Mr. T. S. Davies on Geometry and Georheten. 509 



little circle in Glasgow. Simson was there, what Johnson was 

 in his "Club" in Fleet Street. 



Simpson is the only author referred to by Simson, who was 

 both British and unadorned by academic titles ; and he is 

 introduced into the first and second editions of the Euclid 

 almost by inevitable necessity. Throughout, he is rather a 

 social pay-verm than a scientific brother. In many of the 

 views of the preceding paper I concur: still I cannot but re- 

 gret the tone in which some of them are expressed. The 

 mode, too, in which Dr. Trail refers to Simpson is in too 

 strict keeping with a feeling of contempt towards " those 

 whose works had been criticised in the Doctor's notes;" the 

 reference applying, as far as I have been able to ascertain, 

 to Thomas Simpson only. No other author of the time is 

 mentioneii, or even alluded to, in Simson's Notes, and indeed 

 no other work on the Elements of Geometry was published 

 during the interval in question. The first edition of Emer- 

 son's was in 1763, and 1 find no allusion there to Simson or 

 to Simpson either. 



I have more particularly alluded to the matters in the pre- 

 ceding paragraph for the purpose of remarking that if a ma- 

 thematician of Simpson's eminence (and I may add of Simp- 

 son's Eurojiean reputation too) could be thus sijffie by " titled 

 scholars," we cannot wonder at the general neglect with which 

 the host of geometers in humble life, during the last century and 

 first quarter of the present one, have been treated by academic 

 bodies*. Few of my readers have the least idea of the exist- 

 ence of a body of men who, through several successive ages, 

 have cultivated geometry with an ardour that is probably un- 

 exampled, and with a degree of success commensurate with 

 that ardour. Their reward, as well as their patrimony, was 

 poverty ; and their fame was limited to their own narrow circle. 



• As a specimen of even a somewhat recent manifestation of this spirit, 

 1 may quote Dr. Cressweli's treatise on Maxima and Minima. He says, 

 " the Elements of Thomas Simpson contain a series of propositions on the 

 Maxima and Minima of Geometrical Qnantities, in which there is not 

 mnch that is original" (p. 5). I confess myself unable to find in any 

 writer antecedent to Simpson, a large relative portion of the propositions 

 in his book, and I cannot accede to the dictum of Dr. Cresswell, except in 

 the qualified sense of the chapter itself being a 'little ' one— barely fifteen 

 pages. But when a writer thus becomes critical upon the subject oforigi. 

 natifi/ in others, we have a right to test him by the same criterion. What 

 is there *' new" in Dr. Cressweli's own treatise, either as to principle, me- 

 thod of development, or final result ? Certainly a finer opportunity for the 

 production of a truly classical work on the subject was never thrown away 

 by any writer. Cressweli's volume on this one subject is really larger than 

 Simpson's entire treatise on geometry generally. No man can do much in 

 fifteen pages, but any competent person might do a good deal in 273. 



