=1602.= There is no inquiry which is not finally reducible to a question of Numbers; for there is none which may not be conceived of as consisting in the determination of quantities by each other, according to certain relations.--COMTE, A. _Positive Philosophy [Martineau], Bk. 1, chap. 1._ =1603.= Pythagoras says that number is the origin of all things, and certainly the law of number is the key that unlocks the secrets of the universe. But the law of number possesses an immanent order, which is at first sight mystifying, but on a more intimate acquaintance we easily understand it to be intrinsically necessary; and this law of number explains the wondrous consistency of the laws of nature.--CARUS, PAUL. _Reflections on Magic Squares; Monist, Vol. 16 (1906), p. 139._ =1604.= An ancient writer said that arithmetic and geometry are the _wings of mathematics_; I believe one can say without speaking metaphorically that these two sciences are the foundation and essence of all the sciences which deal with quantity. Not only are they the foundation, they are also, as it were, the capstones; for, whenever a result has been arrived at, in order to use that result, it is necessary to translate it into numbers or into lines; to translate it into numbers requires the aid of arithmetic, to translate it into lines necessitates the use of geometry.--LAGRANGE. _Leçons Elémentaires sur les Mathématiques, Leçon seconde._ =1605.= It is number which regulates everything and it is measure which establishes universal order.... A quiet peace, an inviolable order, an inflexible security amidst all change and turmoil characterize the world which mathematics discloses and whose depths it unlocks.--DILLMANN, E. _Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 12._ =1606.= Number, the inducer of philosophies, The synthesis of letters, .... --AESCHYLUS. _Quoted in, Thomson, J. A., Introduction to Science, chap. 1 (London)._ =1607.= Amongst all the ideas we have, as there is none suggested to the mind by more ways, so there is none more simple, than that of _unity_, or one: it has no shadow of variety or composition in it; every object our senses are employed about; every idea in our understanding; every thought of our minds, brings this idea along with it. And therefore it is the most intimate to our thoughts, as well as it is, in its agreement to all other things, _the most universal idea we have_.--LOCKE, JOHN. _An Essay concerning Human Understanding, Bk. 2, chap. 16, sect. 1._