Elementary Algebra for the Use of Preparatory Schools |
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Page vii
... Unknown Quantities .. 119 IX . Problems .... 122 Miscellaneous Examples II .. 128 X. Factors .. 132 Factors of ax2 + bx + c ...... 142 Factors by Rearrangement of Terms .. 147 Quadratic Equations ... 151 CHAPTER PAGE XI . Highest Common ...
... Unknown Quantities .. 119 IX . Problems .... 122 Miscellaneous Examples II .. 128 X. Factors .. 132 Factors of ax2 + bx + c ...... 142 Factors by Rearrangement of Terms .. 147 Quadratic Equations ... 151 CHAPTER PAGE XI . Highest Common ...
Page 5
... quantities involved in it , the theory of algebra will eventually show that out of it may be evolved , by simple processes , the value of the impor- tant quantity x , the unknown quantity , which , when found , answers the question ...
... quantities involved in it , the theory of algebra will eventually show that out of it may be evolved , by simple processes , the value of the impor- tant quantity x , the unknown quantity , which , when found , answers the question ...
Page 94
... unknown quantity . 93. In the solution of equations frequent use is made of the following axioms : ( i . ) If we add to equals the same quantity , or equal quantities , the sums will be equal . Thus , if a = b , then a + c = b + c ...
... unknown quantity . 93. In the solution of equations frequent use is made of the following axioms : ( i . ) If we add to equals the same quantity , or equal quantities , the sums will be equal . Thus , if a = b , then a + c = b + c ...
Page 101
... unknown quantities must be expressed by means of algebraical symbols : we thus obtain equations , the roots of which are the required values of the unknown quantities . 100. In the present chapter we shall only consider problems in ...
... unknown quantities must be expressed by means of algebraical symbols : we thus obtain equations , the roots of which are the required values of the unknown quantities . 100. In the present chapter we shall only consider problems in ...
Page 109
... unknown . quantities can be satisfied by an indefinite number of pairs of values of the unknown quantities . Consider , for example , the equation x - 3y = 24 . It is clear that the equation is satisfied by the values y = 0 and x = 24 ...
... unknown . quantities can be satisfied by an indefinite number of pairs of values of the unknown quantities . Consider , for example , the equation x - 3y = 24 . It is clear that the equation is satisfied by the values y = 0 and x = 24 ...
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Common terms and phrases
7th term a²b a²b² a²x a²x² a³b ab² ab³ absolutely convergent algebraical expression arithmetic means ax² b₁ binomial theorem cents CHAPTER coefficients contain continued fraction convergent denote determinant difference digits Divide dividend division divisor equal equation x² example Find the factors Find the H. C. F. Find the number Find the square Find the sum Find the value finite formula geometrical progression given expression greater Hence indeterminate forms integer less letters limit logarithms monomial Multiply negative nth root number of terms obtain permutations positive integer powers Prove quadratic equation quotient remainder result Show Simplify simultaneous equations Solve the equation square root subtract surds unknown quantities x²y x²y² xy² xy³ zero
Popular passages
Page 46 - Multiplication is the process of taking one number as many times as there are units in another number.
Page 362 - Find the area of a circle whose radius is 12 feet, from the law that the area of a circle varies as the square of its radius.
Page 349 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 77 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 362 - ... that the volume of a sphere varies as the cube of its radius. 20. Find the radius of a sphere whose volume is equal to the sum of the volumes of three spheres whose radii are r, /, and r".