Have you ever noticed that those who have a turn for arithmetic are, with scarcely an exception, naturally quick in all sciences; and that men of slow intellect, if they be trained and exercised in this study ... become invariably quicker than they were before? Exactly so, he replied. And, moreover, I think you will not easily find that many things give the learner and student more trouble than this. Of course not. On all these accounts, then, we must not omit this branch of science, but those with the best of talents should be instructed therein.--PLATO. _Republic [Davis], Bk. 7, chap. 8._ =1621.= Arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and if visible or tangible objects are obtruding upon the argument, refusing to be satisfied.--PLATO. _Republic [Jowett], Bk. 7, p. 525._ =1622.= Good arithmetic contributes powerfully to purposive effort, to concentration, to tenacity of purpose, to generalship, to faith in right, and to the joy of achievement, which are the elements that make up efficient citizenship.... Good arithmetic exalts thinking, furnishes intellectual pleasure, adds appreciably to love of right, and subordinates pure memory.--MYERS, GEORGE. _Monograph on Arithmetic in Public Education (Chicago), p. 21._ =1623.= On the one side we may say that the purpose of number work is to put a child in possession of the machinery of calculation; on the other side it is to give him a better mastery of the world through a clear (mathematical) insight into the varied physical objects and activities. The whole world, from one point of view, can be definitely interpreted and appreciated by mathematical measurements and estimates. Arithmetic in the common school should give a child this point of view, the ability to see and estimate things with a mathematical eye.--MCMURRAY, C. A. _Special Method in Arithmetic_ (_New York, 1906_), _p. 18._ =1624.= We are so accustomed to hear arithmetic spoken of as one of the three fundamental ingredients in all schemes of instruction, that it seems like inquiring too curiously to ask why this should be. Reading, Writing, and Arithmetic--these three are assumed to be of co-ordinate rank. Are they indeed co-ordinate, and if so on what grounds?