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THE

ECLECTIC EDUCATIONAL SERIES

EMBRACES

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McGuffey's PRIMARY School CHARTS, 6 Nos. MCGUFFEY'S ECLECTIC SPELLER,

1 Book. McGuffey's New ECLECTIC READERS,

7 Books. McGUFFEY's NEW ECLECTIC SPEAKERS,

2 Books. RAY's SERIES OF ARITHMETICS,

7 Books. RAY'S SERIES OF ALGEBRAS,

3 Books. PINNEO's SERIES OF GRAMMARS,

3 Books. GREAT MERIT:—These School Books possess the highest merit, are more widely introduced than any other series published, and have received the cordial indorsement of the most intelligent and successful Teachers, throughout the Union.

ECONOMY TO PARENTS.—They combine the rare advantages of superior intrinsic merit, typographical beauty, Cheapness, and extensive uniformity of adoption and use.

EXTENSIVE POPULARITY.
The ECLECTIC SERIES is recommended, at this time, wholly or
in part, by the following STATE SUPERINTENDENTS OF PUBLIC
INSTRUCTION:
Hon. Anson Smyth,

STATE SUPT. OF Ohio.
Hon. Miles J. FLETCHER, State SUPT. OF Indiang.
Hon. Newton BATEMAN, STATE SUPT. of Illinois.
Hon. T. H. BENTON, JR., State Supt. of Iowa.
Hon. JAMES L. PICKARD, STATE SUPT. OF Wisconsin.
Hox. Bend. F. CRARY, STATE SUPT. OF Minnesota.
Hon. Wm. R. GRIFFITH, STATE SUPT. OF Kansas.

Hon. Wm. B. STARKE, STATE SUPT. OF Missouri. Approved and adopted in many Schools in the NEW ENGLAND STATES, in NEW YORK CITY Public Schools - in the Public Schools of PENNSYLVANIA — and in nearly every other State where liberal attention is given to public instruction.

SARGENT, WILSON & HINKLE, Cincinnati.

From HON. ANSON SMYTH, State Supt. of Public Instruction,

OHIO. I know of no other Readers which I could more earnestly indorse than McGUFFEY'S NEW ECLECTIC SERIES. RAY's ARITHMETICS need no praise. They are their own commendation. I esteem PINNEO's GRAMMARS as among the best text-books extant for guiding the learner to a knowledge of the correct use of our language.

ANSON SMYTH.

From Hon. M. J. FLETCHER, late State Supt. of Pub. Inst.,

INDIANA. The public sentiment, as expressed in Indiana by the almost universal use of the ECLECTIC EDUCATIONAL SERIES, was sufficient of itself to induce the STATE BOARD OF EDUCATION to recommend them.

In addition to this, by careful examination, I am well satisfied that their true intrinsic and comparative merit entitles them to such recommendation.

MILES J. FLETCHER.

From Hon. NEWTON BATEMAN, State Supt. of Pub. Inst.,

ILLINOIS. I believe no series of books ever obtained so many voices of approval from Teachers as McGUFFEY'S ECLECTIC READERS. No other has been so popular throughout the West, we well know. RAY's ARITHMETICS have deservedly shared in the popularity of the Eclectic Series. The ALGEBRAS are clear, full, and comprehensive.

NEWTON BATEMAN.

From Hon. T. H. BENTON, JR., State Supt. of Pub. Inst.gr

IOWA. I have carefully examined the New Editions of McGUFTEY'S ECLECTIC READERS, PINNEO's GRAMMARS, and Ray's SERIES OF ARITHMETICS and ALGEBRAS, and cordially approve them as textbooks for our schools. Taking the whole series together-Readers, Grammars, Arithmetics, and Algebras—I do not believe a similar collection has yet been published which is better adapted to our wants.

Tuomas H. BENTON, JR.

From Hon. B. F. CRARY, State Supt. of Pub. Inst.,

MINNESOTA. I have examined the ECLECTIC EDUCATIONAL SERIES of School Books, and have no hesitation in saying they are Superior to any similar text-books that have come under my observation. I rejoice that a Western House has been able to meet the increasing wants of the West in this great field.

B. F. CRARY.

SARGENT, WILSON & HINKLE, Cincinnati.

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CINCINNATI:
SARGENT, WILSON & IIINKLI.

NEW YORK: CLARK & MAYNARD.
PHILADELPHIA : J. B. LIPPINCOTT & CO.

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NARVARD COLLEGE LIEKARY

BY EXCHANGE FRO
NEW YOKK STATE LIBRARY

FEB 21 1932

Entered according to Act of Congress, in the year 1862, by

W. B. SMITH & CO.,

In the Clerk's Office of the District Court of the United States, for the

Southern District of Ohio.

Electrotyped at the Franklin Type Foundry,

Cincinnati, O.

PREFACE.

The following concise treatise on Geometry has been prepared chiefly for that class of students in our Public Schools and elsewhere, who can not spare the requisite time for mastering the larger works. It is conceived, also, that it will be found useful as a course of first lessons for those who intend to pursue the study more at length.

The writer has aimed, in general, to select those propositions in both Plane and Solid Geometry which have the most important direct applications; omitting a large number of those which serve chiefly as steps to something following them in an extended course of reasoning. In order to do this without breaking the logical connection, he has often found it necessary to present the demonstrations in a considerably modified form; though, in a majority of cases, they are essentially based on those found in Euclid, Legendre, and other standard works.

In the treatment of parallel lines, important hints have been taken from the work of Professor Peirce,

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