Alexander Dyce, A General Glossary to Shakespeare's Works

death — “Took it on his,” KING JOHN, i. 1. 110. This is explained by Steevens,“Entertained it as his fixed opinion, when he was dying;” but I believe that here upon his death is merely an asseveration, or sort of oath, as it is in 1 Henry IV., v. 4. 149, where Falstaff says,“I'll take it upon my death, I gave him this wound in the thigh.” Compare, too:
“Gripe. But I am sure she loues not him.
Will. Nay, I dare take it on my death she loues him.”
Wily Begvilde, sig. C verso, ed. 1606.