Elementary AlgebraMacmillan and Company, 1895 - 478 páginas |
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Página 117
... fraction = = 4ab ( a + b ) ( a - b ) ' 4a2b2 -- 4ab ` ( a2 + b2 ) ( a2 − b2 ) * ( a + b ) ( a − b ) - = 4a2b2 ( a ... Continued Fractions , we begin from the lowest fraction , and simplify step by step . 9x2-64 Example 4. Simplify 1 x ...
... fraction = = 4ab ( a + b ) ( a - b ) ' 4a2b2 -- 4ab ` ( a2 + b2 ) ( a2 − b2 ) * ( a + b ) ( a − b ) - = 4a2b2 ( a ... Continued Fractions , we begin from the lowest fraction , and simplify step by step . 9x2-64 Example 4. Simplify 1 x ...
Página 370
... continued fraction . Example . Reduce to a continued fraction . 832 159 Finding the greatest common measure of 832 and 159 by the usual process , thus : 159 ) 832 ( 5 795 37 ) 159 ( 4 148 11 ) 37 ( 3 33 4 ) 11 ( 2 8 3 ) 4 ( 1 3 1 ) 3 ...
... continued fraction . Example . Reduce to a continued fraction . 832 159 Finding the greatest common measure of 832 and 159 by the usual process , thus : 159 ) 832 ( 5 795 37 ) 159 ( 4 148 11 ) 37 ( 3 33 4 ) 11 ( 2 8 3 ) 4 ( 1 3 1 ) 3 ...
Página 371
... continued fraction are called the first , second , third , convergents , because , as will be shown in Art . 476 , each successive convergent is a nearer approximation to the true value of the continued fraction than any of the ...
... continued fraction are called the first , second , third , convergents , because , as will be shown in Art . 476 , each successive convergent is a nearer approximation to the true value of the continued fraction than any of the ...
Página 372
... continued fraction and calculate 674 313 the successive convergents . 674 By Art . 469 , = 2 + 313 1 1 1 1 1 6+ 1+ 1 ... fraction is a proper fraction , we may consider zero as the first convergent , and proceed as follows : 84 Reduce to ...
... continued fraction and calculate 674 313 the successive convergents . 674 By Art . 469 , = 2 + 313 1 1 1 1 1 6+ 1+ 1 ... fraction is a proper fraction , we may consider zero as the first convergent , and proceed as follows : 84 Reduce to ...
Página 373
... fraction , and calculate the suc- 227 cessive convergents . Proceeding as in Art . 469 , 227 ) 84 ( 0 00 84 ) 227 ( 2 168 59 ) 84 ( 1 59 25 ) 59 ( ... We obtain 0+ 1 1 1 1 ... continued fraction be denoted by a2 + 1 CONTINUED FRACTIONS . 373.
... fraction , and calculate the suc- 227 cessive convergents . Proceeding as in Art . 469 , 227 ) 84 ( 0 00 84 ) 227 ( 2 168 59 ) 84 ( 1 59 25 ) 59 ( ... We obtain 0+ 1 1 1 1 ... continued fraction be denoted by a2 + 1 CONTINUED FRACTIONS . 373.
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Términos y frases comunes
a+3b a+b+c a₁ a²+b² arithmetic means arithmetical arranged ascending powers b₁ beginner Binomial Theorem cents CHAPTER coefficients column compound expression continued fraction convergent cube root decimal denote digits dimes Divide dividend division divisor equal EXAMPLES XI Find the highest find the number Find the square Find the sum find the value following expressions given expressions greater harmonic mean Hence highest common factor integer less letters logarithm lowest common multiple method miles an hour Multiply number of terms numerator and denominator obtain partial fractions prefixed prove quadratic quadratic equation quotient ratio remainder Resolve into factors result rule of signs second term Simplify SIMULTANEOUS EQUATIONS solution square root subtraction Suppose surds symbols Transposing unknown quantity walk whence write yards zero
Pasajes populares
Página 331 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 256 - In a quadratic equation wJiere the coefficient of the first term is unity, (i) the sum of the roots is equal to the coefficient of x with its sign changed ; (ii) the product of the roots is equal to the third term.
Página 168 - Thus the 4th root (2x2) = the square root of the square root ; the sixth root (3x2) = the cube root of the square root, or the square root of the cube root.
Página 178 - A basket of oranges is emptied by one person taking half of them and one more, a second person taking half of the remainder and one more, and a third person taking half of the remainder and six more. How many did the basket contain at first ? 17.
Página 179 - Two vessels contain mixtures of wine and water ; in one there is three times as much wine as water, in the other five times as much water as wine. Find how much must be drawn off from each to fill a third vessel which holds seven gallons, in order that its contents may be half wine and half water.
Página 280 - The pressure of wind on a plane surface varies jointly as the area of the surface, and the square of the wind's velocity. The pressure on a square foot is 1...
Página 213 - Art. 167 we saw that if the number of unknown quantities is greater than the number of independent equations, there will be an unlimited number of solutions, and the equations will be indeterminate. By introducing conditions, however, we can limit the number of solutions. When positive integral values of the unknown quantities are required, the equations are called simple indeterminate equations. The introduction of this restriction enables us to express the solutions in a very simple form. Ex. 1....