# WALLACE, WILLIAM

(b. Dysart, Scotland, 23 September 1768; d. Edinburgh, Scotland, 28 April 1843), mathematics.

Wallace had no schooling after the age of eleven, when he was apprenticed to a bookbinder; he subsequently taught himself mathematics and became a teacher at Perth. In 1803 he was appointed to the Royal Military College at Great Marlow and in 1819 became professor of mathematics at the University of Edinburgh, where he remained until his retirement in 1838. Wallace wrote many articles for encyclopedias and numerous papers in Proceedings of the Royal Society of Edinburgh, including some on mechanical devices. He also played a large part in the establishment of the observatory on Calton Hill, Edinburgh.

The feet of the perpendiculars to the sides of a triangle from a point P on its circumcircle are collinear. This line is sometimes called the pedal line but more often, incorrectly, the Simson line of the triangle relative to P. It was stated by J. S. Mackay that no such theorem is in Simson’s published works. The result appears in an article by Wallace in Thomas Leybourn’s Mathematical Repository (2 [1799-1800], 111), and Mackay could find no earlier publication. In the preceding volume Wallace had proved that if the sides of a triangle touch a parabola, the circumcircle of the triangle passes through the focus of the parabola, a result already obtained by Lambert. To demonstrate this, Wallace showed that the feet of the perpendiculars from the focus to the sides of the triangle lie on the tangent at the vertex of the parabola. which is equivalent to saying that the pedal line of the triangle is the tangent at the vertex. The close connection of this theorem with the pedal line suggests that Wallace was led to the property of the pedal line from the parabolic property.

In 1804 the following result was proposed for proof in Mathematical Repository (n.s. 1. 22): IF four straight lines intersect each other to form four triangles by omitting one line in turn, the circumcircles of these triangles have a point in common. The proposer was “Scoticus” , which Leybourn later said was a pseudonym for Wallace. Two solutions were given in the same volume (170). Miquel later proved that five lines determine five sets of four lines, by omitting each in turn; and the five points, one arising from each such set, lie on a circle. Clifford proved that the theorems of Wallace and Miquel are parts of an endless chain of theorems: 2n lines determine a point as the intersection of 2n circles: taking one more line, 2n + 1 lines determines 2n + 1 sets of 2n lines, each such set determines a point, and these 2n + 1 points lie on a circle.

## BIBLIOGRAPHY

Two articles by J. S. Mackay in Proceedings of the Edinburgh Mathematical Society9 (1891), 83–91, and 23 (1905), 80–85—give the bibliography of Wallace’s two theorems and later extensions and generalizations with scholarly thoroughness.

For a full account of Wallace’s life, see the unsigned but evidently authoritative obituary in Monthly Notices of the Royal Astronomical Society, 6 (1845), 31–36.

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## Wallace, William

Wallace, William (d. 1305). Scottish patriot and commander at the battles of Stirling Bridge (1297) and Falkirk (1298). Wallace came of a middling family, retainers of the Stewarts in the neighbourhood of Paisley. Nothing reliable is known of his date of birth or early life; nor is it easy to explain his emergence as a Scottish leader in 1297.

In that year there were many prominent Scots anxious to resist Edward's ‘take-over’ of the previous year, including Wallace's lord, James, the hereditary steward of Scotland. But there was no co-ordinated or open rising, only miscellaneous outbreaks in the early part of the year. In May Wallace killed the English sheriff of Lanark in an affray. He was joined by Sir William Douglas in an attack on the English justiciar at Scone. Others, including Robert Bruce, earl of Carrick, the future Robert I, were also prepared to join in. This rising might easily have achieved nothing, since determined English action quickly persuaded many of the prominent leaders of the Scots to make terms; but in May another movement had started in Moray, with an attack on Inverness led by the young Andrew Murray, son of a leading baron. These twin risings, by Wallace and Murray, attracted increasing support, including that of the earls of Fife and Buchan, and Bruce openly took the Scottish side. By August, Murray and Wallace had joined forces and threatened Stirling. Their astute tactics at the battle of Stirling Bridge, and the ineptitude of the English commander Earl Warenne, resulted in a dramatic victory, which put Edward I's position in Scotland in peril. Murray, however, was wounded and died a few months later.

