The Elements of Arithmetic

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J. Taylor, 1835 - Arithmetic - 190 pages
 

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Contents

article 40 is shortened and EXERCISES
54
ciphers
61
Process when there are ciphers in the multiplier
63
RULE OF MULTIPLICATION derived from the last two articles
64
Additional RULE when there are ciphers on the right hand
65
either factor 66 Definition of square cube c EXERCISES
66
Algebraic multiplications
67
Page 3656
68
Definition of division
69
Simplest process of division
70
Division the reverse of multiplication
71
Division not always possible without fractions
72
Result expressed algebraically
73
The same process performed by several smaller ones
74
Result expressed algebraically
75
Method of performing several of the subtractions at once
76
Assertions necessary to be understood before proceeding to
77
shortest process of division 78 Shortest process of division explained
78
Simplest way of writing the operations
79
RULE FOR DIVISION
80
Process when the divisor is less than 12 with various abbre
81
Process when the divisor is 1 followed by ciphers
82
Process when there are ciphers on the right hand of the divisor
83
EXERCISES in division and in the combination of the preceding
84
The quotient not altered by multiplying the divisor and dividend
85
by the same number 86 Reverse of this principle
86
If a number be multiplied or divided successively by two others
87
it is multiplied or divided by their product 88 89 If a number be multiplied by a second and divided by
88
third it is multiplied by the quotient of the second divided by the third or divided by the quotient of the third divided by the second 90 Preceding res...
90
Definition of a measure
91
Definition of a common measure and of the greatest common
92
that of the divisor and remainder
98
Method of taking into account the remainder of a division
104
LOWEST TERMS RULE and EXERCISES
110
in the last case consists of ciphers preceded by 1 EXERCISES
116
The same for three or more fractions
119
Simplification of the rules and EXERCISES
120
SION of fractions 122 123 Simplification of the rule and EXERCISES
122
Results of this section expressed algebraically
124
measure
125
Definition of decimal numbers and fractions
126
Use of the cipher in this notation
136
A decimal thus expressed is not altered by putting ciphers
137
its right 138 Reduction of decimals to a common denominator
138
ADDITION of decimal fractions and EXERCISES
139
SUBTRACTION of decimal fractions and EXERCISES
140
Multiplication of a decimal fraction by a decimal number
141
MULTIPLICATION of one decimal fraction by another
142
Division of a decimal fraction by a decimal number
144
Continuation of 128 and RULE
145
Continuation of 129 and RULE
146
first and those which are added by the rule 148 Modification of the rule when there are ciphers in the denomi EXERCISES
148
Process of DIVISION of one decimal by another
149
RULE for the process in the last article and EXERCISES
150
Method of correcting the last place of an approximate decimal
151
and EXAMPLES 152 Degree of dependence which may be placed on the multiplication
152
and division of approximate decimals RULE 153 154 RULE and EXAMPLES of contracted multiplication
153
RULE and EXAMPLES of contracted division For EXERCISE
155
Meaning of the term square root and notation
156
Algebraical illustration
157
Approximate square root
158
Deduction of the extraction of a square root from the formation
159
of a square 160 Example of the same
160
Reduction of the rule to its most convenient form
161
The same for the manner of writing the process
162
RULE for the extraction of the square root
163
Square root of a fraction
164
Approximate square root EXERCISES
165
RULE OF THREE
166
RULE for finding the same and EXAMPLES
167
RULE for doubling the number of decimals obtained
169
Definition of arithmetical proportion
170
Definition of arithmetical progression
171
RULE for summation of arithmetical progressions
172
Method of finding the last term EXERCISES
173
The sum c being given to find the common difference
174
EXERCISES
175
tables
179
means
182
APPENDIX Page
187
proportion without destroying the proportion
188
to d

Common terms and phrases

acres added alter annex ciphers arithmetical arithmetical series called cent column common denominator common difference CONNOP THIRLWALL contains 18 cubic inches decimal fraction decimal number decimal places decimal point DIONYSIUS LARDNER divided dividend division divisor equal example EXERCISES farthings following rule four numbers GEORGE DARLEY given greater greatest common measure Hence hund hundreds INDIANA UNIVERSITY INDIANENSIS last article last terms least common multiple length less mainder MDCCCXX miles multiple-part multiplicand number of ciphers number of decimal number of figures number of terms number or fraction numerator and denominator obtained pebbles pence permutations places of decimals pound proceed proportion quantity question reduced required to multiply result second remainder shew shewn shillings sides SIGILLUM square number square root Suppose it required taken tens thing third thousands twice VERITAS whole number write written

Bibliographic information

TitleThe Elements of Arithmetic
AuthorAugustus De Morgan
Edition3
PublisherJ. Taylor, 1835
Original fromIndiana University
DigitizedJun 22, 2011
Length190 pages
  
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