The rise of Rome at the expense of Greece marked a steep decline in the pursuit of pure mathematics in the western world. Although Roman culture borrowed freely from Greek religion, philosophy, and art, Roman mathematics largely confined itself to what was necessary for commerce and engineering. However, the economies and militaries of both Greece and Rome extended east as far as India, prompting trade not only of goods but of knowledge. Islamic versions of universities attracted thinkers and collected knowledge for the sake of science, acting as transfer points where thinkers carried mathematical ideas between cultures.

The scholar Abu Ali al-Hasan ibn al-Hasan ibn al-Haytham (born 965) acted as such a conduit of knowledge. Born in what is now Iraq, ibn al-Haytham traveled to Egypt to work on a river-control project, interacting with scholars familiar with Greek mathematics. Ibn al-Haytham studied light, particularly its role in eyesight, and produced beautiful results concerning surfaces, reflection, angles, and numbers. In this chapter, we will study one of his arguments that resembles later European methods to the point where it is tempting to believe that his ideas filtered north from Egypt during the intervening 700 years.