Archimedes, Codex C,”The Method of Mechanical Theorems”: Controversy

Time: 6:00 p. m. to 8:00 p.m.

Location: Saint Augustine Center Room 300, Villanova University, Villanova, PA

We begin with conversation and a light supper (donation: $10.00). When the discussion lags, about 6:30 to 6:45, Mr. Robert Naugle of Shepherd University and Hagerstown Community College will speak on:

Archimedes, Codex C,”The Method of Mechanical Theorems”: Controversy

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.

Directions: Villanova University is located on route 30, Lancaster Avenue, just east of I-476. If you drive to the meeting, enter Villanova by the main gate on Ithan Avenue, just north of Lancaster Avenue (route 30), opposite the Pavilion. Tell the guard you are attending the History of Mathematics Seminar. Ask for directions either to the Mendel Lot, where there is limited parking around the greenhouse, or to the St. Augustine lot. From the Mendel Lot, pass under the arch of Mendel Hall and turn left, follow the sidewalk with Mendel Hall on your left. The next building on your left is the Saint Augustine Center. Enter the building, proceed to the rear and take the elevator to the third floor. Exit to the right, then turn left; Room 300 is directly on the opposite side of the building. From the St. Augustine Lot enter the Center via the doorway at the end of the lot. Turn right and follow the hallway to the elevators; take the elevator to the third floor. Follow the directions to Room 300 as above. You can get in touch with me (Alan Gluchoff) at 610-905-1376 if you need help.

Public transportation: Take SEPTA's Paoli - Thorndale train to the Villanova station. If outbound from center city go down through the tunnel to the inbound side. From the inbound platform a few steps lead to the Mendel parking lot. Proceed as above to Saint Augustine 300.