A Treatise on Algebra: For the Use of Schools and CollegesAppleton, 1849 - 336 σελίδες |
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Σελίδα 28
... evidently the same thing as saying , that it is introduced minus five halves of a time . - In other words a indicates , that a product , containing a five times as a factor , is separated into two equal factors , and that one of these ...
... evidently the same thing as saying , that it is introduced minus five halves of a time . - In other words a indicates , that a product , containing a five times as a factor , is separated into two equal factors , and that one of these ...
Σελίδα 30
... evidently true ; for , if a unit be divided into 10 equal parts , one of them will be contained in any quantity 10 times as often as the whole unit is contained in the same quantity ; and , if the unit be divided into a2 equal parts ...
... evidently true ; for , if a unit be divided into 10 equal parts , one of them will be contained in any quantity 10 times as often as the whole unit is contained in the same quantity ; and , if the unit be divided into a2 equal parts ...
Σελίδα 44
... evidently the same as x taken a + b - 2c times , which ( § 2. h ) is expressed ( a + b - 2c ) x . Hence , we may write the coefficients , whether numerical or literal ( § 9. b ) , of the common letter or letters in the several terms ...
... evidently the same as x taken a + b - 2c times , which ( § 2. h ) is expressed ( a + b - 2c ) x . Hence , we may write the coefficients , whether numerical or literal ( § 9. b ) , of the common letter or letters in the several terms ...
Σελίδα 54
... by the unknown quantity . § 51. III . Any equation containing only two powers of the unknown quantity , provided their exponents differ by unity , may evidently be reduced to the common form 54 [ § 49-51 . INTRODUCTION .
... by the unknown quantity . § 51. III . Any equation containing only two powers of the unknown quantity , provided their exponents differ by unity , may evidently be reduced to the common form 54 [ § 49-51 . INTRODUCTION .
Σελίδα 55
For the Use of Schools and Colleges Stephen Chase. unity , may evidently be reduced to the common form of the first degree , by dividing by the lowest power of the unknown quantity ... evidently comes under § 42. c § 52. ] 55 EQUATIONS .
For the Use of Schools and Colleges Stephen Chase. unity , may evidently be reduced to the common form of the first degree , by dividing by the lowest power of the unknown quantity ... evidently comes under § 42. c § 52. ] 55 EQUATIONS .
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A Treatise on Algebra: For the Use of Schools and Colleges (Classic Reprint) S. Chase Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
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Συχνά εμφανιζόμενοι όροι και φράσεις
a₁ algebraic approximately arithm Arithmetic arrangements become zero binomial called coefficient of x¹ Consequently continued fraction convergent corresponding course cube root D₁ D₂ denoted difference divide dividend division equa equal factors equal roots equal to zero equations containing equidifferent evidently expressed find x fourth function Geom given equation greater greatest common divisor harmonic series Hence imaginary roots infinite series last term least common multiple less letter logarithm monomial multiply negative quantity negative root NOTE nth root number of terms obviously odd number permutations polynomial positive or negative positive root primitive equation quan quotient ratio real roots reciprocal reduced remainder result root of X=0 second degree second term square root Sturm's theorem substitution subtract taken terms containing third tion tity unity unknown quantity unlike signs whole number
Δημοφιλή αποσπάσματα
Σελίδα 181 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Σελίδα 80 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Σελίδα 180 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Σελίδα 50 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 118 - 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.
Σελίδα 140 - Divide the first term of the remainder by three times the square of the root already found, and write the quotient for the next term of the root.
Σελίδα 242 - Any positive number being selected as a base, the logarithm of any other positive number is the exponent of the power to which the base must be raised to produce the given number. Thus, if a
Σελίδα 176 - The quantities which are compared together are called the terms of the proportion. The first and last terms are called the two extremes, and the second and third terms, the two means.
Σελίδα 104 - ... multiply each numerator by all the denominators, except its own, for a new numerator, and under it write the common denominator.
Σελίδα 187 - That is, the last term is equal to the first term, plus the product of the common difference by the number of terms less one.