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PLANE AND SPHERICAL
BY BENJAMIN GREENLEAF, A. M.,
AUTHOR OF A MATHEMATICAL SERIES.
IMPROVED ELECTROTYPE EDITION.
PUBLISHED BY ROBERT S. DAVIS & CO.
NEW YORK: WILLIAM WOOD & CO., AND W. I. POOLEY.
PHILADELPHIA: J. B. LIPPINCOTT & COMPANY.
ST. LOUIS: KEITH AND WOODS.
NEW ORLEANS: DUNCAN & CO.
Greenleaf's New Primary Arithmetic,
Upon the Inductive Plan. Designed for Primary Schools. Improved Electrotype Edition, beautifully illustrated.
Greenleaf's Intellectual Arithmetic,
Upon the Inductive Plan. Being an Advanced Intellectual Course for Common Schools and Academies. Improved Edition.
Greenleaf's Common School Arithmetic, Or, Introduction to the National Arithmetic. A complete System for Common Schools. Improved Electrotype Edition. 324 pp.
Greenleaf's National Arithmetic,
Being a Complete Course of Higher Arithmetic, for High Schools, Academies, and Normál Schools. New Electrotype Edition, with Additions and Improvements. 444 pp.
Greenleaf's New Elementary Algebra,
In which the First Principles of Analysis are progressively developed and simplified. For Common Schools and Academies. 324 pp.
Greenleaf's Treatise on Algebra,
For Academies and High Schools, and for advanced Students in Common Schools. Improved Stereotype Edition. 360 pp.
Greenleaf's Geometry and Trigonometry,
With Practical Applications. Designed for High Schools, Academies, and Colleges. Tenth Improved Electrotype Edition. 490 pp.
Complete Keys to the Intellectual, Common School, and National Arithmetics, Algebras, Geometry and Trigonometry; for Teachers only.
Entered according to Act of Congress, in the year 1863, by
in the Clerk's Office of the District Court of the District of Massachusetts.
CAMBRIDGE: PRINTED BY H. O. HOUGHTON AND COMPANY
THE preparation of this treatise was undertaken at the earnest solicitation of many teachers, who, having used the author's Arithmetics, Algebras, and Elements of Geometry with satisfaction, were desirous of seeing his series rendered more nearly complete by the addition of the Elements of Plane and Spherical Trigonometry. It is hoped that the present work will be found to be a complete system, theoretical and practical, fully adapted to the wants of advanced classes.
The trigonometric functions, in this treatise, have been regarded as ratios, since this improved method has not only now superseded the ancient method in English and French works, but has been approved and adopted generally by the best American mathematicians. Reference, however, is made to whatever is especially valuable in the old method.
In the preparation of this work the author has received valuable suggestions from many eminent teachers, to whom he would here express his sincere thanks. Especially would he acknowledge his great obligations to H. B. Maglathlin, A. M., who for many months has been associated with him in his labors, and to whose experience as a teacher, skill as a mathematician, and ability as a writer, the value of this treatise is largely due.
BRADFORD, Mass., July 25, 1861.
THIS System of Trigonometry was designed to be published in connection with the author's Elements of Geometry. It is now published separately, to accommodate those teachers who desire to use it in that form.
January 1, 1863.