_Arithmetic in Public Education (Chicago), p. 18._ =458.= In destroying the predisposition to anger, science of all kind is useful; but the mathematics possess this property in the most eminent degree.--DR. RUSH. _Quoted in Day’s Collacon (London, no date)._ =459.= The mathematics are the friends to religion, inasmuch as they charm the passions, restrain the impetuosity of the imagination, and purge the mind from error and prejudice. Vice is error, confusion and false reasoning; and all truth is more or less opposite to it. Besides, mathematical truth may serve for a pleasant entertainment for those hours which young men are apt to throw away upon their vices; the delightfulness of them being such as to make solitude not only easy but desirable. --ARBUTHNOT, JOHN. _Usefulness of Mathematical Learning._ =460.= There is no prophet which preaches the superpersonal God more plainly than mathematics.--CARUS, PAUL. _Reflections on Magic Squares; Monist (1906), p. 147._ =461.= Mathematics must subdue the flights of our reason; they are the staff of the blind; no one can take a step without them; and to them and experience is due all that is certain in physics. --VOLTAIRE. _Oeuvres Complètes (Paris, 1880), t. 35, p. 219._ CHAPTER V THE TEACHING OF MATHEMATICS =501.= In mathematics two ends are constantly kept in view: First, stimulation of the inventive faculty, exercise of judgment, development of logical reasoning, and the habit of concise statement; second, the association of the branches of pure mathematics with each other and with applied science, that the pupil may see clearly the true relations of principles and things. _International Commission on the Teaching of Mathematics, American Report; U. S. Bureau of Education, Bulletin 1912, No. 4, p. 7._ =502.= The ends to be attained [in the teaching of mathematics in the secondary schools] are the knowledge of a body of geometrical truths, the power to draw correct inferences from given premises, the power to use algebraic processes as a means of finding results in practical problems, and the awakening of interest in the science of mathematics. _International Commission on the Teaching of Mathematics, American Report; U. S. Bureau of Education, Bulletin 1912, No. 4, p. 7._