Dante's interest in the mystic significance of numbers is never again so obtrusive as in the Vita Nuova. But it is quite as pervasive, in his Divine Comedy; and he uses them—and geometrical forms, their related concepts—continually, not only for purposes of exposition and illustration, but also to give the illusion of reality to his Vision. Among the almost innumerable instances of this last use of numerical determinatives, the most striking—from their baldly prosaic injection, in the terms of pure mathematics, outside of any æsthetic qualities—are probably the two cases in Inf., xxix, 9 and xxx, 86, in which the diameters of two circles are given, respectively, as twenty-two, and eleven, miles. The advantages, in the direction of vividness, of this method—although it seems almost to flirt with poetic disaster at times—are great; and its peril is obviated, in the otherwise physically impossible journey within the time limits set, by recourse, sparingly and cannily, in the early cantos of the descent to Hell's apex, to swoons during which the pilgrim poet is advanced indeterminate distances toward his goal; and in the arduous ascent of the Moutain of Purgatory an unspecified but very considerable space is surmounted by the supernatural aid of Lucia.