CONTENTS.

Page.

1

ibid.

General remarks on the different kinds of magnitude or quantity

Of number

Of spoken numeration

Manner of representing numbers by figures, or written numera-

tion

Of reading numbers

Of abstract and concrete numbers

Of Addition.

Of the principles on which addition is founded
General rule for performing addition

Of the principles on which it is founded

Explanation of the terms, remainder, excess, and difference

General rule for subtraction

Method of proof for addition and subtraction

9

10

12

13

Of Multiplication.

The origin of multiplication

14

An explanation of the terms multiplicand, multiplier, product,

and factors

15

Of the principles on which multiplication is performed

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

ibid.

ures

16

Formation of this table

ibid.

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

the factors does not affect the product

17

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

single figure

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

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

any number of ciphers

General rule for multiplication

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

ed by ciphers

Of Division.

The origin of division

Explanation of the terms, dividend, divisor, and quotient

Of the principles on which division is founded

ibid.

Mode of proceeding, when the divisor consists of several figures 27

General rule for division

Method of abbreviating the process of division

28

29

When both the divisor and dividend have ciphers on the right

Multiplication and division mutually prove each other

30

-

îbid.

30

32

ibid.

33

34

ibid.

35

36

38

39

40

41

42

43

44

The origin of fractions

of Fractions.

The manner of reading and writing fractions

An explanation of the terms numerator and denominator
Of the changes which a fraction undergoes, by the increase or
diminution of one of its terms

A Table representing the changes which take place in a fraction,
by the multiplication or division of either of its terms

The value of a fraction not altered by multiplying or dividing

both its terms by the same number

To simplify a fraction without altering its value
The greatest common divisor of two numbers
General rule for finding the greatest common divisor
To distinguish the numbers divisible by 2, 5, or 3
Of prime numbers

General signification of the term multiplier
To multiply a whole number by a fraction

To find the whole number contained in a fraction
To reduce a whole number to a fraction

To multiply one fraction by another

Of compound fractions

Of division in general

Of the division of a whole number by a fraction

To divide one fraction by another

Of the addition and subtraction of fractions

To reduce fractions to a common denominator

Of the addition and subtraction of mixed numbers

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

der in which they are multiplied

Of Decimal Fractions,

The origin of decimal fractions

The manner of reading and writing decimals

A number containing decimals, not altered by annexing ciphers

Addition of decimals

Subtraction of decimals

The effect of changing the place of the decimal point

To multiply a number containing decimals, by a whole number

The multiplication of one decimal by another

To divide a decimal number by a whole number

To divide one decimal by another

ibid.

55

56

57

58

59

ibid.

Method of approximating the quotient of a division by decimals ibid.

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

in fractions of a given denomination

To reduce vulgar fractions to decimals

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

denomination

Of periodical decimals

Tables of Coin, Weight, and Measure.

Of Federal Money

65

66

ibid.

·

ibid.

67

ibid.

ibid.

To reduce pounds and shillings to pence &c.

To reduce shillings to pounds

To reduce other denominations of money, weight, and measure

To reduce a compound number to the lowest denomination con-

-

69

70

71

72

To reduce a number from a lower denomination to a higher ibid.

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

of the highest denomination contained in it

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

of the highest denomination contained in it.

73

ibid.

75

76

77

ibid.

To reduce numbers from one denomination to another, when the

two numbers are not commensurable

78

To reduce a decimal of a higher denomination to a lower

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

pound

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

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

Method of operation, when the divisor is large, and resolvable

into two or more factors

ibid.

Process, when the divisor cannot be so resolved

Multiplication and division mutually prove each other

Of Proportion.

A development of the principles on which the rules of proportion

91

ibid.

92 93 ibid..

94

ibid.

Of the equality of the product of the means to that of the extremes 95 Transposition of the terms of a proportion

To obtain any one term of the proportion from the other three

The Rule of Three

Rules for the stating of questions

ibid.

96

97 ibid.

These principles illustrated by examples

Of the compounding of ratios

General rule for solving questions in compound proportion
Examples for practice

Fellowship.

103

ibid.

108

The use of the rule, and the principles on which it is founded
Commercial use of the terms, capital or stock and dividend
Examples illustrative of the principles of fellowship
Of equidifference in numbers, or arithmetical ratios
Note.-Distinction between geometrical and arithmetical pro-
portion

Manner of writing numbers in equidifference
Questions for practice