The analytical power should not be confounded with simple ingenuity; for while the analyst is necessarily ingenious, the ingenious man is often remarkably incapable of analysis.
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It will be found, in fact, that the ingenious are always fanciful, and the truly imaginative never otherwise than analytic.
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Mathematical reasoning may be regarded...
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. -
Between ingenuity and the analytic ability there exists a difference far greater, indeed, than that between the fancy and the imagination, but of a character very strictly analogous.
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That man is not truly brave who is afraid either to seem or to be, when it suits him, a coward.
