People attribute this to Aristotle largely because Jowett used a contemporary proverb in lieu of what Aristotle wrote: "As the proverb says -- 'Well begun is half done.'" The following alternative translations capture his original meaning more closely:
"The beginning is said to be half of the business." [tr. Ellis (1912)]
"The beginning as the proverb says is half of the whole." [tr. Rackham (1932)]
"The beginning is said to be 'half of the whole.'" [tr. Lord (1984)]
"The starting-point is said to be half the whole." [tr. Reeve (2007)]