Journey Through Genius: The Great Theorems of Mathematics Chapter Summary & Analysis - Euclid's Proof of the Pythagorean Theorem Summary

Euclid's Proof of the Pythagorean Theorem Summary and Analysis

Dunham next turns to Euclid in the first of two chapters devoted to the great mathematician. Euclid major contribution to mathematics is his book on geometry and number theory called the Elements. Euclid's Elements, Dunham writes, is a revolutionary book not so much for what it says, for much if what it contains is already known from earlier authors, but in how it is presented. Euclid begins with some very basic definitions and gradually builds on them to higher conclusions in a methodical way, creating an "axiomatic framework" for his proofs that allows for solid proofs based on consistent definitions.

In the first book of his Elements, Euclid offers 23 definitions, beginning with the definition of a point, a line, and a straight line. He also defines right angles, circles, and in what is to become an important definition to later mathematicians, parallel lines. These Euclid defines as straight...
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