A Treatise on AlgebraHarper & brothers, 1846 - 346 páginas |
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Página 10
... prob- lems , which are too difficult for common Arithmetic . Some of the problems in Sections VII . and VIII . may be solved by Arith- metical methods ; but others cannot be thus resolved , 10 PRELIMINARY DEFINITIONS AND NOTATION .
... prob- lems , which are too difficult for common Arithmetic . Some of the problems in Sections VII . and VIII . may be solved by Arith- metical methods ; but others cannot be thus resolved , 10 PRELIMINARY DEFINITIONS AND NOTATION .
Página 80
... Prob . 2. What number is that , the double of which exceeds its half by 6 ? Let x = the number required . Then by the conditions 2x - Ꮖ = 6 . Clearing of fractions 4x x = 12 or Hence 3x = 12 . x = 4 . To verify this result , double 4 ...
... Prob . 2. What number is that , the double of which exceeds its half by 6 ? Let x = the number required . Then by the conditions 2x - Ꮖ = 6 . Clearing of fractions 4x x = 12 or Hence 3x = 12 . x = 4 . To verify this result , double 4 ...
Página 81
... Prob . 3. The sum of two numbers is 8 , and their difference 2 . What are the two numbers ? Let x = the least number . 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 the two numbers ? Let x = the least number . 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 82
... Prob . 5. From two towns which are 54 miles distant , two travelers set out at the same time with an intention of meeting . One of them goes 4 miles and the other 5 miles per hour . In how many hours will they meet ? Let x represent the ...
... Prob . 5. From two towns which are 54 miles distant , two travelers set out at the same time with an intention of meeting . One of them goes 4 miles and the other 5 miles per hour . In how many hours will they meet ? Let x represent the ...
Página 83
... 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 ...
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Términos y frases comunes
according to Art algebraic arithmetical binomial Charles Anthon coefficient common denominator Completing the square contrary sign cube root cubic equation deduce denotes Divide the number dividend divisible equation containing equation whose roots equation x³ exponent expression Extracting the root extracting the square factors find the values following RULE fourth power fourth root given equation greatest common divisor Hence inequality infinite series last term less logarithm method miles monomial multiplied negative nth root number of terms obtain order of differences original equation polynomial positive Prob problem PROPOSITION quadratic equations quotient radical quantities ratio real roots remainder Required the cube Required the fourth Required the square Required the sum result second degree second term Sheep extra simple form solved square root Sturm's Theorem subtract surd Theorem unknown quantity variation Whence whole number
Pasajes populares
Página 38 - 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.
Página 37 - THEOREM I. 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.
Página 91 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Página 332 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Página 33 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Página 138 - The nth root of the product of any number of factors is equal to the product of the nth roots of those factors.
Página 168 - 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 31 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.
Página 4 - A Grammar of the Greek Language, for the Use of Schools and Colleges. By Charles Anthon, LL.D.
Página 213 - When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of proportionals.