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PREFAO E.

This volume is intended to follow our Primary Arithmetic, or that of any other series, or may be used as a first book with beginners that are not too young. It goes over the ground covered by the Primary, but in a style suited to minds somewhat more mature, enlarging on the subjects there treated, and introducing the pupil to many new ones. Besides the four fundamental operations, it gives a comprehensive view of Fractions, Federal Money, Reduction, and the Compound Rules, presenting under each a large collection of sums, in every variety, not too difficult, but so constructed as to require the pupil to think, and thus make the performance intelligent and not mechanical.

Convinced that too much theory and rule embarrass the young pupil, the author has in this respect sought to strike a happy mean,presenting necessary explanations, but in few words; giving example sometimes the precedence over precept, and making rules intelligible by means of preliminary illustrations. Definitions are made brief and simple. Technical terms unnecessary at this stage of progress are avoided. The difficulties of beginners being appreciated, it is believed that they are here so met as to save the teacher the annoy. ance of constant demands for explanation.

In arrangement we trust some gain will be apparent; particularly in Compound Numbers, where, in stead of presenting the Tables in a body, to be confounded together in the pupil's mind, we immediately apply each Table, as soon as learned, in appropriate exercises, either mental or written. Attention is also invited to the inductive method used in developing the several subjects.

The teacher is requested to see that every principle is mastered as the pupil advances. A single defective link makes a whole chain worthless. If this suggestion is attended to, it is believed that the present work will make the young student thoroughly acquainted with the subjects it embraces, and properly prepare him for the next number of the series, THE PRACTICAL ARITHMETIC,

NEW YORK, August 6, 1863.

ELEMENTARY ARITHMETIC.

WHAT ARITHMETIC Is.

1. We commence with ONE. We have one head, one mouth, one body.

One, a single thing, is called a Unit.

2. A unit joined to another unit, makes TWO. We have two eyes, two hands, two feet.

Another unit joined to two, makes THREE. Each of our fingers has three joints.

Another unit joined to three, makes FOUR.

So we may go on. Adding a unit each time, we get FIVE, SIX, SEVEN, EIGHT, NINE.

3. One, two, three, four, five, six, &c., are called Numbers.

A Number is, therefore, one unit or more. 4. Arithmetic treats of numbers.

5. Repeating the numbers in order--one, two, three, four, five, six, &c., is called Counting.

QUESTIONS.--1. With what do we commence? What is one, a single thing, called ?-2. Of what is two made up? Of what is three made up? If we go on, adding a unit each time, what do we get ?--3. What are one, two, three, four, &c., called ? What is a Number ?–4. Of what does Arithmetic treat ?-5. What is Counting? Count nine. Count nine backwards-nine, eight, seven, &c.

NOTATION.

6. Every number has a name; as, one, two, three. In stead of writing out the name, however, we may represent it by a character; as, 1, 2, 3.

Notation is the art of expressing numbers by characters.

7. There are two systems of Notation, the Ar'abic and the Roman.

The Arabic Notation.

8. The Arabic Notation is so called because it was used by the Arabs. It employs these ten characters, called Figures :

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The first of these figures, 0, implies the absence of number. O cents means not a single cent.

9. The greatest number that can be expressed with one figure is nine. All the numbers above nine are expressed by combining two or more figures.

First, 1 is combined with each of the ten figures ; then 2, forming the twenties; then 3, forming the thirties; then 4, forming the forties, &c.

6. How may numbers be represented ? What is Notation ?–7. How many systems of notation are there? Name them.-8. Why is the Arabic Notation so called? How many characters does it use? What are they called ? Learn how to make the ten figures, and their names What does 0 imply?-9. What is the greatest number that can be expressed with one figure? How are all numbers above nine expressed ?

THE ARABIC NOTATION.

7

10. The numbers formed of two figures are

10 ten

11 eleven

12 twelve

13 thirteen

14 fourteen 15 fifteen 16 sixteen 17 seventeen 18 eighteen 19 nineteen 20 twenty 21 twenty-one 22 twenty-two 23 twenty-three 24 twenty-four 25 twenty-five 26 twenty-six 27 twenty-seven 28 twenty-eight 29 twenty-nine 30 thirty 31 thirty-one 32 thirty-two 33 thirty-three 34 thirty-four 35 thirty-five 36 thirty-six 37 thirty-seven 38 thirty-eight 39 thirty-nine

40 forty 41 forty-one 42 forty-two 43 forty-three 44 forty-four 45 forty-five 46 forty-six 47 forty-seven 48 forty-eight 49forty-nine 50 fifty 51 fifty-one 52 fifty-two 53 fifty-three 54 fifty-four 55 fifty-five 56 fifty-six 57 fifty-sevens 58 fifty-eight 59fifty-nine 60 sixty 61 sixty-one 62 sixty-two 63 sixty-three 64 sixty-four 63 sixty-five 66 sixty-six 67 sixty-seven 68 sixty-eight 69 sixty-nine

70 seventy 71 seventy-one 72 seventy-two 73 seventy-three 74 seventy-four 75 seventy-five 76 seventy-six 77 seventy-seven 78 seventy-eight 79 seventy-nine 80 eighty 81 eighty-one 82 eighty-two 83 eighty-three 84 eighty-four 85 eighty-five 86 eighty-six 87. eighty-seven 88 eighty-eight 89 eighty-nine 90 ninety 91 ninety-one 92 ninety-two 93 ninety-three 94 ninety-four 95 ninety-five 96 ninety-six 97 ninety-seven 98 ninety-eight 99 ninety-nine

EX EROISE.

Count from 1 to 99. Count from 99 to 1, backwards. With what figure do the thirties all begin? The sixties? Write the following numbers in figures :-thirty-seven; eleven; ninety-eight; eighty-nine; twelve; twenty ; five; fifteen; fifty. What system of notation have you just used?

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