professor at Halle, was ambitious to figure as successor of Leibniz, but he "forced the ingenious ideas of Leibniz into a pedantic scholasticism, and had the unenviable reputation of having presented the elements of the arithmetic, algebra, and
analysis developed since the time of the Renaissance in the form of Euclid,–-of course only in outward form, for into the spirit of them he was quite unable to penetrate."16
The contemporaries and immediate successors of Newton in Great Britain were men of no mean merit. We have reference to Cotes, Taylor, Maclaurin, and De Moivre. We are
told that at the death of Roger Cotes (1682–1716), Newton exclaimed, "If Cotes had lived, we might have known something." It was at the request of Dr. Bentley that Cotes undertook the publication of the second edition of Newton's Principia. His mathematical papers were published after his
death by Robert Smith, his successor in the Plumbian professorship
at Trinity College. The title of the work, Harmonia Mensurarum, was suggested by the following theorem contained in it: If on each radius vector, through a fixed point , there be taken a point , such that the reciprocal of be the arithmetic mean of the reciprocals of , then the locus of will be a straight line. In this work progress was made in the application of logarithms and the
properties of the circle to the calculus of fluents. To Cotes we owe a theorem in trigonometry which depends on the
forming of factors of . Chief among the admirers of Newton were Taylor and Maclaurin. The quarrel between English and Continental mathematicians caused them to work quite independently of their great contemporaries across the Channel.
Brook Taylor (1685–1731) was interested in many branches of learning, and in the latter part of his life engaged mainly in religious and philosophic speculations. His principal work, Methodus incrementorum directa et inversa, London, 1715–1717, added a new branch to mathematics, now called "finite differences."
He made many important applications of it, particularly to the study of the form of movement of vibrating
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