Waring's mathematical style is highly analytical. In fact he criticised those British mathematicians who adhered too strictly to geometry. It is indicative that he was one of the subscribers of John Landen's "Residual Analysis" (1764), one of the works in which the tradition of the Newtonian fluxional calculus was more severely criticised. In the preface of "Meditationes Analyticae" Waring showed a good knowledge of continental mathematicians such as Alexis Clairaut, Jean le Rond d'Alembert, and Euler. He lamented the fact that in Great Britain mathematics was cultivated with less interest than on the continent, and clearly desired to be considered as highly as the great names in continental mathematics—there is no doubt that he was reading their work at a level never reached by any other eighteenth-century British mathematician. Most notably, at the end of chapter three of "Meditationes Analyticae" Waring presents some partial fluxional equations (partial differential equations in Leibnizian terminology); such equations are a mathematical instrument of great importance in the study of continuous bodies which was almost completely neglected in Britain before Waring's researches. One of the most interesting results in "Meditationes Analyticae" is a test for the convergence of series generally attributed to d'Alembert (the 'ratio test'). The theory of convergence of series (the object of which is to establish when the summation of an infinite number of terms can be said to have a finite 'sum') was not much advanced in the eighteenth century.