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HISTORICAL VIEW OF THE

Geometry : — Euclid.

In no department are we under greater obligations tothe school of Alexandria than in pure mathematics.One of the first of those eminent men who did so muchhonour to the wise liberality of its founder, was Euclid ;pre-eminently known in every quarter of the globe, andin every age, from his own to the present, by his systemof elementary geometry. We have few particulars ofhis life, and can only assign the period at which heflourished as that immediately succeeding the foundationof the school of Alexandria , or between b. c. 300 and250. Our principal source of information respectinghim, and his works, is from the commentary of Proclus on his Elements. There is no doubt that elements ofgeometry had been previously compiled by Hippocrates ,Eudoxus, and others. Euclid ’s principal design wouldseem to have been that of correcting their errors, sup-plying their deficiencies, and uniting the series of ele-mentary truths into a perfectly systematic chain ofdeduction. The extreme logical precision which isevinced in the style of demonstration, is equalled onlyby the admirable perspicuity and simplicity which, withvery few exceptions, characterise every part of the work.But few treatises, probably, ever suffered more than thisin the course of time, at the hands not only of meretianscribers, but of commentators, and pretended im-provers. Hence it has been the constant object ofmodern editors to restore the text to its probable originalcharacter. Among such attempts, none has been moreconspicuous, or more generally admitted as suecessful,than that of Dr. R. Simson. There still seems, how.ever, to be something wanting to its complete perfection.A certain tinge of mysticism infects some of the defini-tions and axioms ; and the primary defect in the theoryof parallel lines still remains. And though variousremedies have been proposed, none has as yet fulfilledthe conditions of simplicity and conformity to the ele-mentary style, even if admitted to be conclusive.