Examples of Multiplication, with Explanation of the Process 57 30

General Rule and Examples

64

Product of Two General Expressions of Number

Product of Three Factors

67

Proof that axb+a×c=a(b+c)

Product of any Number of Factors

Definitions of the Terms Multiple, Sub-Multiple, Square,

Cube, Square Root, and Cube Root

Number of Figures contained in the Product of Two given

Numbers

Multiplication of General Expressions of Number

72

73

74 38

56 29

70 36

71 37

37

37

26

34

SECTION V. DIVISION OF WHOLE NUMBERS.

Principles

Examples of Division, with Explanation of the Process

Abridged Form of Division

General Rule and Examples

Case of One Dividend and Two or more Divisors

Division by the Factors of a Divisor

Division of General Expressions of Number

Verifications of Multiplication and Division

SECTION VI. DIVISIBILITY OF NUMBERS. GREATEST COMMON

MEASURE AND LEAST COMMON MULTIPLE OF TWO OR

MORE NUMBERS.

Definitions and Principles

103

Investigation of the Greatest Common Measure of Two

Numbers

107

Rule for finding the Greatest Common Measure of Two

Numbers

108

Conditions under which Numbers either are, or are not, prime
with other Numbers

Tests of the Divisibility of Numbers by certain Divisors

Prime Numbers between 1 and 100

109

119 62

130 65

Verifications of Multiplication and Division from Properties

of the Number 9

131 65

Definition of a Composite Number

132

Formula comprehending all Prime Numbers greater than 3

Research of the Prime Factors of a Number

Composition of the Greatest Common Measure of Three or

more Numbers

Least Common Multiple of Two or more Numbers

Remark on Division of whole Numbers

66

68

69

69

SECTION VI.* FRACTIONS.

Definitions and Principles

Reduction of a Fraction to the lowest Terms

Reduction of an Improper Fraction to a Mixed Number

Reduction of a Mixed Number to an Improper Fraction

Reduction of Fractions to the same Denominator

Reduction of Fractions to the Least Common Denominator
Rules and Examples for Articles 160, 161, 162, 163
Addition of Fractions

Remarks on Multiplication and Division of Fractions

Reduction of a Complex to a Simple Fraction

The Number VI. has been given by mistake to the last Section, and also

to this.

SECTION VIII. OF THE SQUARE, SQUARE ROOT, CUBE, AND

CUBE ROOT OF NUMBERS.

Composition of the Square of a Number

Extraction of the Square Root of a Whole Number

Rule and Examples

Tests for the Discovery of Square Numbers

-

Approximation to the Square Root of a Number which is not

a perfect Square

Extraction of the Square Root of a Vulgar Fraction

Extraction of the Square Root of a Decimal Fraction

Examples for Articles 265-269

Composition of the Cube of a Number

Extraction of the Cube Root of a Whole Number

Rule and Examples

Tests for the Discovery of Cube Numbers

Approximation to the Cube Root of a Number which is not

a perfect Cube

Extraction of the Cube Root of a Vulgar Fraction

Extraction of the Cube Root of a Decimal Fraction

Examples for Articles 276-279

SECTION IX. OF DIFFERENT SYSTEMS OF NUMERATION.

General Principles

Reduction of Numbers from one System to another

Of the Names of Numbers in different Systems

Of the Roman and Grecian Notation

Comparison of the Decimal with the ancient Systems

SECTION X. TABLES OF BRITISH WEIGHTS AND MEASURES.

REDUCTION, ADDITION, SUBTRACTION, MULTIPLICATION,

AND DIVISION OF COMPOUND NUMBERS. RULE OF

ALIQUOT PARTS.

Formation and Use of Compound Numbers

Of principal and subordinate Units

293 156

295 157

296 158

Tables of Weights and Measures

297 160

Multiplication Table to 25 × 25

297 163

Reduction of Compound Numbers from higher Denominations

to lower

Of different Expressions of the same absolute Quantity by

means of Compound Numbers

298 164

299 164

Reduction of a Fraction to a Compound Number expressed in

Terms of lower Denominations

Reduction of Numbers from lower Denominations to higher

Reduction of a Compound Number to a Fraction expressed in

Terms of any given Denomination

Reduction from one Weight or Measure to another

Of the Application of the elementary Operations of Arithmetic

to Compound Numbers

317 176

Addition of Compound Numbers

318 177

Subtraction of Compound Numbers

319 180

Multiplication of a Compound Number by a Whole Number

Division of a Compound Number by a Whole Number

320 183

321 187