Author's comments: The article is an exercise in the reading of mathematics from earlier times. An explanation of Descartes's solution of the problem of Pappus as included in the appendix "La géométrie" to "Discours de la méthode" and an explanation of a solution to another form of the same problem by Fermat, described briefly in a letter included in his collected works, are taken as an occasion to compare the mathematical styles of the two men and to observe their mutual debt to Apollonius as well as the differences in their depth of understanding of his work. The purpose is not scientific or historic; it is simply to encourage the private reading of classical mathematics by those who like me have no special knowledge of the history of mathematics.
This article appeared on pages 54-61 of the mathematical magazine Matematik Dünyası, No. 2, 2005. The magazine (as mentioned above, edited by Ali Nesin), is published in Istanbul and has a wide circulation among mathematics students and teachers in Turkey.