Elements of Algebra: Including Sturm's TheoremA. S. Barnes & Company, 1847 - 368 σελίδες |
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Σελίδα 7
... Ratios ... 182 Four Proportionals are Proportional Inversely ... 183 Four Proportionals are in Proportion by Composition or Division 184 Equi - multiples have the same Ratio as the Quantities .... 185 Proportion by augmenting Antecedent ...
... Ratios ... 182 Four Proportionals are Proportional Inversely ... 183 Four Proportionals are in Proportion by Composition or Division 184 Equi - multiples have the same Ratio as the Quantities .... 185 Proportion by augmenting Antecedent ...
Σελίδα 151
... ratio of the squares of these distances . Let the distance AB , between the two lights , be expressed by c ; the intensity of the light A , at the units distance , by a ; that of the light B , at the same distance , by b . Suppose C to ...
... ratio of the squares of these distances . Let the distance AB , between the two lights , be expressed by c ; the intensity of the light A , at the units distance , by a ; that of the light B , at the same distance , by b . Suppose C to ...
Σελίδα 168
... the last , 3xy = 108 ; by subtracting x2 2xy + y2 = 25 : hence , X - y = ± 5 . But , x + y : = 13 : hence , x = 9 , or 4 ; and y = 4 , or 9 . 6. Find the values of x and y , in 168 [ CHAP . VI ELEMENTS OF ALGEBRA . Ratio Defined.
... the last , 3xy = 108 ; by subtracting x2 2xy + y2 = 25 : hence , X - y = ± 5 . But , x + y : = 13 : hence , x = 9 , or 4 ; and y = 4 , or 9 . 6. Find the values of x and y , in 168 [ CHAP . VI ELEMENTS OF ALGEBRA . Ratio Defined.
Σελίδα 180
... Ratio is the quotient arising from dividing one quantity by another quantity of the same kind . Thus , if A and B repre- sent quantities of the same kind , the ratio of A to B is expressed by B Α ́ 169. If there be four magnitudes , A ...
... Ratio is the quotient arising from dividing one quantity by another quantity of the same kind . Thus , if A and B repre- sent quantities of the same kind , the ratio of A to B is expressed by B Α ́ 169. If there be four magnitudes , A ...
Σελίδα 181
... ratios . 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 and read , A is to B , as C is to D. : D , The quantities which are compared together are called the terms of the ...
... ratios . 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 and read , A is to B , as C is to D. : D , The quantities which are compared together are called the terms of the ...
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affected algebraic quantities arithmetical arrangements becomes binomial called co-efficient common difference consequently contain continued fraction contrary signs cube root decimal deduced denominator 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 manner 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 required to find resolved result rule second degree second member second term simplest form square root substituted subtract superior limit suppose take the equation taken third tion transformed transposing unity unknown quantity whence whole number
Δημοφιλή αποσπάσματα
Σελίδα 277 - 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.
Σελίδα 29 - 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.
Σελίδα 348 - 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.
Σελίδα 33 - 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.
Σελίδα 111 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 298 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Σελίδα 204 - 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.
Σελίδα 182 - 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.
Σελίδα 27 - We have seen that multiplying by a whole number is taking the multiplicand as many times as there are units in the multiplier.
Σελίδα 115 - ... equal to the square root of the numerator divided by the square root of the denominator.