PLAYFAIR, JOHN (b. Benvie, near Dundee, Scotland, 10 March 1748; d. Edinburgh, Scotland, 20 July 1819), mathematics, physics, geology.

Playfair was the eldest son of the Reverend James Playfair. At the age of fourteen he went to the University of St. Andrews, primarily to qualify for the ministry, but he also showed remarkable mathematical ability. In 1769 he left St. Andrews for Edinburgh. On the death of his father in 1772, he succeeded him in the living of Benvie, which he resigned in 1782 to become tutor for a private family. From 1785 to 1805 Playfair held a professorship of mathematics at the University of Edinburgh. He edited the Transactions of the Royal Society of Edinburgh for many years, and most of his papers appeared in that periodical. They were concerned almost entirely with mathematics, physics, and biographies. His Elements of Geometry was published in 1795. Following the death in 1797 of his friend James Hutton, Playfair proceeded to make a careful analysis, clarification, and amplification of Hutton's Theory of the Earth, which had originally been presented as a paper read in 1785 to the Royal Society of Edinburgh and was expanded into the two-volume work of 1795. Playfair's efforts resulted in Illustrations of the Huttonian Theory of the Earth (1802). In 1805 he became professor of natural philosophy at Edinburgh, where his lectures now embraced physics and astronomy. His Outlines of Natural Philosophy was published in 1814.

Playfair's professional work was thus in mathematics and physics. His book on geometry is a full presentation of the first six books of Euclid, with much additional material. The formal treatment of linear parallelism requires axioms. Finding Euclid's axioms on this matter to be unsatisfactory, Playfair proposed “that two straight lines, which intersect one another, cannot be both parallel to the same straight line.” This is what became known as “Playfair's axiom,” as it is given in his Elements of Geometry.

Playfair's fame as a scientist, however, rests almost entirely on his work in geology--hardly a “professional” study at the time--in presenting Hutton's momentous theory in a clear and palatable form (which Hutton himself had failed to do), and in adding materially to the geological knowledge of the time. The precision and elegance of the style of his mathematical exposition is here applied to a descriptive, inductive science. As Archibald Geikie remarked (1905): “How different would geological literature be to-day if men had tried to think and write like Playfair!” The publication of the Illustrations is indeed one of the most conspicuous landmarks in the progress of British geology. It ended the early period in the history of that science, a termination that happened to coincide with the end of the eighteenth century. There was a pause in the advance of geology during the early years of the nineteenth century; but powerful forces were gathering an impetus that was released in the second decade with the publication of important works by William Smith, John Farey, and Thomas Webster, which were summarized in the next landmark of the literature, Conybeare and Phillips' Outlines of the Geology of England and Wales (1822). Playfair lived well into this second period of activity but did not take any part in it. A project that was very much in his mind was the preparation of a comprehensive work on geology, which was to have been a greatly amplified edition of his Illustrations. The peace of 1815 enabled Playfair to make an extensive tour of France, Switzerland, and Italy, in order to extend his observations for this purpose; but although we have details of the journey, nothing of the projected work was composed.