Penn Arts & Sciences Logo

Thursday, March 19, 2015 - 6:00pm

Robert Naugle

Shepherd University and Hagerstown Community College

Location

Villanova University

St. Augustine Center 300

Optional light supper ($10 donation)

The only extant copy of "The Method of Mechanical Theorems" in the original Greek has been known to exist in Codex C since Johan Ludvig Heiberg (1854-1928) examined it at the turn of the 20th Century. Heiberg succeeded in deciphering most of its contents using light, a magnifying glass and a camera. Proposition 14, determining the volume of a planar cut of a cylinder encased in a cube, a "hoof", had a large gap hidden from Heiberg in the gutter of Codex C. Heiberg wrote in Latin that "I shall not speculate as to what could have been written in such a large gap."

This gap was exposed by unbinding and modern imaging during the recovery of the Archimedes palimpsest after its sale to a private buyer in 1998. Dr. Reviel Netz, a Classics scholar at Stanford who is fluent in the Doric dialect of Archimedes and who was at the time completing an extensive translation and commentary of Archimedes´ mathematics, was called in to consult after the Codex was unbound.

Dr. Netz subsequently claimed that information hidden in the gutter of Codex C suggests that Archimedes had considered a 19th century concept of infinity (actual, completed infinity) in Proposition 14 of The Method.

We will use this as motivation for examining The Method through Proposition 1 in which Archimedes shows Eratosthenes his heuristic method of realizing that the area of a circumscribing parabola is 4/3 that of the triangle it encloses and move to Proposition 14, show the rudiments of The Method applied again and the Doric Greek hidden in the gutter that led Netz to make his claim.