history, placing the invention of the water mill in the mid-third century BC by the Greeks. Philo's works also contain the oldest known application of a chain drive in a repeating crossbow. Two flat-linked chains were connected to a windlass, which by winding back and forth would automatically fire the machine's arrows until its magazine was empty. Philo also was the first to describe a gimbal: an eight-sided ink pot that could be turned any way without spilling and expose the ink on top. This was done by the suspension of the inkwell at the centre, which was mounted on a series of concentric metal rings which remained stationary no matter which way the pot turns. In his Pneumatics (chapter 31) Philo describes an escapement mechanism, the earliest known, as part of a washstand. A counterweighted spoon, supplied by a water tank, tips over in a basin when full releasing a pumice in the process. Once the spoon has emptied, it is pulled up again by the counterweight, closing the door on the pumice by the tightening string. Remarkably, Philo's comment that "its construction is similar to that of clocks" indicates that such escapements mechanism were already integrated in ancient water clocks. He is also credited with the construction of the first thermoscope (or Philo thermometer), an early version of the thermometer. Mathematics In mathematics, Philo tackled the problem of doubling the cube. The doubling of the cube was necessitated by the following problem: given a catapult, construct a second catapult that is capable of firing a projectile twice as heavy as the projectile of the first catapult. His solution was to find the point of intersection of a rectangular hyperbola and a circle, a solution that is similar to the solution given by Hero of Alexandria several centuries later. See also Chain pump William M. Murray, The Age of Titans – the rise and fall of the great Hellenistic navies. New York, Oxford University Press, 2012. Appenedix E: Book V of Philo's Compendium of Mechanics – The Naval Sections (translated to English), pp. 282–301 . References External links Animation: Philons "Bird and snake" English translation of 'The Seven Wonders of the World' 280s BC births 220s BC deaths 3rd-century BC Greek people 3rd-century BC writers Ancient Byzantines Ancient Greek inventors Ancient Greek military engineers Ancient Greek military writers Ancient Greek physicists Ancient Greek science writers Hellenistic military engineers