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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 labourious task of imparting knowledge to-youth.


Philadelphia, Sept. 16, 1811. AFTER a careful inspection of Mr. S. Pike's System of Arithmetic, I give it a decided preferance 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.


Philadelphia, Sept. 30, 1811. GENTLEMEN,

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

Your's, &c.

SAMUEL B. WYLIE. Messrs. Johnson & Warner.

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equal; as, 208. = L. I.
+ 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.
or Square Root; as, 64 = 8.

Cube Root; as, V 64=4.
♡ Fourth Root; as, V64 = 2, &c.

A Vinculum; denoting the several quantities
over which it is drawn, to be considered jointly
as a simple quantity,


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 miltions, &c.

The following are the figures used in numeration, with their names written aboye them. One two three four five six

seven eight nine 1 2 3 4 5 : 6


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 is exemplified in the following tables.


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Hundred million
Ten million
Hundred thousand
Ten thousand
Thous und

Hundreds of millions

Tens of millions
à Hundreds of thousands

A Tens of thousands


111,1 11,1 1 1

2 2 2,2 2 2,2 2 2 These tables shew 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. I ten and 1 unit are read eleven; 1 ten and 2 units, twelve ; I ten and 3 units, thirteen, &c. 2 tens and I 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.


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Tens of millions
Hundreds of nuillions
Tens of thousands
Hundreds of thousands


One 1 2 .... Twelve 1 2 3 .... One hundred and twenty-three 1, 2 3 4 .... I thousand 234 I 2,3 4 5 .... 12 thousand 345 1.2.3, 4 5 6....123 thousand 456 1,2 3 4, 5 6 7 .... 1 million 234 thousand 567 1 2,3 4 5, 6 7 8 ....

12 millions 345 thousands 678 1 2 3,4 5 6,7 8 9....123 millions 456 thousands 789

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