m/M = M/(M + m) = 1/2 (v5 - 1) = .618 = the key to the most exciting discovery in the history of Vergilian criticism. As a result of intensive research and study in the poetry of Vergil, George Duckworth has made a remarkable find: Vergil, as well as other poets of his century, deliberately used the Golden Mean ratio to give mathematical symmetry to the structure of his poetry. The author gives a full and critical account of the scholarship, which up to now has been devoted to the construction of the Aeneid. In turn, he traces the Golden Mean ratio—famous in mathematics, art, and architecture—everywhere in the main divisions and subdivisions, in the short speeches, and in the long narrative units of the Aeneid. Duckworth proves with his data that consecutive units of the epic are proportionate to one another in the ratio .618. With the longer and shorter passages denoted as M (major) and m (minor), the exact ratio is: m/M = M/(M + m) = 1/2 (v5 - 1) = .618, being achieved most frequently by the Fibonacci series in which each number is the sum of the two preceding numbers. This extraordinary book provides a new awareness of the marvelous structure of Vergil's poetry. It is an essential text for resolving the disputed passages in Vergil. George Duckworth has pioneered a structural analysis that will not only make obsolete much Vergilian criticism but will, in addition, serve as a basis for future research.

Using Vergil's Aeneid as a norm, George E. Duckworth provides an authoritative and comprehensive analysis of the metrics of Vergil and other Latin poets who composed in hexameters—from Ennius to Arator and Corippus, from the second century before Christ to the Age of Justinian. Duckworth begins by describing the various patterns of hexameter poetry and goes on to apply these statistical criteria to poems written over a period of 750 years—thus providing a history as well as an analysis of the genre. The study of metrical variety serves to reveal the influence of earlier poets on later writers and to illuminate successive developments in an individual poet's work. Comparisons support Duckworth's views on the authenticity of works of questionable authorship, and the structural approach aids in the determination of the correct chronology of works written by a specific poet. Also included are juxtapositions of Latin poets with selected Greek hexameter poets—Ennius with Homer, Catullus with Callimachus and Apollonius of Rhodes, the later Roman poets with Quintus of Smyrna and Nonnus. Like his earlier work on the structures of the Aeneid, Duckworth's new book provides material on which to base a heightened appreciation of the genius of Vergil and other Latin poets.