"Aeneid" I and .618

SINCE PAUL MAURY in 1944 propounded his theory that Virgil made use of Neo-Pythagorean symbolic numbers in the composition of the Eclogues,' and Guy Le Grelle, s.j., extending Maury's work, suggested that the first book of the Georgics was constructed in accordance with the Divine Proportion, .618,2 the mathematical approach to structural analysis has become a major aspect of Virgilian scholarship. Although the results produced by mathematical analysis are interesting, the method itself has not won unqualified approval. This is especially the case with the mathematical sections of Professor G. E. Duckworth's Structural Patterns and Proportions in Vergil's Aeneid: A Study in Mathematical Composition, published in 1962. It is his thesis that Virgil deliberately and consistently made use of the arithmetical equivalent of Euclid 2.11 and 6.30, the Golden Mean ratio or Golden Section, .618, as the basis for organizing his narrative: he wrote the short passages with mathematical symmetry and combined them into increasingly larger units, with every part of every book containing exact or approximate Golden Mean ratios ranging from .60 to .636 (p. 73). Professor Duckworth has found at least 1044 Golden Mean ratios in the Aeneid. The supporters of Professor Duckworth's theory have been enthusiastic.8 R. J. Getty went so far as to say He has brought to the analysis of the Aeneid a principle of much aesthetic importance and has defended it stoutly. What is now at stake is not his reputation, but that of his critics if they express their disbelief without being able to refute him. Yet much can be and has been said by those who find themselves unconvinced.4 Most reviewers point out that the validity of the mathematical thesis rests upon the logical relation between suggested mathematical units and coherently interrelated passages of narrative. As yet, however, no systematic attempt has been made to examine in detail the subject-divisions which Professor Duckworth uses. This I propose to do, using the subject-divisions and ratios suggested for Aeneid 1. As a preface to the study, I shall comment briefly on the Golden Mean ratio

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