The algebraic solution of any problem formulated in mathematical symbols takes one of two forms: it is either given in the explicit form x=f(a, b, c,...), where → is some functional form of a, b, c, ... , which are supposed known in any particular case, or the solution required is to be found from an equation F(x, a, b, c, ...)=0, where F is a known functional form of the unknown x and of the quantities a, b, c, ... . The mathematician is generally concerned on the one hand with reducing f(a, b, c, ...) into its simplest, often its “prettiest” form, and on the other hand with investigating what method, if any, exists for “solving” the equation F(x, a, b, c, ...) = 0, i.e. finding x in terms of a, b, c, ... . The course included in any text-book of algebra consists principally of the former, since the latter is distinctly more difficult.