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GIVEN is a term frequently used by mathematicians, to denote something supposed to be known. Thus, if a magnitude be known, it is said to be a given magnitude. If the position of a thing be known, it is given in position ; if a circle be described with a known radius, its centre is given in position, and its circumference given in magnitude, and the circle itself is said to be given both in magnitude and position. If the kind or species of a figure be known, it is said to be given in species ; if the ratio between two quantities be known, these quantities are said to have a given ratio, &c. &c.