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CONTENTS.

Of Numeration.

Page.

General remarks on the different kinds of magnitude or quantity 1

Of number

1

Of spoken numeration

2

Manner of representing numbers by figures, or written numera-

tion

4

of reading numbers

6

Of abstract and concrete numbers

8

Of Addition.

Of the principles on which addition is founded

General rule for performing addition

• 10

Of Subtraction.

Of the principles on which it is founded

Explanation of the terms, remainder, excess, and difference

General rule for subtraction

Method of proving addition and subtraction

11

14

Of Multiplication.

The origin of multiplication

16

An explanation of the terms multiplicand, multiplier, product,

and factors

Of the principles on which multiplication is performed

17

The table of Pythagoras, containing the products of any two fig-

117

Formation of this table

Remarks, from which it is inferred, that a change in the order of

the factors does not affect the product

ures

18

Rule for multiplying a number, consisting of several figures, by a

single figure

20

To multiply by 10, 100, 1000, &c.

21

Rule for multiplying by a number consisting of a single digit and

any number of ciphers

22

General rule for multiplication

23

Manner of abridging the process, when both factors are terminat-

ed by ciphers

Of Division.

The origin of division

24

Explanation of the terms, dividend, divisor, and quotient

25

Of the principles on which division is founded

Mode of proceeding, when the divisor consists of several figures 29

General rule for division

30

Method of abbreviating the process of division

31

When both the divisor and dividend have ciphers on the right 31

Multiplication and division mutually prove each other

32

Of Fractions.

.

The origin of fractions

The manner of reading and writing fractions

34

An explanation of the terms, numerator and denominator

Of the changes wbich a fraction undergoes, by the increase or

diminution of one of its terms

35

A table representing the changes which take place in a fraction,

by the multiplication or division of either of its terms 36

The value of a fraction not altered by multiplying or dividing

both its terms by the same number

36

To simplify a fraction without altering its value

37

The greatest common divisor of two numbers

38

General rule for finding the greatest common divisor

40

To distinguish the numbers divisible by 2, 5, or 3

41

Of prime numbers

42

General signification of the term multiplication

44

To multiply a whole number by a fraction

To find the whole number contained in a fraction

45

To reduce a whole number to a fraction

46

To multiply one fraction by another

Of compound fractions

47

Of division in general

Of the division of a whole number by a fraction

48

To divide one fraction by another

Of the addition and subtraction of fractions

50

To reduce fractions to a common denominator

Of the addition and subtraction of mixed numbers

51

The product of several factors not changed, by changing the or-

der in which they are multiplied

52

Of Decimal Fractions.

The origin of decimal fractions

54

The manner of reading and writing decimals

55

A number containing decimals, not altered by annexing ciphers 56

Addition of decimals

56

Subtraction of decimals

57

The effect of changing the place of the decimal point

58

To multiply a number containing decimals, by a whole number 60

The multiplication of one decimal by another

60

To divide a decimal number by a whole number

61

To divide one decimal by another

62

Method of approximating the quotient of a division by decimals 62

Note.—Method of finding the value of the quotient of a division

in fractions of a given denomination

63

To reduce vulgar fractions to decimals

Note. On the changing of one fraction to another of a lower

denomination

Of periodical decimals

65

64

Tables of Coin, Weight, and Measure.

68

Of Federal Money

69

English Money

Troy Weight

Apothecaries' Weight

Avoirdupois Weight

Long Measure

Cloth Measure

70

71

Square Measure

Dry or Corn Measure

Ale and Beer Measure

Wine Measure

Time

72

73

74

Reduction.

To reduce pounds and shillings to pence &c.

75

To reduce shillings to pounds

. 76

To reduce other denominations of money, weight, and measure 76

To reduce a compound number to the lowest denomination con-

tained in it

78

To reduce a number from a lower denomination to a higher - 78

To reduce the several parts of a compound number to a fraction

of the highest denomination contained in it

79

To find the value of a fraction of a higher denomination, in the

terms of a lower

To reduce the several parts of a compound number to a decimal

81

To reduce a decimal of a higher denomination to a lower 82

To convert shillings, pence, and farthings, to the decimal of a

pound

83

To convert the decimal of a pound to shillings &c.

To reduce numbers from one denomination to another, when the

two numbers are not commensurable

84

Of Compound Numbers.

General rule for the addition of compound numbers

Method of proving the addition of compound numbers

Of the subtraction of compound numbers

To prove subtraction of compound numbers

Multiplication of compound numbers

General rule for the multiplication of compound numbers

Mode of proceeding, when the multiplier exceeds 12

Of duodecimals

General rule for the multiplication of duodecimals

of the division of compound numbers

General rule for compound division

86

87

89

90

91

93

94

95

96