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In page River Clyde:

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The exact etymology of the river's name is unclear, though it is known that the name is ancient. In 50AD, the Egyptian mathematician, astronomer and geographer Claudius Ptolemy wrote of the river as "Klōta",[1] It was called Clut or Clud by the Britons and Clota by the Romans. It is therefore likely that the name comes from a Celtic language—most likely Old British. But there is more than one old Celtic word that the river's name could plausibly derive from. One possible root is the Common Brittonic Clywwd, meaning 'loud' or 'loudly'.[citation needed] More likely, the river was named after a local Celtic goddess, Clōta. The goddess's name in turn derives from an older, Proto-Celtic word meaning 'the strongly flowing one' or 'the holy cleanser'.