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Mathematical Treasure: Playfair’s Elements of Geometry

Frank J. Swetz (Pennsylvania State University)

John Playfair (1748-1819) in his Elements of Geometry, first published in 1795, helped reform the teaching of geometry in Great Britain. Firstly, Playfair helped to abbreviate the exposition of proofs by introducing algebraic notation into the proof process and, secondly, he provided an alternative to Euclid’s definition of parallelism. Euclid’s Fifth Postulate had been the subject of much contention.

“Playfair’s Axiom” states:

Given a line and a point not on the line, it is possible to draw exactly one line through the point parallel to the given line.

The title page shown above is from the 1832 American edition of Playfair’s Elements of Geometry.

Sample content in Playfair’s Geometry

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in “Mathematical Treasures.” In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Playfair’s Elements of Geometry," Convergence (September 2013)