**John Playfair** FRSE, FRS (10 March 1748 – 20 July
1819) was a Scottish scientist and mathematician, and a 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 summarized the
work of

James Hutton. It was through
this book that Hutton's principle of

uniformitarianism, later taken
up by

Charles Lyell, first reached a
wide audience. Playfair also is remembered for his proposal of an
alternative to

Euclid's parallel postulate
.

## Early life

Born at
Benvie, Angus, Scotland,
where his father was parish minister, Playfair was educated at home
until the age of fourteen, when he entered the University of St
Andrews. In 1766, when only eighteen, he was a
candidate for the chair of mathematics in Marischal
College (now part of the University of Aberdeen), and,
although he was unsuccessful, his claims were admitted to be
high.
Six years
later he applied 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. Playfair continued,
however, 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,
Playfair 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.

Interestingly, (Alhazen of the fame of Alhazen Plain on the
moon)Ibn al-Haytham's work (800 years before Playfair) of simple
substitution of Euclidean theory was the original from which John
Playfair managed to 'formulate' his revolutionary theory of
parallel postulates.

## Mature work

In 1795 Playfair published an alternative, more stringent
formulation of Euclid's parallel postulate, which is now called

Playfair's axiom; though the axiom
bears Playfair's name, he did not create it, but credited others,
in particular William Ludlam (1718 - 1788), with the prior use of
it.

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
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 on

John Smeaton and

William Hyde Wollaston's work
championing the theory.

## Family

John's brothers were architect

James
Playfair and engineer

William
Playfair.

## Honours

## Critical bibliography

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 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 has 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.

## Notes

## External links