A treatise on the elements of algebra, by G. Ainsworth and J. Yeats1854 |
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Side
... Root Cube Root • VIII . Greatest Common Measure Demonstration of the Rule Least Common Multiple IX . Fractions Reduction • Addition and Subtraction Multiplication Division Miscellaneous Exercises on the foregoing X. Simple Equations ...
... Root Cube Root • VIII . Greatest Common Measure Demonstration of the Rule Least Common Multiple IX . Fractions Reduction • Addition and Subtraction Multiplication Division Miscellaneous Exercises on the foregoing X. Simple Equations ...
Side 2
... root , and it shows what root is to be extracted : thus c denotes the cube root of c . In expressing the square root , the index 2 is omitted . The index of a root shows how often that root has to be multiplied into itself to equal the ...
... root , and it shows what root is to be extracted : thus c denotes the cube root of c . In expressing the square root , the index 2 is omitted . The index of a root shows how often that root has to be multiplied into itself to equal the ...
Side 36
... cube of q is to be written down in the fourth power ; also the quotient of 8 in the third power , divided by r in ... root of their sum ? 11. How must we write the product of the sum of p and q in the second power , and the square root ...
... cube of q is to be written down in the fourth power ; also the quotient of 8 in the third power , divided by r in ... root of their sum ? 11. How must we write the product of the sum of p and q in the second power , and the square root ...
Side 38
... cube root of a3 ; : . a2 is the square root of aa ; .. a4 is the cube root of a12 . As 3 is the square root of 26 , because ( x3 ) 2 = x6 , so x2 is the cube root of 26 , because ( x2 ) 3 = x6 ; √a ^ = a2 , 16a8b4 = 2a2b , & c .; hence ...
... cube root of a3 ; : . a2 is the square root of aa ; .. a4 is the cube root of a12 . As 3 is the square root of 26 , because ( x3 ) 2 = x6 , so x2 is the cube root of 26 , because ( x2 ) 3 = x6 ; √a ^ = a2 , 16a8b4 = 2a2b , & c .; hence ...
Side 44
... CUBE ROOT . We have already seen how binomials and multinomials raised to a given power are developed in a certain and fixed order . ( a + b ) 3 = a3 + 3a2b + 3ab2 + b3 , and this expansion consists of the third power of each ... Cube Root •
... CUBE ROOT . We have already seen how binomials and multinomials raised to a given power are developed in a certain and fixed order . ( a + b ) 3 = a3 + 3a2b + 3ab2 + b3 , and this expansion consists of the third power of each ... Cube Root •
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A Treatise on the Elements of Algebra, by G. Ainsworth and J. Yeats G Ainsworth Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
a+b-c a+b+c a²+2ab+b² abcd added algebraic fraction arithmetical means arithmetical progression arithmetical series binomial Binomial Theorem brackets casks cent coefficients common difference compound cube root decimal denoted digits dividend divisible divisor equal equation example EXERCISE XXXI exponent expression factors feet find the number four numbers fourth geometrical progression geometrical series greatest common measure harmonical harmonical mean Hence least common multiple letters lowest terms multinomial multiplied negative number of terms number of variations numerator and denominator obtain permutations positive preceding proportion quadratic quan quotient ratio Reduce remainder Required the number rule second term Simplify square root subtracted suppose surd Theorem things taken third power unknown quantity whole number write x+y=a x²-y² x²+2xy
Populære passager
Side 160 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Side 19 - The square of the sum of two numbers is equal to the square of the first number plus twice the product of the first and second number plus the square of the second number.
Side 131 - 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 as much as 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Ans. 300.
Side 109 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Side 124 - 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...
Side 164 - To find a number consisting of three places, whose digits are in arithmetical progression; if this number be divided by the sum of its digits, the quotient will be 48 ; and if from the number be subtracted 198, the digits will be inverted.
Side 80 - 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.
Side 119 - There are four numbers in arithmetical progression : the sum of the squares of the two first is 34 ; and the sum of the squares of the two last is 130. What are the numbers?
Side 65 - The product of two or more fractions is the product of their numerators divided by the product of their denominators. Exam ¡île \. Example 2. IX f о. x Г...
Side 156 - A certain number, consisting of two places, a unit and a ten, is four times the sum of its digits, and if 27 be added to it, the digits will be inverted. What is the number ? NOTE.