Algebra for Colleges and SchoolsMacmillan, 1897 - 516 páginas |
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Página 1
... considering . Moreover , we may operate with symbols without assigning to them any par- ticular numerical value ; indeed it is with such operations that Algebra is chiefly concerned . We begin with the definitions of Algebra , premising ...
... considering . Moreover , we may operate with symbols without assigning to them any par- ticular numerical value ; indeed it is with such operations that Algebra is chiefly concerned . We begin with the definitions of Algebra , premising ...
Página 2
... consider any factor , or factors , of a product as the coefficient of the remaining factors . Thus , in the product 6 abc , 6 a may be appropriately called the coefficient of bc . A coefficient which is not 2 ALGEBRA .
... consider any factor , or factors , of a product as the coefficient of the remaining factors . Thus , in the product 6 abc , 6 a may be appropriately called the coefficient of bc . A coefficient which is not 2 ALGEBRA .
Página 14
... considering the results ( 1 ) , ( 2 ) , ( 3 ) , ( 4 ) , we are led to the following rule : Rule . When an expression within brackets is preceded by the sign + , the brackets can be removed without making any change in the expression ...
... considering the results ( 1 ) , ( 2 ) , ( 3 ) , ( 4 ) , we are led to the following rule : Rule . When an expression within brackets is preceded by the sign + , the brackets can be removed without making any change in the expression ...
Página 28
... consider each term on the right - hand side of this last result , and the way in which it arises , we find that ( + α ) x ( + c ) = + ac , - ( − b ) x ( −d ) = + bd , ( b ) x ( + c ) = bc , ( + a ) x ( −d ) = — ad . These results ...
... consider each term on the right - hand side of this last result , and the way in which it arises , we find that ( + α ) x ( + c ) = + ac , - ( − b ) x ( −d ) = + bd , ( b ) x ( + c ) = bc , ( + a ) x ( −d ) = — ad . These results ...
Página 56
... Consider the equation 7 x = 14 . It is required to find what numerical value x must have consistent with this statement . Dividing both sides by 7 , we get x = 2 • • ( Axiom 4 ) . x Similarly , if 6 , 2 multiplying both sides by 2 , we ...
... Consider the equation 7 x = 14 . It is required to find what numerical value x must have consistent with this statement . Dividing both sides by 7 , we get x = 2 • • ( Axiom 4 ) . x Similarly , if 6 , 2 multiplying both sides by 2 , we ...
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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...