The Undefined Notions
Before we can talk about objects or concepts in geometry, we need actual material work with. Without them, we're no better than a lumberjack without any lumber. (Would that just make him a jack?)
Well, it's easy for lumberjacks. They can go out and get what they need without a second thought. When discussing geometry, on the other hand, we might not even have a clue as to where to start. It's like a big empty void of nothingness, and we're expected to somehow create these building blocks of geometry using only logic. (Thank goodness for the previous chapter, huh?)
Fine, then. We'll make these basic units of geometry—the point, the line, and the plane—and call them undefined notions. Since there was nothing that existed before them, we can't use anything to define them—but that doesn't mean we can't explain them.