An ingenious instrument for drawing ellipses and hyperbolas has recently been invented which is so arranged that if a pen be used it will keep the latter at all times tangent to the curve. The instrument is based on the principle that the sum or the difference respectively of the distances from any point of an ellipse or a hyperbola to the foci of such curve is constant. It is constructed with two posts provided with points to be placed at the foci of the ellipse or hyperbola. These two posts are connected by slotted beams clamped together by a thumb screw. On the top of each post is a stationary pinion, about which is swiveled a head. Passing freely through the two heads, and engaging each pinion are two racks, crossing each other and both engaging a traveling pinion. Passing through the traveling pinion is a vertical shaft, at the bottom of which is connected a pen or pencil. Around the pinion are two heads adapted to travel along the racks. If the instrument is put in motion by placing the hand at the top of the shaft, the traveling pinion will revolve, taking up on one rack and letting out exactly the same distance on the other rack, thereby causing the pen to describe an ellipse which is mathematically correct. By reassembling the instrument so that the traveling pinion will pass between the two foci, the pen or pencil will describe a hyperbola. For drawing an ellipse with ink, it is necessary that the pen always travel tangent to the point of the* curve which it is drawing. The mechanism which achieves this purpose is based on the well-known property of the ellipse or hyberbola, that the tangent in each point of the curve bisects the angle between the two connecting lines of said point with the foci of said ellipse. Each of the traveling heads is provided with a flange, in which is cut a spiral-shaped groove running in opposite directions. Between the two flanges there is a steel plate swiveled around the pinion and having a slot running in a radial direction. The pin engaging both of these grooves, and also a slot in the plate between the two flanges, causes this plate to revolve around the vertical shaft whenever the instrument is put in motion. The steel plate has an extension at the point opposite the radial slot, in the end of which is riveted a short vertical pin engaging a hole at the end of a horizontal arm, which is threaded into the head carrying the pen. By this arrangement the revolving motion of the steel plate is conveyed to the pen, and thereby the pen is properly directed. By using an attachment not shown in the cut to take the place of one of the posts at the foci, and having this slide along a T square, the pen or pencil will describe a parabola.