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 understand 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 said quantities.

APPARENT CONJUNCTION of the planets, is when a right line, supposed to be drawn through their centres, passes through the eye of the spectator, and not through the centre of the earth. And, in general, the apparent conjunction of any objects, is when they appear or are placed in the same right line with the eye.

APPARENT DIAMETER of a planet or other heavenly body, is not the real length of the diameter of that body, but the angle which it subtends at the eye, or under which it appears.