Postulates: the board's own rules
Axioms never mention a line. So where do a line's rules come from? Sort the cards below.
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The rice test
A line's rules come from postulates. These are agreements about the drawing board. The drawing board is where we draw points, lines and circles. Like an axiom, a postulate is agreed, not proved. Ask one question of any statement. Could you say it about rice, rods or rupees?
Nobody has drawn a perfect line or circle. A pencil line has thickness. A drawn circle wobbles. So the rules for perfect lines and circles are agreed in words.
| Statement | About rice? | Shelf |
|---|---|---|
| Equals added to equals give equal wholes. | Yes. | Axiom |
| A circle can be drawn with any centre and any radius. | No. Rice has no centre. | Postulate |
| A line can be extended further. | No. Only the board has lines. | Postulate |
Rule: A statement you could say about rice is an axiom. A statement about a point, line, circle or angle is a postulate.