I never met an epigraph. . .

Circles
I chose this answer: ". . . this epigraph comments or elucidates the meaning of the text." as the purpose of Emerson's use of his "Circles" epigraph:

Nature centres into balls,
And her proud ephemerals,
Fast to surface and outside,
Scan the profile of the sphere;
Knew they what that signified,
A new genesis is here.

In using just a few, spare words to form his epigraph, Emerson has given us a large message: Nature (life) is an omniscient, never-ending sphere (circle). The circle has both physical attributes (ball)--which are constantly replenishing (ephemeral), and the circle has human attributes. . ."Scan the profile of the sphere: Knew they what that signified, A new genesis is here." This is his hello to readers. . .Man, are you Thinking? Man. . .what is your character and did you know you form your character by a circle of truth, which is then surrounded by another circle of truth, without end?

Emerson completely supports his epigraph through the use of a monster-size ecliptic salvo in the first paragraph of "Circles." He sets us up to expect (and delivers) many great ideas (Nature, Man Thinking, Circles, Character, Ephemeral qualities of life), throughout this essay, with this opening paragraph:

"The eye is the first circle; the horizon which it forms is the second; and throughout nature this primary figure is repeated without end. St. Augustine described the nature of God as a circle whose centre was everywhere, and its copious circumference nowhere. We are all our lifetime reading the copious sense of this first of forms. One moral we have already deduced in considering the circular or compensatory character of every human action. Another analogy we shall now trace; that every action admits of being outdone. Our life is an apprenticeship to the truth, that around every circle another can be drawn; that there is no end in nature, but every end is a beginning; that there is always another dawn rise on mid-noon, and under every deep a lower deep opens."

Paragraph 3:
"There are no fixtures in nature (ephemeral). The universe is fluid and volatile. Permanence is but a word of degrees. Our globe (earth, ball, circle) seen by God is a transparent law, not a mass of facts."

Paragraph 5:
He is again discussing character, the human condition: "The key to every man is his thought. . ."The life of man is a self-evolving circle, which, from a ring imperceptibly small, rushes on all sides outward to a new and larger (ephemeral) circles, and that without end."

Paragraph 20:
He reminds us again in this paragraph, we are humans; and our world is a fleeting, passing, replenishing thing:
"The natural world may be conceived as a system of concentric circles, and we now and then detect in nature slight dislocations, which apprize us that this surface on which we now stand is not fixed, but sliding."

A reader can easily find connections to the epigraph in ALL of the "Circle."

"Beware when the great God lets loose a thinker on this planet"
He did just that with Emerson.
-30-
COMPLETE ASIDE:
I was one of the students from this class who admitted to overlooking reading one of the epigraphs from Emerson or Thoreau earlier this week. Although I used one myself for my Keats Fact Sheet, I didn't read the one from the esteemed author. Be sure I won't do it again. Now I am haunted by them, I see them everywhere (feel like this could be a Seinfield episode, "Jerry, ya should have heard the epigraph that guy used on me. . ."). I added one purposefully to a project due for my Rhetoric class. Upon peer review of the project, only one comment on the epigraph was received. While the message of MY epigraph, in my mind, could not have been more clear and purposeful, my peer reviewer asked what I meant by it. So then I started thinking. . .why did they not understand it when it was perfectly clear to me!