Greeks and Geometry

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Geometry as a word itself originates from the Greek language: Geo=earth, metria=measurement. Geometry therefore is the measurement of earth. But not only for those reasons, Geometry was mathematics for ancient Greeks. All geometry before Greeks seems to have been intuitive - this means that the people were looking for facts relating to measurement without attempting to demonstrate or prove them by a process of deductive reasoning. Greeks brought about a great change to geometry by demonstrating the truth of a proposition. This means that, for example, they sought to understand rules for all right angled triangles through few examples and then apply it to any and all right-angled triangle without exception.

Geometry, because of Greeks, is a science of the properties and relationships of points, lines and surfaces in space.

Try to think for yourself what the following words would mean:

Plane geometry
Geometry of 3 dimensions
Euclidean geometry.

Thales is first of the Greek mathematicians who is credited with taking up the demonstration as the main tool for generalisation of properties of geometrical objects. Some of his most important discoveries are the following:

Any circle is bisected by its diameter.
The angles at the base of an isosceles triangle are equal.
When two lines intersect, the vertical angels are equal.
An angle in a semicircle is a right angle.
The sides of similar triangles are proportional.
Two triangles are congruent if they have two angles and a side respectively equal.

It may seem to you that these are so easy that there is no great achievement in what Thales did. But actually this is precisely where his main achievement lay - he took some of the intuitive statements and suggested a type of geometry where things had to be explained, proved, and applied to any and every case in question. This means that he made geometry abstract.

See other topics in the history of Greek Mathematics

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