The student's algebra

Front Cover
1881
0 Reviews
Reviews aren't verified, but Google checks for and removes fake content when it's identified
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Multiplication of one Compound Quantity by another
53
When Divisor and Dividend contain more than one Letter
66
Division of one Compound Quantity by another
72
88899
76
When Coefficient of first Term of Divisor is greater than unity
79
Greatest Common Measure
83
Reversal of order of Terms in dividing
89
Least Common Multiple by Inspection
99
Least Common Multiple by finding G C M
101
Complex Fractions and their simplification
102
Continued Fractions
103
Addition and Subtraction of Fractions
104
Substitutions in Fractions
105
Fractions of the form
106
Fractions of the form the sign
107
Multiplication of a Fraction by a Fraction
115
PAGE 121
123
142
142
Fractions of the form Vanishing Fractions 109 General Theorems in Fractions signs 110 Fractional Equations
147
Problems involving Fractions
153
CHAPTER IX
162
162
163
164
164
First Method of Solution Substitution 114 Second MethodEquating or Comparison 115 Third Method Equalizing Coefficients 116 Problems produ...
171
Equations with three Unknown Quantities 118 Equations with four or more Unknown Quantities 171
178
Quantities
184
Indeterminate Multipliers
185
Cross Multiplication
189
Surd Equations 123 Meaning of the signs 124 Definition of a Surd 125 Multiplication of Surds
192
Multiplication by Detached Coefficients when Terms
193
Solution of Equations 127 Unsatisfactory Solutions
195
MISCELLANEOUS EXAMPLES
197
Propositions in Variation
206
EXAMINATION PAPERS
207
ANSWERS
215
PART II
233
ART CHAPTER XI PAGE 128 Involution
235
Signs of Odd and Even Powers
236
Definition of Binomial Trinomial etc
237
Expansion of Binomials of the form ax
238
Expansion of Trinomials and Polynomials
239
Evolution
241
Surds and Imaginary Quantities
242
Square Root of Compound Quantities
243
Adfected Quadratics
258
Rule for First Method
259
Second Method of Solution by completing Square
262
Rule for Second Method
263
Third Method by rendering Coefficient of x a Square
267
Equations that may be Solved like Quadratics
268
Problems Producing Quadratic Equations with One Un known Quantity
271
Double Value of Unknown Quantity in Problems yielding Quadratic Equations
272
Simultaneous Quadratic Equations
279
When the Equations are Symmetrical
280
When the Equations are Homogeneous
281
Method of Equating Constant Terms
282
Method of Symmetrical Solution
284
286
286
Quadratic Equations of Three Unknown Quantities 165 Problems Producing Quadratic Equations of two or more Unknown Quantities
292
Surds CHAPTER XIII
300
Different Kinds of Surds 170 Reduction of Surds 171 Preliminary Proposition
301
302
302
To bring a Product partly Rational partly Surd entirely to the Surd Form
303
To change the Index of a Surd
304
To bring two or more Surds to a Common Index
305
Addition and Subtraction of Surds 178 Multiplication and Division of Surds 179 Multiplication and Division by Fractional Indices 180 Compound S...
308
185
319
Theorems in Multiplication
324
Factors of Expressions of the form a+62 192 Surd Equations 325 327 185 Extraction of Roots of Surds
325
192
327
193
332
332
333
Equations involving Multiplication
334
197
336
CHAPTER IV
353
Geometrical Progression Definitions
364
215
365
To find the Sum to Infinity of a Decreasing Geometrical Series
370
CHAPTER XVII
385
The Number of Combinations of n things taken nr at
391
General Term
403
CHAPTER XIX
413
Common Logarithms
419
52
425
CHAPTER XX
427
59
436
EXAMINATION PAPERS
445

Other editions - View all

Common terms and phrases

Popular passages

Page 322 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 187 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Page 187 - A cask A contains 12 gallons of wine and 18 gallons of water; and another cask B contains 9 gallons of wine and 3 gallons of water; how many gallons must be drawn from each cask so as to produce by their mixture 7 gallons of wine and 7 gallons of water t 33.
Page 365 - Therefore the number of permutations of n things taken r at a time is n (n - l) (n - 2) (n-r+l).
Page 42 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — b) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 350 - ... the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.
Page 42 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Page 194 - A ship sails with a supply of biscuit for 60 days, at a daily allowance of a pound a head ; after being at sea 20 days she encounters a storm in which 5 men are washed overboard, and damage sustained that will cause a delay of 24 days, and it is found that each man's daily allowance must be reduced to fivesevenths of a pound.
Page 164 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Page 194 - A and B are two towns situated 24 miles apart, on the same bank of a river. A man goes from A to B in 7 hours, by rowing the first half of the distance, and walking the second half.

Bibliographic information