Euclidean Geometry: Reason Made Manifest

“Let no one come to our school, who has not first learnt the elements of Euclid.”
– Notice posted on school doors by Greek philosophers, notably Plato’s Academy

A youth who had begun to read geometry with Euclid, when he had learnt the first proposition, inquired, “What do I get by learning these things?” So Euclid called a slave and said “Give him three pence, since he must make a gain out of what he learns.”
– Stobaeus, Extracts

“The laws of nature are but the mathematical thoughts of God.”
– Euclid

“If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker.”
– Albert Einstein

“I tell you that I accept God simply. But you must note this: If God exists and if He really did create the world, then, as we all know, He created it according to the geometry of Euclid.”
– Ivan, in The Brothers Karamazov, by Fyodor Dostoyevsky (1821-1881)

“Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.”
– Eric Temple Bell

Lincoln explains why he was motivated to read Euclid:

“In the course of my law reading I constantly came upon the word “demonstrate”. I thought at first that I understood its meaning, but soon became satisfied that I did not. I said to myself, What do I do when I demonstrate more than when I reason or prove? How does demonstration differ from any other proof?I consulted Webster’s Dictionary. They told of ‘certain proof,’ ‘proof beyond the possibility of doubt’; but I could form no idea of what sort of proof that was. I thought a great many things were proved beyond the possibility of doubt, without recourse to any such extraordinary process of reasoning as I understood demonstration to be. I consulted all the dictionaries and books of reference I could find, but with no better results. You might as well have defined blue to a blind man.At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies.”

 

I’m currently reading Euclid’s elements. I decided that I should employ a method to guide my madness. To begin, I will read each book within the Elements, completing all the propositions within each as they are demonstrated with a compass and straight edge. I will transcribe every definition, postulate, common notion, and proposition as I come to them. I will memorize every proposition until I have demonstrated mastery of every book of the Elements until perfection.

Reading Euclid’s Elements is apart of a larger goal of mine: I wish to master Newton’s Principia, eventually gaining confidence and knowledge of higher order physics and mathematics that I might apply to economic, social, and biological systems.

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