A Treatise on AlgebraHarper & Brothers, 1873 - 360 páginas |
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Página 28
... equivalent to or to or to a - b - c + d a— ( b + c ― d ) , a - b- ( c - d ) , a + d- ( b + c ) . These expressions are all equivalent , the first form being the simplest . EXAMPLES . Reduce the following expressions to their simplest ...
... equivalent to or to or to a - b - c + d a— ( b + c ― d ) , a - b- ( c - d ) , a + d- ( b + c ) . These expressions are all equivalent , the first form being the simplest . EXAMPLES . Reduce the following expressions to their simplest ...
Página 29
... equivalent to m + n , and m + ( - n ) But m − ( + n ) and m - ( - n ) " " " 6 " " m - n . m — n , m + n . The sign immediately preceding n is called the sign of the quantity ; the sign preceding the parenthesis may be called the sign ...
... equivalent to m + n , and m + ( - n ) But m − ( + n ) and m - ( - n ) " " " 6 " " m - n . m — n , m + n . The sign immediately preceding n is called the sign of the quantity ; the sign preceding the parenthesis may be called the sign ...
Página 33
... equivalent to aaa , and a2 to aa . Therefore the product will be aaaaa , which may be written a3 , a result which is obtained by adding together 3 and 2 , the exponents of the common letter a . Hence we see that the exponent of any ...
... equivalent to aaa , and a2 to aa . Therefore the product will be aaaaa , which may be written a3 , a result which is obtained by adding together 3 and 2 , the exponents of the common letter a . Hence we see that the exponent of any ...
Página 43
... equivalent to a2 ' Hence a - 2 is equivalent to 1 So , also , if a2 is to be divided by a5 , this may be written a2 = 1 a In the same manner , we find 1 - · = that is , any quantity having a negative exponent is equal to the reciprocal ...
... equivalent to a2 ' Hence a - 2 is equivalent to 1 So , also , if a2 is to be divided by a5 , this may be written a2 = 1 a In the same manner , we find 1 - · = that is , any quantity having a negative exponent is equal to the reciprocal ...
Página 64
... equivalent to + - Ꮳ When no sign is prefixed either to the terms of a fraction or to its dividing line , plus is always to be understood . Reduction of Fractions . 112. To reduce a Fraction to its Lowest Terms . - A fraction is in its ...
... equivalent to + - Ꮳ When no sign is prefixed either to the terms of a fraction or to its dividing line , plus is always to be understood . Reduction of Fractions . 112. To reduce a Fraction to its Lowest Terms . - A fraction is in its ...
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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.