42 UNIVERSITY OF MISSOURI BULLETIN 



in a desire to express facts briefly, to derive results which 

 will enable us to perform operations without excessive labor. 

 At least mathematics proper, and even reckoning does not 

 depend upon the particular symbolism which we use; the 

 question of symbolism is a chapter in shorthand, and not a 

 chapter in mathematics. 



Leaving this obvious phase of mathematics, which is 

 already too firmly embedded in the public mind, I should 

 pass quickly to geometry, which also finds common recogni- 

 tion as a part of mathematics. That it deals with position 

 and space, with figures in space, and with the relations exist- 

 ing between those figures in trite. That its scope includes 

 also drawing and measurement of all kinds is perhaps less 

 commonly thought. 



An entirely mistaken idea is that geometry is closely 

 allied to formal logic. Indeed, logic is necessary in geometry, 

 but there is no reason why the formalities of logic should 

 not be utterly divorced from geometry, in the sense that formal 

 logic is divorced from physics and other sciences in which 

 reasoning certainly occurs. It is to be hoped that that reason- 

 ing remains just as logical. 



Beyond these two, which form perhaps the greater basis 

 of the common conception of mathematics, the usual course 

 proceeds to trigonometry, itself indeed nothing but a chapter 

 in geometry. The reason that trigonometry is excepted is 

 curious. It is because our great geometer, Euclid, was ignor- 

 ant of trigonometry, and his great book which has for two 

 thousand years formed the basis for every course in elemen- 

 tary geometry happened not to contain that chapter. Its 

 subject matter is simply the rules for finding the remaining 

 parts of a triangle when sufficient number of parts (namely, 

 three) are given. These rules are quite simple ; they were 

 forecast entirely in Euclidean geometry, and might easily be 

 stated there. As usually taught, trigonometry includes also 

 a few extensions of the orignial ideas, but these extensions 



