Lesson 9 of 11
The big picture
Show on a big screenEight ideas, one screen.
| Idea | The rule |
|---|---|
| Examples are not a reason | One failing case ends the claim. |
| Definitions | Use only words already defined. Point and line are undefined. |
| The two axioms | Things equal to the same thing are equal. Equals added to equals stay equal. |
| Postulates | A statement about a point, line, circle or angle. It is not about rice. |
| The five postulates | Three moves that draw. Two claims that later steps use. |
| Construction | Each drawing step is allowed by a postulate. Nothing is measured. |
| The equal square | Its side, times itself, gives the area. Equal ground does not mean an equal way round. |
| Proof parts | A proof starts from undefined words, definitions, axioms and postulates. Reasoning does the rest. |
This is the chapter Introduction to Euclid's Geometry: Axioms and Postulates.
The next chapter starts proving. Each proof uses a layer from this one.