The classic treatise in geometry written by Euclid and used as a textbook for more than 
years in western Europe. An Arabic
version The Elements appears at the end of the eighth century, and the first
printed version was produced in 1482 (Tietze 1965, p. 8). The Elements,
which went through more than 
editions and consisted of 465 propositions, are divided into 13 "books"
(an archaic word for "chapters").
| book | contents |
| 1 | triangles |
| 2 | rectangles |
| 3 | circles |
| 4 | polygons |
| 5 | proportion |
| 6 | similarity |
| 7-10 | number theory |
| 11 | solid geometry |
| 12 | pyramids |
| 13 | Platonic solids |
The elements started with 23 definitions, five postulates, and five "common notions," and systematically built the rest of plane and solid geometry upon this foundation. The five Euclid's postulates are
1. It is possible to draw a straight line from any point to another point.
2. It is possible to produce a finite straight line continuously in a straight line.
3. It is possible to describe a circle with any center and 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 less than two right angles, the straight lines (if extended indefinitely) meet on the side on which the angles which are less than two right angles lie.
(Dunham 1990). Euclid's fifth postulate is known as the parallel postulate. After more than two millennia of study, this postulate was found to be independent of the others. In fact, equally valid non-Euclidean geometries were found to be possible by changing the assumption of this postulate. Unfortunately, Euclid's postulates were not rigorously complete and left a large number of gaps. Hilbert needed a total of 20 postulates to construct a logically complete geometry.
