the inhabitants of the Moon, as he has to us, a power of apprehending, in a very general and abstract form, the relations of that space in which he performs his works. We should judge, that having been led so far in their speculations, they must, in all probability, have been led also to a conception of the Universe, as the field of action of a universal and Divine Mind; that having thus become geometers, they must have ascended to the Idea of a God who works by geometry. 4. But yet, by such a supposition, on further consideration, we find ourselves introduced to views entirely different from those to which we are led by the supposition of mere animal life, existing in other worlds than the earth. For, not to dwell here upon any speculations as to how far the operations of our minds may resemble the operations of the Divine Mind;--a subject which we shall hereafter endeavor to discuss;--we know that the advance to such truths as those of geometry has been, among the inhabitants of the earth, gradual and progressive. Though the human mind have had the same powers and faculties, from the beginning of the existence of the race up to the present time, (as we cannot but suppose,) the results of the exercise of these powers and faculties have been very different in different ages; and have gradually grown up, from small beginnings, to the vast and complex body of knowledge concerning the scheme and relations of the Universe, which is at present accessible to the minds of human speculators. It is, as we have said, probably about four thousand years, since the first steps in such knowledge were made. Geometry is said to have had its origin in Egypt; but it assumed its abstract and speculative character first among the Greeks. Pythagoras is related to have been the first who saw, in the clear light of demonstration, the property of the right-angled triangle, of which we have spoken. The Greeks, from the time of Socrates, stimulated especially by Plato, pursued, with wonderful success, the investigation of this kind of truths. They saw that such truths had their application in the heavens, far more extensively than on the earth. They were enabled, by such speculations, to unravel, in a great degree, the scheme of the universe, before so seemingly entangled and perplexed. They determined, to a very considerable extent, the relative motions of the planets and of the stars. And in modern times, after a long interval, in which such knowledge was nearly stationary, the progress again began; and further advances were successively made in man's knowledge of the scheme and structure of the visible heavens; till at length the intellect of man was led to those views of the extent of the Universe and the nature of the stars, which are the basis of the discussions in which we are now engaged. And thus man, having probably been, in the earliest ages of the existence of the species, entirely ignorant of abstract truth, and of the relations which, by the knowledge