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C O N T A I N I N G T H E
PRINCIPAL PROPOSITIONs

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witH NOTES C R ITICAL AND EXPLAN AT OR Y.

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OF all the works of antiquity which have been transmitted to the present times, none are more universally and deservedly esteemed than the Elements of Geometry which go under the name of EUCLID. In many other branches of science the moderns have far surpassed their masters ; but, after a lapse of more than two thousand years, this performance still maintains its original preeminence, and has even acquired additional celebrity from the fruitless attempts which have been made to establish a different

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It is, however, generally allowed, that the Elements, as they now stand, are attended with many difficulties, which greatly retard the progress of learners, on their first entrance upon this study, and prevent them from applying to other branches of knowledge, which, in the present advanced state of the sciences, are equally useful and important. Among other obstacles of this kind A 2 may

may be mentioned the theory of parallel lines, the doćtrine of proportion, and many things in the eleventh and twelfth books, relating to solids, which are usually found extremely embarrassing; and notwithstanding the numberless efforts which have been made to elucidate and explain them, are still liable to many objećtions. On this account, it has been found necessary, in most of our academical institutions, to have recourse to some of the more compendious rudiments of later writers, who, by means of a different arrangement, have endeavoured to new-model the subject, and to render it less complex and elaborate. But the greater part of them are so ill digested that they serve rather to mislead the learner than to afford him any assistance. For, besides being deficient in order and method, some of these authors have treated the subjećt algebraically ; and others, by introducing a number of exceptionable principles, and a vague unsatisfactory mode of demonstration, have degraded the science, and deprived it of some of its most striking advantages.

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