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Sometimes the New Critics illustrated big points with one tiny example. Like when Yvor Winters analyzed Robert Browning's poem in his book, In Defense of Reason—he didn't analyze the whole poem, he just concentrated on two lines.
Winters only needed the two lines though to make his point, you see. As he argued, the "precision of a word"—a.k.a., its exact meaning in context—cannot be understood from the word alone. You have to go looking at the words around it.
Keep in mind that nailing down the definition of one word, completely out of context, is complicated enough. Words, of course, carry with them both dictionary meanings (or denotation) and whole fuzzy fields of associations (or connotations). So when you combine words into sentences, all of their meanings start to play off each other giving you a much more complex overall impression of each individual word's meaning.
To illustrate this point, Winters used the following lines from Browning's "Serenade at the Villa."