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CONTAINING

THE ELEMENTARY AND THE HIGHER PRINCIPLES

AND APPLICATIONS OF THE SCIENCE,

WITH THE MOST USEFUL

ABBREVIATED METHODS OF CALCULATION;

PRACTICAL MENSURATION;

AND

APPENDICES

ON EXCHANGE, AND MATHEMATICAL PROBABILITIES ;

WITH APPLICATIONS OF THE LATTER TO

LIFE ANNUITIES AND LIFE INSURANCE.

BY

JAMES B. DODD, A. M.,

MORRISON PROF. OF MATHEMATICS AND NAT. PHILOSOPHY, IN TRANSYLVANIA UNIVERSITY.

SECOND EDITION

NEW-YORK:
PUBLISHED BY PRATT, WOODFORD & CO.

HARVA
UNIVEDC!"
LIBRA

OH*122

Entered according to Act of Congress, in the Year 1851, by

JAMES B. DODD,

In the Clerk's Office of the District Court of Kentucky.

PRE FACE.

The greater portion of the following work, under the title of “Elementary and Practical Arithmetic,” was published about two years ago, and has met with the most gratifying reception from eminent Teachers wherever it has become known.

In enlarging the work with a view to meet the wants of Schools in which a more extensive course of arithmetical study is pursued, the object has been to add whatever seemed wanting to a complete theoretical and practical treatise; to present the supplemental principles and processes in the clearest light of which they are susceptible; to furnish Exercises which shall be found well adapted to the expanding capacity of the Studentprove a means and a test of his intellectual development and discipline and inure him to some of the more recondite, as well as to the more obvious applications of the science.

But in the completeness aimed at, a regard has been entertained only for what appeared to be really useful. One or two subjects, therefore, of merely theoretical interest, may be found in some of the Higher Arithmetics, which have been omitted, or partially presented in this; whịle others have been pursued to an unusual extent; and two of three, of much theoretical and practical interest, have been introduced; which, so far as is known to the author, have not hitherto been treated in any work designed for educational purposes.

To place in the hands of his fellow laborers the best instrumental aid towards an able performance of their duty, in a department of their labors which is peculiarly liable to suffer from indolence or incompetency in Authors, as well as in Teachers,-has been the earnest endeavor of the writer, in the composition of every part of this work.

To those who, in various, even the remotest parts of the country, have so strongly commended his former publicationwho, with comparatively few exceptions, are personally unknown to him, the author will do himself the pleasure, on this occasion, to offer the expression of his grateful acknowledgments. TRANSYLVANIA UNIVERSITY,

September 24th, 1851.

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