Euclidean Geometry : What Euclid actually said...

by Stu Savory, 2005.

Euclid's Definitions
1. A point is that which has no parts.
2. A line is that which has length without breadth.
3. The limits of a line are points.
4. A straight line is that which lies equally to the points on it.
5. A surface is that which has only length and breadth.
6. The limits of a surface are lines.
7. A plane surface is that which lies equally to the straight lines on it.
Euclid's Axioms
1. Things which are equal to the same thing are also equal to one another.
2. If equals be added to equals, the wholes are equal.
3. If equals be subtracted from equals, the remainders are equal.
4. Things which coincide with one another are equal to one another.
5. The whole is greater than the part.
Euclid's Postulates
1. A straight line can be drawn between any two points.
2. A finite line can be extended infinitely in both directions.
3. A circle can be drawn with any centre and any radius.
4. All right angles are equal to each other.
5. Given a line and a point not on the line, only one line can be drawn through the point parallel to the line.

And you can deduce all the rest, given the things above :-)