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FIRST SIX BOOKS
ELEMENTS OF EUCLID,
PRINTED AT THE UNIVERSITY PRESS,
FOR RICHARD MILLIKEN AND SON,
AND WILLIAM CURRY, JUN. AND CO.,
TO THE READER.
IN preparing this edition, designed solely for the use of the Undergraduates in the University of Dublin, it was the object of the Editor to retain the original strictness of the demonstrations as given by Euclid, and at the same time to throw them into the most simple form. For this purpose the syllogistic mode of argument, in which all the direct proofs had usually been drawn up, has been abandoned; and the arrangement approved of by Locke adopted in its stead. But the theory of Proportion in the fifth book has been entirely altered, for reasons assigned in the notes. To defend the definition of proportional quantities given by Euclid, it has been asserted, that there is no other principle from which the doctrine can be demonstrated; but that defence, it is hoped, must now be abandoned, as the demonstrations here given are derived from a more simple and natural definition.