But this rule applies not always to the tradesmen, and still less often to the soldiers, and to the workmen; who indeed can hardly be said to deserve the name of human Figures, since they have not all their sides equal. With them therefore the law of Nature does not hold; and the son of an Isosceles ( i.e. a Triangle with two sides equal) remains Isosceles still. Nevertheless, all hope is not shut out, even from the Isosceles, that his posterity may ultimately rise above his degraded condition. For, after a long series of military successes, or diligent and skilful labours, it is generally found that the more intelligent among the artisan and soldier classes manifest a slight increase of their third side or base, and a shrinkage of the two other sides. Intermarriages (arranged by the Priests) between the sons and daughters of these more intellectual members of the lower classes generally result in an offspring approximating still more to the type of the Equal-Sided Triangle.

Rarely⁠—in proportion to the vast numbers of Isosceles births⁠—is a genuine and certifiable Equal-Sided Triangle produced from Isosceles parents. 2 Such a birth requires, as its antecedents, not only a series of carefully arranged intermarriages, but also a long, continued exercise of frugality and self-control on the part of the would-be ancestors of the coming Equilateral, and a patient, systematic, and continuous development of the Isosceles intellect through many generations.