Abstract
THE BASIC THESIS IN G. E. DucKWORTH'S Structural Patterns and Proportions in Vergil's Aeneid (Ann Arbor 1962) is that Vergil deliberately shaped his poetry to embody the extreme and mean ratio.' The same idea had been suggested earlier by G. LeGrelle,2 and has been taken up by E. L. Brown.3 Classicists have argued for and against the thesis,4 but no one seems to have approached it from a background in mathematics. I have tried to consider the subject in the context of ancient mathematical thought, and the arguments presented below have forced me to conclude that Duckworth's thesis is extremely improbable. Most of the discussion will apply to all three authors, but I have concentrated on Duckworth's book because it is the most detailed presentation of the thesis (Brown devotes space to things like acrostic signatures,5 and LeGrelle introduces a great deal of unrelated number symbolism6).
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