The earliest reference is in the Pipe Rolls of 1203, which spells the place FROGGEGATE. Next in 1225, the 'Rotuli Litteranum Clausanum' (published by the Royal Commission, London, in 1833-44) spells the place FROGGECOT or FROGGECOTE, which also appears in 1330 (Assize Rolls) and 1424. Other spellings are FROGGCOATE (1423), FROGCOT(E) (Edward I charters, so some time between 1239&1307; 1348). The more familiar FROGGOT(E) appears in 1319, 1355, 1392 and 1416; and FROGGAT(T) in 1339. Source: 'The Place Names of Derbyshire' (Publications of the Record Commission, London, 1959)
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