_Quoted in Young’s Teaching of Mathematics (London, 1907), p. 44._ =307.= The reasoning of mathematics is a type of perfect reasoning.--BARNETT, P. A. _Common Sense in Education and Teaching (New York, 1905), p. 222._ =308.= Mathematics, once fairly established on the foundation of a few axioms and definitions, as upon a rock, has grown from age to age, so as to become the most solid fabric that human reason can boast.--REID, THOMAS. _Essays on the Intellectual Powers of Man, 4th. Ed., p. 461._ =309.= The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method--more daring than anything that the history of philosophy records--of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.--BUTLER, NICHOLAS MURRAY. _The Meaning of Education and other Essays and Addresses (New York, 1905), p. 45._ =310.= Mathematics is the gate and key of the sciences.... Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus ignorant are unable to perceive their own ignorance and so do not seek a remedy.--BACON, ROGER. _Opus Majus, Part 4, Distinctia Prima, cap. 1._ =311.= Just as it will never be successfully challenged that the French language, progressively developing and growing more perfect day by day, has the better claim to serve as a developed court and world language, so no one will venture to estimate lightly the debt which the world owes to mathematicians, in that they treat in their own language matters of the utmost importance, and govern, determine and decide whatever is subject, using the word in the highest sense, to number and measurement. --GOETHE. _Sprüche in Prosa, Natur, III, 868._ =312.= Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.--THOMSON, W. (LORD KELVIN). _Thompson, S. P.: Life of Lord Kelvin (London, 1910), p. 1139._ =313.= The advancement and perfection of mathematics are intimately connected with the prosperity of the State.--NAPOLEON I. _Correspondance de Napoléon, t. 24 (1868), p. 112._