OF ARTS AND SCIENCES. 165 



Pythagoras and his disciples, had more than a merely speculative inter- 

 est : it had a substantial foundation, and a practical application. For, 

 while in the early progress of the arts numerical relations gave to them 

 their primal and universal laws, the mystical conceptions in respect to 

 the absolute and inherent qualities of numbers themselves quickened the 

 fancy of the artist, and gave him confidence in the performance of his 

 work. " Number and figure were the greatest instruments of thought 

 which were possessed by the Greek philosopher ; having the same power 

 over the mind which was exerted by abstract ideas, they were also capa- 

 ble of practical application. . . . They were the measure of all things, 

 and seemed to give law to all things ; nature was rescued from chaos 

 and confusion by their power ; the notes of music, the motions of the 

 stars, the forms of atoms, the recurrence and evolutions of days, months, 

 years, the military divisions of an army, the civil division of a state, — 

 seemed to afford a present witness of them : what would have become 

 of man, or of the world, if deprived of number?"* 



It was not strange that the Pythagoreans, having recognized that the 

 material laws of the universe could be expressed by numbers, should 

 have mistaken this condition for the essence of the thing itself. Such 

 a mistake is frequent in the history of thought ; and it may serve to 

 illustrate how superstitious fancies become often mingled with the most 

 solid truths. 



But to return to the number which is the special subject of this 

 inquiry, 735, we may observe, that it not only presents in its digits the 

 first three numeri inpares, but is itself composed of them, as fol- 

 lows : — 



7X3X5 X7 = 735; 



and this analysis suggests another and (as I propose to show) highly 

 characteristic and interesting set of factors ; namely, — 



35 X 21 == 735. 



In the well-known obscure and much discussed passage in the 

 " Timaeus," in which the Pythagorean Timaeus gives account of the 

 process of making of the soul, we are told that when God had mingled 

 the three elements of which the soul is composed, and out of the three 



* Jowett, Introduction to Timaeus, in " The Dialogues of Plato translated," 

 2d ed. III. 564. The whole passage from which the preceding extract is taken 

 is full of striking and original reflections. Plato's own views in regard to num- 

 ber, and the science of arithmetic as a guide to truth, are set forth in a remark- 

 able passage in his " Republic," book vii. 525, 526. 



