Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools and CollegesWinthrop B. Smith & Company, 1852 - 396 σελίδες |
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Σελίδα iv
... Second Degree have re- ceived more than usual attention . The same may be said of Radicals , of the Binomial Theorem , and of Logarithms , all of which are so useful in other branches of mathematics . On some subjects it was necessary ...
... Second Degree have re- ceived more than usual attention . The same may be said of Radicals , of the Binomial Theorem , and of Logarithms , all of which are so useful in other branches of mathematics . On some subjects it was necessary ...
Σελίδα vi
... Degree - Rule .. .152-153 Questions involving Equations of the First Degree .. 154 Simultaneous Equations of the First Degree containing two unknown quantities . 155 Elimination by Substitution . 156 by Comparison . 157 by Addition and ...
... Degree - Rule .. .152-153 Questions involving Equations of the First Degree .. 154 Simultaneous Equations of the First Degree containing two unknown quantities . 155 Elimination by Substitution . 156 by Comparison . 157 by Addition and ...
Σελίδα vii
... Degree containing Radicals . 214 216 INEQUALITIES - Propositions I to V ...... .217-224 Examples involving the principles of Inequalities 224 CHAPTER VII . EQUATIONS OF THE SECOND ... Second Degree .. 230 Completing the Square- General Rule ...
... Degree containing Radicals . 214 216 INEQUALITIES - Propositions I to V ...... .217-224 Examples involving the principles of Inequalities 224 CHAPTER VII . EQUATIONS OF THE SECOND ... Second Degree .. 230 Completing the Square- General Rule ...
Σελίδα viii
... Second Degree .. Formulæ - General Solutions Special Solutions and Examples .. CHAPTER VIII . RATIO - PROPORTION - PROGRESSIONS . Arithmetical - Geometrical . ARTICLES . 245 .246-250 251 252 253 RATIO - 254 - Antecedent and Consequent ...
... Second Degree .. Formulæ - General Solutions Special Solutions and Examples .. CHAPTER VIII . RATIO - PROPORTION - PROGRESSIONS . Arithmetical - Geometrical . ARTICLES . 245 .246-250 251 252 253 RATIO - 254 - Antecedent and Consequent ...
Σελίδα x
... Degree has n roots ... An Equation of the nth Degree has only n roots Relations of the Roots and Coëfficients of an ... SECOND . CHAPTER I. DEFINITIONS AND X CONTENTS .
... Degree has n roots ... An Equation of the nth Degree has only n roots Relations of the Roots and Coëfficients of an ... SECOND . CHAPTER I. DEFINITIONS AND X CONTENTS .
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Άλλες εκδόσεις - Προβολή όλων
Ray's Algebra, Part Second: An Analytical Treatise, Designed for High ... Joseph Ray Πλήρης προβολή - 1857 |
Συχνά εμφανιζόμενοι όροι και φράσεις
algebraic algebraic quantity arithmetical progression Binomial Theorem coëfficient continued fraction converging fraction cube root denominator denotes dividend divisible equa equal equation whose roots evident exactly divide EXAMPLES FOR PRACTICE exponent expressed extract the square Find the cube Find the greatest Find the number Find the square Find the sum find the value geometrical progression given number gives greater greatest common divisor Hence least common multiple less letters logarithm method minus monomial Multiply nth root nth term number of balls number of permutations number of terms operation perfect square polynomial positive root preceding proportion proposed equation quotient ratio real roots reduced remainder Required the numbers required to find result second degree second term square root Sturm's theorem substitute subtracted taken theorem third tion transformed transposing unknown quantity whence whole number zero
Δημοφιλή αποσπάσματα
Σελίδα 83 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 42 - 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 39 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Σελίδα 128 - 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 43 - 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 35 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.
Σελίδα 140 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Σελίδα 220 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12 ? Ans.
Σελίδα 183 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...
Σελίδα 28 - Multiply the coefficients of the two terms together, and to their product annex all the letters in both quantities, giving to each letter an exponent equal to the sum of its exponents in the two factors.