DEVELOPMENT OF MATHEMATICAL THOUGHT. 733 



exhibited the slovenliness of a man who talks at the 

 same time in more than one language, because he is 

 too negligent to arrange his thoughts clearly. Then 

 there come in the demands of the teacher who has 

 to introduce abstract and difficult subjects in a clear, 

 consistent, and simple manner, taking heed that with 

 the elements he does not introduce the sources of 

 future error. The same interest that led in ancient 

 times to the composition of the Elements of Euclid has 

 led, in the higher education of the nineteenth century, 

 beginning with the Ecole Polytechnique and ending with 

 Weierstrass's famous courses of lectures at Berlin, to 

 a revision and recasting of the whole elementary frame- 

 work of mathematics. In the mean time the resource- 

 fulness in applied mathematical thought which ever 

 since the age of Newton has characterised the in- 

 dividual research of this country, has opened out new 

 vistas and afforded much material for critical siftings 

 and strict definitions. Both qualities were united in 

 the great mind of Gauss with a regrettable absence of 

 the love of teaching and the communicative faculty. 

 Like Newton's ' Principia,' his greatest works will 

 always remain great storehouses of thought; while his 

 unpublished remains might be compared to the Queries 

 appended to the ' Opticks ' and to the ' Portsmouth 

 Papers.' 



Several eminent mathematicians in France, Germany, 

 and Italy have been for many years l working at the 



1 The literature of this sub- 

 ject has been rapidly increasing 

 since the year 1872, the ap- 

 proximate date of the following 



publications, which created an 

 epoch : R. Dedekind, ' Stetigkeit 

 und irrationale Zahlen ' (Braunsch- 

 weig, 1872) ; E. Heine, " Die 



