Euclid Definition
Euclid Definition
Euclid Definition
INTRODUCTION :
The word ' Geometry ' comes from the greek words 'geo' meaning the 'earth', and 'metrien' , mening ' to measure'. Geometry appears to have originated from the need for measuring land. This branch of mathematics was studied in various forms in every ancient civilisation, be it in Egypt, Babylonia, China, India, Greece the Incas, etc. The people of these civilisation faced several practical problems which required the development of geometry in various ways. The greek mathematicians of Euclid's time thought of geometry as an abstract model of the world in which they lived. The notions of point, line, plane (or surface) and so on were derived from what was seen around them. From studies of the sapce and solids in the space around them, an abstract geometerical notion of a solid objects was developed. A solid has shape, size, positions and can be moved from one place to another. Its boundaries are called surfaces. They separate one part of the space from another, and aresaid to have no thickness. The boundaries of the surfaces are curves or straight . These lines end in points.
Consider the three steps from solids to points (solids-surfaces-lines-points).In each steps we lose extension, also called a dimension. So, a solid has three dimensions, a surface has two, a lines has ones and a point has none.Euclid summarised these statements as definitions. He began his exposition by listing 23 definitions in Book 1 of the 'Elements'. A few of them are given below :
If you carefully study these definitions, you find that some of the terms like part, breadth, length, evenly, etc. need to be further explained clearly. For example, consider his definition of a point. In this definition, 'apart ' needs to be defined. Suppose if you define 'a part ' to be that which occupies 'area' , again 'an area' needs to be ddefined. So, to define one thing, you need to define many other things, and you may get a long chain of definitions without an end. For such reasons, mathematicians agree to leave some geometeric terms undefined.
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