Euclid of Megara

For centuries, medieval scholars confused two Greek men named Euclid who lived roughly a century apart and had nothing philosophically in common beyond the accident of sharing a name. Euclid of Megara, born around 435 BCE, was a companion of Socrates present, according to Plato's Phaedo, at his execution in 399 BCE, and afterward founded a school at his native Megara that fused Socratic ethics with the Eleatic doctrine that being is one and unchanging, arguing that the good itself is a single unified reality that goes by many names, wisdom among them, and that its supposed opposite has no real existence at all. Euclid of Alexandria, the mathematician who wrote the Elements roughly a century later and gave the Western world its model of geometric proof, is an entirely distinct figure with no connection to Megara or to Socrates. The confusion is old enough to have a name of its own: medieval manuscripts and commentators sometimes styled the mathematician Megarensis, as though he were the Megarian philosopher, an error modern scholarship has fully untangled but which still surfaces in casual references to Euclid. The philosopher's own writings, a set of Socratic dialogues, have not survived, and what is known of Megarian philosophy after him comes chiefly through his successors, Eubulides and later Stilpo, whose sharp logical puzzles and dialectical arguments fed directly into the development of Stoic logic a generation afterward.

This article records tradition as it has been passed down and reported. Its sources are not yet part of the atlas's verified catalogue.

Diogenes Laertius preserves a specific story about how far Euclid of Megara was willing to go to keep learning from Socrates. During a period of hostility between Athens and Megara, Athens is said to have decreed death for any Megarian caught entering the city. Euclid, unwilling to give up attending Socrates's teaching in Athens, reportedly disguised himself in a long woman's robe and veil and traveled the roughly twenty mile distance from Megara after dark, arriving to hear Socrates and departing again before daybreak to avoid discovery, a nightly round trip undertaken purely to keep studying under a teacher he could otherwise no longer legally approach.

The anecdote, whatever its precise historical reliability, was already circulating in antiquity as an illustration of the depth of Euclid's attachment to Socrates specifically, distinct from the philosophical doctrine Euclid later built combining Socratic ethics with Eleatic metaphysics after Socrates's death. It also places Euclid inside the same small circle Plato's Phaedo names as present at Socrates's execution in 399 BCE, a circle the disguise story suggests Euclid had been risking real legal danger to remain part of for some time before that final scene.

A political ban meant to keep Megarians out of Athens, and one philosopher's readiness to defy it under disguise rather than miss his teacher's lessons, is a smaller and more personal story than the doctrine Euclid is chiefly remembered for, but it is the story ancient tradition chose to preserve about why he kept coming back.