Mr. T. S. Davies on Geometry and Geometers. 499 



at the head identifies its authorship and purpose. The paper 

 itself has much the appearance of being intended for press, 

 though there is not the least reason to think it ever was 

 printed. On this account I give it entire. Probably it was 

 cancelled on account of Simpson's intimacy with Nourse. 



" Remarks upon some of Mr. Thomas Simpson's notes at the end of 

 the second edition of his Elements of Geometry. 



"Art. 1 . In page 257 and the next there is a long note, one design 

 of which is to show the impropriety of conceiving one figure to be 

 transferred from one place to another when the thing in hand can be 

 done another way ; he says Euclid has never recourse to this in other 

 cases ; but Euclid not only uses it in the 4 Prop. 1 and in the 24 

 Prop. 3. but also in the*4 Prop. 6. where he might instead of con- 

 ceiving one of the triangles contiguous to the other with its base in 

 the same straight line with the base of the other, have constructed a 

 triangle in that position, having its sides equal, each to each, to the 

 sides of the other ; and in like manner the corollary of 1 Prop. 6 

 might have been shewn ; but it would have been quite needless in 

 either case. Mr. Simpson himself uses this method in the axiom 

 before his 7'^ Book, where without the least necessity he conceives 

 the figure PQR to be formed equal and similar to the bases ABC, 

 DEF and the prisms upon these last bases to be placed upon the 

 base PQR ; whereas he needed only have conceived the prism on the 

 base ABC to be applied to the prism on the base DEF so as their 

 bases may coincide ; but he has been afraid that they could not stand 

 both together upon one base, and therefore he bids place them suc- 

 cessively upon the base PQR." 



The reader will remark the quaint humour of the close of 

 this article : but long experience convinces me that very few 

 pupils are able to abstract all notions of impeiietrahility when 

 considering the geometry of solids. The term "solid" is 

 indeed an unfortunate one to have chosen, by which to desig- 

 nate a fifjure of three dimensions; and it is difficult to remove 

 from the young mind some vague notion of the impossibility 

 (or absurdity of directing it) of applying one solid to another 

 so that both shall be in the same place at the same time. The 

 method of Simson's Euclid is unquestionably legitimate : but 

 something must be conceded in the outset of a new course of 



• • • m 



study to the youthful incapacity for abstraction. The con- 

 ception of both solids being successively fitted into the same 

 matrix, or in the form that Simpson gives it, is less likely to 

 violate previous notions, than the more abstract and certainly 

 more philosophical process. Neither is it inaccurate under 

 any aspect as a method of reasoning; and the more desirable 

 view will easily present itselfto the mind of the careful student 

 at a stage of reading not very remote. 



But is the supraposition of a plane figure upon another 



2 K2 



