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Explanation of Characters used in this Book.

Equal to, as 12d.

= 18. signifies that 12 pence are equal to 1 shilling. + More, the sign of Addition, as 5+7=12, signifies that

6 and 7 added together, are equal to 12. - Minus, or less, the sign of Subtraction, as 6--2-4,

signifies that 2 subtracted from 6, leaves 4. x Multiply, or with, the sign of Multiplication ; as

4x3=12, signifies that 4 multiplied by 3, is equal to

12. • The sign of Division; as 8-2=4, signifies that 8

divided by 2, is equal to 4 ; or thus, : =4, each of

which signify the same thing. : : Four points set in the middle of four numbers, denote

them tù be proportional to one arother, by the rule of three ; as 2:4::8:16 ; that is, as 2 to 4, so is 8 to

16. ✓ Prefixed to any number, supposes that the square root

of that number is required. Prefixed to any number, supposes the cube root of that number is required. Denotes the biquadrate root, or fourth power, &c.

ARITHMETIC,

ARITHMETIC is the art of computing oy numbers, and has five principal rules for its operation, viz. Numeration, Addition, Subtraction, Multiplication, and Division.

NUMERATION.

Numeration is the art of numbering. It teaches to express the value of any proposed number by the following characters, or figures :

1, 2, 3, 4, 5, 6, 7, 8, 9, 0-or cypher Besides the simple value of figures, each has a local value, which depends upon the place it stands in, viz. any figure in the place of units, represents only its simple value, or so many ones, but in the second place, or

Note.-Although a cypher standing alone signifies nothing; yet when it is placed on the right hand of figures, it increases their value in a centold proportion, by throwing them into higher places. Thus ? with a cypher annexed io it becomes 20, iweniy, and with two cyphers, thus, 200, two hundreu.

2. When numbers consisting of many figures, are given to be read, it will be found convenient to divide them into as inany periods as we can, of six bgures cach, reckoning from the right hand towards the leat, calling the first the period of units, the second that of millions, the third biliions, the fourtb trillions, &c. as in the following nuinher:

807 36 % 5 4 6 2 7 8 9 0 1 2 5 0 6 793 4. Period of 3. Period uf

2. Period of 1. l'eriod of Trilliuns. Billions. Millions.

Units.

500792

8073
695462

7890:2 The foregoing number is read thus-Eighi thousand and seventy-three tril. lions; sin hundred and twenty-five

thousarid, four hundred ard sixty-two bilo lions, seven hundred and eighty-nine thousand and twelve millions ; five hundred and six thousand seven liundred and ninety-two.

N. B. Billions is substitu!ed for inillions of millions.
Trillions for millions of millions of millions.
Quatrillions for millions of millions of miliions of millions, &e.

place of tens, it becomes so many tens, or ten times its simple value, and in the third place or place of hundrede, it becomes a hundred times its simple value, and so on, as in the following

TABLE.

Millions,
C. of Millions,
Teos,
X, of Millions,
Units,
C. of Thousands,
Hundreds,
X. of Thousands,
Thousands,

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1 One,
2 1 - Twenty-one.

3 2 1 Three hundred & twenty-one. 1 4 3 2 1 - Four thousand 321.

5 4 3 2 1 · Fifty-four thousand 321.

6 5 4 3 2 1 - 654 thousand 321. in 6 5 4 3 2 1 .7 million 654 thousand 321, 18 7 6 5 4 3 2 1 87 million 654 thousand 321,

8 mp 6 5 4 3 2 1 - 987 million 654 thousand 321. 1 2 3 4 5 6 7 8 9 -123 million 456 thousand 789, 9 8 7 6 5 4 3 4 8 - 987 inillion 654 thousand 348.

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To know the value of any number of figures.

RULE.

1. Numer ate from the right to the left hand, each figure in its proper place, by saying, units, tens, hundreds, &c. as in the Numeration Table.

2. To the simple value of each figure, join the name of its place, beginning at the left hand, and reading to

the right.

EXAMPLES.

Read the following numbers.

365, Three hundred and sixty-five. 6461, Five thousand four hundred and sixty-one, 1234,.One thousand two hundred and thirty-four. 64026, Fifty-four thousand and twenty-six.

123461, One hundred and twenty-three thousand four

hundred and sixty-one. 4656240, Four millions, six hundred and sixty-six

thousand two hundred and forty. Note.--For convenience in reading large numbers, they may be divided into periods of three figures each, as follows:

987, Nine hundred and eignty-seven. 987-000, Nine hundred and eighty-seven thousand. 957 OCO 000, Nine hundred and eighty-seven million. 997 654 321, Nine hundred and eighty-seven million,

six hundred ad fifty-four thousand, three hundred and twenty-one.

To write numbers.

RULE.

Begin on the right hand, write units in the units place, tens in the tens place, hundreds in the hundreds place, and so on, towards the left hand, writing each figure according to its proper value in numeration ; taking care to supply those places of the natural order with cyphers which are omitted in the question.

EXAMPLES.

Write down in proper figures the following numbers :
Thirty-six
Two hundred and seventy-nine.
Thirty-seven thousand, five hundred and fourteen.
Nire millions, seventy-two thousand and two hundreds

Eight hundred miHions, forty-four thousand and fiftyfive.

SIMPLE ADDITION, IS putting together several smaller numbers, of the same denomination, into one larger, equal to the whole or sum total; as 4 dollars and six dollars in one sum is 10 dollars

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RULE.

Having placed units under units, tens under tens, &c draw a line underncath, and begin with the units ; afteradding up every figure in that column, consider how many tens are contained in their sum ; set down the remainder under the units, and carry so many as you have tens, to the next column of tens; proceed in the same manner through every column, or row, and set down the whole amount of the last row.

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