Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems : and Practical Examples |
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Page 93
... equation by 3 and the second by 4 ; and since the co - efficients of z have contrary signs , add the two results ... proposed equations becomes , 15-24 + 4x = 15 , whence z = 6 . If we have a group of m simultaneous equations ...
... equation by 3 and the second by 4 ; and since the co - efficients of z have contrary signs , add the two results ... proposed equations becomes , 15-24 + 4x = 15 , whence z = 6 . If we have a group of m simultaneous equations ...
Page 94
... equation containing one unknown quantity . IV . Find the value of this unknown quantity by the rule for solving ... proposed equations do not contain all the unknown quantities . In this case , with a little address , the ...
... equation containing one unknown quantity . IV . Find the value of this unknown quantity by the rule for solving ... proposed equations do not contain all the unknown quantities . In this case , with a little address , the ...
Page 173
... equation of the second degree , containing two unknown quantities , is of the general form ay2 + bxy + cx2 + dy + fx ... proposed equations , will give a final equation , involving only y . But without effecting the substitution ...
... equation of the second degree , containing two unknown quantities , is of the general form ay2 + bxy + cx2 + dy + fx ... proposed equations , will give a final equation , involving only y . But without effecting the substitution ...
Page 204
... equation to the mth power a = bmn . Extracting the mnth root of both members of the last equation , we have , and ... proposed number . Extraction of Roots by Approximation . 144. When it is 204 [ CHAP . VIL ELEMENTS OF ALGEBRA .
... equation to the mth power a = bmn . Extracting the mnth root of both members of the last equation , we have , and ... proposed number . Extraction of Roots by Approximation . 144. When it is 204 [ CHAP . VIL ELEMENTS OF ALGEBRA .
Page 252
... equation containing but one indeterminate quan- tity , the co - efficients of the like powers of that quantity in ... proposed form , 252 [ CHAP . VIII . ELEMENTS OF ALGEBRA .
... equation containing but one indeterminate quan- tity , the co - efficients of the like powers of that quantity in ... proposed form , 252 [ CHAP . VIII . ELEMENTS OF ALGEBRA .
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Common terms and phrases
algebraic quantity approximating fraction arithmetical arithmetical progression becomes binomial formula called co-efficient common difference continued fraction contrary signs cube root deduce denote the number derived polynomial divide dividend division entire number equal example exponent extract the square figures Find the square find the values following RULE formula given equation given number gives greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple less logarithm monomial multiplicand multiplied negative roots nth power nth root number of terms obtain operation perfect square positive roots preceding problem progression proposed equation quotient radical sign real roots Reduce remainder required root required to find result second degree second member second term simplest form square root subtract superior limit suppose taken third transformed equation unknown quantity whence whole number X₁
Popular passages
Page 99 - A person has two horses, and a saddle worth £50 ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first ; what is the value of each horse ? Ans.
Page 364 - 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 118 - X 6 62 + 3 x 3; and taken 3 tens times, 32 + 2 (3 X 6) + 6s gives 3 x 6 + 32 ; and their sum is, 33 + 2 (3 x 6) + 63 : that is, Rule. — The square of a number is equal to the square of the tens, plus twice the product of the tens by the units, plus the square of the units.
Page 174 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 39 - 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 200 - Subtract the cube of this number from the first period, and to the remainder bring down the first figure of the next period for a, dividend.
Page 242 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 215 - Resolve the quantity under the radical sign into two factors, one of which is the highest perfect power of the same degree as the radical. Extract the required root of this factor, and prefix the result to the indicated root of the other.
Page 41 - Divide the coefficient of the dividend by the coefficient of the divisor.
Page 10 - Logic is a portion of the art of thinking; language is evidently, and by the admission of all philosophers, one of the principal instruments or helps of thought; and any imperfection in the instrument or in the mode of employing it is confessedly liable, still more than in almost any other art, to confuse and impede the process and destroy all ground of confidence in the result.