A Treatise on AlgebraHarper & Brothers, 1868 - 384 páginas |
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Página 88
... Prob . 1. What number is that , to the double of which if 16 be added , the sum is equal to four times the required number ? Let x represent the number required . The double of this will be 2x . This increased by 16 should equal 4x ...
... Prob . 1. What number is that , to the double of which if 16 be added , the sum is equal to four times the required number ? Let x represent the number required . The double of this will be 2x . This increased by 16 should equal 4x ...
Página 89
... Prob . 3. The sum of two numbers is 8 , and their difference 2. What are those numbers ? Let the least number . x = Then x + 2 will be the greater number . The sum of these is 2x + 2 , which is required to equal 8 . Hence we have By ...
... Prob . 3. The sum of two numbers is 8 , and their difference 2. What are those numbers ? Let the least number . x = Then x + 2 will be the greater number . The sum of these is 2x + 2 , which is required to equal 8 . Hence we have By ...
Página 90
... Prob . 5. From two towns which are 54 miles distant , two travelers set out at the same time with an intention of meet- ing . One of them goes 4 miles and the other 5 miles per hour . In how many hours will they meet ? Let x represent ...
... Prob . 5. From two towns which are 54 miles distant , two travelers set out at the same time with an intention of meet- ing . One of them goes 4 miles and the other 5 miles per hour . In how many hours will they meet ? Let x represent ...
Página 91
... Prob . 5 ; but they are all solved by the formula of Prob . 6. We also see what is necessary in order that the answers may be obtained in whole numbers . The given distance ( a ) must be exactly divisible by m + n . Prob . 7. A ...
... Prob . 5 ; but they are all solved by the formula of Prob . 6. We also see what is necessary in order that the answers may be obtained in whole numbers . The given distance ( a ) must be exactly divisible by m + n . Prob . 7. A ...
Página 92
... Prob . 10. Find a number such that when multiplied success- ively by m and by n , the difference of the products shall be a Ans . α m- m — n Prob . 11. A gentleman , dying , bequeathed 1000 dollars to three servants . A was to have ...
... Prob . 10. Find a number such that when multiplied success- ively by m and by n , the difference of the products shall be a Ans . α m- m — n Prob . 11. A gentleman , dying , bequeathed 1000 dollars to three servants . A was to have ...
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Términos y frases comunes
algebraic arithmetical progression binomial binomial theorem cent coefficient common denominator common difference compound interest continued fraction cube root decimal denote digits Divide the number dividend divisible dollars equa equal equation whose roots EXAMPLES exponent expression Extract the square factors figure Find the cube Find the fifth Find the fourth Find the number Find the square Find the sum find the values following RULE fourth power geometrical progression Given greatest common divisor Hence indicates infinite series last term least common multiple less logarithm miles monomial Multiply negative nth root number of terms obtain polynomial positive preceding Prob problem quotient radical sign ratio real roots Reduce remainder represent Resolve result second degree second term Solve the equation square root Sturm's Theorem subtract suppose surd third tion unity unknown quantity whence whole number zero
Pasajes populares
Página 72 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Página 141 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Página 39 - ... the square of the second. In the second case, (ab)2 = a?-2ab + bi. (2) That is, the square of the difference of two numbers is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Página 54 - Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.
Página 46 - 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.
Página 181 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left. How much wine did he draw each time ? 50.
Página 227 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.
Página 204 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Página 220 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Página 202 - A , where m=c 9. Find two numbers such that their sum, their product, and the difference of their squares may be all equal to one another.