THE

AMERICAN ARITHMETIC,

AND

PRACTICAL MENSURATOR.

ARITHMETIC is the art of computing by numbers; these numbers are called Figures, viz. 0, 1, 2, 3, 4, 5, 6, 7,8,9,-0, of itself has no value, but when joined to the right of other numbers, it increases their value in a tenfold proportion. Thus, 1 is one. 10 is ten, 2 is two, 20 is twenty.

Of other Characters used in Arithmetic. This mark+ Is the sign of Addition; and shews, that the number which follows the sign, must be ad

ded to the number before it. Thus 9+10
signifies that 9 and 10 are to be added.
Is the sign of Subtraction; and denotes
the number following it, must be sub-
tracted from the one before it. Thus,
16-4 signifies that 4 must be taken from

16.

X Is the sign of Multiplication; and denotes. that all the numbers, between which it is placed, are to be multiplied together. Thus, 9x9 signifies that 9 is to be multipled by 9, or 9X9×9 must be multiplied. Is the sign of Divison; and denotes the number standing before it, is to be divided by the number following it. Thus, 943 signifies that 9 is to be divided by 3.

This is the signofequality, and signifies the sum or product of the numbers before it, is equal to the number after it, 2+4+5

I mean that 2, 4 and 5 added, their sum

would be 11; and 2×4×540 mean, that
2 and 4 multiplied, and that product mul-
tiplied again by 5 the product is equal to
40; and also 9X8÷126, means that 9
and 8 multiplied, and the product divided
by 12, the quotient will be equal to 6.
: Are the signs of proportion as 7:14::8
16, and are read as 7 to 14, so is 8 to
16.

2 This shews the Square Root of the number
is required.

This shews the Cube Root of the number is required.

Numeration Table.

2

Millions of Millions.

Hundreds of Thousands of Millions.

∞∞∞ Tens of Thousands of Millions.

3. 4

→ A Thousands of Millions.

∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ Hundreds of Thousands.

The use of this Table in

Addition.

stands 20, the sum regle of the two lines ly over, and in the anon the top stands directlong on that line till 13 or right, and move a look for 7 on the left, ed to add 7 with 13, required.--It is requirmeet, stands the sum angle in which the lines and in the corner, or would add it on the top,

number with which you or right hand, and the to be added on the left

Look for the number

the left or right hand, from 15, look for 9 on Required to take 9 EXAMPLE.

find 15, and on the top directly over 15 is 6, the remainthen follow that line towards the right or left till you

der required.

1

SIMPLE ADDITION.

DEFINITION. Simlpe Addition teaches to add togeth. er several sums of the same denomination.

RULE.-Set down units under units, tens under tens, and hundreds under hundreds, &c. Begin to add in the place of units, add all in that column, carry one for eveten that is in the sum of units, to the place of tens, and set down all that is over ten, or tens; add up the col umn of tens, carry one for every ten to the next column, and set down all that is over; thus proceed through all the columns to the last; observe to set down the whole sum in the last column.

PROOF-Begin at the top add downwards, carry as be. fore, and if the work is right, the sum will be the same as it was when added upwards.

1. Add together 345674, 98736, 456752 and 7654.

Ans. 908816.

2. Add 94321, 675431, 1234 and 76432 together.

3. Add 6421, 94742, 6752 and 875432 together.

Ans. 847418.

Ans. 983347.

Ans. 309385.

5. Add 9944, 2343, 78764 and 94929 together.

Ans. 185980.

4: Add 67432, 98891, 65641 and 77421 together.

6. I lent a friend 942 dollars, at one time, at another 741, at another 91; what is the whole sum lent?

Ans. 1774 dolls.

7. A man killed 4 hogs, weighing as follows; one 396, one 472, one 510 and one 371; what did they all weigh? Ans. 1749.

8. I killed an ox, his quarters weighed 642, his hide 105, his tallow 92; what did they all weigh? Ans. 839.

9. A man gave to three sons as follows, to one 3427 dolls. to another 3025 dolls. to another 2947 dolls. ; what did he give to all of them? Ans. 9399.

10. A man's taxes were as follows for 3 years; the first 142 dolls. second 165, the third 210 dolls.

did he

pay in three years.

what

Ans. 517.

SIMPLE SUBTRACTION.

DEFINITION.-Simple Subtraction teaches to take a less number from a greater, that is of the same denomination, and thereby find the difference, or remainder. RULE. Write the largest number down first; and the smallest underneath, units under units, &c. begin to subtract in the place of units; and take the under from the upper figure; set down the remainder: If at any time any particular figure in the lower line is larger than the one immediately over it, subtract the under figure from ten; to the remainder add the upper figure and set it down; and carry one to the next figure in the lower line; thus proceed through the whole.

PROOF. Add the remainder and the lower line together, and if the work is right the sum will be like the upper line.