"Geometry is the Science of figured Space. Figured Space is of one two or three dimensions according as it consists of lines surfaces or solids. The boundaries of solids are surfaces; of surfaces lines; and of lines points. Thus it is the province of Geometry to investigate the properties of solids of surfaces and of the figures described on surfaces. The simplest of all surfaces is the plane and that department of Geometry which is occupied with the lines and curves drawn on a plane is called Plane Geometry; that which demonstrates the properties of solids of curved surfaces and the figures described on curved surfaces is Geometry of Three Dimensions. The simplest lines that can be drawn on a plane are the right line and circle and the study of the properties of the point the right line and the circle is the introduction to Geometry of which it forms an extensive and important department. This is the part of Geometry on which the oldest Mathematical Book in existence namely Euclid's Elements is written and is the subject of the present volume. The conic sections and other curves that can be described on a plane form special branches and complete the divisions of this the most comprehensive of all the Sciences. The student will find in Chasles' Aperçu Historique a valuable history of the origin and the development of the methods of Geometry."