DATA

(I.at. things ginn.) A term used in geometry to denote certain things or quantities determined by the con. ditions of the problem, and at the same time known as a ignable. According to Simson (Preface to Euclid's Data), a thing is said in general to.be given which is either actually exhibited or ran be found out; that is, which is either known by hypothesis or can be demonstrated to be known; so that in the analysis or Investigation of a problem, from the things thai are laid down to be known or given, by the help of known propositions other things are demonstrated to be given, and from these other things are again shown to be given, and so on, until that which was proposed to be found out in (he problem is demonstrated to he given. When this is done the problem is solved, and its composition is made and derived from the compositions of the data which were made use of in the analysis. In the language of the ancient mathematicians, geometrical quantities are given in species, magnitude, or position. Thus, a triangle is given in species when its three angles, or the ratio are known. A straight line is given in magnitude when we know its length, or the area of a triangle of which the three sides are given. And lastly, a line is given in position when we know its inclination to another given line. The Book of Data, ascribed to Euclid, is the first in order of the ancient treatises on the geometrical analysis. There are numerous editions of this work. of Sanson and Ilorsley are the best [s. 331]