Many people have been mixing drinks for 100s of years, but it was not before 17th and 18th centuries that the precursors of the cocktail (the Slings, Fizzes, Toddies and Juleps) became well known enough to be noted in the history books. It is undecided where, who, and what went into the creation of the first cocktail, but it seems to be a particular drink instead of a list of mixed drinks during that time.
The first publicized quotation to the cocktail shows up in the Farmer's Cabinet (Amherst, New Hampshire, April 28, 1803). The spoof editorial narrates of a "lounger" who, with an 11 who, with an 11 am hangover." Sipped a glass of cocktail - fantastic for the head..."
In Imbibe! David Wondrich stages the first known cocktail recipe in print to Captain J.E. Alexander in 1831 who calls for gin, whiskey or rum in a mix of "... a third of the spirit to two-thirds of the water; add bitters, and enrich with sugar and nutmeg."