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Professor John Playfair FRSE (March 10, 1748 – July 20, 1819) was a Scottish scientist.

Playfair was professor of mathematics and later professor of natural philosophy at the University of Edinburgh. He is perhaps best known for his book Illustrations of the Huttonian Theory of the Earth (1802), which was a summary of the work of James Hutton. It was through this that Hutton's principle of uniformitarianism, later taken up by Charles Lyell, first reached a wide audience.

In 1795 Playfair created an alternative formulation of Euclid's parallel postulate called Playfair's axiom.

Contents 1 Early life 2 Mature work 3 Family 4 Honours 5 Notes 6 Critical bibliography 7 External links 8 References

Born at Benvie, Angus, Scotland, where his father was parish minister, he was educated at home until the age of fourteen, when he entered the University of St Andrews. In 1766, when only eighteen, he was candidate for the chair of mathematics in Marischal College, Aberdeen, and, although he was unsuccessful, his claims were admitted to be high.

Six years later he made application for the chair of natural philosophy in his own university, but again without success, and in 1773 he was offered and accepted the benefice of the united parishes of Liff and Benvie, vacant by the death of his father. He continued, however, to carry on his mathematical and physical studies, and in 1782 he resigned his charge in order to become the tutor of Ferguson of Raith. By this arrangement he was able to be frequently in Edinburgh and to cultivate the literary and scientific society for which it 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 Edinburgh chair of moral philosophy, Playfair succeeded the former in that of mathematics.

In 1802, he 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 he 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 connexion with Sir John Leslie's appointment to the post he had vacated, and published a satirical Letter (1806).

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^[1] on John Smeaton and William Hyde Wollaston's work championing the theory.

He died in Edinburgh.

John's brothers were the celebrated architect James Playfair who died in 1794 and the engineer William Playfair ^[2].

• Fellow of the Royal Society of Edinburgh
• Fellow of the Royal Society of London, 1807
• Craters on Mars and the Moon were named in his honor.

1. ^ Edinburgh Review, 12, 1808, 120–130
2. ^ Biographical Dictionary of Eminent Scotsmen (1856), reproduced in Significant Scots

A collected edition of Playfair's works, with a memoir by James G. Playfair, appeared at Edinburgh in 4 vols. 8vo.

His writings include a number of essays contributed to the Edinburgh Review from 1804 onwards, various papers in the Phil. Trans. (including his earliest publication, " On the Arithmetic of Impossible Quantities," 1779, and an " Account of the Lithological Survey of Schehallion," 1811) and in the Transactions of the Royal Society of Edinburgh (" On the Causes which affect the Accuracy of Barometrical Measurements," &c.), also 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 (Supplement to fourth, fifth and sixth editions).

His Elements of Geometry first appeared in 1795 and have passed through many editions; his Outlines of Natural Philosophy (2 vols., 1812-1816) consist of the propositions and formulae which were the basis of his class lectures. Playfair's contributions to pure mathematics were not considerable, his paper "On the Arithmetic of Impossible Quantities," that " 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, Robison, many of his reviews, and above all his "Dissertation" are of the utmost value.

• Dictionary of Scientific Biography
• O'Connor, John J., and Edmund F. Robertson. "John Playfair". MacTutor History of Mathematics archive.
• Significant Scots: John Playfair
• National Portrait Gallery

• This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.