Final answer:
Odysseus is the speaker in the Odyssey excerpt, addressing Circe. He demands an oath from Circe for his safety, reflecting his control and wariness of enchantment.
Step-by-step explanation:
The speaker in the excerpt from the Odyssey is Odysseus, who is addressing Circe, a sorceress who has transformed his men into swine and is now attempting to seduce him.
The significance of this quote lies in Odysseus's assertion of control and demand for an oath from Circe, ensuring that she will do him no harm before he agrees to her advances. This demand for an oath symbolizes a moment of regaining power and ensuring his safety in a treacherous and enchanting environment.