What are the two things that are being compared (metaphor) in Emerson's, "to draw a new circle"?

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Did you mean Emerson's essay, entitled "Circles"?

In "Circles" Emerson compares the eye and horizon to circles with all of nature following this pattern: "The eye is the first circle; the horizon which it forms, the second; and, throughout nature this primary figure is repeated without end."

Emerson also states that "our culture is the predominance of an idea which draws after it this train of cities and institutions. For example, the Puritan culture of Colonial America had its concept, or idea of God being actively involved in one's life; the Puritans built their colleges for the instruction of young men in the ministry of this faith. The cities and institutions were citadels of this faith: "one circle leads to another with the primary figure repeated." The original ideology is the first circle; the "train of cities and institutions" are cultural horizons, the second circle.

The emanaitng self becoming a widening circle is the metaphor. Emerson writes that the key to every man is his thought; all his facts are clarified by a "certain helm" of thought. The central beliefs of a man are the "helm" of his thought that lead him to the widening circles of thought and culture.

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