DOUBLING TEE CUBE was a celebrated geometrical problem among the ancients. The object was to find the side of a cube whose content should be twice that of another given cube; and various accounts are given of how the problem was sug gested. One legend brings the matter into connection with Delos (hence the name of " the Delian problem"), and relates that the oracle of Apollo in that island, being consulted by the inhabitants during the prevalence of a pestilence, gave for answer, that they should make the altar of Apollo, which was in the form of a cube, as large again. This was done, and yet the pestilence continued; and the oracle being again consulted, replied, that the altar must retain its cubic form, which had not been attended to in the enlargement. This problem perplexed the Delians, as it did mathe maticians of after-ages. Even Plato, whom they consulted on the difficulty, could give them no solution, and had recourse, according to the story, to evasion.
The problem, however, is older than Plato; before his time, it had occupied Hip pocrates of Chios (not the physician Hippocrates), and was studied afterwards by Era tosthenes, Nicomedes, Hero, and others. Apollonius applied conic sections to the solu
tion of the question, as did also Mentechmus; Nicomedes invented a curve, which ho called the conchoid, for the express purpose, and Diocles the cissoid. The analytical method introduced into geometry by Descartes showed this problem in its true light. It was seen to be only a special case of the solution of a cubic equation—a solution which is impossible by geometry, i.e., by the use of the circle and straight line. It may, however, be represented by the intersection of two conic sections, of which one may be a circle. DesraatC,S ,_ni,tele use of the parabola with the circle, which is the simplest way. With numbers, the question is merely'one of the extraction of the cube root. If the side of a cube be one foot, its solid content is 1 X 1 X 1=-1 cubic foot. The side of a cube of double that content, or 2 cubic feet, is V2 = 1.259921.