This classic treatise on geometry is a must-read for students and practitioners of mathematics alike. Edward Olney's clear and concise exposition of the subject is ideal for both beginners and experts, and his insights will deepen your understanding and appreciation of the subject. This edition includes new material on recent developments in the field, making it an essential resource for anyone interested in this fascinating area of study. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.