In learning a foreign and especially a dead language, these are indispensable and necessary aids, which greatly promote and facilitate its acquisition; so also mathematics furnish indispensable helps and a most valuable organon for the cognition of nature. But with them alone man will never learn to understand even a word, not to talk of a whole proposition, out of nature’s strangely-sounding and most difficult hieroglyphics. Somewhat different is it, when man seeks to understand the true living geometry in nature herself, _i.e._, attempts to discover the place which the circle and eclipse (passing from these up to the spheres in their sidereal orbits), or which the triangle, the square, the hexagon, and so forth, assume in the scale of its creations--or when, in a similar spirit, he investigates and ascertains the really dominant rule in the arithmetic of life; those numbers which the physician observes in the periodic developments of life, and which, in the fluctuating states of an abating and heightening malady, enable him, under certain conditions, to predict the moment of its crisis. Of a still higher kind is that spiritual, we might almost call it divine chronology, which, in universal history, marks out definite epochs of the mental development of the human race, and traces therein the influence of certain grades of life, or ages of the world, and the alternating phases of disease in whole communities, and those decisive moments and great critical emergencies in which God Himself appears as the healing Physician and Restorer of life. It was, in all probability, in reference to such an arithmetic, or in some similar sense, that Pythagoras taught that numbers are, or contain the essence of things. For such an arithmetic of life and geometry of nature do afford a positive cognition and a real knowledge. As commonly understood, however, mathematics are nothing more than a formal science--in other words, they are simply a scientific organon, rather than a science. But now, if nature be not regarded as dead, but living, who can doubt that it--or, as we are now speaking of man’s nearest neighbor--that the earth is akin to man? Was he not formed out of the dust of the earth, and is he not therefore the son, nay, in truth, the first-born of the earth?--does he not receive from it food and nourishment? and when the irrevocable summons goes forth from above, does he not give back again to its bosom the earthly tabernacle of his flesh? Do not chemists tell us that the principal constituent of the purest wheat-corn has a great affinity to the substance of man’s blood? and does not the blood, moreover, derive one of its ingredients from iron--the principal among the metals of the earth? And are not gold and other metallic substances either wholesome medicines or deadly poisons? And is there not also an inexhaustible store of both in the wonderful varieties of herbs and plants? Do not invigorating and healing springs