What is A Postulate?
- Mathew Purser
Euclid's meaning of a postulate is a little different than what we tend to mean in modern times. Today, postulates and axioms mean the same thing now, a statement that does not require proof; Euclid's means a true statement that may not be initially obvious. We will go over true axioms in the next chapter and focus on Euclid's style of postulate now. Think of this section as the slightly more advanced tutorial while the definitions were the basics. Think about the tutorial in a video game, after they show you what each button does you learn combinations and mechanics that are less obvious , that's what this section is about! There are five basic postulates that we will cover individually, read through them and see if you can explain them in your own words what each means: 1. To draw a straight line from any point to any point. 2. To produce a finite straight line continuously in a straight line. 3. To describe a circle with any center and radius. 4. That all right angles equal one another. 5. That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.