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It occurred to him that when the moon is precisely dichotomized that is to say, precisely at the half-the line of vision from the earth to the moon must be precisely at right angles with the line of light passing from the sun to the moon. At this moment, then, the imaginary lines joining the sun, the moon, and the earth, make a right angle triangle.
No man of the world, to say nothing of a man of faith or imagination, has ever yet trusted to a purely intellectual judgment. So we reject the old dualism, its dichotomized universe, its two sorts of authority, its prodigious and arbitrary supernaturalism. But we do not reject what lay behind it.
It strikes a powerful blow at the scholastic notion of a dichotomized universe divided between nature and supernature, divine and human. It reinforced humanism by minimizing, if not making unnecessary, the objective and external source and external interpretations of religions. It pushes back the initial creative act until it is lost in the mists and chaos of an unimaginably remote past.
Indeed, Aristarchus of Samos attempted to ascertain the distance of the sun from the earth on the principle of observing the moon when she is dichotomized, a method quite significant of the knowledge of the time, though in practice untrustworthy; Aristarchus thus finding that the sun's distance is eighteen times that of the moon, whereas it is in reality 400.
"If we admit these six hypotheses," Aristarchus continues, "it follows that the sun is more than eighteen times more distant from the earth than is the moon, and that it is less than twenty times more distant, and that the diameter of the sun bears a corresponding relation to the diameter of the moon; which is proved by the position of the moon when dichotomized.
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