The city of Euclid, OH, is a suburb on the shore of Lake Erie, to the east of Cleveland, OH. It was settled in 1798. It is 25 square miles, and has a population (1994) of 54,875.
Moses Cleaveland, for whom Cleveland is named, employed a group of surveyors to survey the Western Reserve of Connecticut, in the 1790s. The Western Reserve is a parcel of 3 million acres in Northeast Ohio, the southern border of which corresponds with the southern boundary of Connecticut. The surveyors divided the Western Reserve into 25 square mile parcels, five miles by five miles, except those on Lake Erie, which, due to their irregular shape are sometimes larger and sometimes smaller.
As part of the payment for their work, the surveyors were allowed to name some of the townships. They were students of classical mathematics, and felt heavily indebted to the writings of Euclid, and thus, named one of the townships after him.
David Dille, a Revolutionary War lieutenant from Virginia, is generally credited as the first settler, in 1798. The township was incorportated in 1809.
It is for the city of Euclid that things in the Cleveland area are named Euclid, most notably, Euclid Avenue, the road that runs from downtown Cleveland to Euclid, and the Euclid Tavern, a small club and great place to hear music, on Euclid Avenue.
Euclid is mostly a commuter suburb, devoid of significant landmarks and attractions. It is, however, home to the National Cleveland-Style Polka Hall of Fame.
Sources:
http://www.ci.euclid.oh.us/history.htm
http://www.clevelandstyle.com/phof_001.htm
Coates, Wiliam R. A History of Cuyahoga County and the City of Cleveland, American Historican Society, Chicago, 1924
Personal knowledge as a resident of the Cleveland area.