older than King Edwin of Northumbria (who often is credited as the source of the name); originally Din Eidyn, Celtic, perhaps literally "fort on a slope." Later the first element was trimmed off and Old English burh "fort" added in its place." Dunedin in New Zealand represents an attempt at the original form.

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Definitions of Edinburgh from WordNet

Edinburgh (n.)
the capital of Scotland; located in the Lothian Region on the south side of the Firth of Forth;