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Equal to, as 12d. = 1s. signifies that 12 penge are

equal to 1 shilling. + More, the sign of addition, as 5+7=12, signifies

that 5 and 7 added together, are equal to 12.

---- Minus, or less, the sign of subtraction, as 6-=

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.

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• 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 to be proportional to one another, by the rule
of three; as 2:4::8:16.; that is, as 2 to 4, so is 8
to 16.

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Prefixed to any number, supposes that the square root

of that number is required.

v Prefixed to any number, supposes the cube root of that number is required.

Denotes the biquadrate root, or fourth power, &c.'

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

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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, Omor 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

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NOTE. Although a cypher standing alone signifies vothing; yet when it is placed on the right hand of figures, it increases their valne in a tenfold proportion, by throwing them into higher places. Thus 2 with a cypher annexed to it, becomes 20, twenty, and with two cyphers, thus, 200, two hundred.

2. When pumbers consisting of many figures, are given to be read, it will br found convenient to divide them into as many periods as we can, of six figures each, reckoning from the right hand towards the left, calling the first the period of units, the second that of millions, the third billions, the fourth trillions, &c. as in the following number:

807 8 6 2 5 4 6 7 8 9 0 1 25 0 6 7 9 %
4. Period of 1 3. Period of 12. Period of 11. Period of

Trillions, Billions. 1 Millions, Units.

3078

625462 7 89012: 1 506792 The foregoing number is read thus-Eight thousand and seventy-three trillions; six hundred and twenty-five thousand, four hundred and sixty-two billions ; seven hur dred and eighty-nine thousand and twelve millions; five hopdred and six thousand, seven hundred and ninety-two. N. B. Billions is substituted for millions of millions.. Trillions for millions of millions of millions. Quatrillions for millions of millions of millions of millions,

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

TABLE:

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'1-One.
!! 21. Twenty-one.

2 1 - Three hundred twenty-one.

21 - Four thousand 321.
5 4 3 2 1 - Fifty-four thousand 321.
5 4 3 2 1 - 654 thousand 321.

5 4 3 2 1 - 7 million 654 thousand 321.
8 7 6 5 4 3 2 1 - 87 million 654 thousand 321.
8 7 6 5 4 3 2 1 - 987 million 654 thousand 321.

3 4 5 6 7 8 9 - 123 million 456 thousand 789. 9 8 7 6 5 4 3 4 8 - 987 million 654 thousand 348.

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To know the value of any number of figures.

RULE. 1. Numerate from the right to the left hand, each figure in its proper place, by saying, units, tens, hundrede, &c. as in the Nuineration 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.
5461, Five thousand four hundred and sixty-one.

1254, One thousand two hundred and thirty-four.
54026, Fifty-four thousand and twenty-six.

123461, One hundred and twenty-three thousand four

hundred and sixty-one.

4666240, Four millions, six hundred and sixty-six thou.

sand 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 eighty-seven.

987 000, Nine hundred and eighty-seven thousand. 987 000 000, Nine hundred and eighty-seven million. 987 654 321, Nine hundred and eighty-seven million,

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

To write numbers.

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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 ac-
cording 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.
Nine millions, seventy-two thousand and two hundred.

Eight hundred millions, forty-four thousand and fiftyfive.

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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.

RULE.

Having placed units under units, tens under tens, &c. draw a line underneath, and begin with the units; after adding up every figure in that column, consider how ma. ny 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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