There were the warlike Symbols, who had borne the royal flag through many perilous campaigns; tall people of fight, lordly with plumes and armor. There were the mysterious Surds, the princely Polynomials, and the uneasy Radicals, who were suspected of Red Republicanism: also all signs and expressions, homogeneous or heterogeneous, all tribes , all clans which hold estates , honors, dignities and franchises from the throne. The doors of the hall were open; a four- decker with the admiral of Britain could have sailed through. Behind , you looked down upon the ocean, but on the wide area in front, the stand ing army of the empire , the innumerable Logarithms, were drawn up in solid columns even to the edge of the precipices. Their venerable Radix , a weather- beaten, invulnerable, unterrified old hero, sat like cast-iron, in a conspicious chariot above all the hosts. The heavy field and battering formulae, were planted in battery at inter vals among the deep masses, and the Sines and Cotangents spread in clouds on the flank; their squadrons seeming like the locusts for multitude .

Among the Unknown Quantities assembled at Court, there was none of more brilliant promise than the hero of our tale . Young x was descended from a family of Symbols , which abstractly considered as the representatives of a mathematical truth , could have had no beginning : but without venturing on such dangerous metaphysics as speculations on this point would lead to, it is sufficient to know that our hero's ancestors had been people of consideration ever since the discovery of algebra ; ever since the light of reason pierced the obscuring fog banks and touched the cliffs of that continent where the disciples of science will forever wander as in a paradise. His grand father had been raised to the sixth power and enjoyed the confidence of his sovereign in an especial degree.