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 strings, first reduced to mechanical principles by him. This work contains also "Taylor's theorem," the importance of which was not recognised by analysts for over fifty years, until Lagrange pointed out its power. His proof of it does not consider the question of convergency, and is quite worthless. The first rigorous proof was given a century later by Cauchy. Taylor's work contains the first correct explanation of astronomical refraction. He wrote also a work on linear perspective, a treatise which, like his other writings, suffers for want of fulness and clearness of expression. At the age of twenty-three he gave a remarkable solution of the problem of the centre of oscillation, published in 1714. His claim to priority was unjustly disputed by John Bernoulli.

Colin Maclaurin (1698–1746) was elected professor of mathematics at Aberdeen at the age of nineteen by competitive examination, and in 1725 succeeded James Gregory at the University of Edinburgh. He enjoyed the friendship of Newton, and, inspired by Newton's discoveries, he published in 1719 his Geometria Organica, containing a new and remarkable mode of generating conics, known by his name. A second tract, De Linearum geometricarum Proprietatibus, 1720, is remarkable for the elegance of its demonstrations. It is based upon two theorems: the first is the theorem of Cotes; the second is Maclaurin's: If through any point O a line be drawn meeting the curve in n points, and at these points tangents be drawn, and if any other line through O cut the curve in $$\scriptstyle{R_1,~R_2,}$$ etc., and the system of n tangents in $$\scriptstyle{r_1,~r_2,}$$ etc., then $\scriptstyle{\sum\frac{1}{OR}=\sum\frac{1}{Or}}$.|undefined This and Cotes' theorem are generalisations of theorems of Newton. Maclaurin uses these in his treatment of curves of the second and third degree, culminating in the remarkable theorem that if a quadrangle has its vertices and the two points of intersection of its opposite sides upon a curve of the