his most mathematically productive time. Two books, which appeared in 1715, Methodus incrementorum directa et inversa and Linear Perspective are extremely important in the history of mathematics. Taylor made several visits to France. These were made partly for health reasons and partly to visit friends he had made there. He met Pierre Remond de Montmort and corresponded with him on various mathematical topics after his return. In particular, they discussed infinite series and probability. Taylor also corresponded with de Moivre on probability and at times there was a three-way discussion going on between them. Between 1712 and 1724, Taylor published 13 articles on topics as diverse as describing experiments in capillary action, magnetism and thermometers. He gave an account of an experiment to discover the law of magnetic attraction (1715) and an improved method for approximating the roots of an equation by giving a new method for computing logarithms (1717).Taylor added to mathematics a new branch now called the calculus of finite differences, invented integration by parts, and discovered the celebrated series known as Taylors expansion. These ideas appear in his first book mentioned previously. Other important ideas, which are contained in said book, are singular solutions to differential equations, a change of variables formula, and a way of relating the derivative of a function to the derivative of the inverse function. Also contained is a discussion on vibrating strings, an interest which almost certainly comes from his early love of music.Taylor also devised the basic principles of perspective in Linear Perspective (1715). The main theorem in this work was that the projection of a straight line not parallel to the plane of the picture passes through its intersection and its vanishing point....
