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connexion with the second, has been frequently reprinted in the United States. The Boston edition of both volumes, which appeared in 1821, translates the quotations not in English. Mr. Stewart, however, seems not to have been satisfied with the version, for he has left, I am informed, eight quarto pages of corrections in his copy of the book. I do not know whether these translations are the same with those given in Wright's London edition of the two volumes, in 1843.

In the present collection,—the fragment of the Outlines was printed from the seventh edition, collated with the fourth, and with the first three editions in which the author's annotations are found.—The First Volume of the Elements was printed from its fourth edition, (1811,) collated with the sixth, (1818;) and the insertions from the Addenda in the third volume are distinguished by square brackets.—The Second Volume was printed from the third edition, (1821,) collated with the second, (1816,) and also with the first, in which last Mr. Stewart's annotations were written.—The Third Volume was, of course,

— printed from the one edition ; and to this part of the Elements nothing has been added by the author.

In regard to what I have myself contributed to this collection,-I may repeat, that I have limited my interference strictly to the province of an editor; and it was manifestly no part of my official duty to meddle with the author's reasonings. Accordingly, there has been nothing added by me, in the view of vindicating, of supplementing or confirming, of qualifying or criticising, Mr. Stewart's doctrines. I have proposed, exclusively, to render this edition the one in which these might be most conveniently studied. To this end, however, it was necessary that the authorities and their citations should be occasionally rectified and filled up; and it was necessary that the reader, let him open the book where he might, should be

made at once aware of the special matter under discussion.
But this last could only be accomplished by a total change of
the plan previously adopted, in what is called the heading of
the pages; the running titles now first indicating as minutely as
possible the local argument.* This pervading improvement
has not, however, been overtly distinguished. It should also
be noted, that in the Table of Contents and in the relative
places of the text, the Editor's supplement of titles has only
been ambiguously marked, as new, by the brackets. All formal
distinction of insertion by the Editor, has likewise been omitted
in the case of references appended to quotations, and, in general,
to all short and merely explicative interpolations. It should
perhaps be observed, that Notes referred to from the text,
and not by numerals, are all the Editor's; but indeed, any
brief insertion, whether in text or note, is usually by him.-
As the work proceeded, it was found expedient to pay greater
attention to punctuality of reference; and this may account
for, if not excuse, any earlier omission.

W. H.
July, 1854.

* The First Volume is occupied with
Part First; the Second, with Part
Second, First Subdivision. But what
has been overlooked,—to the left hand
heading of the former should be added
the number, -1.; and to that of the

latter, the numbers,—II. 1. In the
Third Volume, the omission has been
supplied. On the right hand heading,
also, of this volume, the sections (28),
especially in the Outlines, have not
always been marked.

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