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which contain rules and examples sufficient for practice, to which the Reader is referred.

No pains have been spared to render the work as correct as possible, by a thorough examination of the proof-sheets; many errors may, however, have escaped correction, if any such should be pointed out, it would be considered as a mark of favor and friendship, by

SOLOMON PARKER.

KEY

TO THE FIRST TABLES.

THESE Tables, though simple, contain not only the squares and cubes but even the roots of all powers; which shew at once their great use and facility.

The first tables are numbered from 1 in a numerical succession to 99-each table is again numbered from 1 to 199 numerically, where it breaks off. abruptly, and is then numbered 365, where it ends. The letters NO. signify the numbers at the top of the tables, and the letter N, signifies the numbers standing in the table. The NO. may be called any name or number required, only observing to give the right hand figure of the answer the same name which is in the place of units, the next figure to the left hand in the place of tens, &c. and as many cyphers as you add to NO. so many you must add to the answer, in the table; still observing that the right hand cypher, thus added, bears the same name as before directed. N. may be augmented or di minished in, like proportion, even to infinite numbers. When

bers, the right and N. are both decimal num

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figure of the answer will stand in the place of hundredths. I shall therefore explain the use of the tables by giving rules and work. ing them, It is a rule in arithmetic that any number multiplied by itself produces a square; and any number multiplied by its square produces a cube. To find one side of any square number is called the extraction of the square root of that number.

If a

cube

cube be given to find out a number which being multiplied into its square produceth the number given-this is called the extraction of the cube root.

EXAMPLE.

Find the square and cube of 7.-Take NO. 7, then under N. in the same table, take 7, against which stands 49-the square. Then against N. 49, found in the same table, stands 343-the cube required. Then NO. 7 becomes the square root of 49, and the cube root of 343. In like manner may the squares and cubes of the nine powers be found, either in whole or in decimal numbers; observing in decimal numbers to call the right hand figure of the answer after the same name of your given decimal note. For 7. 5-tenths, take NO. 75; for 4. 3-tenths, take NO. 43; for 1. 7-tenths take NO. 17; for 2. 9-tenths, take NO. 29; for 6. 8-tenths, take NO. 68, &c, and in like proportion for any other number.

EXAMPLE.

What is the square and cube of 1. 2-tenths? For. the given number, 1. 2-tenths, take NO. 12, then under N. find 12, against which stands 1. 44-hundredths, the square-then against N. 144 stands 17. 28-hundredths, the cube-then r. 2-tenths becomes the square root of 1. 44-hundredths, and the cube root of 17. 28-hundredths. In like manner you may proceed to infinite numbers. ◊

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To find the product of any two numbers multiplied together. Rule.-Call NO. the multiplier, and N. the multiplicand-in an angle of meeting stands the product or answer.

EXAMPLES.

1. Find the product of 197 multiplied by 83.Find NO. 83 for the multiplier, then find N. 197 for the multiplicand, against which stands 16351, the product or answer.`

2. What is the product of 57, multiplied by 19? 1083, the Answer.

3. Find the product of 1990, multiplied by 99.— Find NO. 99, then find N. 199, to which add a cypher; it then becomes 1990, against which stands (remembering to pay the borrowed cypher) 197010, the product or answer.

-Note-The product of any two numbers can be found by addition of cyphers, remembering to place as many cyphers to the right hand of the answer, as you borrow to augment the numbers required. To use this table for multiplying of decimal numbersRule Call NO. and N. the given decimals, and in an angle of meeting stands the answer. Example-What is the product of 2. 3 multiplied by 1.7? For 1.7 take, NO. 17, then for 2. 3 take N. 23, against which stands 3. 91-hundredths, the answer.

Note-If NO. 17 is assumed as a decimal number, and N. 23 as a whole number, the answer will stand thus-39. 1-tenth.

To find the price of any number or quantity of goods or merchandize. Rule-With the given price of one ounce, pound, hundred, &c. enter the tables, and find NO. to agree with the given price; then under N. find the given quantity, against which, in the right hand column, stands the answer required.

EXAMPLES.

1. What is the value of 79 lb. of butter, at 17 cents per pound. Here the given price for one pound is 17 cents with this price enter the tables and find NO. 17, then in the same table under N. find 79, the number of pounds, against which stands $13 43 cents, the answer.

2. What is the value of 143 yards of tape, at 3 cents per yard? Find NO. 3, the price of one yard, then under N. find 143, the number of yards, against which stands $4 29 cents, the answer.

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3. What is the value of 73 bushels of corn, at 69 cents per bushel? Find NO. 69, the price of one bushel, then under N. find 73, the number of bushels, against which stands £50 37 cents the an

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4. What is the value of 27lbs of cheese at 9 cents per pound? Find NO. 9, the given price of one pound, then under N. find 27, the number of pounds, against which stands $2 43 cents--the answer.

5. Find the value of 78lbs. of butter, at 9 cents 9 mills per pound. Here 9 cents 9 mills becomes 99 mills; take NO. 99, which call mills, then under N. find 78, the number of pounds, against which stands 7. 72.2; which is 7 dollars 72 cents 2 mills -the answer.

Note Here NO. 99 receives the name of mills; and, according to the rule, the right hand figure of: the answer receives the same name, in which the decimal point or space must be removed one figure to the left hand.

6. What is the income or expences for 365 days, at 6 cents per day? For the 6 cents take NO: 6, then under N. find 365, the number of days, against which stands $21 90 cents-the answer.

7. What is the value of 750 bushels of wheat, at $1.59 cents per bushel? For the number of bushels take NO. 75 for the two first figures, then by adding a cypher it becomes 750; then in the same table under N. find 159, the number of cents for one bushel, against which (remembering to add the cy, pher as the rule directs) stands $1192 50 centsthe answer.

Note-Here the decimal space is removed one figure to the right hand.

8. What is the amount or wages for 11 days labor, at $125 cents per day? For the number of days take NO. 11, then for $125 cents, the price of one day,

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