The determination of the true relation between the length of a pendulum and the time of its oscillation; the invention of the theory of evolutes; the discovery, hence ensuing, that the cycloid is its own evolute, and is strictly **isochronous**; the ingenious although practically inoperative idea of correcting the "circular error" of the pendulum by applying cycloidal cheeks to clocks - were all contained in this remarkable treatise.

As an additional claim to remembrance, he was the first to solve Leibnitz's problem of the **isochronous** curve (Acta Eruditorum, 1690).

In so far as the vibrations may be regarded as **isochronous**, the distance between consecutive corresponding points of the recurrent figure, or, as it may be called, the wavelength of the figure, is directly proportional to the velocity of the jet, i.e.