Infernal Geometry

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Dante guides the reader as Apelles paints, who through his high genius, illustrated by a subtle mind and by mathematical knowledge, places before our eyes the form and measurements of Hell.

—Cristoforo Landino, 1481

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How far into Hell would you have to travel to reach the center of the earth? Approximately 3,400 miles, according to Antonio Manetti. Manetti’s measurements of Hell went virtually unchallenged until Alessandro Vellutello proposed a radically different mathematical model in his 1544 commentary on the Comedy (1). He proposed new figures for the height of Lucifer, which was triangulated from the circumference of the earth, the height of the giants (in Hell’s ninth circle) and the distance of Hell’s lowest circles. Manetti’s calculations were eventually adopted, but only after 40 years of fierce debate among Dante scholars.

Rendered in a spare style, the engraved map frontispiece of the Crusca Academy’s edition of the Comedy (2) presents a more mathematical approach to representing the underworld. The three different projections represent the width, length and depth of Hell according to the measurements of Manetti. Although other mathematicians offered different models for the dimensions of Hell, Galileo confirmed Manetti’s findings in his lectures on “the site, form, and measurements of the Inferno” that he delivered to the Florentine Academy in 1588. In these lectures, Galileo used drawings to prove his calculations, which demonstrates how images played a significant role in sustaining mathematical arguments about the poem’s structure. Indeed, some scholars argue that the 1595 engraving was based on Galileo’s own drawings of Hell.

The Crusca Academy, a group of Florentine intellectuals, was concerned with standardizing the Italian language. Its members were responsible for publishing the first modern dictionary of Italian. To prepare their edition of the Comedy, they collected almost 100 manuscripts and printed editions of Dante’s poem in order to restore the poem to its original linguistic state. The Crusca text is considered to be the first critical edition of Dante’s poem: Its frontispiece’s notably flat and linear style perhaps reflects the rigorous and systematic approach to Dante’s text.

The Crusca’s diagram of Hell engraving drew upon the visual tradition of infernal cartography, while in simultaneous conversation with illustrations of mathematical and astronomical books, such as Euclid’s Elements (3), Ptolemy’s Almagest and Sacrobosco’s Sphere (4), the primary math and astronomy textbooks in the medieval and early modern periods. These books also laid the groundwork for innovative printing techniques of geometrical figures, mathematical models and planetary motion. In many cases, the diagrams were annotated, copied, colored or cut out to create instruments to help readers calculate the movement of the hours, planets and stars. The resemblance between the 1595 frontispiece and the instrument (5) depicted in Christopher Clavius’s Gnomonices (referring to the part of the sundial that casts a shadow) suggests that the engraving also served as a tool for readers to calculate Hell’s dimensions more precisely, and perhaps, to experiment with their own models of Hell.