A Treatise on AlgebraHarper & Brothers, 1873 - 360 páginas |
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Página 9
... assumed standard is called the unit of measure . 2. Mathematics is the science of quantity , or the science which treats of the properties and relations of quantities . It employs a variety of symbols to express the values and relations ...
... assumed standard is called the unit of measure . 2. Mathematics is the science of quantity , or the science which treats of the properties and relations of quantities . It employs a variety of symbols to express the values and relations ...
Página 114
... assume for particular hy- potheses made upon the values of the given quantities , and to interpret the peculiar results obtained . We have seen that if the sum of two numbers is represented by a , and their differ- the less by ab 2 a + ...
... assume for particular hy- potheses made upon the values of the given quantities , and to interpret the peculiar results obtained . We have seen that if the sum of two numbers is represented by a , and their differ- the less by ab 2 a + ...
Página 172
... assume √a + √b = √x + √y . ( 1. ) By squaring , a + √b = x + 2√xy + y . ( 2. ) By Art . 243 , a = x + y , ( 3. ) and √b = 2√xy . ( 4. ) Subtracting ( 4 ) from ( 3 ) , we have a − √b = x - 2√xy + y . By evolution , √a_√b ...
... assume √a + √b = √x + √y . ( 1. ) By squaring , a + √b = x + 2√xy + y . ( 2. ) By Art . 243 , a = x + y , ( 3. ) and √b = 2√xy . ( 4. ) Subtracting ( 4 ) from ( 3 ) , we have a − √b = x - 2√xy + y . By evolution , √a_√b ...
Página 180
... assume a principle employed in Arithmetic , viz . , If four quantities are proportional , the product of the extremes is equal to the product of the means . Thus , if then a : b :: c : d , ad = bc . Prob . 8. Divide the number a into ...
... assume a principle employed in Arithmetic , viz . , If four quantities are proportional , the product of the extremes is equal to the product of the means . Thus , if then a : b :: c : d , ad = bc . Prob . 8. Divide the number a into ...
Página 188
... assume y = x " , then y = x , and this equation y2 + py = q ; becomes whence - p 土√2 + 2 = 4 ' Extracting the nth root of each member , we have n x = p2 ㄓ 2+ : 4 Ex . 1. Solve the equation x - 13x2 —— 36 . Assuming x2 = y , the above ...
... assume y = x " , then y = x , and this equation y2 + py = q ; becomes whence - p 土√2 + 2 = 4 ' Extracting the nth root of each member , we have n x = p2 ㄓ 2+ : 4 Ex . 1. Solve the equation x - 13x2 —— 36 . Assuming x2 = y , the above ...
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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.