much the author as the compiler of the work which bears his name. Geometry had engaged, from an early age, the earnest attention of the most eminent Greek philosophers; but the fruits of their ingenuity lay widely scattered, till Euclid, collecting them together, linked them into a system, and gave to the body of hitherto isolated and disjointed truths, plan, |