Elements of Algebra |
From inside the book
Results 1-5 of 6
Page 12
... inequality , and is used to express that one quantity is greater or less than another . Thus , a > b is read , a greater than b ; and a < b is read , a less than b ; that is , the opening of the sign is turned towards the greater ...
... inequality , and is used to express that one quantity is greater or less than another . Thus , a > b is read , a greater than b ; and a < b is read , a less than b ; that is , the opening of the sign is turned towards the greater ...
Page 105
... inequality . These exceptions arise from the introduction of negative expressions into the calculus , as quantities . In order that we may be clearly understood , we will take exam . ples of the different transformations that ...
... inequality . These exceptions arise from the introduction of negative expressions into the calculus , as quantities . In order that we may be clearly understood , we will take exam . ples of the different transformations that ...
Page 106
... inequality to the other . Take , for ex- ample , the inequality a2 + b2 > 3b - 2a2 ; there will result from it a2 + 2a2 > 362 - b2 , or 3a2 > 262 . 2. If two inequalities subsist in the same sense , and we add them member to member ...
... inequality to the other . Take , for ex- ample , the inequality a2 + b2 > 3b - 2a2 ; there will result from it a2 + 2a2 > 362 - b2 , or 3a2 > 262 . 2. If two inequalities subsist in the same sense , and we add them member to member ...
Page 107
... inequality would exist in a contrary sense . 4. It is not permitted to change the signs of the two members of an inequality unless we establish the resulting inequality in a contrary sense ; for this transformation is evidently the ...
... inequality would exist in a contrary sense . 4. It is not permitted to change the signs of the two members of an inequality unless we establish the resulting inequality in a contrary sense ; for this transformation is evidently the ...
Page 333
... inequality will become xm > kxm - 1 + kxm - 2 + ... + kx + k . It is evident that every number substituted for a which will satisfy this condition , will for a stronger reason , satisfy the preceding . Now , dividing this inequality by ...
... inequality will become xm > kxm - 1 + kxm - 2 + ... + kx + k . It is evident that every number substituted for a which will satisfy this condition , will for a stronger reason , satisfy the preceding . Now , dividing this inequality by ...
Other editions - View all
Elements of Algebra: Translated from the French of M. Bourdon; Revised and ... Charles Davies No preview available - 2017 |
Elements of Algebra: Translated From the French of M. Bourdon; Revised and ... Charles Davies No preview available - 2015 |
Common terms and phrases
affected algebraic quantities arithmetical arithmetical means arithmetical progression binomial cents co-efficient common difference common factor consequently contain contrary signs cube root decimal deduce denominator denote divide dividend division entire number enunciation equa equal equation involving example expression extract the cube extract the square figure find the values formula fourth fraction given number gives greater greatest common divisor Hence inequality last term least common multiple less letters taken logarithm manner monomial multiplicand multiplied negative nth power nth root number of terms obtain operation perfect square polynomial preceding problem progression proportion proposed equation proposed number quotient radical reduced remainder required root reserved letters result rule second degree second member second term square root substituted subtract suppose take the equation tens third tion total number transformation unity unknown quantity vulgar fraction whence whole number
Popular passages
Page 181 - C' then A is said to have the same ratio to B that C has to D ; or, the ratio of A to B is equal to the ratio of C to D.
Page 183 - D, we have — =— , (Art. 169) ; nj\ and by clearing the equation of fractions, we have BC=AD; that is, of four proportional quantities, the product of the two extremes is equal to the product of the two means.
Page 122 - These expressions may sometimes be simplified, upon the principle that, the square root of the product of two or more factors is equal to the product of the square roots of these factors; or, in algebraic language, V'abed . . . = i/a.
Page 181 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Page 114 - ... the entire part of the root sought. For example, if it were required to extract the square root of 665, we should find 25 for the entire part of the root, and a remainder of 40, which shows that 665 is not a perfect square. But is the square of 25 the greatest perfect square contained in 665 ? that is, is 25 the entire part of the root ? To prove this, we will first show that, the difference between the squares of two consecutive numbers, is equal to twice the less number augmented by unity.
Page 28 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
Page 33 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.
Page 267 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 146 - B, departed from different places at the same time, and travelled towards each other. On meeting, it appeared that A had travelled 18 miles more than B ; and that A could have gone B's journey in 15| days, but B would have been 28 days in performing A's journey. How far did each travel ? Ans.
Page 90 - If A and B together can perform a piece of work in 8 days, A and c together in 9 days, and B and c in 10 days, how many days will it take each person to perform the same work alone.