We have every reason to believe that the publication of Newton's _Principia_ had a powerful effect in diffusing a semi-geometrical taste amongst the academical class of students in this country, and it is equally certain that this diffusion became much more general, when Motte, in 1729, published his translation of that admirable work. The nature of the contents of the _Principia_, however, precluded the possibility of its being adapted to form the taste of novices in the study of geometry; it served rather to exhibit the _ne plus ultra_ of the science, and produced its effect by inducing the student to master the rudimentary treatises thoroughly, in order to qualify himself for understanding its demonstrations, rather than by providing a series of models for his imitation. A powerful inducement to the study of pure geometry was therefore created by the publication of Motte's translation: ordinary students had here a desirable object to obtain by its careful cultivation, which hitherto had not existed, and hence when Professor Simpson, of Woolwich, published his _Algebra_ and the _Elements of Geometry_ in 1745 and 1747, a select reading public had been formed which hailed these excellent works as valuable accessions to the then scanty means of study. Nor must the labours of Simpson's talented associates, Rollinson and Turner, be forgotten when sketching the progress of this revival. The pages of the _Ladies' Diary_, the _Mathematician_, and the _Mathematical Exercises_, of which these gentlemen were severally editors and contributors, soon began to exhibit a goodly array of geometrical exercises, whilst their lists of correspondents evince a gradual increase in numbers and ability. The publication of Stewart's _General Theorems_ and Simson's edition of _Euclid_, in 1746 and 1756, probably to some extent assisted the movement; but the most active elements at work were undoubtedly the mathematical periodicals of the time, aided by such powerful auxiliaries as Simpson's _Select Exercises_ (1752) and his other treatises previously mentioned. It may further be observed that up to this period the mere English reader had few, if any means of obtaining access to the elegant remains of the ancient geometers. Dr. Halley had indeed given his restoration of Apollonius's _De Sectione Rationis_ and _Sectione Spatii_ in 1706. Dr. Simson had also issued his edition of the _Locis Planis_ in 1749; but unfortunately the very language in which these valuable works were written, precluded the possibility of {59} these unlettered students being able to derive any material advantages from their publication: and hence arises another weighty reason why Simpson's writings were so eagerly studied, seeing they contained the leading propositions of some of the most interesting researches of the Alexandrian School.