to adjure
Horkizo is used for directly binding or pressing someone by an appeal to God or to Jesus' name.
The two occurrences show a direct, first-person appeal that invokes a higher name: one speaker appeals by God to prevent torment, and others invoke Jesus' name over people with evil spirits.
Senses in use
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Binding appeal by an invoked name · dominant
Both occurrences use the first-person present active indicative form in direct speech. In Mark 5:7 the speaker appeals by God, asking Jesus not to torment him; in Acts 19:13 the speakers invoke Jesus' name over those with evil spirits, and the APB renders the clause "I adjure you by Jesus whom Paul proclaims."
In the Anselm Project Bible: The APB presents the term with "I adjure you" in both direct-speech clauses, followed by an appeal "by God" or "by Jesus whom Paul proclaims." This rendering confirms the overall appeal rather than isolating every element of the Greek form.