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CHARACTERS USED IN THIS WORK.

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Contraction, for U. S. United States' currency, and is prefixed to dollars and cents.

= Sign of equality; as 12 inches =1 foot, signifies, that 12 inches are equal to one foot.

Sign of addition; as 8+6=14, signifies, that 8 added to 6 is equal to 14.

Sign of subtraction; 8-6-2, that is, 8 less 6 is equal to 2.

× Sign of multiplication; as 7×6=42, that is, 7 multiplied by 6, is equal to 42.

Sign of division; as 42-6-7, that is, 42 divided by 6 is equal to 7.

72 Numbers placed in this manner imply, that the upper line is to be divided by the lower line.

:

Signs of proportion; thus, 2:4::6: 12, that is,

2 has the same ratio to 4, that 6 has to 12; and such numbers are called proportionals.

12—3+4=13. Numbers placed in this manner show, that 3

is to be taken from 12, and 4 added to the remainder. The line at the top is called a vinculum, and connects all the numbers over which it is drawn.

9* Implies, that 9 is to be raised to the second power; that is, multiplied by itself.

83

Implies, that 8 is to be multiplied into its square.

✔ This sign prefixed to any number shows, that the square root is to be extracted.

This sign prefixed to a number, shows, that the cube root is to be extracted.

By Edwards Lo Woldery

ARITHMETIC.

SECTION I.

ARITHMETIC is the art of computing by numbers. Its five principal rules are Numeration, Addition, Subtraction, Multiplication, and Division.

NUMERATION.

Numeration teaches to express the value of numbers either by words or characters.

The numbers in Arithmetic are expressed by the following ten characters, or Arabic numeral figures, which the Moors introduced into Europe about nine hundred years ago; viz. 1 one, 2 two, 3 three, 4 four, 5 five, 6 six, 7 seven, 8 eight, 9 nine, 0 cipher, or nothing.

The first nine are called significant figures, as distinguished from the cipher, which is of itself insignificant.

Besides this value of those figures, they have also another, which depends on the place in which they stand, when connected together; as in the following table.

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Here any figure in the first place, reckoning from right to left, denotes only its simple vaiue; but that in the second place, denotes ten times its simple value; and that in the third place a hundred times its simple value; and so on; the value of any successive place being always ten times its former value.

Thus in the number 1834, the 4 in the first place denotes only four units, or simply 4; 3 in the second place signifies three tens, or thirty; 8 in the third place signifies eighty tens or eight hundred; and the 1, in the fourth place, one thousand; so that the whole number is read thus,-one thousand eight hundred and thirty-four.

As to the cipher, 0, though it signify nothing of itself, yet being joined to the right hand of other figures, it increases their value in a tenfold proportion; thus 5 signifies only five, but 50 denotes 5 tens or fifty; 500 is five hundred; and so on.

NOTE. The idea of number is the latest and most difficult to form. Before the mind can arrive at such an abstract conception, it must be familiar with that process of classification, by which we successively remount from individuals to species, from species to genera, from genera to orders. The savage is lost in his attempts at numeration, and significantly expresses his inability to proceed, by holding up his expanded fingers or pointing to the hair of his head. See Lacroix.

NUMERATION TABLE.

317,897;431,032; 639,864; 361,316: 461,315; 123,675; 816,131; 123,456; 123,614; 315,131; 398,832; 563,871; 351,615; 123,561.

Thousands.

Tridecillions.

Thousands.

Duodecillions.

Thousands.
Undecillions.

Thousands.
Decillions.

Thousands.

Nonillions.

Thousands.

Octillions.

Thousands.

Septillions.

Thousands.

Sextillions.
Thousands.
Quintillions.

Thousands.
Quatrillions.
Thousands.

Trillions.
Thousands.

Billions.
Thousands.

Millions.

Thousands.

Units.

In order to enumerate any number of figures, they must be separated by semicolons into divisions of six figures each, and each division by a comma, as in the annexed table. Each division will be known by a different name. The first three figures in each division will be so many thousands of that name, and the next three will be so many of that name, that is over its unit place. The value of the numbers in the annexed table, expressed in words, is Three hundred and seventeen thousand, eight hundred and ninety-seven tridecillions; four hundred and thirty-one thousand, thirty-two duodecillions; six hundred thirty-nine thousand, eight hundred sixtyfour undecillions; three hundred sixty-one thousand, three hundred sixteen decillions ; four hundred sixty-one thousand, three hundred fifteen nonillions; one hundred twenty-three thousand, six hundred seventy-five octillions; eight hundred sixteen thousand, one hundred thirty-one septillions; one hundred twenty-three thousand, four hundred fifty-six sextillions; one hundred twenty-three thousand, six hundred fourteen quintillions; three hundred fifteen thousand, one hundred thirty-one quatrillions; three hundred ninety-eight thousand, eight hundred thirty-two trillions; five hundred sixty-three thousand, eight hundred seventy-one billions; three hundred fiftyone thousand, six hundred fifteen millions; one hundred twenty-three thousand five hundred sixty-one.

NOTE.-The student must be familiar with the names, from Units to Tridecillions, and from Tridecillions to Units, so that he may repeat them with facility either way.

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