Copyright © Lucas Amiras 2017

In the "Elements" of Euclid (3th century B.C.) the primitive notions (point, line, surface, straight line, flat surface) are defined in a very problematic way.

Book I, Definitions

1. A point is that which has no part.

2. A line is breadthless length.

3. The ends of a line are points.

4. A straight line is a line which lies evenly with the points on itself.

5. A surface is that which has length and breadth only.

6. The edges of a surface are lines.

7. A plane surface is a surface which lies evenly with the straight lines on itself.

The struggle to define the primitive geometric notions in Euclid can be understood
as coming up of a philosophical tradition aiming at clarifying geometrical notions
and determining them terminologically. In the writings of Aristotle (384-

Ancient Geometry and Philosophy