( 36 )
thing by ten minus thing; it is ten things minus a square. Then multiply it by four, because the instance states “four times as much.” The result will be four times the product of one of the parts multiplied by the other. This is forty things minus four squares. After this you multiply thing by thing, that is to say, one of the portions by itself. This is a square, which is equal to forty things minus four squares. Reduce it now by the four squares, and add them to the one square. Then the equation is: forty things are equal to five squares; and one square will be equal to eight roots, that is, sixty-four; the root of this is eight, and this is one of the two portions, namely, that which is to (26) be multiplied by itself. The remainder from the ten is two, and that is the other portion. Thus the question leads you to one of the six cases, namely, that of “squares equal to roots.” Remark this.
Second Problem.
I have divided ten into two portions: I have multiplied each of the parts by itself, and afterwards ten by itself: the product often by itself is equal to one of the two parts multiplied by itself; and afterwards by two and seven-ninths; or equal to the other-multiplied by itself, and afterwards by six and one-fourth.[1]
