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EASTERN DISTRICT OF PENNSYLVANIA, to wit:

BE JT REMEMBERED, THAT on the twenty-second day of L.S.

, *** America, A. D. 1828, Francis Nichols, of the said District, hath deposited in this office the title of a book, the right whereof he claims as proprietor, in the words following, to wit: ELEMENTS OF GEOMETRY. Being chiefly a Selection

from PLAYPAIR'S GEOMETRY, with additions and improvements. From the fifth English edition. In conformity to the Aet of the Congress of the United States, entitled “An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the Authors and Proprietors of such copies, during the times therein mentioned ;'-And also to the Act, entitled« An Act supplementary to an Act, entitled " An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the times therein mentioned,” and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints »

D. CALDWELL,

Clerk of the Eastern District of Pennsylvania,

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PREFACE.

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Many years ago the editor of this book published two large impressions of Play fair’s Geometry, with some alterations and improvements, which rendered the American edition more convenient to students than the English. The work has been long out of print, and a republication of it has been often requested by public and private teachers of geometry. It is therefore again presented to the public without an adequate compensation for the time and labour bestowed on the preparation of a new and improved edition.

The books of geometry, used in places of education in this country, are two large, and otherwise exceptionable. The best editions of Euclid's Elements are difficult and repulsive to students. They require some alterations to render them fit for the use of youth in schools and colleges. False reverence of antiquity, and old prejudice, have assigned to Euclid's Geometry a higher rank in mathematical science than its intrinsic merit can justly claim. But it is capable of alterations and improvements, and may be made a good introduction to geometry.

This book is partly an abridgment of the fifth English edition of Playfair's Geometry. It differs from Piayfair's Geometry chiefly in additions, omissions, and alterations.

Many teachers of mathematics in our colleges and higher schools have often expressed a wish that a se

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lection from Euclid's Elements might be published, if it could be executed without deviating much from the form of the original. To accomplish this desirable object is the main design of the present perform

Euclid's Geometry contains parts which are never read, with obscurities and difficulties which discourage youth, and impede the study of mathematics. The prejudices of education and custom have retained an old book in schools and colleges, to the exclusion of modern works of greater merit. We find that on the continent of Europe Euclid's Geometry has nearly sunk into oblivion, and modern systems now occupy its place. But still, as the ruins of ancient edifices furnish the materials of elegant modern structures, so Euclid's treatise of geometry may be so modified as to be converted into a plain and useful book for youth.

Some definitions, postulates, and axioms, have been added by the editor, on the supposition that they might be wanted in the course of the work, for the purpose of rendering the demonstrations of certain propositions shorter or plainer than those of Euclid. Some useful propositions, which were not known to the ancients, have been added to this treatise; and many propositions have been omitted, which are either useless, or merely auxiliary to the demonstrations of others. Some demonstrations which were long and tedious, or difficult to learners, have been rejected, and others have been adopted from modern books instead of them. But no new demonstrations have been given unless they were decidedly preferable to Euclid's.

The enunciations of many propositions are expressed with more precision and brevity than they are in former editions of Euclid's Elements. Repetitions and circumlocutions in the demonstrations have been generally avoided.

Numerous articles, marked Ed., are not found in

Playfair's Geometry, and have been taken chiefly from other books. They were collected at different times, but the editor does not recollect the names of the authors of many of them. In the latter part of the volume many references have been designedly omitted; for it appeared useless to repeat the references to preceding articles, which must have become familiar to the reader by their frequent recurrence. But the teacher should require his pupils to supply such omissions when they are reciting a demonstration.

Toward the ends of the first, third, and sixth Books there is a number of elementary propositions, which are not necessary in a course of mathematics, and may be either read or omitted. They will serve as exercises for students.

On revising the printed sheets I have observed that some changes might be made with advantage to the work. In its present form however I am confident that it will be found plainer and more convenient to students than any book of geometry which is now used in the higher places of education.

If this attempt to facilitate the study of geometry be favourably received by the public, it will be followed by another work, which is partly executed, and will contain a large collection of Geometrical Problems, Trigonometry, &c.

EDITOR.

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