Saturday, April 7, 2012


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Geometry is the branch of mathematics dealing with the relations, properties, and the measurements of solids, surfaces, lines, points, and angles. The mathematician Euclid is often considered the Father of geometry. He is most well known for his book, The Elements. He was also the author of the most successful textbook next to Autolycusi’s Sphere.

Euclid was born around 5 BC and died about 65 BC in Alexandria, Egypt. His birthplace is unknown. Very little is known about Euclid’s life because the name Euclid was very popular at that time5. He was most likely a Greek that traveled to Alexandria to learn and teach. In Alexandria, he most likely founded a school of mathematics. Also, it is a possibility that he studied with Plato’s students due to his familiarity to the geometry of Eudoxus and Theaetetus5.

Euclid wrote his famous book The Elements when he was around thirty years old. It is quite long, spanning thirteen books. In it, Euclid compiled and systematically arranged many of the major mathematical results known during his time, besides adding his own findings. His book makes up the core of basic mathematics even today. Unfortunately, no original copies from his time have been found. However, some fragments of The Elements have been found in potshards in Egypt and on pieces of papyrus dating around 100 BC. The earliest copy of his book dates around 888 BC. The Elements has been used in schools until 1014.

The beginning of his book starts with a list of definitions, postulates, and axioms, which he used to prove proposition after proposition. His method has served as the standard for scientific argumentation for other generations (proofs). The volumes are Books 1-6 Plane Geometry. Books 7- Number Theory. Book 10 Euxodus’ Theory of Irrational numbers. Books 11-1 Solid Geometry.

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The first five postulates in his book are these1

1. (It is possible) to draw a straight line from any point to any point.

. (It is possible) to produce (continue) a finite straight line in a straight line.

. (It is possible) to describe a circle with any center and distance (radius).

4. All right angles are equal to each other.

5. If a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

The first three postulates are postulates of construction. These postulates assume the existence of points, lines, and circles as well as other geometric objects that can be derived from the fact that these exist. The fourth and the fifth are very different from the first three. The fourth postulate look obvious, but in truth, it assumes that space is homogeneous. The fifth postulate is one of the more famous ones and basically states that one and only one line can be drawn through a point parallel to a given line5.

Euclid also included axioms, which Euclid called ‘common notations’. Common notations are not specific geometric properties, but are instead, general assumptions that are the basis of mathematics and which allows it to continue to be a deductive science5. His five common notations are1

1. Things which are equal to the same thing are equal to one another.

. If equals be added to equals, the wholes are equal.

. If equals be subtracted from equals, the remainders are equal.

4. Things which coincide with one another are equal to one another.

5. The whole is greater than the part.

Euclid was often portrayed as a kind, fair, and patient man who was quick to help others and to encourage and praise them. However, he was rather sarcastic as well. One well known story about his sarcasm was when one of his students complained that there was no point use for any of the mathematics he was learning. Euclid then called his slave to give the boy a coin because “he must make gain out of what he learns.” Euclid was man of great wisdom who has greatly affected, modern mathematics. He will live on in the books of history forever.


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