MACLAURIN, COLIN

born February 1698, Kilmodan, Argyllshire, Scot. died June 14, 1746, Edinburgh Scottish mathematician who developed and extended Sir Isaac Newton's work in calculus, geometry, and gravitation. A child prodigy, he entered the University of Glasgow at age 11. At the age of 19, he was elected professor of mathematics at Marischal College, Aberdeen, and two years later he became a fellow of the Royal Society of London. At this time he became acquainted with Newton. In his most important work, Geometrica Organica; Sive Descriptio Linearum Curvarum Universalis (1720; Organic Geometry, with the Description of the Universal Linear Curves), Maclaurin developed several theorems similar to some in Newton's Principia, introduced the method of generating conics (the circle, ellipse, hyperbola, and parabola) that bears his name, and showed that certain types of curves (of the third and fourth degree) can be described by the intersection of two movable angles. On the recommendation of Newton, he was made professor of mathematics at the University of Edinburgh in 1725. In 1740 he shared, with the mathematicians Leonhard Euler and Daniel Bernoulli, the prize offered by the Acadmie des Sciences for an essay on tides. His Treatise of Fluxions (1742) was written in reply to criticisms by George Berkeley of England that Newton's calculus was based on faulty reasoning. In this essay he showed that stable figures for a homogeneous rotating fluid mass are the ellipsoids of revolution, later known as Maclaurin's ellipsoids. He also gave in his Fluxions, for the first time, the correct theory for distinguishing between maxima and minima in general and pointed out the importance of the distinction in the theory of the multiple points of curves. The Maclaurin series, a special case of the Taylor series, was named in his honour. In 1745, when Jacobites (supporters of the Stuart king James II and his descendants) were marching on Edinburgh, Maclaurin took a prominent part in preparing trenches and barricades for the city's defense. As soon as the rebel army captured Edinburgh, Maclaurin fled to England until it was safe to return. The ordeal of his escape ruined his health, and he died at age 48. Maclaurin's Account of Sir Isaac Newton's Philosophical Discoveries was published posthumously, as was his Treatise of Algebra (1748). De Linearum Geometricarum Proprietatibus Generalibus tractatus (A Tract on the General Properties of Geometrical Lines), noted for its elegant geometric demonstrations, was appended to his Algebra.