DATA

, in General Mathematics, denote certain things or quantities, supposed given or known, from which other quantities are discovered that were unknown, or sought. A problem or question usually consists of two parts, data and quæsita.

Euclid has an express and excellent treatise of Data; in which he uses the word for such spaces, lines, angles, &c, as are given; or to which others can be found equal.

Euclid's Data is the first in order of the books that have been written by the ancient geometricians, to facilitate and promote the method of resolution or analysis. In general a thing is said to be given which is either actually exhibited, or can be found out, that is, which is either known by hypothesis, or that can be demonstrated to be known: and the propositions in the book of Euclid's Data shew what things can be found out or known, from those that by hypothesis are already known: so that in the analysis or investigation of a problem, from the things that are laid down as given | or known, by the help of these propositions, it is demonstrated that other things are given, and from these last that others again are given, and so on, till it is demonstrated that that which was proposed to be found out in the problem is given; and when this is done, the problem is solved, and its composition is made and derived from the compositions of the Data which were employed in the analysis. And thus the Data of Euclid are of the most general and necessary use in the solution of problems of every kind.

Marinus, at the end of his Preface to the Data, is mistaken in asserting that Euclid has not used the synthetical, but the analytical method in delivering them: for, though in the analysis of a theorem, the thing to be demonstrated is assumed in the analysis; yet, in the demonstrations of the Data, the thing to be demonstrated, which is, that something is given, is never once assumed in the demonstration; from which it is manifest that every one of them is demonstrated synthetlcally: though indeed if a proposition of the Data be turned into a problem, the demonstration of the proposition becomes the analysis of the problem. See Simson's edition of Euclid's Data, which is esteemed the best.

DAVIS's Quadrant, the common sea quadrant, or back-staff. See Back-Staff. See also Robertson's Navigation, book 9, sect. 7.