Taylor's magic splines

Although the presentation of the spline is routine for many of us, classica l textbooks have not paid sufficient tribute to Brook Taylor in explaining such a concept whose roots can be found on his historic work Methodus Incre mentorum Directa et Inversa, published in London in 1715. As our modest mem orial to such a genius, we discuss the development of polynomial splines on the basis of Taylor's series. The specific steps for the construction of p arabolic, cubic, tetra and quintic splines are given here.