UNCIA

, a term generally used for the 12th part of a thing. In which sense it occurs in Latin writers, both for a weight, called by us an ounce, and a measure called an inch.

UNCIÆ, in Algebra, first used by Vieta, are the numbers prefixed to the letters in the terms of any power of a binomial; now more usually, and generally, called coefficients. Thus, in the 4th power of a + b, viz, a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴, the Unciæ are 1, 4, 6, 4, 1.

Briggs first shewed how to find these Unciæ, one from another, in any power, independent of the foregoing powers. They are now usually found by what is called Newton's binomial theorem, which is the same rule as Briggs's in another form. See Binomial.