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“The art of seeing nature, or, in other words, the art of using models, is in reality the great object, the point to which all our studies are directed.”

“To view an object in the proper light we must stand away from it. The study of the classical literatures gives the aloofness which cultivates insight. In learning to live with peoples and civilizations that have long ceased to be alive, we gain a vantage point, acquire an enlargement and elevation of thought, which enable us to study with a more impartial and liberal mind the condition of the society around us.”

“The science of the church is neglected for the study of geometry, and they lose sight of Heaven while they are employed in measuring the earth. Euclid is perpetually in their hands. Aristotle and Theophrastus are the objects of their admiration; and they express an uncommon reverence for the works of Galen. Their errors are derived from the abuse of the arts and sciences of the infidels, and they corrupt the simplicity of the gospel by the refinements of human reason.”

“It reflects no great honor on a painter to be able to execute only one thing well -- such as a head, an academy figure, or draperies, animals, landscapes, or the like -- in other words, confining himself to some particular object of study. This is so because there is scarcely a person so devoid of genius as to fail of success if he applies himself earnestly to one branch of study and practices it continually.”

“In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency towards intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations.”

“In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.”

“So abundant and novel are the objects of interest in a pure wilderness that unless you are pursuing special studies it matters little where you go, or how often to the same place. Wherever you chance to be always seems at the moment of all places the best; and you feel that there can be no happiness in this world or in any other for those who may not be happy there.”