The elements of algebra |
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Página xiv
... continued proportion , and also the signs for common proportion , except that he placed only one dot instead of two between the first and second , and the third and fourth terms thus , a.b :: c.d . By the radical sign , with q placed ...
... continued proportion , and also the signs for common proportion , except that he placed only one dot instead of two between the first and second , and the third and fourth terms thus , a.b :: c.d . By the radical sign , with q placed ...
Página xvii
... Continued Fractions ( 1670 ) . He discovered a fraction of this kind that expressed the ratio of the square of the ... continued fraction given by Lord Brounker for this purpose ; and a series expressing the length of a quadrantal are ...
... Continued Fractions ( 1670 ) . He discovered a fraction of this kind that expressed the ratio of the square of the ... continued fraction given by Lord Brounker for this purpose ; and a series expressing the length of a quadrantal are ...
Página xviii
... continued fractions to the solution of equations ; the value of the root , by his method of solu- tion , being exhibited in the form of a continued fraction . Gauss published a work on the theory of numbers , which also contained the ...
... continued fractions to the solution of equations ; the value of the root , by his method of solu- tion , being exhibited in the form of a continued fraction . Gauss published a work on the theory of numbers , which also contained the ...
Página xxii
... CONTINUED FRACTIONS . Definition 409 Conversion of Common into Continued Fractions 412 Convergent Fractions 415 Periodical Continued Fractions - 422 INDETERMINATE EQUATIONS . Simple Indeterminate Equations One Equation with two Unknown ...
... CONTINUED FRACTIONS . Definition 409 Conversion of Common into Continued Fractions 412 Convergent Fractions 415 Periodical Continued Fractions - 422 INDETERMINATE EQUATIONS . Simple Indeterminate Equations One Equation with two Unknown ...
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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.