in Antiquity, the name given to a per- son who leapt from one horse to another as a feat of dexterity. In the *Iliad* (xv. 679) a performer of this kind is represented keeping four horses at full speed and leaping from one to another like equestrian performers in the modern circus. These exhibitions were very popular among the Romans, who appear, however, to have used but two horses for the purpose. The Greeks and the Romans appear to have borrowed this kind of equestrian exercise from the Numidians, who, it seems, applied it to the purposes of war. Livy (xxiii. 29) mentions a troop of Numidian horse, of which each man was provided with two horses, which were used alternately as occasion required. The Scythians, Armenians, and some Indian tribes, were likewise noted for feats of this kind.

**DETERMINATE Problem**, in *Geometry* and *Analysis*, is that which has but one solution, or a certain limited number of solutions; in contradistinction to an indeterminate problem, which admits of an infinite number of solutions.

**DETERMINATE Section**, the name of a tract or general problem, written by the ancient geometrician Apollonius. None of this work has come down to us, excepting some extracts, and an account of it by Pappus, in the Preface to the 7th book of his Mathematical Collections. He there says that the general problem was "To cut an infinite right line in one point, so that, of the segments contained between the point of section sought, and given points in the said line, either the square on one of them, or the rectangle contained by two of them, may have a given ratio, either to the rectangle contained by one of them and a given line, or to the rectangle contained by two of them."