Binomial Theorem

(Math.) In algebra, a formula discovered by Newton, for expre ing any power of a binomial quantity. It is usually written thus: n (n-1) (1+x)=1+nz+x2+ 1. 2. n (n-1) (n-2) -x3+, . from which four terms the law of the whole series will be sufficiently apparent. The method of obtaining the formula, and of proving its validity for all values of n , will be found in any good algebra. When n is a positive integer, the series is finite, and consists of n +1 terms; in all other cases it is infinite, but convergent whenever z is numerically le than 1, no matter what n may be. It would be usele to attempt to describe the applications of this formula in mathematics; it is beyond question the most important one of elementary algebra. Binom'inal, Binom'inous, a . [Lat. bis , double, and nomen , name.] Having two names; double-named. Binor'mal, n. [Lat. bis , and norma , a rule.] ( Geom .) А term employed by Saint-Venant ( Jour . de l'Ecole Poly technique , cap. 30) to denote the line through a point of a non-plane curve which is perpendicular to two consecutive elements. It lies of course in the normal plane, and is perpendicular to the osculating-plane. The locus IMG:content-0623.jpg:[blocks in formation]