Mathematician; born at Edmonton, near London, Aug. 18, 1685; entered St. John’s College, Cambridge, in 1701; distinguished himself in music, painting, and mathematics; in 1708 wrote a treatise on “The Center of Oscillation,” which was published in the “Philosophical Transactions” for 1713; in 1712 was chosen a fellow of the Royal Society, of which he became secretary two years later; and in 1715 he had a controversial correspondence with Count Raymond de Montmort upon the philosophical theories of Malebranche. He published “Methodus Incrementorum,” etc. (1715), which contains the foundation of the calculus of finite differences and the first announcement of the famous “Taylor’s theorem,” the latter almost unnoticed by mathematicians until 1772, when Lagrange adopted it as the basis of the differential calculus. Among his other works were “New Principles of Linear Perspective” (1719); and “Contemplatio Philosophica,” which was published, with a memoir by his grandson, Sir William Young (1793). Died in London Dec. 29, 1731.

Personal

  We have a remarkable evidence of domestic unhappiness annihilating the very faculty of genius itself, in the case of Dr. Brook Taylor, the celebrated author of the “Linear Perspective.” This great mathematician in early life distinguished himself as an inventor in science, and the most sanguine hopes of his future discoveries were raised both at home and abroad. Two unexpected events in domestic life extinguished his inventive faculties. After the loss of two wives, whom he regarded with no common affection, he became unfitted for profound studies; he carried his own personal despair into his favourite objects of pursuit, and abandoned them. The inventor of the most original work suffered the last fifteen years of his life to drop away, without hope, and without exertion.

General

  A single analytical formula in the “Method of Increments” has conferred a celebrity on its author, which the most voluminous works have not often been able to bestow. It is known by the name of Taylor’s Theorem, and expresses the value of any function of a variable quantity in terms of the successive orders of increments, whether finite or infinitely small. If any one proposition can be said to comprehend in it a whole science, it is this: for from it almost every truth and every method of the new analysis may be deduced. It is difficult to say, whether the theorem does most credit to the genius of the author, or the power of the language which is capable of concentrating such a vast body of knowledge in a single expression.

  Successively modified, transformed, and extended by Maclaurin, Lagrange, and Laplace, whose names are attached to their respective formulæ.

  I have made this extract from a very short tract, called “Contemplatio Philosophica,” by Brook Taylor, which I found in an unpublished memoir of his life printed by the late Sir William Young in 1793. It bespeaks the clear and acute understanding of the celebrated philosopher, and appears to me an entire refutation of the scholastic argument of Descartes; one more fit for the Anselms and such dealers in words, from whom it came, than for himself.

  In 1715 he published his “Methodus Incrementorum Directa et Inversa” (London, 4to), which was in reality the first treatise dealing with the calculus of finite differences. It contained the celebrated formula known as “Taylor’s theorem” which was the first general expression for the expansions of functions of a single variable in infinite series, and of which Mercator’s expansion of log. (1 + x), Sir Isaac Newton’s binomial theorem, and his expansions of sin x, cos x, e^x, &c., were but particular cases. The importance of the discovery was not fully recognised, however, until it was pointed out by La Grange in 1772. In this work Taylor also applied the calculus for the solution of several problems which had baffled previous investigators. He obtained a formula showing that the rapidity of vibration of a string varies directly as the weight stretching it and inversely as its own length and weight. For the first time he determined the differential equation of the path of a ray of light when traversing a heterogeneous medium. He also discussed the form of the catenary and the determination of the centres of oscillation and percussion.