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ROBINSON'S MATHEMATICAL SERIES.

ELEMENTS

GEOMETRY,

AND

PLANE AND SPHERICAL TRIGONOMETRY;

WITH

AQUILAR

Free Library.
PROEWYORK
"NEW YORK

NUMEROUS PRACTICAL PROBLEMS

BY

HORATIO N. ROBINSON, LL. D.,

AUTHOR OF A FULL COURSE OF MATHEMATICS.

NEW YORK:

IVISON, PHINNEY, BLAKEMAN & CO.,
CHICAGO: S. C. GRIGGS & CO.

1867.

Series of Mathematics,

THE The most COMPLETE, most PRACTICAL, and most SCIENTIFIC SERIES of PUBLIC LIBMATHEMATICAL TEXT-BOOKS ever issued in this country.

475126

(IN

ASTOR, LENOX AND

TILDEN FOUNDATIONS.

ENTY-TWO VOLUMES.)

II. Robinson's Progressive Primary Arithmetic, -
III. Robinson's Progressive Intellectual Arithmetic,
IV. Robinson's Rudiments of Written Arithmetic,
V. Robinson's Progressive Practical Arithmetic,
VI. Robinson's Key to Practical Arithmetic, -
VII. Robinson's Progressive Higher Arithmetic,
VIII. Robinson's Key to Higher Arithmetic,
IX. Robinson's New Elementary Algebra,
X. Robinson's Key to Elementary Algebra, -
XI. Robinson's University Algebra,

XII. Robinson's Key to University Algebra,
XIII. Robinson's New University Algebra,

XIV. Robinson's Key to New University Algebra,·

XV. Robinson's New Geometry and Trigonometry,
XVI. Robinson's Surveying and Navigation,

XVII. Robinson's Analyt. Geometry and Conic Sections,

XVIII. Robinson's Differen. and Int. Calculus, (in preparation,)-
XIX. Robinson's Elementary Astronomy,

XX. Robinson's University Astronomy,

XXI. Robinson's Mathematical Operations,

XXII. Robinson's Key to Geometry and Trigonometry, Conic
Sections and Analytical Geometry,

Entered, according to Act of Congress, in the year 1862, by
HORATIO N. ROBINSON, LL. D.,

In the Clerk's Office of the District Court of the United States for the Northern
District of New York.

P R E F A СЕ.

IN the preparation of this work, the Author's previous treatise "Elements of Geometry, Plane and Spherical Trigonometry, and Conie Sections," has formed the ground-work of construction. But in

apting the work to the present advanced state of Mathematical education in our best Institutions, it was found necessary to so alter the plan, and the arrangement of subjects, as to make this essentially hew work. The demonstrations of propositions have undergone radical changes, many new propositions have been introduced, and the number

Practical Problems greatly increased, so that the work is now believed to be as full and complete as could be desired in an elementary treatise.

In view of the fact that the Seventh Book is so much larger than the others, it may be asked why it is not divided into two? We answer, that classifications and divisions are based upon differences, and that the differences seized upon for this purpose must be determined by the nature of the properties and relations we wish to investigate. There is such a close resemblance between the geometrical properties of the polyedrons and the round bodies, and the demonstrations relating to the former require such slight modifications to become applicable to the latter, that there seems no sufficient reason for separating into two Books that part of Geometry which treats of them.

The subject of Spherical Geometry, which has been much extended in the present edition, is placed as before, as an introduction to Spherial Trigonometry. The propriety of this arrangement may be questioned by some; but it is believed that much of the difficulty which the student meets in mastering the propositions of Spherical Trigonometry, arises from the fact that he is not sufficiently familiar with the geometry of the surface of the sphere; and that, by having the propositions of Spherical Geometry fresh in his mind when he begins the study of Spherical Trigonometry, he will be as little embarrassed with it as with Plane Trigonometry.