In 1620 the English mathematician William Gunter (1581-1621) recognised that the same principle, coupled with the ideas underlying logarithms, could be exploited to construct a device with which rough estimates of division and multiplication calculations could be made. Thus instead of using marks which were placed equidistantly, successive marks were placed at (appropriately) decreasing distances, e.g. the distance from the mark representing 1 and the mark representing 2 would be same as the distance between the mark representing 2 and that representing 4, etc. Gunter's calculating aid consisted of a grid on which numbers could be multiplied and divided by adding and subtracting lengths with the assistance of a compass.