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through want of direct incitement. Abstract pursuits will be found nowise unfriendly to the cultivation of elegant literature, or incompatible with the most vigorous play of imagination. When the connexion and mutual dependence of the several branches of knowledge are clearly understood, it may be expected that our academical institutions, happily released from the trammels of antiquated forms, will hasten to show their liberality, in extending to the mathematical studies the same protection which has hitherto been almost exclusively confined to the scholastic arrangements.

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It is the nature of mathematical science to advance in continual progression. Each step carries it to others still higher. As its domain swells on the sight, new relations are descried, and the more distant objects seem gradually to approximate. But, while science thus enlarges its bounds, it likewise tends uniformly to simplicity and concentration. The discoveries of one age are, perhaps in the next, melted down into the mass of elementary truths. What are deemed at first merely objects of enlightened curiosity, become, in due time,

subservient to the most important interests.

The ory soon descends to guide and assist the operations of practice. To the geometrical speculations of the Greeks, we may distinctly trace whatever progress the moderns have been enabled to achieve in mechanics, navigation, and the various complicated arts of life. A refined analysis has disclosed the harmony of the celestial motions, and conducted the philosopher, through a maze of intricate phænomena, to the great laws appointed for the government of the Universe.

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1.-TABLE of Correspondence between these Books of Geometry and the

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II-TABLE of Correspondence of the Elements of EUCLID with these Books

of Geometry.

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