undertake solemnly

"Monsieur le President," cried Danton, "if the traitors venture to present themselves, I undertake solemnly either that my head shall fall on the scaffold, or to prove that their heads should roll at the feet of the nation they have betrayed."

Since, therefore, the assembled representatives refused to take the oaths at Thebes, the Thebans sent to the different states, one by one in turn, urging each to undertake solemnly to act in accordance with the great king's rescript.