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The Romans used both fixed and floating water wheels and introduced water power to other provinces of the Roman Empire.
So-called 'Greek Mills' used water wheels with a horizontal wheel (and vertical shaft).
The former type can be further divided, depending on where the water hits the wheel paddles, into undershot, overshot, breastshot and pitchback (backshot or reverse shot) waterwheel mills.
Another way to classify water mills is by an essential trait about their location: tide mills use the movement of the tide; ship mills are water mills onboard (and constituting) a ship. Lewis has shown that those portions of Philo of Byzantium's mechanical treatise which describe water wheels and which have been previously regarded as later Arabic interpolations, actually date back to the Greek 3rd-century BC original.
The Tang Dynasty (618–907 AD) 'Ordinances of the Department of Waterways' written in 737 AD stated that watermills should not interrupt riverine transport and in some cases were restricted to use in certain seasons of the year.Reynolds suggests that the first water wheels were Norias and, by the 2nd century BC, evolved into the vertical watermill in Syria and Asia Minor, from where it spread to ancient Greece and the Roman Empire. Lewis assigns the date of the invention of the horizontal-wheeled mill to the Greek colony of Byzantium in the first half of the 3rd century BC, and that of the vertical-wheeled mill to Ptolemaic Alexandria around 240 BC.Engineers in the Hellenistic world used the two main components of watermills, the waterwheel and toothed gearing, and, along with the Roman Empire, operated undershot, overshot and breastshot waterwheel mills. Hold back your hand from the mill, you grinding girls; even if the cockcrow heralds the dawn, sleep on.Similar anvil stones have been found at other Roman mines across Europe, especially in Spain and Portugal.The 1st-century AD multiple mill complex of Barbegal in southern France has been described as "the greatest known concentration of mechanical power in the ancient world".