Coupon Accepted Successfully!


Euclid’s Definitions

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 space and solids in the space around them, an abstract geometrical notion of a solid object was developed. A solid has shape, size, position and can be moved from one place to another. Its boundaries are called surfaces. They separate one part of the space from another, and are said to have no thickness. The boundaries of the surfaces are curves or straight lines. These lines end in points.

Consider the three steps from solids to points (solids-surfaces-lines-points). In each step we lose one extension, also called a dimension. So, a solid has three dimensions, a surface has two, a line has one and a point has none. Euclid summarized 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:

1. A point is that which has no part.
2. A line is breadthless length.
3. The ends of a line are points.
4. A straight line is a line which lies evenly with the points on itself.
5. A surface is that which has length and breadth only.
6. The edges of a surface are lines.
7. A plane surface is a surface which lies evenly with the straight lines on itself.

In these definitions some of the terms like part, breadth, length etc., are not defined. For defining these terms we need to define many other things, and we may get a long chain of definitions without an end. For such reasons, mathematicians agree to leave some geometric terms undefined. In geometry, we take a point, a line and a plane as undefined terms. We will take only those things that we can represent intuitively or explain them with the help of physical models.


Test Your Skills Now!
Take a Quiz now
Reviewer Name