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The Author having submitted his Manuscript to the inspection of the Hon. A. CALDWELL, Judge of the United States Court for the Western District of Virginia, received from him the following

RECOMMENDATION.

Wheeling, 21st July, 1823. Mr. Wm. Slocomb:

Sir-Upon a careful examination of your treatise of Arithmetick, it affords me pleasure to state, that I highly approve of it, and prefer it, decidedly, to any other I am acquainted with. So far as it is a compilation from other systems, you have the merit of having made the most judicious selections, having excluded what is redundant and simplificd what is complex. Your mode of calculating interest is quite new, and in my opinion will do complete justice both to creditor and debtor, which cannot be said of any of the rules now in use; some give to the creditor too much, while others deprive him of what he is fairly entitled to. Yours respectfully,

A. CALDWELL.

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ARITHMETICK.

INTRODUCTION.

a Arithmetick is the Art, or Science, which treats of nun bers, and consists of two kinds, theoretical and practical.

6 The THEORY of Arithmetick explains the nature and quality of numbers, and demonstrates the reasons of practical operations.

c PRACTICAL ARITHMETICK shows the method of working by numbers, so as to be most useful and expeditious for business.

The first thing which should engage the attention of the learner, is

NUMERATION, With which he should be well acquainted, before entering upon the study of the fundamental rules of Aritmetick.

à Numeratton teaches the different value of figures by their different places, and to read or write any sum or number by these ten characters 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, The first nine are called significant figures, each of which standing by itself, invariably expresses a particular or certain number, but in a combination of figures, its value depends upon its local situation, thus 5 standing by itself signifies fire; but when placed at the left of another fige] ure, or 0, it is increased in value, in a tenfold proportion; thus 50 signifies ten times five, or fifty; and 500, ten times fifty, or five hundred. By the above example the use of the cypher is obvious. When standing alone it has no signification; but when placed at the right hand of another figure, it increases that figure in a ten fold proportion.

The value of figures in conjunction, and how to read any sum or number, by giving to each figure its proper value, will be rendered easy, by careful attention to the following

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A Thousand millions

o Hundred millions

v Ten millions

Billions

A Hundred thousands

Ten thousands

Millions

00 Thousands

w Hundreds

A l'ens

er Units

1,
, 7 9,

8, 3 In order to assist the learner in enumeration, when the f] number of figures is large, the following directions may be of use. Point off the sum into periods of six figures each, commencing at the right hand, calling the six right hand figures the unit period, the next six the million period, after which billion, trillion, &e. Next divide each period into half periods) The above figures may then be easily read, thus-One billion, two hundred and sixty tour thousand and seventy nine million, four hundred and ninety cight thousand, three hundred and forty five.

Thus by the use of ten characters the whole operation in Arithmetick is performed, and every thing may be reckoned which can be numbered. . After the foregoing table has been carefully studied, and is well understood, the learner will do well to write a few figures upon his slate, and enumerate them, without looking at the table, gradually increasing the number till he is able to read, at least ten or twelve figures. He may then write the following numbers in figures.

Six hundred and twenty five.
Three thousand two hundred and forty nine.
One hundred and twenty thousand eight hundred and forty.,
STwo millions, three hundred and twenty seven thou-

sand, six hundred and thirty four.
Seven hundred and sixty nine thousand, four hundred

twenty four millions, two hundred and three thousand,

five hundred and twenty eight. Two billions, three hundred twenty one thousand, nine

hundred and three millions, sixty five thousand, ene. hundred and forty three.

Explanation of the Characters made use of in this work.

= The sign of equality; as 100 cts.=to 1 dollar.
+ The sign of addition; as 4+5=to 9. That is, four

added to five are equal to nine.
The sign of subtraction; as 9-5=4. That is, five

taken from nine leaves four. * The sign of multiplication; as 5x4=20. That is,

four times five are equal to twenty. ; or ( The sign of division; as 4 205, or 20-435.

That is, twenty divided by four, the quotient is five. :::: The sign of proportion; as 2:4::6:12. That is,

as two is to four, so is six to twelve.

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FUNDAMENTAL RULES OF ARITHMETICK. g These are four, Addition, Subtraction, Multiplication, and Division; they may be either simple or compound.

h: They are called principal, or fundamental rules, because all other rules and operations in Arithmetick, are the various uses and repetitions of these four rules.

QUESTIONS,
a What is Arithmetick?
b What is the theory of Arithmetick!
c What is practical Arithmetick?
d What is Numeration?

e How are figures increased in value by being placed at the left hand of another figure or cypher?

f What directions are given to facilitate the reading of figures?

What are the fundamental rules of Arithmetick? ? Why are they called principal or fundamental rulesi

SIMPLE ADDITION. a Simple Addition is the putting together of two or more numbers of the same denomination, so as to make them one whole number, called sum, or amount..

6 Place the numbers to be added one under another, with units under units, tens under tens, &c. and draw a line be low them.

RULE.

c Begin the addition with the unit column, and having added all the figures, consider how many tens are contained d] in their sum, and placing the excess under the unit column, carry as many to the next column as there are tens in the one added. Proceed in like manner to add the other columns, carrying as before, and set down the full sum of the last column.

PROOF.

e Reckon the figures from the top downwards, and if the work be right, the amount of the last addition will correspond with the first.

f Note. The reason for carrying for ten in all simple numbers, will be evident from what has been taught in Numeration. It is because 1 in a superior column, is equil to 10 in the inferiour: thus, 1, by itself is one; but place it in a superiour column, or, which is the same thing, place a cypher at the right hand of it, thus 10, and it is ten,

ADDITION AND SUBTRACTION TABLE.

1 | 2 | 31 41 51 61 7 | 8 | 9110111|12 21 41 51 61 71 81 9 | 10 |11| 12 |13|14 31 51 61 71 81 9110 111 112 113 114 115 461 71 81 9 10 11 12 13 14 15 16 51 p 1 81 9110111|12|13|14|15|1612 61 81 9110111 | 12 13 14 15 16 17 18 7 | 9 | 10111|12|13|14 (15 116 117 118 119 8| 10 | 11 |12|13|1415|16|17|18|19 120 9111 | 12 | 13 | 14 | 15 16 | 17 | 18 | 19 | 20 | 21 10 | 12 | 13|11|15|16|17 18 19 20 21 22

سریر مینی حما

:

When you would add two numbers, look for one of them in the left hand column, and the other at top; and under the top number you will find their sum: as 6 and 4 are 10. When

you would subtract, find the number to be subtracted in the left hand column; in the same line to the right, find the number from which it is to be taken, and directly over it at top, you will find the difference; as 6 taken from 10, leaves 4.

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