Born at Benvie, slightly west of Dundee to Margaret Young and Reverend James Playfair, the kirk minister at Benvie. Playfair was educated at home until the age of 14, when he entered the University of St Andrews to study divinity. He also did further studies at Edinburgh University. In 1766, when only 18, he was a candidate for the chair of mathematics in Marischal College, and, although he was unsuccessful, his claims were admitted to be high. Six years later he applied for the chair of natural philosophy at St Andrews University, but again without success. In 1773 he was licensed to preach by the Church of Scotland and was offered the united parishes of Liff and his home parish of Benvie. However, Playfair chose to continue his studies in mathematics and physics, and in 1782 he resigned his charge to become the tutor of Adam Ferguson. By this arrangement Playfair regularly visited Edinburgh and went on to cultivate the literary and scientific society for which the city was at that time specially distinguished. In particular, he attended the natural history course of John Walker. Through Nevil Maskelyne, whose acquaintance he had first made in the course of the celebrated Schiehallion experiments in 1774, he also gained access to the scientific circles of London. In 1785 when Dugald Stewart succeeded Ferguson in the University of Edinburgh Chair of Moral Philosophy, Playfair succeeded the former to become the chair of mathematics.
Mature work
In 1795 Playfair published an alternative, more stringent formulation of Euclid's parallel postulate, which is now called Playfair's axiom. Although the axiom bears Playfair's name, he did not create it, but credited others, in particular William Ludlam with its prior use. In 1802 Playfair published his celebrated volume entitled Illustrations of the Huttonian Theory of the Earth. The influence exerted by James Hutton on the development of geology is thought to be largely due to its publication. In 1805 Playfair exchanged the Chair of Mathematics for that of natural philosophy in succession to John Robison, whom also he succeeded as general secretary to the Royal Society of Edinburgh. He took a prominent part, on the liberal side, in the ecclesiastical controversy that arose in connection with Sir John Leslie's appointment to the post he had vacated, and published a satirical letter. Playfair was an opponent of Gottfried Leibniz's vis viva principle, an early version of the conservation of energy. In 1808, he launched an attack on John Smeaton and William Hyde Wollaston's work championing the theory. In 1808 he also published a review of Laplace's Traité de Mécanique Celeste.
Family
Playfair's brothers were architect James Playfair, solicitor Robert Playfair and engineer William Playfair. His nephew, William Henry Playfair was an eminent architect in Scotland. In later life he admired and proposed to the wealthy widow Jane Apreece. She turned him down and married Sir Humphry Davy. He died of strangury on 20 July 1819, and although an eminent man was buried in an unmarked grave in Old Calton Burial Ground, on Waterloo Place in Edinburgh. His, and his brother, James's graves were marked by a plaque unveiled in 2011 following a local campaign. The monument to his memory by William Henry Playfair, on Calton Hill, is visible from the spot.
A four-volume collected edition of Playfair's works, with a memoir by James G. Playfair, appeared at Edinburgh in 1822. His writings include a number of essays contributed to the Edinburgh Review from 1804 onwards, various papers in the Philosophical Transactions of the Royal Society and in the Transactions of the Royal Society of Edinburgh, the articles "Aepinus" and "Physical Astronomy", and a "Dissertation on the Progress of Mathematical and Physical Science since the Revival of Learning in Europe" in the Encyclopædia Britannica. He also took an interest in Indian astronomy and compared them with traditional and ancient astronomy from Egypt and Greece. He also examined Indian concepts in trigonometry. His Elements of Geometry first appeared in 1795 and has passed through many editions; his Outlines of Natural Philosophy consist of the propositions and formulae which were the basis of his class lectures. Playfair's contributions to pure mathematics were not considerable, his papers "On the Arithmetic of Impossible Quantities" and "On the Causes which Affect the Accuracy of Barometrical Measurements", and his Elements of Geometry, all already referred to, being the most important. His lives of Matthew Stewart, Hutton, and Robison, many of his reviews, and above all his "Dissertation" are of the utmost value.
