[318]. Those who assert that the mathematical sciences make no affirmation about what is fair or good make a false assertion; for they do speak of these and frame demonstrations of them in the most eminent sense of the word. For if they do not actually employ these names, they do not exhibit even the results and the reasons of these, and therefore can be hardly said to make any assertion about them. Of what is fair, however, the most important species are order and symmetry, and that which is definite, which the mathematical sciences make manifest in a most eminent degree. And since, at least, these appear to be the causes of many things—now, I mean, for example, order, and that which is a definite thing, it is evident that they would assert, also, the existence of a cause of this description, and its subsistence after the same manner as that which is fair subsists in.—Aristotle.
Metaphysics [MacMahon] Bk. 12, chap. 3.
[319]. Many arts there are which beautify the mind of man; of all other none do more garnish and beautify it than those arts which are called mathematical.—Billingsley, H.
The Elements of Geometrie of the most ancient Philosopher Euclide of Megara (London, 1570), Note to the Reader.
[320]. As the sun eclipses the stars by his brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them.—Brahmagupta.
Quoted in Cajori’s History of Mathematics (New York, 1897), p. 92.
[321]. So highly did the ancients esteem the power of figures and numbers, that Democritus ascribed to the figures of atoms the first principles of the variety of things; and Pythagoras asserted that the nature of things consisted of numbers.—Bacon, Lord.
De Augmentis, Bk. 3; Advancement of Learning, Bk. 2.
[322]. There has not been any science so much esteemed and honored as this of mathematics, nor with so much industry and vigilance become the care of great men, and labored in by the potentates of the world, viz. emperors, kings, princes, etc.—Franklin, Benjamin.
On the Usefulness of Mathematics, Works (Boston, 1840), Vol. 2, p. 28.