The Philadelphia Area Seminar on History of Mathematics: John Playfair and His Misnamed Axiom

The term "Playfair's Axiom" is a mainstay of school geometry textbooks as well as one of the few things many mathematicians know about John Playfair (1748–1819), Professor of Mathematics and then of Natural Philosophy at the University of Edinburgh. However, the ubiquity of the phrase masks considerable historical complexity. At least three different versions of the statement circulate among speakers of English—only two of which appeared in the editions of Playfair's Elements of Geometry—while the underlying concept dates back to Proclus. Additionally, the versions are not logically equivalent with each other. I will discuss recent research that has revealed new information about when and why "Playfair's Axiom" became commonplace as a label. 

 

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. By order of the Parking Office, all parking is now in the Saint Augustine Center lot, newly refurbished to a multistory structure.  You will need to display a parking pass, which will follow in a later email.  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.