Number, place, and combination . . . the three intersecting but…

It has been said that to appreciate what virtue and morals mean, men must live virtuous and moral lives. It is equally true, that a knowledge of the objects of science is not to be attained by any scheme of definitions, however carefully …

It seems to be expected of every pilgrim up the slopes of the mathematical Parnassus, that he will at some point or other of his journey sit down and invent a definite integral or two towards the increase of the common stock.

As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.

The object of pure Physic[s] is the unfolding of the laws of the intelligible world; the object of pure Mathematic[s] that of unfolding the laws of human intelligence.

The scene was changed. It was a bark that slowly held its way, And o'er its lee the coast of France in the light of evening lay; And on its deck a lady sat, who gazed with tearful eyes Upon the fast receding hills that dim and distant rise.

So All is diff’rent, and yet All is One.