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TICKNOR'S PRACTICAL MENSURATION,

For the Academies and Common Schools of the United States.

Easton, January 2, 1849. We, the undersigned, Teachers of the Public Schools of Easton, Pa. after a careful examination of Mr. Ticknor's “ Treatise on Mensuration, do not hesitate in saying that we are decidedly pleased with its arrangement, and in particular with the plainness with which its rules and examples are written. That a work of this kind has been long needed in our public schools, no teacher will deny, since most other publications of the kind, being abstruse and difficult, are better suited for the college than the public school. But this little work, containing all the information necessary for the carpenter, mason, bricklayer, &c., "' and which is so happily adapted to the comprehension of school-boys, is just the thing to teach them what they will want to practice when they become men." We therefore hope it may meet with the cordial reception it deserves, by both scholars and teachers. We shall adopt it in our schools immediately. B. H. SAXTON,

CHAS. S. EMMONS,
NEWTON KIRKPATRICK, HENRY GRIFFITHS,
D. MULFORD JAMES,

JAS. JAY OKILL, A. M.
Prin. Pub. School, S. Easton, Pa.

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City of Reading, January 1, 1849. We, the undersigned, having examined Mr. Ticknor's Mensuration, are happy in expressing our entire approbation of the work. The arrangement is very judicious; the questions well selected; the number of questions such as will insure a thorough knowledge of each problem, without subjecting the pupil to drudgery ; and the rationale so simply stated that none will find the study of his book either tedious or dry.

We cordially recommend the work, and hope its circulation will be as extensive as its merit is undoubted.

STEPHEN ENGLISH, Teacher of the N. Ward Grammar School.
JOSEPH MALSBERGER, Principal N. E. Ward.
JOHN RYAN, Principal S. E. Ward P. S.
B. M. HOAG, Principal N. Ward Pub. School.
T. STOCKDALE, Principal Bingaman St. Pub. School.
GEO. F. SPAYD, Principal S. W. Ward Grammar School.

MR. TICKNOR—Dear Sir: I cheerfully endorse the above, and certify further, that your endeavours to bring the practical advantages of science to the mass of the people, in a cheap form, is highly commendable.

GEO. W. F. EMERSON.

OR,

SQUARE AND TRIANGLE:

BEING A PRACTICAL AND CONCISE SYSTEM

OF

GEOMETRY AND MENSURATION.

ADAPTED TO THE USE OF SCHOOLS AND ACADEMIES

IN THE AMERICAN REPUBLIC.

BY ALMON TICKNOR,

AUTHOR OF THE

COLUMBIAN CALCULATOR, YOUTH'S COLUMBIAN CALCULATOR, COLUMBIAN SPELLING-BOOK, TABLE

BOOK, ACCOUNTANT'S ASSISTANT, MATHEMATICAL TABLES, ETC.

“ Education is a better safeguard of liberty than a standing army. If we retrench
the wages of the schoolmaster, we must raise those of the recruiting sergeant.”—Hon.
EDWARD EVERETT.

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POTTSVILLE:
PUBLISHED BY B. BANNAN.

AND FOR SALE BY
KAY & TROUTMAN, PHILADELPHIA-HUNTINGDON & SAVAGE, NEW YORK
-B. B. MUSSEY & CO., BOSTON–W.T. TRUMAN, CINCINNATI.

Entered, according to Act of Congress, in the year 1849, by

ALMON TICKNOR, in the Clerk's Office of the District Court of the Eastern District of

Pennsylvania.

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REMARKS.

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HAVING for many years witnessed the necessity of a practical elementary treatise on Geometry and Mensuration in our DistrictSchools and Academies, and as no work answering this description is at present before the public, this, it is presumed, will be a sufficient apology for the attempt to supply a vacancy in this department of science.

Next to a correct knowledge of Arithmetic, we may rank that of Mensuration, a branch of mathematics which embraces a variety of pleasing and interesting subjects of the greatest importance and utility to the man of business, the merchant, artisan, manufacturer, farmer, mechanist, and indeed almost every person whose transactions are of sufficient importance to require the application of figures. Even its introduction into “ Female Seminariesshould not be considered as derogatory, or too rudefor the exercise of the female mind, as a substitute for less

useful studies and employment, when it is known that many ladies have distinguished themselves, as much by their attainments in

the abstruse sciences of mathematics and astronomy, as they have by their contributions to our periodical literature. The daily and constant intercourse of men, in the transaction of business, will continually demand the application of the principles of Mensuration, almost as frequently as that of common Arithmetic, and notwithstanding the demand for the application of those rules and principles, it is believed that not more than one person in fifty is even partially acquainted with the science. This practi

part of mathematics has been quite too much neglected in our district schools as a part of elementary instruction, and seldom receives that attention necessary to acquire a correct knowledge of the science even in many of our High Schools and Academies.This may be attributed either to the want of suitable books, or to the neglect of the teacher. In a work of this kind, but little new or original can be written or pected, beyond the arrangement, the selection of appropriate practical questions, and the general adaptation of the volume to the use of the man of business, and the capacity of those for whom it is intended as an introductory course of instruction to the higher branches of mathematics. In the selection of suitable

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matter in the following pages, much care and attention have been bestowed, with a view to introduce such, and such only as appeared the most useful, and to omit all extraneous subjects as irrelevant in a text-book on elementary science, as well as a fruitful source of complaint with many teachers. A series of examples in Decimals and Evolution has been introduced as a preliminary course, a correct knowledge of which is indispensable in the solution of the following problems, for the reason, that this part of Arithmetic is but partially, or imperfectly taught by authors or teachers, particularly decimals, they being considered of “no kind of use," and the time of the pupil is therefore employed on "mental arithmetic," and "foreign currency,much to the detriment of the pupil, injustice to the public, and a hinderance to the advancement of mathematical science and general information : a system that never has been, nor never can be attended with the least benefit to any one, and should be prohibited and discountenanced in every school in the Union. This no doubt will be the case when the “public mind” becomes enlightened on the pernicious consequences, and convinced of the folly of a superficial education, and the great loss of time and money in the vain pursuit of a phantom,_ in truth, a most consummate humbug."

This volume, with the two “ Columbian Calculators,embraces about FOUR THOUSAND TWO HUNDRED questions for solution, a large proportion of which are original, a number sufficient to make the pupil a proficient in the various subjects introduced. If this volume should merit and receive the approbation of TEACHERS and others interested, the author will consider himself sufficiently rewarded for all his care and labor, and his most sanguine expectations fully realized.

July 4, 1849.

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