APOTOME, is a term employed by Euclid to denote the difference between two lines or quantities which are only commensurable in power. Such is the difference between 1 and \sqrt{2}, or the difference between the side of a square and its diagonal. The doctrine of apotomes in lines, as delivered by this ancient mathematician in the tenth book of his Elements, is a very curious subject, and has always been admired by such as understood it. The first algebraical writers in Europe, such as Lucas de Burgo, Cardan, Tartalea, Stifelius, &c. employed a considerable portion of their works on an algebraical exposition of that which led them to the doctrine of surd quantities.