There is no linear covariant, since it is impossible to form a symbolic product which will contain x once and at the same time appertain to a quadratic. (v.) is the Jacobian; geometrically it denotes the bisectors of the angles between the lines ax, or, as we may say, the common harmonic conjugates of the lines and the lines x x .
If we form all the partitions of 6 into not more than three parts, these are 6, 51, 4 2, 33, 411, 321, 222, and the conjugates are Iiiiii, 21iii, 221i, 222, 311i, 321, 33, where no part is greater than 3; and so in general we have the theorem, the number of partitions of n into not more than k parts is equal to the number of partitions of n with no part greater than k.
What has just been said as to the treatment of the final vowels in Catalan must be understood as applying only to pure Catalan, unaltered by the predominance of the Castilian, for the actual language is no longer faithful to the principle we have laid down; it allows the.final o atonic in a number of substantives and adjectives, and in the verb it now conjugates canto, temo, sentoa thing unknown in the ancient language.