principle. The device was impractical to build with the technology of Leibniz's time, and was never realized. In 1706 John Perks built a tractional machine in order to realise the hyperbolic quadrature. In 1729 Giovanni Poleni built a tractional device that enabled logarithmic functions to be drawn. A history of all these machines can be seen in an article by H. J. M. Bos. See also Dini's surface Hyperbolic functions for , , , Natural logarithm for Sign function for Trigonometric functions for , , , , Notes References External links Tractrix on MathWorld Module: Leibniz's Pocket Watch ODE at PHASER Plane curves Mathematical physics