A Treatise on AlgebraHarper & Brothers, 1873 - 360 páginas |
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Página 25
... proposed to be subtracted is less than c by d , too much has been taken away by d , and there- fore the true remainder will be greater than a - b - c by d , and may hence be expressed thus , a - b - c + d , where the signs of the last ...
... proposed to be subtracted is less than c by d , too much has been taken away by d , and there- fore the true remainder will be greater than a - b - c by d , and may hence be expressed thus , a - b - c + d , where the signs of the last ...
Página 35
... proposed to multiply 8-5 by 6-2 ; that is , the quantity 8-5 is to be repeated as many times as there are units in 6-2 . If we multiply 8-5 by 6 , we obtain 48-30 ; that is , we have repeated 8-5 six times . But it was only required to ...
... proposed to multiply 8-5 by 6-2 ; that is , the quantity 8-5 is to be repeated as many times as there are units in 6-2 . If we multiply 8-5 by 6 , we obtain 48-30 ; that is , we have repeated 8-5 six times . But it was only required to ...
Página 45
... proposed dividend , the remainder may be regarded as the product of the divisor by the remaining terms of the quotient . We shall then ob- tain another term of the quotient by dividing that term of the remainder which is affected with ...
... proposed dividend , the remainder may be regarded as the product of the divisor by the remaining terms of the quotient . We shall then ob- tain another term of the quotient by dividing that term of the remainder which is affected with ...
Página 67
... proposed fractions , and they have the common denominator bdn . Hence we have the following RULE . Multiply each numerator into all the denominators , except its own , for a new numerator , and all the denominators together for the ...
... proposed fractions , and they have the common denominator bdn . Hence we have the following RULE . Multiply each numerator into all the denominators , except its own , for a new numerator , and all the denominators together for the ...
Página 72
... proposed multiplier was ; that is , we have used a multiplier d times too great . We must therefore divide the result by d ; and , according to the second principle of Art . 109 , we obtain ac bd a с ас ; that is , & = bd bd Hence we ...
... proposed multiplier was ; that is , we have used a multiplier d times too great . We must therefore divide the result by d ; and , according to the second principle of Art . 109 , we obtain ac bd a с ас ; that is , & = bd bd Hence we ...
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Términos y frases comunes
algebraic algebraic quantity arithmetical progression binomial binomial theorem cent Clearing of fractions coefficient common difference continued fraction cube root decimal denote digits diminished Divide the number dividend divisible dollars equa equal equation whose roots equations containing 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 four fourth power fourth root geometrical progression greatest common divisor Hence indicates inequality infinite series last term least common multiple less logarithm monomial negative nth root number of terms obtain positive pounds preceding problem quotient radical sign ratio real roots Reduce remainder represent Resolve result second degree second term simultaneous equations Solve the equation square root Sturm's Theorem suppose surd three numbers tion unity unknown quantity whence whole number zero
Pasajes populares
Página 97 - 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 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.
Página 284 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Página 258 - We may obtain the sixth root by extracting the cube root of the square root, or the square root of the cube root. It is, however, best to extract the roots of the lowest degrees first, because the operation is less laborious. We may obtain the eighth root by extracting the square root three times successively.
Página 371 - ... force of attraction to vary directly as the quantity of matter, and inversely as the square of the distance, at what point between them will a third body be equally attracted by the earth and moon ? Ans.
Página 42 - Divide the coefficient of the dividend by the coefficient of the divisor.
Página 38 - 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 101 - RULE. Find an expression for the value of one of the unknown quantities in one of the equations, and substitute this value for the same unknown quantity in the other equation.
Página 139 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.