Elements of Algebra: Including Sturms' Theorem |
From inside the book
Results 1-5 of 27
Page 24
... units contained in 26 , the number taken away from 4a , is too great by the number of units contained in 3c , and the result 26 is therefore too small by 3c ; this remainder must there- fore be corrected by adding 3c to it . Hence ...
... units contained in 26 , the number taken away from 4a , is too great by the number of units contained in 3c , and the result 26 is therefore too small by 3c ; this remainder must there- fore be corrected by adding 3c to it . Hence ...
Page 26
... units expressed by a , and the number of units expressed by b . Consequently , this result is numerically less than a . To distinguish this sum from an arithmetical sum , it is called the algebraic sum . Thus , the polynomial , 2a3 ...
... units expressed by a , and the number of units expressed by b . Consequently , this result is numerically less than a . To distinguish this sum from an arithmetical sum , it is called the algebraic sum . Thus , the polynomial , 2a3 ...
Page 27
Including Sturms' Theorem Charles Davies. cal difference between the sum of the units contained in the ad- ditive terms , and the sum of the units contained in the subtractive terms . It follows from this , that an algebraic sum may , in ...
Including Sturms' Theorem Charles Davies. cal difference between the sum of the units contained in the ad- ditive terms , and the sum of the units contained in the subtractive terms . It follows from this , that an algebraic sum may , in ...
Page 28
... units in cd . Let us first multiply by c ; that is , take a - b as many times as there are units in c . We begin by wri- ting ac , which is too great by b taken - a b C - d ac - ac - bc ad + bd - bc ― ad + bd . c times ; for it is only ...
... units in cd . Let us first multiply by c ; that is , take a - b as many times as there are units in c . We begin by wri- ting ac , which is too great by b taken - a b C - d ac - ac - bc ad + bd - bc ― ad + bd . c times ; for it is only ...
Page 47
... units in the denominator , and one of these parts is supposed to be taken as many times as there are units in the numerator . Thus , in the fractional expression a + b c + ď a given unit is supposed to be divided into as many equal ...
... units in the denominator , and one of these parts is supposed to be taken as many times as there are units in the numerator . Thus , in the fractional expression a + b c + ď a given unit is supposed to be divided into as many equal ...
Contents
70 | |
98 | |
104 | |
113 | |
119 | |
126 | |
132 | |
144 | |
151 | |
157 | |
163 | |
169 | |
175 | |
187 | |
193 | |
262 | |
272 | |
279 | |
286 | |
292 | |
300 | |
307 | |
318 | |
327 | |
333 | |
341 | |
349 | |
361 | |
367 | |
Other editions - View all
Common terms and phrases
affected algebraic quantities arithmetical arrangements becomes binomial called co-efficient common difference consequently contain continued fraction contrary signs cube root decimal deduced denominator divide dividend division entire number enunciation equa equal equation involving example exponent factors figure formula fourth given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm method monomial multiply nth root number of terms obtain operation ounces perfect square positive roots preceding problem progression proposed equation quan quotient real roots Reduce remainder resolved result rule second degree second member second term simplest form square root substituted subtract superior limit suppose take the equation taken third tion tities transformed transposing unity unknown quantity whence whole number
Popular passages
Page 30 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 275 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 27 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Page 179 - 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 180 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
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 would it take each person to perform the same work alone ? Ans.
Page 346 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots to , the number of permanences.
Page 34 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Page 108 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 202 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.