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A root is any quantity which is to be multiplied by itself, consisting of units, or numbers ascending, or fractions descending.[1]
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.”[2]
(4) Of the case in which squares are equal to roots, this is an example, “A square is equal to five roots of the same;”[3] 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;”[4] 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;”[5] then one square is equal to two roots; the root of the square is two, and its square is four.
