Algebra for Colleges and SchoolsMacmillan, 1897 - 516 páginas |
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Página 1
... letters of our own alphabet ; and , though there is no restriction as to the numerical values a symbol may represent , it is under- stood that in the same piece of work it keeps the same value throughout . Thus , when we say " let a ...
... letters of our own alphabet ; and , though there is no restriction as to the numerical values a symbol may represent , it is under- stood that in the same piece of work it keeps the same value throughout . Thus , when we say " let a ...
Página 4
... letters a and b , and have therefore the same value . Although it is immaterial in what order the factors of a product are written , it is usual to arrange them alphabetically . Fractional co- efficients which are greater than unity are ...
... letters a and b , and have therefore the same value . Although it is immaterial in what order the factors of a product are written , it is usual to arrange them alphabetically . Fractional co- efficients which are greater than unity are ...
Página 17
... letters composing a term is called a dimension of the term , and the number of letters involved is called the degree of the term . Thus the product abc is said to be of three dimensions , or of the third degree ; and ax1 is said to be ...
... letters composing a term is called a dimension of the term , and the number of letters involved is called the degree of the term . Thus the product abc is said to be of three dimensions , or of the third degree ; and ax1 is said to be ...
Página 18
... letter , it will be found convenient to arrange all the expressions in descending or ascending powers of that letter . This will be made clear by the following examples . Ex . 1. Add together 4x - 2x8 + 3x2 ; 3x8 + 7 +6 x 5 x2 ; 2 x2 ...
... letter , it will be found convenient to arrange all the expressions in descending or ascending powers of that letter . This will be made clear by the following examples . Ex . 1. Add together 4x - 2x8 + 3x2 ; 3x8 + 7 +6 x 5 x2 ; 2 x2 ...
Página 21
... letter being unlike must stand in different columns . - x8 3x2 2 x +1 x3 - 3x2 + 2x + 1 Subtract The rearrangement of terms in the first line is not necessary , but it is convenient , because it gives the result of subtraction in ...
... letter being unlike must stand in different columns . - x8 3x2 2 x +1 x3 - 3x2 + 2x + 1 Subtract The rearrangement of terms in the first line is not necessary , but it is convenient , because it gives the result of subtraction in ...
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Términos y frases comunes
a²b a²b² a²x a²x² a³b ab² ab³ algebraic arithmetic means arithmetical ascending powers ax² ax³ b₁ binomial Binomial Theorem bx² cents CHAPTER coefficient column compound expressions continued fraction convergent cube denote digits dimes Divide dividend divisible divisor equal equation EXAMPLES Find the highest find the number Find the square Find the sum find the value fraction harmonic means Hence highest common factor integer letters logarithm lowest common multiple miles an hour Multiply negative number of terms numerator and denominator obtain positive quadratic quadratic equation quotient ratio remainder Resolve into factors result rule of signs Simplify Solve square root Subtract surd symbols unknown quantity whence whole number x²y x²y² x³y xy² xy³ yards zero
Pasajes populares
Página 167 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Página 264 - That is, if a quadratic equation be reduced to the form x?+px = q, the algebraic sum of the roots is equal to the coefficient of x with its sign changed, and the product of the roots is equal to the second member, with its sign changed.
Página 351 - The logarithm of a product is the sum of the logarithms of its factors.
Página 352 - The Integral Part of a logarithm is called the Characteristic, and the decimal part the Mantissa.
Página 183 - The sixth root of an expression is found by taking the cube root of the square root, or the square root of the cube root.
Página 102 - ... remainder. The lowest common multiple of two or more algebraic expressions is the expression of lowest degree which will contain them all without a remainder.
Página 289 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Página 328 - A telegraph has 5 arms, and each arm has 4 distinct positions, including the position of rest: find the total number of signals that can be made.
Página 322 - From 7 Englishmen and 4 Americans a committee of 6 Is to be formed: in how many ways can this be done, (1) when the committee contains exactly 2 Americans, (2) at least 2 Americans...
Página 290 - Hence if any three terms of a proportion are given, the fourth may be found. Thus if a...