Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems : and Practical ExamplesA.S. Barnes & Burr, 1860 - 400 σελίδες |
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Σελίδα 7
... Exponents . CHAPTER VIII . .159-160 ..160-162 .162-164 ..164-171 OF SERIES.- . -ARITHMETICAL PROGRESSION . GEOMETRICAL PROFORTION AND PROGRESSION . - RECURRING SERIES.BINOMIAL SUMMATION OF SERIES .-- PILING OF SHOT AND SHELLS . FORMULA ...
... Exponents . CHAPTER VIII . .159-160 ..160-162 .162-164 ..164-171 OF SERIES.- . -ARITHMETICAL PROGRESSION . GEOMETRICAL PROFORTION AND PROGRESSION . - RECURRING SERIES.BINOMIAL SUMMATION OF SERIES .-- PILING OF SHOT AND SHELLS . FORMULA ...
Σελίδα 18
... exponent , and indicates that a is taken 5 times as a factor . Hence , an exponent is a number written to the right and above a quantity , to show how many times it is taken as a factor . If no exponent is written , the exponent 1 is ...
... exponent , and indicates that a is taken 5 times as a factor . Hence , an exponent is a number written to the right and above a quantity , to show how many times it is taken as a factor . If no exponent is written , the exponent 1 is ...
Σελίδα 21
... exponents of the letters which enter it . For example , the term Sa2bcd3 is of the seventh degree , since the sum of the expo- nents , 2 + 1 + 1 + 3 , is equal to 7 . 26. A polynomial is said to be homogeneous , when all of its terms ...
... exponents of the letters which enter it . For example , the term Sa2bcd3 is of the seventh degree , since the sum of the expo- nents , 2 + 1 + 1 + 3 , is equal to 7 . 26. A polynomial is said to be homogeneous , when all of its terms ...
Σελίδα 23
... exponents . 30. A THEOREM is a general truth , which is made evident by a course of reasoning called a demonstration . A PROBLEM is a question proposed which requires a solution . 31. We shall now illustrate the utility and brevity of ...
... exponents . 30. A THEOREM is a general truth , which is made evident by a course of reasoning called a demonstration . A PROBLEM is a question proposed which requires a solution . 31. We shall now illustrate the utility and brevity of ...
Σελίδα 33
... exponent of each letter is equal to the sum of the exponents of that letter in both multiplicand and multiplier . And since the same course of reasoning may be applied 3 CHAP . II . ] 33 MULTIPLICATION .
... exponent of each letter is equal to the sum of the exponents of that letter in both multiplicand and multiplier . And since the same course of reasoning may be applied 3 CHAP . II . ] 33 MULTIPLICATION .
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algebraic expression algebraic quantities approximating fraction arithmetical arithmetical progression becomes binomial called co-efficient common difference contrary signs cube root deduce denote the number derived polynomial Divide dividend entire number equal exactly divisible example exponent extract the square figures Find the factors find the values following RULE formula fractional unit given equation given number gives greater number greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple logarithm mixed quantity monomial multiplicand and multiplier nth power nth root number of terms obtain operation perfect square positive roots preceding problem proposed equation quotient radical sign real roots Reduce the polynomial remainder required to find result second degree second member second term simplest form square root substituted subtract suppose taken third transformed equation unknown quantity whence whole number X₁
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 174 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 41 - Divide the coefficient of the dividend by the coefficient of the divisor.
Σελίδα 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.