Page:The Algebra of Mohammed Ben Musa (1831).djvu/22

 A root is any quantity which is to be multiplied by itself, consisting of units, or numbers ascending, or fractions descending.

A square is the whole amount of the root multiplied by itself.

A simple number is any number which may be pronounced without reference to root or square.

A number belonging to one of these three classes may be equal to a number of another class; you may say, for instance, “squares are equal to roots,” or “squares are equal to numbers,” or “roots are equal to numbers.”

Of the case in which squares are equal to roots, this is an example, “A square is equal to five roots of the same;” the root of the square is five, and the square is twenty-five, which is equal to five times its root.

So you say, “one third of the square is equal to four roots;” then the whole square is equal to twelve roots; that is a hundred and forty-four; and its root is twelve.

Or you say, “five squares are equal to ten roots;” then one square is equal to two roots; the root of the square is two, and its square is four.