among mathematicians, a term for such things or quantities as are given or known, in order thereby to find other things that are unknown. The data of Euclid is the first in order of the books which have been written by the ancient geometers, 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 show 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, it is demonstrated, by the help of these propositions, 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 synthetic, 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 synthetically; though indeed if a proposition of the data be turned into a problem, the demonstration of the proposition becomes the analysis of the problem.

From the primary use of the word data in mathematics, it has been transplanted into other branches, as philosophy, medicine, and the like, where it expresses any quantity which, for the sake of a present calculation, is taken for granted to be such, without requiring an immediate proof of its certainty, and is also called the given quantity, number, or power. And hence also such things as are known, and from which, either in natural philosophy, the animal mechanism, or the operation of medicine, we come to the knowledge of others unknown, are now frequently in physical writers called data.