208 Mr. T. S. Davies on Geometry and Geometers. 



luable for the great number of properties which the author 

 has brought together, of which a fair portion were original. 

 As geometry, however, both works are extremely impure, every 

 geometrical difficulty being unceremoniously got over by an 

 algebraical equation — a practice only too common amongst 

 the so-called geometrical writers of our own time. This, 

 however, is not the geometry bequeathed us by the Greeks, 

 and exemplified by the Andersons, the Gregories, the Halleys, 

 the Simsons, and the Stewarts of these isles. 



The popular error to which I referred is, that Emerson 

 was the Coryphaeus of the non-academic class of geometers. 

 He has never been recognized by themselves as the head, the 

 founder, or the leader of their class; but I suppose the fre- 

 quency of his books on the stalls has led men little acquainted 

 with the history of English geometry to infer that they either 

 are, or have been, in great demand, and consulted as oracles. 

 This never-ending reappearance is more due to the almost 

 indestructible paper on which they were printed, and the firm 

 bindings in which they were issued, than to any other cause; 

 as very few of them ever reached a second edition, and a 

 great number lay on the bookseller's hands at the time of 

 Emerson's death. They were pushed into notice by the per- 



almost the only marked exception — or perhaps also Euclid's Porisms. We 

 find at all events, extremely little (if anything, properly speaking) concern- 

 ing lines meeting in a point, or points ranging in a straight line. The 

 modern French geometers were the first to enter upon this class of re- 

 searches with any degree of system ; and the results have justified their 

 expectations, however sanguine. We need not then, after all, feel much 

 surprise at finding the proposition in question claiming so recent a place in 

 geometry; and the same may be said of a great number of now-familiar 

 truths. 



Postscript, August 24. — Whilst reading the proof sheets, the Mechanics' 

 Magazine of this date reached me, containing one of Mr. Wilkinson's able 

 and elaborate analyses of our English mathematical periodicals, viz. of the 

 Miscellanea Curiosa Mathematica, 1745-53, edited by Holliday, whose 

 name has been already mentioned. As there is one passage which renders 

 a slight modification of the preceding paragraph necessary, I quote it as it 

 stands — from its offering less trouble, both to myself and the printer at the 

 last moment, than recomposition and resetting would do. 



Speaking of art. xxxix., " A new Proposition in Geometry demonstrated, 

 by Mr. William Chappie," he says : — 



" This proposition is the new well-known property, that ' the three per- 

 pendiculars of any triangle intersect in the same point,' and although taken 

 for granted in the solutions of Quest. 45 Gentleman's Diary for 1743-44; 

 Quest. 260 Ladies'" Diary, 1745-46, the honour of a formal enunciation 

 and demonstration appears to be due to Mr. Chappie. The property is 

 stated both for the acute and obtuse-angled triangle, ' the same demonstra- 

 tion serving for both, which however is not conducted in so purely geo- 

 metrical a manner as one could wish.' " He then mentions some more re- 

 cent researches, which, however, need not be introduced here. 



