*By Jocelyn Hitchcock, Contributing Writer, Classical Wisdom*

**Euclid’s Early Life**

**Euclid’s Career**

*the Elements*, to which Euclid replied that there was no royal road to geometry.” This would suggest that not only was Euclid noteworthy among mathematicians and scientists in Alexandria, but was prominent enough to have an audience with the ruler of Egypt. As with details of his early life, we don’t know specifics regarding his career, save for his extant works and the fact that he was a prominent teacher in Alexandria.

**Euclid’s Works and Achievements**

*The Elements*, is a proto-textbook of 13 sections pulling together definitions, theories, and constructions of mathematics at the time. He covers geometry, number theory, and incommensurate lines- all subjects that have proved to be invaluable over the development of mathematics.

*The Elements*consisted of five general axioms and five geometrical postulates. Euclid provided the basic model for mathematical argument that follows logical deductions from initial assumptions. For those of us (including myself) who are not so mathematically inclined to understand the nitty-gritty details of Euclid’s

*Elements*, Sir Thomas Heath sums them up in his 1908 publication

*The Elements of Euclid*:

**The 5 Axioms of Euclid:**

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

2. If equals are added to equals, the whole (sums) are equal

3. If equals are subtracted from equals, the remainders (differences) are equal

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

5. The whole is greater than the part

**The 5 Geometric Postulates:**

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

2. It is possible to extend a finite straight line continuously in a straight line

3. It is possible to create a circle with any center and distance

4. All right angles are equal to one another

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

*the Elements*, five other works of Euclid have come down to us and have been able to be interpreted: Data, dealing with the nature and implications of “given” information in geometry;

*On Divisions of Figures*, dealing with the division of geometrical figures into two or more equal parts or into parts in given ratios;

*Catoptrics*, dealing with the theory of mirrors and the images formed in plane and spherical concave mirrors;

*Phaenomena*, a treatise on spherical astronomy; and

*Optics*the earliest surviving Greek treatise on perspective.

**Euclid’s Death and Legacy**

*the Euclid Spacecraft*.