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IVISON, PHINNEY & CO., 48 AND 50 WALKER ST.
CHICAGO: S. C. GRIGGS & CO., 39 AND 41 LAKE ST.

BOSTON: BROWN & TAGGARD. PHILADELPHIA: SOWER, BARNES & CO., AND
J. B. LIPPINCOTT & CO. CINCINNATI: MOORE, WILSTACH, KEYS & Co.
SAVANNAH: J. M. COOPER & CO. ST. LOUIS: KEITH & WOODS.
NEW ORLEANS: E. R. STEVENS & CO. DETROIT: RAYMOND
& LAPHAM. BALTIMORE: CUSHING & BAILEY.

ROBINSON'S SYSTEM OF MATHEMATICS, Recently revised and enlarged, is now the most extensive, completė, practical and scientific Mathematical Series published in this country.

1. Robinson's Progressive Primary Arithmetic. Illustrated. $0 15
2. Robinson's Progressive Intellectual Arithmetic, for ad-
vanced Classes, with an Original and Comprehensive System
of Analysis.

3. Robinson's Progressive Practical Arithmetic; a complete
work for Common Schools and Academies.

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7. Robinson's New Elementary Algebra: a clear and simple

Treatise for Beginners.

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8. Key to Robinson's New Elementary Algebra.

9. Robinson's University Algebra: a full and complete Trea-
tise for Academies and Colleges.

10. Key to Robinson's University Algebra; separate.

11. Robinson's Geometry and Trigonometry; with applications to practical examples.

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100

1 50

12. Robinson's Surveying and Navigation; combining theory with practice.

1 50

13. Robinson's Analytical Geometry and Conic Sections; made clear and comprehensive to common minds.

1 50

14. Robinson's Differential and Integral Calculus; a full and complete Treatise.

1 50

15. Robinson's Elementary Astronomy; designed to teach the first principles of this Science.

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16. Robinson's University Astronomy; for advanced classes in Academies and Colleges.

1 75

17. Robinson's Concise Mathematical Operations: a book of reference for the Teacher, embracing the gems of Mathematical Science.

2 25

18. Key to Robinson's University Algebra, Geometry, Surveying, and Calculus; in 1 vol.

Entered, according to Act of Congress, in the year 1860, by

H. N. ROBINSON, LL.D.,

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in the Clerk's Office of the District Court of the United States for the Northern District

of New York.

JOHN FAGAN, STEREOTYPER, PHILADELPHIA.

PREFACE.

In the preparation of this work, the Author's previous treatise, "Elements of Geometry, Plane and Spherical Trigonometry, and Conic Sections," has formed the ground-work of construction. But in adapting 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 a new work. The demonstrations of propositions have undergone radical changes, many new propositions have been introduced, and the number of 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 Spherical 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.

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(iii)

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