A point is that which has no part. A line is breadth less length. The ends of lines are points. A straight line is a line which lies evenly with the points on itself. A surface is that which has length and breadth only.
The edges of a surface are lines. A plane surface is a surface which lies evenly with the straight lines on itself. Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction. Euclid’s Axioms (or common notions)
Some of the Euclid’s axioms not in the order are given below:
1. Things which are equal to the same thing are equal to one another.
2. If equals are added to equals, the wholes are equal.
3. If equals are 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.
6. Things which are double of the same things are equal to one another.
7. Things which are halves of the same things are equal to one another.
Euclid’s Postulates
1. A straight line may be drawn from any point to any other point.
2. A terminated line can be produced indefinitely.
3. A circle can be drawn with any centre and any radius.
4. All right angles are equal to one another.
5. If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles are less than two right angles