The elements of algebra |
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Página iii
... assumed without demonstration . The summation of some of those species of Infinite Series that are usually given in similar treatises to the present , is here accom- plished by a new and simple method , which is both concise and general ...
... assumed without demonstration . The summation of some of those species of Infinite Series that are usually given in similar treatises to the present , is here accom- plished by a new and simple method , which is both concise and general ...
Página v
... assumed - hence the necessity and the origin of algebraical language . By reasoning in regard to particular numbers , general properties may sometimes be discovered , and their truth satisfactorily established ; but , * See the ...
... assumed - hence the necessity and the origin of algebraical language . By reasoning in regard to particular numbers , general properties may sometimes be discovered , and their truth satisfactorily established ; but , * See the ...
Página 1
... assumed portion of the same kind of quantity by which it is to be measured . Thus , to measure the length of a line , some unit of measure , as a foot , is assumed , and the number of feet in the line can then be ascertained . ( 5 ...
... assumed portion of the same kind of quantity by which it is to be measured . Thus , to measure the length of a line , some unit of measure , as a foot , is assumed , and the number of feet in the line can then be ascertained . ( 5 ...
Página 96
... assumed that the product of ( n - 1 ) factors is the same in whatever order they are taken ; and hence all the pro- ducts in the first group are equal . So if P ' be the product of ( n − 1 ) factors , excluding the second or b , any ...
... assumed that the product of ( n - 1 ) factors is the same in whatever order they are taken ; and hence all the pro- ducts in the first group are equal . So if P ' be the product of ( n − 1 ) factors , excluding the second or b , any ...
Página 135
... assumed for the compound quantity under the parenthesis ; thus , let ( ax ) = z , or ( x2 + y2 ) 2 = x2 , and then apply the rule , and afterwards substitute for z its value . So when the quantity under the radical sign is the product ...
... assumed for the compound quantity under the parenthesis ; thus , let ( ax ) = z , or ( x2 + y2 ) 2 = x2 , and then apply the rule , and afterwards substitute for z its value . So when the quantity under the radical sign is the product ...
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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.