Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools and Colleges |
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Page iii
... principle , and to fur- nish the student the means of understanding clearly the rationale of every process he is required to perform . No effort has been made to simplify subjects by omitting that which is difficult , but rather to ...
... principle , and to fur- nish the student the means of understanding clearly the rationale of every process he is required to perform . No effort has been made to simplify subjects by omitting that which is difficult , but rather to ...
Page iv
... principles . The limits of a preface will not permit a statement of the pecu- liarities of the work , nor is it necessary , as those who are in- terested to know , will examine it for themselves . It is , however , proper to remark ...
... principles . The limits of a preface will not permit a statement of the pecu- liarities of the work , nor is it necessary , as those who are in- terested to know , will examine it for themselves . It is , however , proper to remark ...
Page v
... principle 47-51 52-53 Rule of the Coëfficients Rule of the Exponents . Rule of the Signs 55 56 60 61 62 63-66 ... Principles of factoring numbers . Factoring of Algebraic quantities GREATEST COMMON DIVISOR . LEAST COMMON MULTIPLE 128 78 ...
... principle 47-51 52-53 Rule of the Coëfficients Rule of the Exponents . Rule of the Signs 55 56 60 61 62 63-66 ... Principles of factoring numbers . Factoring of Algebraic quantities GREATEST COMMON DIVISOR . LEAST COMMON MULTIPLE 128 78 ...
Page vi
... principles 140-149 Transposition ..... 150 To clear an Equation of Fractions .. 151 Solution of Equations of the First Degree - Rule .. .152-153 Questions involving Equations of the First Degree .. 154 Simultaneous Equations of the ...
... principles 140-149 Transposition ..... 150 To clear an Equation of Fractions .. 151 Solution of Equations of the First Degree - Rule .. .152-153 Questions involving Equations of the First Degree .. 154 Simultaneous Equations of the ...
Page vii
... principles of Inequalities 224 CHAPTER VII . EQUATIONS OF THE SECOND DEGREE . Definitions and Forms 224-226 Incomplete Equations 227-228 Questions producing Incomplete Equations .. 229 Complete Equations of the Second Degree .. 230 ...
... principles of Inequalities 224 CHAPTER VII . EQUATIONS OF THE SECOND DEGREE . Definitions and Forms 224-226 Incomplete Equations 227-228 Questions producing Incomplete Equations .. 229 Complete Equations of the Second Degree .. 230 ...
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Common terms and phrases
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
Popular passages
Page 83 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.
Page 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...
Page 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.