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phy, History, Literature, and Mythology of the Ancients. Revised,
corrected, and arranged in a new form, by Lorenzo L. da Ponte and

John D. Ogilby. 8vo.
LATIN READER; Parts I. & II. by Frederick Jacobs and

Frederick William Doring; with Notes and Illustrations, partly trans-
lated from the German and partly drawn from other sources. By John

D. Ogilby. 12mo.
ADAM’S LATIN GRAMMAR; containing the ancient and
modern Pronunciation of the Latin Language ; together with Obser-
vations on the Declinable Parts of Speech, Rules for the Government
of the Subjunctive Mood, and various other Improvements and Correc-

tions. By David Patterson, A. M. 12mo.
MAIR'S INTRODUCTION to Latin Syntax : from the Edin-

burgh Stereotype Edition; revised and corrected by A. R. Carson,
Rector of the High School of Edinburgh. To which is added, Copi-
ous Exercises upon the Declinable Parts of Speech, and an Exempli-
fication of the several Moods and Tenses. By David.

Patterson,
A. M. 12mo.
VIRGIL: with English Notes. By John D. Ogilby. ' 12mo.
CÆSAR'S COMMENTARIES: illustrated with English

Notes, and an Index of Proper Names. By David Patterson, Ă. M.

12mo.
BLACKSTONE'S COMMENTARIES on the Laws of Eng-
land : with Notes by Christian, Chitty, Lee, Hovenden, and Ryland.
Also a life of the Author: and References to American Cases. By

a Member of the New-York bar. 2 vols. 8vo.
MURRAY'S MATERIA MEDICA AND PHARMACY,

including Translations of the Edinburgh, London, and Dublin Phar-

macopeias. With Notes and Additions, by John B. Beck, M. D. 8vo.
PARIS' PHARMACOLOGIA : with Notes and Additions, by

John B. Beck, M. D. 8vo.
RICHERAND'S PHYSIOLOGY: translated from the French,

by G. J. M. de Lys, M. D. With Notes and a copious Appendix, by

James Copland, M. D. 8vo.
ÆSOP'S FABLES: with instructive Applications, by Samuel

Croxall, D. D. Embellished with a print before each Fable. 18mo.
GOLDSMITH'S NATURAL HISTORY; abridged for the

use of Schools : with 16 elegant copper-plates. By John D. Godman,
M. D. 12mo.

:

In Press.ADAM'S ROMAN ANTIQUITIES : a new Edition, from
a late English Copy, illustrated with upwards of 100 Engravings on
steel and wood, with notes and improvements, by L. L. da Ponte,
Professor of Italian Literature in the University of the City of New-

York.
Preparing for Press.-A new Edition of HUTTON'S MATHEMA-

TICS, complete in one large 8vo. volume; entirely remodelled by Pro-
fessor Ramsay, of Trinity College, Cambridge. The above Edition
will contain a full and complete Treatise on Arithmetic, Algebra, Ge-
ometry, Conic Sections, Plane Trigonometry, Mensuration, Surveying,
Analytical Plane and Spherical Trigonometry, Analytical Geometry,
the Differential and Integral Calculus. Also, a new Treatise on Me-
chanics, compiled chiefly from the works of Laplace, Lagrange, Pois-
son, Pontecoulant, Boucharlat, Somerville, Gregory, Young, &c.
By James Ryan, A. M.

पा

ELEMENTS

OF

G E O M E T RY:

CONTAINING

THE FIRST SIX BOOKS OF EUCLID,

WITH A

SUPPLEMENT

ON THE

QUADRATURE OF THE CIRCLE, AND THE

GEOMETRY OF SOLIDS:

TO WHICH ARE ADDED,

ELEMENTS OF PLANE AND SPHERICAL

TRIGONOMETRY.

BY

JOHN PLAYFAIR, F.R.S. LOND. & EDIN.
PROFESSOR OF NATURAL PHILOSOPHY, FORMERLY OF MATHEMATICS, IN THE

UNIVERSITY OF EDINBURGH.

A NEW EDITION, ENTIRELY REMODELLED,

BY JAMES RYAN,
AUTHOR OF AN ELEMENTARY TREATISE ON ALGEBRA, THEORETICAL AND PRACTICAL, THE
DIFFERENTIAL AND INTEGRAL CALCULUS; THE NEW AMERICAN

GRAMMAR OF ASTRONOMY, &c.

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W. E. DEAN, PRINTER AND PUBLISHER, No. 2 ANN-STREET,

B. & s. COLLINS, AND N. & J. WHITE.

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Entered according to the Act of Congress, in the year One Thousand

Eight Hundred and Thirty-five, by W. E. DEAN, in the Clerk's Office of the Southern District of New-York.

In offering to the American Public a new edition of Professor PLAYFAIR's Elements of Geometry, it may not be improper to enumerate a few of the considerable alterations, and, it is hoped, the important improvements, made in a work which has acquired great and just celebrity, not only in Europe, but also in the United States, since its republication in this country.

The alterations made are chiefly in the First and Third Books; the arrangement of those Books is similar to that of LEGENDRE, in his Elements of Geometry and Trigonometry.

As the properties of the sections of straight lines are easily derived from Algebra, the demonstrations of the principal propositions in the Second Book are expressed Algebraically, by way of Scholium, to each proposition.

Several Theorems, Lemmas, Corollaries, and Scholiums, are interspersed throughout the whole work, not contained in any previous edition.

A few useful Problems, especially in Surveying, are also added to the Sixth Book; so that this edition of PLAYFAIR'S Geometry, it is presumed, will be found better adapted for the instruction of youth in the Elements of Geometry, according to the present state of Science, than any that has as yet been published.

JAMES RYAN.

New-York, January 1st, 1835.

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