A figure from Descartes’s [i]Geometry [/i](1637). For the modern reader, consider ray AK as the positive [i]y [/i]axis and AG as the positive [i]x [/i]axis (even though it points to the left). KNL is a rigid triangle whose side KL slides on the [i]y[/i] axis. An infinitely long “ruler” is fixed at G on the [i]x[/i] axis, and is attached to the moving point L of the triangle. The side KN of the triangle is extended so that it intersects the ruler at C. As the triangle moves on the [i]y[/i] axis, point C traces a curve.[br][br]This curve is one nappe of a hyperbola. Why? You can read Descartes, or a paper by David Dennis: Rene Descartes' Curve-Drawing Devices: Experiments in the Relations Between Mechanical Motion and Symbolic Language. [i]Mathematics Magazine[/i], 1997, [i]70[/i](3), 163-174.