The simplest and perhaps the oldest one among the ellipsographs is maden up of a rod with two points A and B fixed on it :on these points are pivoted two cursors moving on a two perpendicular slots . Every point of the rod describes an ellipse, whose axis are on the slots.

We name p the plane of the slots and we name t the moving plane on which is the segment AB . The motion of t on p is called motion on fixed perpendicular slots . The facts are:

1) If C is the circle circumscribing the triangle OAB (on the plane t ) and D is the circle on the plane p with centre on O and radius twice as much as the radius of C , the motion of t on p is obtained rotating C about D .

2) Every point of the plane t (except that lying on circle C, who moves on diameters of D) describe an ellipse.
3) Every diameter of D envelops a ipocycloid with four cusps.

We have built also an instruments with two slots not perpendicular. Here every point of the segment AB describes an ellipse : two conjugated diameters are on the lines on which are the slots.