To John Sowner Esquine with the best respects of the

Author

OF

GEOMETRY,

THEORETICAL AND PRACTICAL:

INCLUDING

CONSTRUCTIONS BY THE RIGHT LINE AND BY THE CIRCLE;

TOGETHER WITH THE

MENSURATION OF ALL THE ELEMENTARY PLANE FIGURES
AND SOLIDS;

SYSTEMATICALLY ARRANGED,

AND

ADAPTED TO PUBLIC AND PRIVATE INSTRUCTION.

BY EUGENIUS NULTY,

MEMBER OF THE PHILOSOPHICAL SOCIETY, PHILADELPHIA; AND OF THE ACADEMY OF
ARTS AND SCIENCES, BOSTON.

Nil nisi certo ordine et certa via sciri posse.-BACON, DIS. Or.

PHILADELPHIA:

J. WHETHAM, 22 S. FOURTH STREET.

1836.

KE 10299

HARVARD
UNIVERSITY
LIBRARY

047*172

Entered, according to the act of congress, in the year 1836, by EUGENIUS NULTY, in the clerk's office of the district court of the eastern district of Pennsylvania.

PREFACE.

THE present work has been written under the influence of opinions in which the author cannot be regarded as singular. He has presumed that a modern systematical treatise on the Elements of Geometry is essential to modern scientific education, and that any attempt to present those elements with the view of facilitating their more effectual acquirement would meet the approbation of mathematical instructors.

In an elementary course of exact science, the principal requisites are conceived to be a natural sequence of its different parts, and a suitable degree of brevity in their exposition. These have been constantly kept in view in the Treatise now offered to the public; and their observance must greatly contribute to the improvement of students in Geometry, and to the removal of difficulties which have hitherto retarded their progress. With respect to the importance of arrangement, and its effects in the study of this science, the author has had ample experience. He has long observed, that in proportion as the different subjects occupying the attention of students succeeded in natural or in artificial connexion, their ideas appeared distinct or confused, and the impressions left in their minds were of permanent or of momentary continuance.

From these and other considerations relative to demonstrative and inductive science, the author premised in the composition of this work, the following as fundamental principles in regard to the manner and order in which the objects of synthetic Geometry should be introduced and treated.

First, that the possible existence and characteristic property of every object considered, should be established previously to forming its definition.

Secondly, that every object defined should be regarded as establishing the existence of an equal object.