1728 solid inches make

40 feet of round timber, or 50 feet of hewn timber, 128 solid feet or 8 feet long,

4 wide, and 4 high,

1 square foot. 1 square yard. 1 square rod.

1 square rood. 1 square acre. 1 square mile

1 solid foot.

1 ton or load.

1 cord of wood

All solids, or things that have length, breadth and depth, are measured by this measure. N. B. The wine gallon contains 231 solid or cubic inches, and the beer gallon, 282. A bushel contains 2150,42 solid inches.

mo.

yr.

13 months, 1 day and 6 hours, 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 bath 29 days.

12. Circular Motion.

1 month,

Julian year,

30 degrees,

1 minute,

1 degree,

1 sign,

S.

12 sigus, er 360 degrees, the whole great circle of the

Zodiac.

=

Explanation of Characters used in this Book.

Equal to, as 12d. 1s. 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, signifies that 2 subtracted from 6, leaves 4.

× Multiply, or with, the sign of Multiplication; as 4x3=12, significs 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 to be proportional to one another, by the rule of three; as 24::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 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:

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

Nors. Although a cypher standing alone signifies nothing; yet when it is placed on the right hand of figures, it increases their value in a tenfold proportion, by threwing 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 numbers consisting of many figures, are given to be read, it will be found oonvenient 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:

80 7 3 6 2 5 4 6 2 7 8 9 0 1 2 506 7 9 2

4. Period of 3. Period of 2. Period of 1. Period of

Trillions.

8073

Billions.

625462

Millions.

789012

Units.

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 mil. lions; five hundred and six thousand seven hundred and ninety-two. N. B. Billions is substituted for millions of millions.

Trillious for millions of millions of millions.

Quatrillions for millions of millions of millions of millions, &c,

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

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, undreds, &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.

5461, Five thousand four hundred 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 four hundred and 'xty-one.

4666240, 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 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 hun dred 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. Nine millions, seventy-two thousand and two hundred. Eight hundred millions, forty-four thousand and fiftyfive.

SIMPLE ADDITION,

Sputting together several smaller numbers, of the same denomination, into one larger, equal to the whole or sura tal; as 4 dollars and six dollars in one sum is 10 dollars.