The classic treatise in geometry written by Euclid and used as a textbook for more than 1,000 years in western
Europe. *The Elements*, which went through more than 2,000 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.

**References**

Casey, J. *A Sequel to the First Six Books of the Elements of Euclid, 6th ed.* Dublin: Hodges, Figgis, & Co., 1892.

Dixon, R. *Mathographics.* New York: Dover, pp. 26-27, 1991.

Dunham, W. *Journey Through Genius: The Great Theorems of Mathematics.* New York: Wiley, pp. 30-83, 1990.

Heath, T. L. *The Thirteen Books of the Elements, 2nd ed., Vol. 1: Books I and II.* New York: Dover, 1956.

Heath, T. L. *The Thirteen Books of the Elements, 2nd ed., Vol. 2: Books III-IX.* New York: Dover, 1956.

Heath, T. L. *The Thirteen Books of the Elements, 2nd ed., Vol. 3: Books X-XIII.* New York: Dover, 1956.

Joyce, D. E. ``Euclid's Elements.'' http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

© 1996-9

1999-05-25