a city of the principality of Lippe-Detmold, in Germany, the capital of the bailiwick of Brake. It is situated on the river Vega, and is the largest place in the dominion, containing the palace of the sovereign, the courts of justice, the institutions for education, and 640 houses, with 3570 inhabitants. It was formerly one of the Hans Towns, but has now little trade, and only manufactures fine linen. Long. 8° 49'. 13. E. Lat. 52° 1'. 40. N.

**LEMMA** (from λεγω, I assue), 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 shorter and more easy. Thus, to prove a pyramid one third of a prism or parallelopiped, of the same base and altitude, the demonstration of which 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, certain lemmata are necessary to be allowed, as that there is no penetration of dimensions, that all matter is divisible, and the like.