The elements of algebra |
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Página vii
... latter method that the more general truth is established , that this property is possessed by no other curves : the former method affords one means of reaching a certain point , the latter shows by what and by how many ways it may be ...
... latter method that the more general truth is established , that this property is possessed by no other curves : the former method affords one means of reaching a certain point , the latter shows by what and by how many ways it may be ...
Página xiii
... latter , quantities . Previous to this improvement , algebraists considered only numerical equations , and could have no formulas for the values of their roots , although the method of solving one numerical equation might be easily ...
... latter , quantities . Previous to this improvement , algebraists considered only numerical equations , and could have no formulas for the values of their roots , although the method of solving one numerical equation might be easily ...
Página xvi
... latter , and he thus has a rival claim for the honour of inventing the method of Analytical Geometry . The analogous theories of indivisibles , and of the arith- metic of infinities , were published by their respective inven- tors ...
... latter , and he thus has a rival claim for the honour of inventing the method of Analytical Geometry . The analogous theories of indivisibles , and of the arith- metic of infinities , were published by their respective inven- tors ...
Página 3
... latter the negative sign ; and they are said to be contrary or opposite . ( 17. ) Quantities having a positive sign , are said to be positive ; and those having negative signs , are called nega- tive . When a quantity has no sign ...
... latter the negative sign ; and they are said to be contrary or opposite . ( 17. ) Quantities having a positive sign , are said to be positive ; and those having negative signs , are called nega- tive . When a quantity has no sign ...
Página 14
... then whatever quantity the former repre- sents , the latter denotes the same kind of quantity in reversed circumstances ; that is , if a be a number of miles travelled west , [ 6 ] is a number travelled east 14 ELEMENTS OF ALGEBRA .
... then whatever quantity the former repre- sents , the latter denotes the same kind of quantity in reversed circumstances ; that is , if a be a number of miles travelled west , [ 6 ] is a number travelled east 14 ELEMENTS OF ALGEBRA .
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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.