What Did Glaucon Draw?: A Diagrammatic Proof for Plato's Divided Line

Despite the frequency and intensity of scholarly attention to Plato's important divided line passage in Republic 6, an ancient puzzle has repeatedly baffled interpreters: the two middle segments of the line are of equal length, although Socrates declares that the degree of clarity and truth increases in proportion to the contents of each of the line's four segments. The missing piece of the puzzle, I argue, is provided by the practice of ancient Greek geometry: diagrams were drawn with a compass and straightedge. Thus, as actually constructed in the fifth and fourth centuries BCE, the diagram itself vindicates Plato's text.