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OF

GEOMETRY,

WITH PRACTICAL APPLICATIONS,

FOR THE USE OF SCHOOLS.

BY T. WALKER,
· TEACHER OF MATHEMATICS IN THE ROUND HILL SCHOOL,

AT NORTHAMPTON, MASS.

SECOND EDITION, IMPROVED.

BOSTON:
PUBLISHED. BY RICHARDSON, LORD & HOLBROOK,

133 WASHINGTON-STREET.

MUNROB AND FRANCIS, PRINTERS.

1829.

DISTRICT OF MASSACHUSETTS, TO WIT :

District Clerk's Office. Be it remembered, that on the seventeenth day of November, A. D. 1829, and in the fifty-fourth year of the Independence of the United States of America, RICHARDSON, LORD & HOLBROOK, of the said District, have deposited in this Office the title of a book, the right whereof they claim as proprietors, in the words following, to wit :

Elements of Geometry, with Practical Applications, for the Use of Schools. By T. Walker, Teacher of Mathematics in the Round Hill School, at Northampton, Mass. Second Edition, Improved.

In conformity to the act 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 an 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.”

JOIN W. DAVIS, Clerk of the District of Massachusetts.

Tuuli n-21-38 26926

PREFACE TO THE FIRST EDITION.

In preparing the following work, two objects have o been kept constantly in view. First, I have endeasvoured to bring the essential principles of Geometry

within a small compass ; and, secondly, to make their connexion easy to be understood. That such a book is wanted, I am convinced from personal experience. The works of Euclid and Legendre, the two most generally studied in New-England, though each is nearly perfect in its kind, are, for that very reason, suited only to the highest seminaries of learning. They cost too much and they require too much time, to be generally studied in academies and schools. Moreover they are too abstruse and difficult for the comprehension of very young pupils. All this is a necessary consequence of their fulness and perfection, as treatises on this branch of Mathematics. They necessarily contain many propositions, which are not requisite for the understanding of subsequent branches, such as Trigonometry and Conic Sections; and which are not made use of in the more important practical applications, such as Mensuration, Surveying and Navigation. To study them would be an excellent discipline for the mind, if there were time : but this detains the pupil too long from the subsequent higher branches, which afford an equally salutary discipline for the mind, and, in addition to this, are absolutely essential to a complete practical education.

Under these impressions, I have omitted all such propositions as are not absolutely necessary for the understanding of the subsequent parts of a mathemati

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