It was a grisly start to the new era for Libya, broadcast around the world. The dictator was dragged from the sewer pipe where he was hiding, tossed around by frenzied rebel soldiers, beaten bloody and sodomized with a bayonet. A shaky cellphone video showed the pocked face of Col. Muammar el-Qaddafi, “the Leader” who had terrified Libyans for four decades, looking frightened and bewildered. He would soon be dead.

The first news reports of Colonel Qaddafi’s capture and killing in October 2011 reached the secretary of state in Kabul, Afghanistan, where she had just sat down for a televised interview. “Wow!” she said, looking at an aide’s BlackBerry before cautiously noting that the report had not yet been confirmed. But Hillary Clinton seemed impatient for a conclusion to the multinational military intervention she had done so much to organize, and in a rare unguarded moment, she dropped her reserve.

“We came, we saw, he died!” she exclaimed.

Two days before, Mrs. Clinton had taken a triumphal tour of the Libyan capital, Tripoli, and for weeks top aides had been circulating a “ticktock” that described her starring role in the events that had led to this moment. The timeline, her top policy aide, Jake Sullivan, wrote, demonstrated Mrs. Clinton’s “leadership/ownership/stewardship of this country’s Libya policy from start to finish.” The memo’s language put her at the center of everything: “HRC announces … HRC directs … HRC travels … HRC engages,” it read.