1. Origin of Geometry. Egyptian Geometry. Geometry is one of the most ancient of all arts and sciences It arose in Babylonia and Egypt in connection with such practical activities as building, surveying, navigating, etc. In fact, the word "geometry" means earth measurement. Herodotus, a Greek historian who traveled in Egypt, says that the annual overflowing of the Nile changed many boundaries in the adjoining farm land. Thus it became necessary to measure the land of each taxpayer every year in order that taxes might be properly adjusted. In this way, he claims, geometry originated in Egypt, and all the classical writers agree with him in calling Egypt the home of geometry. Much new light was thrown on early geometry by the discovery, in recent years, of Babylonian inscriptions and Egyptian .. papyri: A's early as 1700 в.с. an Egyptian scribe, Ahmes, wrote a mathematical treatise containing a number of geometric rules. Even without such written records the enormous architectural works of the ancients their pyramids, obelisks, temples, palaces, and canals would indicate a very respectable insight into geometric relations. 2. Greek Geometry. The early geometry, however valuable it may have been for practical purposes, was deficient in that it consisted simply of a set of rules obtained after centuries of experimenting. How to get a result seemed to be its important question. That this condition did not last indefinitely is due to the genius of the Greeks. Being a race of thinkers and poets, they wished to know why a certain result must follow under a given set of conditions. For many years their wise men studied in Egypt. Upon returning they aroused among their followers a great interest in the study of geometry. Many new truths were now discovered, which were gradually arranged in a system. In this way geometry became a science. After about three hundred years of persistent study the Greeks produced a great masterpiece in the form of Euclid's "Elements of Geometry" (300 в.с.). This was a textbook on geometry, divided into thirteen chapters or "books." It was accepted at once as the great authority on all geometric questions, and has retained much of its importance to this day. 3. Purpose of Geometry. Geometry, in the form given it by the Greeks, is no longer primarily concerned with such practical activities as surveying. Its main purpose is the discovery and classification of the most important properties of points, lines, surfaces, and solids, in their relation to each other. Hence we must find out how the words "solid," "surface," "line," "point," are used in geometry. 4. Space, Solids, and Surfaces. Every intelligent being has a notion of what space is. The schoolroom represents a portion of space. If it were not bounded by walls, or surfaces, it would extend indefinitely. Therefore we see that a completely inclosed por tion of space arises only when there exist bounding surfaces. Any limited portion of space is a geometric solid. Solids are bounded by surfaces. 5. Lines and Points. Again, the walls of the schoolroom would extend indefinitely if they were not bounded. But they are bounded by their intersections, the edges of the room. These edges are lines. Finally, these edges, or lines, would extend indefinitely if they did not terminate each other by their intersections. The intersections of lines are points. 6. A surface may be considered by itself, without reference to a solid. A line may be considered by itself, without reference to a surface. A point may be considered by itself, without reference to a line. |