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CONTENTS.
Of Numeration.
Page.
General remarks on the different kinds of magnitude or quantity 1
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 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
1
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
The table of Pythagoras, containing the products of any two fig-
17
ures
Formation of this table
Remarks, from which it is inferred, that a change in the order of
the factors does not affect the product
18
}
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
20
21
22
23
Of Division.
The origin of division
24
Explanation of the terms, dividend, divisor, and quotient
Of the principles on which division is founded
Mode of proceeding, when the divisor consists of several figures 29
General rule for division
-
Method of abbreviating the process of division
30
31
When both the divisor and dividend have ciphers on the right 31
Multiplication and division mutually prove each other
32
Of the changes which 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
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 multiplication
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
46
47
48
50
51
52
54
55
A number containing decimals, not altered by annexing ciphers 56
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 60
The multiplication of one decimal by another
To divide a decimal number by a whole number
To divide one decimal by another
·
Method of approximating the quotient of a division by decimals
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
English Money
Troy Weight
Apothecaries' Weight
Avoirdupois Weight
Long Measure
Cloth Measure
68
69
70
71
To reduce other denominations of money, weight, and measure
To reduce a compound number to the lowest denomination con-
tained in it
88888
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
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
79
81
82
To reduce a decimal of a higher denomination to a lower
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