PHILADELPHIA — Breaking a historic barrier, Hillary Clinton triumphantly captured the Democratic nomination for president Tuesday night, the first woman ever to lead a major political party in the race for the White House. Delegates erupted in cheers as Clinton's primary rival, Bernie Sanders, helped make it official when the roll call got to his home state of Vermont — an important show of unity for a party trying to heal deep divisions. "I move that Hillary Clinton be selected as the nominee of the Democratic Party for president of the United States," Sanders declared, asking that it be by acclamation.