The elements of algebra |
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Página 125
... constant divisor . Divide the first term of the remainder by this divisor , and the quotient will be the next term of the root . Involve the part of the root now found to the corresponding power , and subtract this power from the ...
... constant divisor . Divide the first term of the remainder by this divisor , and the quotient will be the next term of the root . Involve the part of the root now found to the corresponding power , and subtract this power from the ...
Página 127
... constant divisor 4a3 , gives b , the second term of the root . After subtracting ( a + b ) 1 = a1 + 4a3b + . the first term of the remainder is 4a3c ; and this being divided by 4 a3 , gives c , the third term of the root . Again , after ...
... constant divisor 4a3 , gives b , the second term of the root . After subtracting ( a + b ) 1 = a1 + 4a3b + . the first term of the remainder is 4a3c ; and this being divided by 4 a3 , gives c , the third term of the root . Again , after ...
Página 226
... constant terms to another quantity n , and then the equation becomes or if r = - - N , mx2 = n , or mx2 . mx2 + r = = 0 --- n = 0 So an adfected quadratic may be similarly reduced ; for all the terms containing 2 may be reduced to one ...
... constant terms to another quantity n , and then the equation becomes or if r = - - N , mx2 = n , or mx2 . mx2 + r = = 0 --- n = 0 So an adfected quadratic may be similarly reduced ; for all the terms containing 2 may be reduced to one ...
Página 264
... constant term . ( 290. ) ' Assume one of the unknown quantities equal to the product of the other by a new or auxiliary unknown quantity , and substitute this product instead of it in the two equations ; and the equations will now ...
... constant term . ( 290. ) ' Assume one of the unknown quantities equal to the product of the other by a new or auxiliary unknown quantity , and substitute this product instead of it in the two equations ; and the equations will now ...
Página 298
... constant quantity of a proper value , my For if x , y , and a " , y " , be any two systems of values of x and y , x ' : x " = y ' : y ' ' ( 381 ) , therefore ( 355 ) x'y ' = x'y ' ; therefore x ' x " = y " y ' If now a " " and y ' " be ...
... constant quantity of a proper value , my For if x , y , and a " , y " , be any two systems of values of x and y , x ' : x " = y ' : y ' ' ( 381 ) , therefore ( 355 ) x'y ' = x'y ' ; therefore x ' x " = y " y ' If now a " " and y ' " be ...
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Términos y frases comunes
a²x a²x² a³x algebraical Algebraical Fractions annuity assumed ax² ax³ binomial coefficients continued fraction cube root cubic equation denote Divide dividend divisible divisor equa equal equations containing equidifferent evident EXAMPLES EXERCISES exponent expressed factors Find a number Find the cube Find the least Find the square Find the sum Find the value Find two numbers former given equations given quantity greatest common measure harmonic mean hence last term latter least common multiple Let the number logarithms method Multiply nth root number of terms permutations positive preceding prefixed proportional equation quadratic quan quotient radical sign ratio Rationalise the denominator Reduce relatively prime remainder required the numbers result rule second term solution square root subtract system of values taken theorem third tion tity unknown quantities vulgar fraction ах
Pasajes populares
Página 76 - Multiply each numerator by all the denominators except its own, for the new numerators ; and all the denominators together for A COMMON denominator. NOTE 1.
Página 317 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Página 339 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.
Página 309 - Find the nth term, and the sum of n terms of the natural series of numbers 1, 2, 3, 4 . . . . Ans.
Página 223 - If A and В together can perform a piece of work in 8 days, A and С together in 9 days, and В and С in 10 days; how many days would it take each person to perform the same work alone?
Página 353 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 286 - If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Página 178 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...
Página 176 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Página 352 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.