Euclid's Proof Of The Pythagorean Theorem Summary

In Chapter 2 of Journey Through Genius, titled “Euclid’s Proof of the Pythagorean Theorem,” the author, William Dunham begins by introducing the Greek contributions to mathematics. The first figure introduced, Plato, brought enthusiasm to the subject. He was not an actual mathematician; he was a philosopher. His main contribution to math was establishing the Academy, a center devoted to “learning and contemplation for talented scholars.” The Academy was mainly focused on mathematics and produced talented scholars, such as Eudoxus. Eudoxus was another important figure in math, as he created the theory of proportion and the method of exhaustion. When Alexander the Great set out to “conquer the world,” he set up a city in Egypt called Alexandria

Euclid’s definitions are subject of much controversy today because his definitions are undefined, meaning that they themselves are composed of terms. His later definitions, however, were more successful than his early ones. AFter finishing definitions, he created 5 postulates, “the self-evident truths of his system.” Postulate 5, the parallel postulate, is today very controversial. Next, Euclid created a list of five common notions, of which only the fourth sparked a little debate. These common notions were more general and were not specific to geometry. After completing all these “preliminaries,” Euclid proved 48 propositions in Book 1. His first proposition was the equilateral triangle construction. However, this proof sparked a lot of controversy because EUclid didn’t prove that the two circles intersected. He relied on the “existence of point C that showed up plainly in the diagram.” Furthermore, Euclid disliked the “reliance of pictures to serve as proofs,” as he believed that one cannot “let the pictures do the talking.” Overall, there are several “holes” in Euclid’s propositions, but have been filled by many mathematicians over time, and have therefore, withstood the test of time. The most prominent proposition was Proposition 1.47, the Pythagorean Theorem. It reads that, “In right angles, the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.” This is where a2+b2=c2 stems from. His proof of this was one of the most important proofs in all of mathematics. Overall, “The Elements” was a significant work in