1. A point is that of which there is no part.

2. And a line is a length without breadth.
3. And the extremities of a line are points.
4. A straight-line is (any) one which lies evenly with points on itself.
5. And a surface is that which has length and breadth only.

Those five definitions are the first five of twenty-three that form the introduction to Euclid’s Elements. They’re the things our second semester freshmen must know before beginning Proposition #1, the start of a mathematical journey that will last through fall semester sophomore year.

Dr. Henry Zepeda, who regularly teaches Euclid, discusses this seminal mathematician and The Elements before commenting on Euclid’s understanding of proportions.