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Euclidean Geometry

From Sir Thomas L. Heath's translation of Euclid's Elements
Postulates

Let the following be postulated:
1. To draw a straight line from any point to any point.
2. To produce a finite straight line continuously in a straight line.
3. To describe a circle with any centre and distance.
4. That all right angles are equal to one another.
5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Some definitions from the same source:

1. A point is that which has no part.
2. A line is breadthless length.
3. The extremities of a line are points
4. A straight line is a line which lies evenly with the the points on itself.
5. A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
6. When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right ....

Common Notions

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.
5. The whole is greater than the part.