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PLANE AND SOLID

G E O M E T R Y.

TO WHICH IS ADDED

PLANE AND SPHERICAL

TRIGONOMETRY

AND

MENSURATION.

AOOOMPANIED WITH ALL TIE NEOESSARY

LOGARITHMIC AND TRIGONOMETRIC

TABLES.

BY GEORGE R. PERKINS, LL.D.

NEW YORK:
D. APPLETON & CO., 443. & 445 BROADWAY,

AND 16 LITTLE BRITAIN, LONDON.

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Entered according to Act of Congress, in the year 1854,

BY GEORGE R. PERKINS, La the Clerk's Office of the District Court for the Northern District of New York

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PREFACE.

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This work is not designed to take the place of the “ ELEMENTS
OF GEOMETRY,” but rather to give a more extended and com
prehensive course, better adapted to the use of Advanced
Schools and Colleges.

In the First Part of the work, which is confined to the theo-
retical principles of Geometry, great care has been taken to
classify and arrange the various Theorems, by bringing together
such as correspond to analogous subjects. We have also ar-
ranged the Problems by themselves, and have in no case mixed
them up with the Theorems.

In the preparation of the Geometrical portion of this work,
we have made free use of the admirable work of VINCENT.
The edition used is the fifth, revised by its author, with the
assistance of the distinguished Bourdon. This is a most excel-

BOURDON.
lent and valuable French work, but it is not in all respects
well adapted to the wants of our Higher Institutions; we have,
therefore, preferred to make selections from it, rather than to
give a translation of the whole. We have endeavored to ar-
range and present the different Propositions in the manner
which to us appeared best calculated to impart a thorough
knowledge of the most important principles of the science of
Geometry. As a general thing, we have adhered to the ordi-
nary method of conducting our demonstrations; still we have
Lot hesitated to introduce the algebraic notation, when by so

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