EVOLUTION OF 'I'HK SCI KNTIFIC INVESTKJ ATOK. 225 



plu'iioini'iia of iiaduv wore I'luloly ohsorvod, aiul strikiiii; occiii'i'ouces 

 in llic earth oi- in (he licaxciis recorded in (he annals of (he nation. 



\'as( was the proiiress of knowledgfe (hii'in*^- (he in(erva] l)etwcen 

 these empires and (he century in which modern science he<>;an. "^'et, 

 if I am riiild in makin<; a (listinc(i()n between the slow and i-e<2:uhir 

 steps of j)r()g-ress, each <>'rowini>' naturally out of that which pre- 

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

 into an entirely new sphei'c of ac(ivi(y, it would appear that there 

 was only one such epoch (hirinii; (he en(ii-e in(erval. This was wdien 

 abstract acometi'ical reasonin<>' connnenced, and astronomical observa- 

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

 Closely associated with it nuist have been the construction of the 

 forms of loo:ic. The radical diti'erence l)etween the demonstration 

 of a theorem of geometiT and the reasoning of everyday life which 

 the masses of men must have practiced from the beginning, and 

 which few even to-day ever get l)eyond, is so evident at a glance 

 that I need not (hvell upon it. The principal feature of this ad- 

 vance is that, by one of those antinomies of the human intellect of 

 Avhich examples are not Avanting even in our time, the develop- 

 ment of abstract ideas jn-eceded the concrete knowledge of 

 natural phenomena. AVhen we reflect that in the geometry of 

 Kuclid 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 can not av^oid the feeling that 

 a very slight change in the direction of the intellectual activity of 

 the (ireeks 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 w^ay of any extension or 

 application of its methods and spirit to the field of nature. One 

 exam))le of this is worthy of attention. In modern teaching the 

 idea of magnitiuU' 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 concejition finds no place in the Euclidian system. But we may 

 regard the omission as a mark of k)gical purity and rigor. Had the 

 real or supposed advantages of introducing motion into geometrical 

 conceptions been suggested to Euclid, we nuiy sup])ose him to have 

 replied that the theorems of space are independent of time; that the 

 idea of motion necessarih^ implies time, and that, in consequence, tp 

 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 apjilication of their science, which has continued 

 in' some form to our own time, and which is not altogether unwhole- 

 SM 1904 15 



