Excerpt from The Theory of Equations: With an Introduction to the Theory of Binary Algebraic Forms

We shall be employed mainly with such algebraical func tions as are rational and integral. By a rational function of a quantity is meant one which contains that quantity in a rational form only; that is, a form free from fractional indices or radical signs. By an integral function of a quantity is meant one in which the quantity enters in an integral form only; that is, never in the denominator of a fraction. The following expres sion, for example, in which n is a positive integer, is a rational and integral algebraical function of a.

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