L’Hôpital’s Synthesis of Calculus and Geometry

Thursday, February 19, 2015

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, Dr. Robert Bradley, chair, Department of Mathematics and Computer Science, Adelphi University, will speak on:

L’Hôpital’s Synthesis of Calculus and Geometry

Abstract:

Guillaume François Antoine, the Marquis de l’Hôpital, wrote the first differential calculus textbook, which he published in 1696. Leibniz’ calculus, which the Marquis had learned from Johann Bernoulli, was at this time a calculus of algebraic functions only. Nevertheless, by combining the techniques of the new calculus with methods of Euclidean geometry, Leibniz and the Bernoullis were able to investigate the properties of wide a variety of transcendental curves, including the cycloid, the quadratrix, and various spirals. Through his groundbreaking textbook, the Marquis de l’Hôpital shared these new methods with the French mathematical community.

In this talk, I will describe l’Hôpital’s calculus, providing a variety of examples drawn from my forthcoming translation of Analyse des infiniment petits, a joint project with Sal Petrilli and Ed Sandifer.

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.