Elements
The classic treatise in geometry written by Euclid 
and used as a textbook for more than 1,000 years in westernEurope. The Elements, which went through more than 2,000 editions and consisted of 465 propositions, are dividedinto 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,'' andsystematically built the rest of plane and solid geometry upon this foundation. The five Euclid's Postulatesare
- 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 interiorAngles on the same side less than two Right Angles, the straightLines (if extended indefinitely) meet on the side on which the Angles which are less thantwo Right Angles lie.
fifth postulate is known as the Parallel Postulate. After more than two millenniaof study, this Postulate was found to be independent of the others. In fact, equally valid Non-EuclideanGeometries 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.See also Parallel Postulate
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
- Truncated Hexahedron
- Truncated Icosahedron
- Truncated Icosidodecahedron
- Truncated Octahedral Number
- Truncated Octahedron
- Truncated Polyhedron
- Truncated Pyramid
- Truncated Square Pyramid
- Truncated Tetrahedral Number
- Truncated Tetrahedron
- Truncation
- Truth Table
- Tschebyshev
- Tschirnhausen Cubic
- Tschirnhausen Cubic Caustic
- Tschirnhausen Cubic Pedal Curve
- Tschirnhausen Transformation
- Tubular Neighborhood
- Tucker Circles
- Tukey's Biweight
- Tukey's Trimean
- Tunnel Number
- Turbine
- Turing Machine
- Turning Angle