Origin of the word 'cop'

Where did the word "cop" come from? Here's the origin story from Do's, Don'ts, and Maybes of English Usage by Theodore Bernstein:

"Cops are, of course, policemen. The slang word is neither of recent derivation nor an Americanism. The Oxford English Dictionary records a quotation using the word cop that is dated 1704. The slang verb cop meant to catch or arrest and one, who did that was a copper. Then copper was shortened to cop. One school of thought relates-copper to the copper buttons once used on police uniforms. Anyway, the cops themselves would rather be called officers. "