# Page:Scientific Memoirs, Vol. 3 (1843).djvu/695

Let us consider a term of the form $\scriptstyle{ab^n}$; since the cards are but a translation of the analytical formula, their number in this particular case must be the same, whatever be the value of $\scriptstyle{n}$; that is to say, whatever be the number of multiplications required for elevating $\scriptstyle{b}$ to the $\scriptstyle{n}$th power (we are supposing for the moment that $\scriptstyle{n}$ is a whole number). Now, since the exponent $\scriptstyle{n}$ indicates that $\scriptstyle{b}$ is to be multiplied $\scriptstyle{n}$ times by itself, and all these operations are of the same nature, it will be sufficient to employ