taken and added to the other, this latter exceeds the former by twice that portion: if it had been merely taken from the former and not added to the latter, then the latter would have exceeded the former only by that one portion; but in the other case, the greater exceeds the mean by one, and the mean exceeds also by one that magnitude from which the portion was taken. By this illustration, then, we obtain a rule to determine what one ought to take from him who has the greater, and what to add to him who has the less. The excess of the mean over the less must be added to the less, and the excess of the greater over the mean be taken from the greater.
Thus let there be three straight lines equal to one another. From one of them cut off a portion, and add as much to another of them. The whole line thus made will exceed the remainder of the first-named line, by twice the portion added, and will exceed the untouched line by that