Euclid
Euclid Book 1, Proposition 13
As I work steadily through Euclid’s early propositions, one thing is becoming very clear. In spite of my desire to doggedly work through the logic of Euclid, I will never have the patience for this. The problem is, Euclid assumes nothing. NOTHING, I tell you. And while I have a certain amount of patience for slogging through complex proofs of things I already know are true, I simply don’t have the time to actually digest all of Euclid’s first book of Elements.
I offer Proposition 13 as an example. Proposition 13 demonstrates the proof that when a straight line intersects another straight line, the adjacent angles will always add up to 180 degrees.
In the above image, Euclid postulates that angles A and B combined will equal 180 degrees, no matter how the lines are drawn. You and I already know this. It’s obvious to us. And you might expect that the
Euclid Book 1, Proposition 1
On a given straight line to construct an equilateral triangle.
The beauty of this proof is what first captured my imagination. Having very little idea of what Euclid was about, I read the introduction and some of the axioms. Then I turned to the first proposition. The pure, unadulterated beauty of it hit me like a punch in the face. You have a line running from point A to point B. That’s all you have. How will you create an equilateral triangle, using that line as one of the sides and only with your trusty compass and straightedge?
My drawing and notes from the first proposition.
The drawing of the proof itself was beautiful to me, as was the simplicity of it’s solution. Remember that Euclid always states the obvious. You could draw a shorter version of this proof by
Real Live Preacher Meets Euclid
You would be hard pressed to find an educated person before the 20th century who had not studied Euclid’s famous Elements. All of the founding fathers of our country would have known Euclid’s postulates, propositions, and proofs. Einstein cut his teeth on Euclid, as did all the early mathematicians and physicists. Abraham Lincoln took up Euclid at 40, hoping to understand in the depths of his soul the meanings of demonstration and proof. He carried a copy of Euclid in his saddlebags, studying at night by candlelight, until he could demonstrate every proof in the first 6 books by memory.
Having come across Euclid so often in biographies, I decided to get a copy for myself to see what all the fuss is about. I should say that while I was fair at mathematics in high school, I never liked math, favoring instead literature, history, science, and writing. I managed to avoid the one required math course for my Bachelor of Arts degree by taking a 5th semester of Greek. My willingness to make that trade should probably tell you something. After all these years, I wouldn’t know the quadratic equation from my daughter’s phone number, assuming I could remember her phone number, which, in fact, I cannot. Even so, I have always had an intuitive grasp of the beauty of numbers, our most universal and precise language. And I have always wished I could understand the mathematical language that is required for advanced physics and cosmology, though clearly I will never do anything more than dabble in such subjects.
I’d been thinking about getting a copy of Euclid for months but was spurred into action when I came across a satchel of professional drafting tools in a junk store. The price was five dollars, so I
All of my books are for sale though me. I've not had the energy or inclination to send them to Amazon or any other place.
Click here for purchase links at my new blog.