58 



NOTES AND QUERIES. 



[No. 34. 



ancient geometry from its favoured retreat in the 

 British Isles; the Professor seemed not to be 

 aware that there existed a devoted band of men in 

 the north, resolutely bound to the pure and ancient 

 forms of geometry, who in the midst of the tumult 

 of steam engines, cultivated it with unyielding 

 ardour, preserving the sacred fire under circum- 

 stances which would seem from their nature most 

 calculated to extinguish it." Mr. Harvey, however, 

 admitted his inability clearly to trace the " true 

 cause of this remarkable phenomenon," but at the 

 same time suggested that " a taste for pure geo- 

 metry, something like that for entomology among 

 the weavers of Spitalfields, may have been trans- 

 mitted from father to son ; but who was the dis- 

 tinguished individual' _/!>«< to create it, in the 

 peculiar race of men here adverted to, seems not 

 to be known." However, as " the two great re- 

 storers of ancient geometry, Matthew Stewart and 

 Robert Simson, it may be observed, lived in Scot- 

 land," he asks the important questions: — "Did 

 their proximity encourage the growth of this spirit? 

 Or were their writings cultivated by some teacher 

 of a village school, who communicated by a method, 

 which genius of a transcendental order knows so 

 well how to employ, a taste for these sublime in- 

 quiries, so that at length they gradually worked 

 their way to the anvil and the loom ? " 



An attentive consideration of these questions in 

 all their bearings has produced in the mind of the 

 writer a full conviction that we must look to other 

 sources for the revival of the study of the ancient 

 geometry than either the writings of Stewart or 

 Simson. It has been well observed by the most 

 eminent geometer of our own times, Professor 

 Davies — whose signature of Pen-and-Ink (Vol. ii., 

 p. 8.) affords but a flimsy disguise for his well- 

 known propria persona — that " it was a great mis- 

 take for these authors to have written their prin- 

 cipal works in the Latin language, as it has done 

 more than anything else to prevent their study 

 among the only geometers of the eighteenth cen- 

 tury who were competent to understand and value 

 them ;" and it is no less singular than true, as 

 the same writer elsewhere observes, " that whilst 

 Dr. Stewart's writings were of a kind calculated 

 to render them peculiarly attractive to the non- 

 academic school of English geometers, they remain 

 to this day less generally known than the writings 

 of any geometer of these kingdoms." The same 

 reuiarks, in a slightly qualified form, may be applied 

 to most of the writings of Simson ; for although his 

 edition of Euclid is now the almost universally 

 adopted text-book of geometry in England, at the 

 time of its first appearance in 1756 it did not differ 

 so much from existing translations as to attract 

 particular attention by the novelty of its contents. 

 Moreover, at this time the impulse had already 

 been given and was silently exerting its influence 

 upon a class of students of whose existence Dr. 



Simson appears to have been completely ignorant. 

 In one of his letters to Nourse {Phil. Mag., Sept. 

 1848, p. 204.) he regrets that "the taste for the 

 ancient geometry, or indeed any geometry, seems 

 to be quite worn out ; " but had he instituted an 

 examination of those contemporary pei'iodicals 

 either wholly or partially devoted to mathematics, 

 he would have been furnished with ample reasons 

 for entertaining a different opinion. 



We have every reason to believe that the publi- 

 cation 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 de- 

 monstrations, 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 Simp- 

 son, 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 editoi's and 

 contributors, soon began to exhibit a goodly array 

 of geometrical exercises, whilst their lists of cor- 

 respondents 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 Sections Rationis and Sectione 

 Spatii in 1706. Dr. Simson had also issued his 

 edition of the Locis Planis in 1749 ; but unfortu- 

 nately the very language in which these valuable 

 works were written, precluded the possibility of 



