(of λεμνον, "I affume.") in Mathematics, denotes a previous proposition, laid down in order to clear the way for some following demonstration; and prefixed either to theorems, in order to render their demonstration less perplexed and intricate; or to problems, to make their resolution more easy and short. Thus, to prove a pyramid one-third of a prism, or parallelopiped, of the same base and height with it, the demonstration whereof in the ordinary way is difficult and troublesome; this lemma may be premised, which is proved in the rules of progression, that the sum of the series of the squares, in numbers in arithmetical progression, beginning from 0, and going on 1, 4, 9, 16, 25, 36, &c. is always subtriple of the sum of as many terms, each equal to the greatest; or is always one-third of the greatest term multiplied by the number of terms. Thus, to find the inflection of a curve line, this lemma is first premised, that a tangent may be drawn to the given curve in a given point.

So in physics, to the demonstration of most propositions, such lemmata as these are necessary first to be allowed: that there is no penetration of dimensions; that all matter is divisible; and the like. As also in the theory of medicine, that where the blood circulates, there is life, &c.