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RECOMMENDATIONS.

Philadelphia, Sept. 23, 1811. AGREFABLY to your request, I have examined Mr. Piķe's Treatise of Arithmetic, and am much pleased with it. His mode of exemplifying the rules, is, I think, extremely well accommodated to the comprehension of juvenile pupils; while the general arrangement, extent, and scientific execution of the work renders it worthy of adoption in both public and private seminaries.

JAMES ABERCROMBIE, D. D.

Director of the Philadelphia Academy. Messrs. Johnson & Warner.

Philadelphia, Ninth mo. 26, 1811. I Have examined the System of Arithmetic compiled by S. PIKE, and am of opinion that it is well calculated for conveying to youth, in a short time, a general knowledge of that science.

The commendable attention which the compiler has paid to a clear elucidation of his subject, as well as his careful exclusion of any thing which would unnecessarily perplex, entitles him to the thanks of those who are engaged in the laborious task of imparting knowledge to youth.

BENJAMIN TUCKER.

Philadelphia, Sept. 16, 1811. After a careful inspection of Mr. S. Pike's System of Arithmetic, I gʻve it a decided preference to every other I have yet seen, and shall be glad of the publication of a work, that, in my opinion, will deduct from the labour of teaching, and conduce to the advantage of learners.

JOANSON TAYLOR.

GENTLEMEN,

Philadelphia, Sept. 30, 1811. I have no hesitation in declaring my belief, in concurrence with the gentlemen who have already recommended S. Pike's System of Arithmetic, that its publication will conduce to the public and private utility of the arithmetical student.

Your's, &c. Messrs. Johnson & Warner.

SAMUEL B. WILIE.

The System of Arithmetic compiled by S. Pike, is, in my opinion, a very judicious performance. The arrangement of the parts, the perspicuity of the rules, and the appropriate and familiar nature of the examples, are peculiarly calculated to facilitate the progress of the learner. I therefore give the work a decided preference to any other on the subject, with which I am acquainted.

John GUMMERE, Principal and Teacher of Burlington Boarding School.

EXPLANATION OF CHARACTERS

Х

Signs.

Significations.
equal; as 20s.=L.1.
more; as, 6+2=8.
less; as, 8-2=6.
into, with, or multiplied by; as, 6x2=12.

by (i. e. divided by) as, 6:2=3; or, 2)6(3.
::: : proportionality; as, 2 : 4 :: 6 : 12.
Vor/Square Root; as, 3/64=8.

3 Cube Root; as, 364=4.

Fourth Root; as, *16=2, &c.
A Vinculum; denoting the several quantities
over which it is drawn, to be considered jointly
as a simple quantity.

ARITHMETIC.

ARITHMETIC is the art of computing by numbers. It has five principal rules for its operations; viz. numeration, addition, subtraction, multiplication, and division.

NUMERATION

Numeration teaches to write or express

numbers by figures, and to read numbers thus written or expressed.

In treating of numbers, the following terms are employed: viz. unit, ten, hundred, thousand, and million; as also billion, trillion, and some others. But the latter are seldom used.

A unit is a single one.
A ten is ten units.
A hundred is ten tens.
A thousand is ten hundreds..
A million is ten hundred thousands.

Note. -As it takes ten hundred thousands to make a million, when we express a number, greater than a thousand, and less than a million, we use tens of thousands, or hundreds of thousands, or both, as the case requires. Likewise, to express a number, greater than a million, we employ tens of millions, or hundreds of millions, &c.

The following are the figures used in numeration, with their names above them. One two three four five six seven eight nine

1 2 3 4 5 6 7 8 9

Each of these figures represents the number which its name denotes; but it is understood to be that number of units, or that number of tens, or that number of hundreds, &c. according to its relative place: which

1:.

fal

lor

TABLE FIRST.

TABLE SECOND.

Hundred million
Ten million
Hundred thousand
--Million
Ten thousand
-Thousand

Hundred

Ten
Unit

Hundreds of millions
Tens of millions
Hundreds of thousands

Tens of thousands
LoMillions
Ô Thousands

Hundreds
Tens
VUnits

These tables show that in using figures to express numbers they are placed in a horizontal row—the first figure at the right hand representing one or more units, the next tens, the next hundreds, &c. Thus a 1 is one unit, or one ten, or one hundred, &c. according to the place in which it stands; and in like manner, a 2 is two units, or two tens, or two hundreds, &c. The same rule determines the value of each of the other figures.

In reading numbers, the units and tens are taken together. 1 ten and 1 unit are read eleven; 1 ten and 2 units, twelve; 1 ten and 3 units, thirteen, &c.; 2 tens and 1 unit are read, twenty-one; 3 tens and 1 unit, thirty-one, &c. Thus the number expressed by the row of figures in table first is read-one hundred and eleven millions, one hundred and eleven thousands, one hundred and eleven. That expressed by the figures in table second is read-two hundred and twenty-two millions, two hundred and twenty-two thousands, two hundred and twenty-two..

The succeeding tables will further illustrate the subject.

TABLE THIRD.

Millions
Tens
Units
Hundreds
Hundreds of millions
Tens of millions
Thousands
Tens of thousands
Hundreds of thousands

1 1 2 1 2 3 1, 2 3 4 -1 2,3 4 5 1 2 3,4 5 6 1,2 3 4, 5 6 7 1 2,3 4 5, 6 7 8 1 2 3,4 5 6,7 8 9

One
Twelve
One hundred and twenty-three

1 thousand 234
12 thousand 345
123 thousand 456

1 million 234 thousands 567 12 millions 345 thousands 678 123 millions 456 thousands 789

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