A Treatise on AlgebraHarper & brothers, 1846 - 346 páginas |
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Página 12
... whole numbers , they are in some cases confined within certain limits , and in others the problem may be impossible . ( 10. ) The solution of a problem is the process by which we obtain the answer to it . A numerical solution is the ...
... whole numbers , they are in some cases confined within certain limits , and in others the problem may be impossible . ( 10. ) The solution of a problem is the process by which we obtain the answer to it . A numerical solution is the ...
Página 15
... whole number or a fraction . Thus , a signifies three - fourths of a . coefficient is expressed , 1 is always to be understood . and a signify the same thing . When no Thus , 1 a The coefficient may be a letter as well as a figure . In ...
... whole number or a fraction . Thus , a signifies three - fourths of a . coefficient is expressed , 1 is always to be understood . and a signify the same thing . When no Thus , 1 a The coefficient may be a letter as well as a figure . In ...
Página 28
... whole may be expressed algebraically , thus : + 50-27 + 15-22 which reduced , equals 16. The positive sign of the result , indicates that the ship was 16 miles north of the equa- tor . Suppose the same ship sails again 8 miles north ...
... whole may be expressed algebraically , thus : + 50-27 + 15-22 which reduced , equals 16. The positive sign of the result , indicates that the ship was 16 miles north of the equa- tor . Suppose the same ship sails again 8 miles north ...
Página 29
... whole may be expressed algebraically , thus : + 1000- 300 + 100 - - 400 which reduced , equals +400 . The + sign of the result indicates that he has now 400 dollars remaining in his possession . Sup- pose he further gains 50 dollars and ...
... whole may be expressed algebraically , thus : + 1000- 300 + 100 - - 400 which reduced , equals +400 . The + sign of the result indicates that he has now 400 dollars remaining in his possession . Sup- pose he further gains 50 dollars and ...
Página 35
... whole doctrine of multiplication . Multiply each term of the multiplicand , by each term of the multi- plier , and add together all the partial products , observing that like signs require + in the product , and unlike signs ...
... whole doctrine of multiplication . Multiply each term of the multiplicand , by each term of the multi- plier , and add together all the partial products , observing that like signs require + in the product , and unlike signs ...
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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.