. . . Hektor would not give ground but kept unquenched the
fury within him
and sloped his shining shield against the jut of
the bastion.
Deeply troubled he spoke to his own great-
hearted spirit:

". . . . it would be much better
. . . to go against Achilleus, and slay him, and come back,
or else be killed by him in glory in front of the city."

–The Iliad of Homer,
Richard Lattimore

What is Hektor thinking about in this passage?

What ancient Greek belief does this passage most clearly suggest?