EVOLUTION OF THE SCIENTIFIC INVESTIGATOR 139 



conditions as our laws are to ours, in which the phenomena of 

 nature were rudely observed, and striking occurrences in the earth 

 or in the heavens recorded in the annals of the nation. 



Vast was the progress of knowledge during the interval between 

 these empires and the century in which modern science began. Yet, 

 if I am right in making a distinction between the slow and regular 

 steps of progress, each growing naturally out of that which preceded 

 it, and the entrance of the mind at some fairly definite epoch into an 

 entirely new sphere of activity, it would appear that there was only 

 one such epoch during the entire interval. This was when abstract 

 geometrical reasoning commenced, and astronomical observations 

 aiming at precision were recorded, compared, and discussed. Closely 

 associated with it must have been the construction of the forms of 

 logic. The radical difference between the demonstration of a theorem 

 of geometry and the reasoning of every-day life which the masses of 

 men must have practiced from the beginning, and which few even 

 to-day ever get beyond, is so evident at a glance that I need not 

 dwell upon it. The principal feature of this advance is that, by one 

 of those antinomies of the human intellect of which examples are not 

 wanting even in our own time, the development of abstract ideas 

 preceded the concrete knowledge of natural phenomena. When we 

 reflect that in the geometry of Euclid the science of space was 

 brought to such logical perfection that even to-day its teachers are 

 not agreed as to the practicability of any great improvement upon 

 it, we cannot avoid the feeling that a very slight change in the 

 direction of the intellectual activity of the Greeks would have led to 

 the beginning of natural science. But it would seem that the very 

 purity and perfection which was aimed at in their system of geometry 

 stood in the way of any extension or application of its methods and 

 spirit to the field of nature. One example of this is worthy of atten- 

 tion. In modern teaching the idea of magnitude as generated by 

 motion is freely introduced. A line is described by a moving point; 

 a plane by a moving line; a solid by a moving plane. It may, at first 

 sight, seem singular that this conception finds no place in the Euclid- 

 ian system. But we may regard the omission as a mark of logical 

 purity and rigor. Had the real or supposed advantages of introduc- 

 ing motion into geometrical conceptions been suggested to Euclid, 

 we may suppose him to have replied that the theorems of space are 

 independent of time; that the idea of motion necessarily implies 

 time, and that, in consequence, to avail ourselves of it would be to 

 introduce an extraneous element into geometry. 



It is quite possible that the contempt of the ancient philosophers 

 for the practical application of their science, which has continued in 

 some form to our own time, and which is not altogether unwholesome, 

 was a powerful factor in the same direction. The result was that, 



