Classical Theorems

For each of the mathematicians that lends his name to the title of this section, there is at least one famous theorem that bears his name. As we shall see, the Alexandrian Greek mathematician Pappus can be paired with either of the seventeenth-century French mathematicians Desargues or Pascal. However, the Alexandrian Greek mathematician Menelaus and the seventeenthcentury Italian mathematician Ceva are invariably mentioned together. Menelaus’ Theorem, which involves a test for the collinearity of three points, and Ceva’s Theorem, which involves a test for the concurrency of three lines, are frequently called the Twin Theorems. These theorems should have been discovered together, and it is not insignificant that such a long period separates Menelaus and Ceva. During the 1500 years that separate the two there was little development in mathematics.