The first goal of this article to show the profound difference between how equality and similarity are understood in Greek geometry and how they are presented in modern mathematics classes. It highlights that the formula "equal-and-similar" reflects the distinct character of "equal" and "similar" as signs in Greek mathematical discourse. The second goal of the article is to demonstrate how such a treatment of history of mathematics defines the teacher's task as one of positioning students with respect to the past, leading them out beyond their parochial modernity to a place where they may begin to see their inescapable relationship with the past. Historical understanding, in this way, becomes not just a tool for motivating students or providing additional classroom examples, but an important end in itself for mathematics education.