Kepler gave given construction for the hyperbola with foci at A and B and with one vertex at C:
Consider pins be placed at A and B. To A let the thread with length AC be tied, and to B a thread with length BC. Consider each thread be lengthened by the amount equal to itself. Then grasp two threads together with one hand (starting at C) and little by little move away from C, paying out two threads. With other hand, draw path of join of the two threads at fingers. Illustrate that path is a hyperbola.