The elements of algebra |
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Página 6
... hence x is the fourth root of 24 , for the continued product of a repeated four times as a factor is a1 . - ( 34. ) To extract any root of a quantity , is to find that root . ( 35. ) The sign , called the radical sign , placed before a ...
... hence x is the fourth root of 24 , for the continued product of a repeated four times as a factor is a1 . - ( 34. ) To extract any root of a quantity , is to find that root . ( 35. ) The sign , called the radical sign , placed before a ...
Página 14
... hence the sum is + 2x . In the second example , the sum of the positive quantities is 8ay , and of the negative 12xy , and the difference between 12 and 8 is 4 , the sign of the greater being ; hence the sum is - 4 xy2 by the rule . In ...
... hence the sum is + 2x . In the second example , the sum of the positive quantities is 8ay , and of the negative 12xy , and the difference between 12 and 8 is 4 , the sign of the greater being ; hence the sum is - 4 xy2 by the rule . In ...
Página 19
... hence a- The rule , therefore , is proved in all these cases , and it only remains to prove it in the following case : - * ( 60. ) When an insulated negative quantity as [ -c ] is to be subtracted from any quantity as b . The sum of a ...
... hence a- The rule , therefore , is proved in all these cases , and it only remains to prove it in the following case : - * ( 60. ) When an insulated negative quantity as [ -c ] is to be subtracted from any quantity as b . The sum of a ...
Página 39
... hence- ( 81. ) The rule for this case of division may also be expressed as in article 78 . EXAMPLES . 1. Divide 12 * by 8 ax 12 a6x4 3a2 × 4a4x4 = = 3 a2 8a4x5 2x × 4α1x1 2x In this example , 4 ata is a factor common to both divisor and ...
... hence- ( 81. ) The rule for this case of division may also be expressed as in article 78 . EXAMPLES . 1. Divide 12 * by 8 ax 12 a6x4 3a2 × 4a4x4 = = 3 a2 8a4x5 2x × 4α1x1 2x In this example , 4 ata is a factor common to both divisor and ...
Página 59
... hence also of B , and therefore of p B or p B + C ( 102 ) , and therefore also of A. Hence M is a measure of A and B. It is also the greatest common measure ; for C = A - p B , MBq C , and any common measure of A and B , or of A and p B ...
... hence also of B , and therefore of p B or p B + C ( 102 ) , and therefore also of A. Hence M is a measure of A and B. It is also the greatest common measure ; for C = A - p B , MBq C , and any common measure of A and B , or of A and p B ...
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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.