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9. Land, or Square Measure. 144 square inches make

square foot. 9 square feet,

I square yard 301 square yards, or

1 square rod. 272 square feet, 40 squarc rods,

1 square rood. 4 square roods,

1.square acre, 640 square acres,

1 square mile. 10. Solid, or Cubic Measure. 1928 solid inches make

I solid foot.. 40 feet of round timber, or /

I tun or load. 50 feet of hewn timber, I 128 solid feet, or 8 feet long,

I cord of wood. 4 wide, and 4 high, All solids, or things that have length, breadth, and depth, pre measured by this measure. N. B. The wine gallon o intains 231 solid or cubic inches, and the beer gallon, 282.. i. bushel contains 2150,42 solid inches.

11. T'ime. 60 seconds (S.) make 1 minute, marked 60 minutes,

1 hour, 24 hours,

I day, 7 days,

I week, : 4 weeks,

I month, 13 months, 1 day and 6 hours, 1 Julian year, yr. Thirty days hath September, April, June, and November, February twenty-eight alone, all the rest have thirty-one. N. B. In Bissextile, or leap year, February hath 29 days.

12. Circular Motion. 60 seconds (") make 1 minute, 60 minutes,

1 degree, 30 degrees,

I sign, 12 signs, or 360 degrees, the whole great circle of the Zodiack.

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Explanation of Characters used in this Book.

= Equal to, as 12d. = ls. signifies that 12 pence 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, 6–2=4, sig.

nifies 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 di. vided by 2, is equal to 4; or thus, 54, 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.

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 is the art of computing by 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 : lebo 1, , 3, 4, 5, 6, 7, 8, 9, 1--or cipher.

Besides the simpe value of figures, each has a local · value, which depena i upon the place it stands in, viz, any

ligure in the place of units, represents only its simple value, or so many ones; but in the second place, or place of tens, it becomes so many tens, or ten times its simple yalue; and in che third place, or place of hundreds, it becomes a hundred rimes its simple value, and so on, as in the following

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Note.-Although a cipher standing alone signisies nothing; yet when it Is placed on the right hard uf figures, it increases their value in a tenfold proportion, by throwing them into higher places. Thus, 2 with a cipher annexed to it, becomes 20, twenty, and with two ciphers, thus, 200,two hundred.

2. When numbers consisting of many figures, are given to be read, it will be 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:

S O 7 3 6 2 5 4 6 2 7 8 9 0 1 2 5 0 6 7 9 2
4. Period of 3. Period of 1 2. Period of 1. Period of
Trillions.
Billions.
Millions.

Unils.
va
8073
625462

789012
789012

506792 The foregoing number is read thus-Eight thousand and seventy-three trillions ; six hundred and twenty-five thousand, four hundred and sixtytwo billions ; seven hundred and eighty-nine thousand and twelve millions ; frve hundred and six thousand seven hundred and ninety-two:

N. B. Billions is substituted for millions of millicris.
Trillions for millions of millions of millions.
Quatrillions for millions of millions of millions of millions, fc.

TABLE.

C. of Millions, ...
X. of Millions,
Millions, -.--..
Thousands,
C. of Thousands, ...
X. of Thousands, i. 2.9 1.9

- •; •

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III -One

2 1 -Twenty-one.

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

4 3 2 1 - Fifty-four thousand 321. ii, 6 5 1 3 2 1 -654 thousand 321.

6 5 4 3 2 1-7 inillion 651 thousand 321. 18 7 6 5 4 3 2 1 -87 inillion 65 1 thousand 321. 9 8 7 6 5 4 3 2 1 -987 million 65-thousand 321 1 2 3 4 5 6 7 8 9 -123 million -150 thousand 789. 9 8 7 6 5 4 3 4 8 -997 milliou 654 thousand 318.

To know the value of any number of figures : Rule.-1. Numerate from tho right to the left hand, each figuro i its proper place, by saying, units, tens, hundreds, &c. as in the Num. ration Table.

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

EXAMPLES."
Rear the following numbers.
365, Three hundred and sixty-five.
5161, Five thousand four lundred and sixty-one.

1234, One thousand two hundred and thirty-four. 54026, Fifty-four thousand and twenty-six. 123461, One hundred and twenty-three thousand foui

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

sand two hundred and forty. Note. For convenience in eading large numbers, they inay 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, Nive hundred and eighty-seven million. 937 (5.1 321, Nine hundred and eighty-seven million, sro

Humired and fifty-four thousand, three hun dred and wenty-one.

To write numbers.. Rock. - Begin on the right hand, write units in the units place, vens in ihu 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 ciphers 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 inillions, forty-four thousand and fifty-five.

SIMPLE ADDITION. IS putting together several smaller numbers, of the same lenomination, into one larger, equal to the whole or sum fotal; as 4 dollars and 6 dollars inyone sum is 10 dollars.

Rule.-Having placed units under units, tens under tcns, &c, draw Le line underneath, and begin with the units ; after adding up every hgure 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 manher through every column or row, and set down the whole amount of the last row.

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