AUTHOR AND ORIGINATOR OF A SERIES OF ARITHMETICS IN TWO
COURSES; THE FIRST COURSE (PUBLISHED 1849),

AND THE SECOND COURSE (1844).

“I had rather speak five words with my understanding, that by my voice I
might teach others also, than ten thousand words in an unknown tongue."

I Cor. XIV. 19.
“If I know not the meaning of the voice, I shall be unto him that speaketh a
barbarian, and he that speaketn shall be a barbarian unto me."-Ibid. Ver II

REVISED EDITION.

NEW YORK:
PUBLISHED BY J. M. BRADSTREET & SON,

18 BEEKMAN STREET.

1870.

ALSO FOR SALE BY J. W. SCHERMERHORN & Co., 14 BOND ST., AND

BY BOOKSELLERS GENERALLY.

Sitate Historical Society

1882

OF WISCONSIN

Entered, according to Act of Congress, in the year 1869,

BY DAVID H. CRUTTENDEN,
In the Clerk's Office of the District Court of the United States, for the

Southern District of New York.

Re-Entered, according to Act of Congress, in the year 1866,

BY DAVID H. CRUTTENDEN,
In the Clerk's Office of the District Court of the United States, for tho

District of Michigan.

Re-Entered, according to Act of Congress, in the year 1869,

BY DAVID H. CRUTTENDEN,
In the Clerk's Office of the District Court of the United States, for the

Southern District of New York,

MOCREA & MILLER, STEREOTYPERS.

XG (95

PREFAOE.

The Works, composing The AMERICAN Series of Text Books, are arranged according to the following Theory

In the first place, Knowledge is to be gained; in the second place, this Knowledge is to be made useful.

Now the order, in which knowledge is gained, is exactly the opposite of the order, in which it is used. Just as gaining is exactly the opposite of giving.

In gaining knowledge, we go from the art to the science; from the object concerning which we would learn, to what we would learn about that object. For instance; a new object is found-new being another name for the unknown—we observe it, and by so doing we learn all that we finally know about it. In short, knowledge is gained in the order of discovery.

You will see the order of its development in the comparison below, under the First Course.

To make knowledge useful we go from the science to the art. Something is to be done. We recall what we know about it; if that be insufficient, we ask aid from those who possess either more knowledge than we do; or, from those who know better how to apply their knowledge. A temple is to be built. He, who knows how to plan it, what materials should be used, how the parts should be shaped and how properly joined, is first employed. His is knowledge applied to artmuseful, or practical knowledge.

You will see the order of its development in the comparison below, under the Second Course.

The following comparison may assist in distinguish