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AUTHOR OF FIRST LESSONS IN ARITHMETIC, ELEMENTARY ALGEBRA,
PRACTICAL GEOMETRY, ELEMENTS OF SURVEYING, ELEMENTS
OF DESCRIPTIVE GEOMETRY, SHADES, SHADOWS AND

PERSPECTIVE, ANALYTICAL GEOMETRY,
DIFFERENTIAL AND INTEGRAL

CALCULUS,

NEW YORK:

PUBLISHED BY A. S. BARNES & CO.
No. 51 JOHN STREET.

PUBLIC Schools, BALTIMORE,

August, 1842. At a meeting of the Board of Commissioners of Public Schools, Baltimore, to hear the report of the Book Committee, upon Davies' Elementary Series. The following resolution was offered, and adopted:

Resolved,—That Davies' First Lessons in ARITHMETIC, Davies'
ARITHMETIC, Davies' Algebra, Davies' Practical GEOMETRY,
and Davies' ELEMENTARY GEOMETRY, be introduced into the Public
Schools of Baltimore.

JAMES LUCAS,
MICHAEL TONER,
JOHN F. MONMONIER,

Commissioners.
From the Minutes,

John F. TILYARD, Clerk.

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CHAMBER OF THE CONTROLLERS or Public Schools,
First School District of PENNSYLVANIA.

Philadelphia, September 15, 1842.
At a meeting of the Board of Controllers of the Public Schools of
the First School District of Pennsylvania, held at the Controllers'
Chamber, on Tuesday afternoon, September 13, 18-12, it was

Resolved,—That Davies' First Lessons in ArTUMETIC, and
Davies' ARITHMETIC, be introduced into the Public Schools of tho
District; and also, that Davies' ALGEBRA be introduced therein; the
latter under the Resolution of the 12th day of November, 1839.
From the Minutes,

THOMAS B. FLORENCE,

Secretary.

1

Entered according to the Act of Congress, in the year one thousand eight hundred and thirty-eight, by Cuarles DaVIES, in the Clerk's Office of the District Court of the United States, for the Southern District of New York.

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C. A. Alvord, PRINTER, cor. of John & Dutch sts., New York.

PREFACE.

A CORRECT and accurate knowledge of Arithmetic is one of the most important elements of a liberal or practical education. The public should, therefore, receive with indulgence every attempt that may be made to improve this department of instruction.

The Elementary Treatise, which is here presented, is an enlargede and it is hoped, an improved edition of the Common School Arithmetic, published in 1833. The suggestions of several experienced teachers have been incorporated with the body of the work in its new form, and, indeed, nothing has been omitted which it was thought would give it value to those for whose use it is designed. It has been the intention to render the whole subject as plain as it is capable of being made, and at the same time, to treat it as concisely as possible.

The name, Compound Numbers, which has heretofore been given to all numbers in which the kind of unit is expressed, has been changed to that of Denominate Numbers. This change has not been made with any ambitious spirit of innovation, but because it is deemed an improvement. It is not easy to form an idea of what is meant by the term, Compound Number, and especially so, when we find it applied to such numbers as 3 pounds, 3 dollars, 3 shillings, &c. Why is 3 pounds a compound number any more than 3? If it be answered that 3 pounds is composed or compounded of three single pounds, that does not remove the difficulty, for 3 is also composed of three units 1. Is it not then the better way to call the first a denominate number, and the other a simple number, as is done in $ 45.

Mr. Hasler, in his Arithmetic, has called this class of numbers, De dominate Fractions.

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