The Scottish kingdom existed once more, and was to maintain its existence, nominally in the name of the absent King John, till 1304. By early 1298 Wallace had been knighted, and emerged as sole guardian. By June, however, Edward was leading an army of some 12,000 men to repress what he regarded as a revolt. At Falkirk, in more open ground than at Stirling, the English knights and archers were devastating. The Scots were routed and Wallace escaped into hiding, resigning his guardianship immediately.

His next task was abroad. In 1299 he led a mission to the French court to get more active support from Philip IV, and seems to have stayed in Paris for most of the next year. By 1303 Wallace was back in Scotland, again fighting in the south. By 1304, Edward had triumphed. Almost all the Scottish leaders submitted on negotiated terms. On 24 July Stirling, the last castle to be held against Edward, surrendered, and only Wallace and John de Soules remained in resistance.

Wallace was now a fugitive. In August 1305 he was captured, and there followed a show trial on 23 August, and immediate execution for ‘treason’, of which, as he had never sworn allegiance to Edward, he could not justly be accused. From that day, Wallace has been regarded as one of the greatest heroes in Scotland's national history.

Bruce Webster

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## Bruce, Sir William

Bruce, Sir William (c.1630–1710). The founder of Classical architecture in Scotland. A Perthshire laird, he became Surveyor-General and Overseer of the King's Buildings in Scotland (1671–8), creating a symmetrical and very French façade at Holyroodhouse (1671–9). He was consulted by many members of the Scottish aristocracy who wanted to improve their houses. At Kinross House (1686–93) he adopted the highly accomplished manner of Pratt and Webb, and the architecture is enhanced by its formal setting. The main vista is terminated by the ruins of Lochleven Castle, so Bruce, like Vanbrugh, has a position in the history of the Picturesque. He designed Lauder Church, Berwickshire (1673), Hopetoun House, West Lothian (1699–1710), the Town House, Stirling (1703–5), and (probably) the Hope Aisle, Abercorn Church, West Lothian (1707–8).

Bibliography

Colvin (1995);
Dunbar (1970, 1978);
Fenwick (1970)

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## Wallace, William

Wallace, William (d. 1631). Scottish architect. He was Master-Mason to the Scottish Crown from 1617 until his death, and carried out works including the King's Lodging, Edinburgh Castle (1615–17), the north quarter of Linlithgow Palace, West Lothian (1618–21), and parts of Stirling Castle. He was responsible for Heriot's Hospital, Edinburgh (1628–59), a showy work with Anglo-Flemish Mannerist decorations. Indeed, he was a major figure in the introduction of this style to Scotland. Among his other designs were Wintoun Castle, East Lothian (c.1620–30), and the monument of John Byres of Coates (d. 1629) in the Greyfriars Cemetery, Edinburgh, in which exuberant strapwork abounds.

Bibliography

Colvin (1995);
Dunbar (1966, 1978);
Gifford,, McWilliam,, & and Walker (1984);
Mylne (1893)

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## Bruce, William Speirs

William Speirs Bruce (spĬrz), 1867–1921, Scottish explorer and authority on the polar regions. He first went to the Antarctic as ship's surgeon in 1892 and later did survey work in Franz Josef Land and oceanographic work in the Arctic Ocean. He led (1902–4) the Scottish National Antarctic Expedition in the Scotia, performing much valuable scientific research in the Weddell Sea and discovering Coats Land. Bruce established a meteorological station on Laurie Island (in the South Orkney group). He edited the reports of the expedition (6 vol.) and wrote Polar Exploration (1911). Bruce made a number of voyages to Spitsbergen and became an authority on the islands.

See R. N. Rudmose Brown, A Naturalist at the Poles (1923).

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## Wallace, William

Wallace, William (b Greenock, 1860; d Malmesbury, 1940). Scottish composer and writer. Entered RAM 1889 after practising as surgeon. Hon. Sec., Phil. Soc. 1911–13. Wrote 6 sym.-poems, The Passing of Beatrice (1892) being said to be first Brit. work in the genre. Others included William Wallace (1905) and François Villon (1909). Also comp. sym., suites The Lady from the Sea (after Ibsen, 1892) and Pelléas et Mélisande (1900), songs, etc. Prof. at RAM. Wrote Richard Wagner as he lived (1925).