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 6
... Inequalities ... 92-93 CHAPTER V. EXTRACTION OF THE SQUARE ROOT OF NUMBERS . - OF ALGEBRAIC QUAN- TITIES . TRANSFORMATION OF RADICALS OF THE SECOND DEGREE . Extraction of the Square Root of Numbers . 93-96 Extraction of the Square Root ...
... Inequalities ... 92-93 CHAPTER V. EXTRACTION OF THE SQUARE ROOT OF NUMBERS . - OF ALGEBRAIC QUAN- TITIES . TRANSFORMATION OF RADICALS OF THE SECOND DEGREE . Extraction of the Square Root of Numbers . 93-96 Extraction of the Square Root ...
Σελίδα 13
... to be repeated here . These , with Davies ' Logic and Utility of Mathematics . § 278 . the signs of equality and inequality , together with the INTRODUCTION . 13 To Multiply Fractions 68-VII To Divide Fractions 68-VIII.
... to be repeated here . These , with Davies ' Logic and Utility of Mathematics . § 278 . the signs of equality and inequality , together with the INTRODUCTION . 13 To Multiply Fractions 68-VII To Divide Fractions 68-VIII.
Σελίδα 14
... inequality , together with the letters of the alphabet , are the elements of the algebraic language . The interpretation of the language of Algebra is the first thing to which the attention of a pupil should be directed ; and he should ...
... inequality , together with the letters of the alphabet , are the elements of the algebraic language . The interpretation of the language of Algebra is the first thing to which the attention of a pupil should be directed ; and he should ...
Σελίδα 17
... inequality , and is used to indicate 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 toward the greater ...
... inequality , and is used to indicate 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 toward the greater ...
Σελίδα 113
... inequality is the expression of two unequal quantities connected by the sign of inequality . Thus , ab is an ... INEQUALITIES . Inequalities 92-93.
... inequality is the expression of two unequal quantities connected by the sign of inequality . Thus , ab is an ... INEQUALITIES . Inequalities 92-93.
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Συχνά εμφανιζόμενοι όροι και φράσεις
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.