A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 - Algebra |
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Page 86
... recurring , and that the number of places included in each period must always be less than the denominator of the frac- tion in its lowest terms . 161. The following are examples : ( 1 ) To convert into a recurring decimal 3 3 ) 1.00000 ...
... recurring , and that the number of places included in each period must always be less than the denominator of the frac- tion in its lowest terms . 161. The following are examples : ( 1 ) To convert into a recurring decimal 3 3 ) 1.00000 ...
Page 87
... recurring period consists of 16 places . Fractions , in their lowest terms , whose denominators are 19 , 23 , 29 , 47 , 59 , 61 , 97 , 109 , 113 , 131 , 149 , 167 , 181 , 193 , will produce recurring decimals , the number of places in ...
... recurring period consists of 16 places . Fractions , in their lowest terms , whose denominators are 19 , 23 , 29 , 47 , 59 , 61 , 97 , 109 , 113 , 131 , 149 , 167 , 181 , 193 , will produce recurring decimals , the number of places in ...
Page 88
... recurring periods only be- ginning from the decimal point . ( 13 ) - .523809523809 ... 21 1 ( 14 ) 49 .020408163265306122448979591836734693877551 . The recurring period consists of 42 places . 162. The converse problem of determining ...
... recurring periods only be- ginning from the decimal point . ( 13 ) - .523809523809 ... 21 1 ( 14 ) 49 .020408163265306122448979591836734693877551 . The recurring period consists of 42 places . 162. The converse problem of determining ...
Page 89
... recurring deci- mal , whether integral or not , will not partake of the repetition : in this case , we must add the number or equivalent fraction which expresses this non - repeating portion , to the fraction which expresses the value ...
... recurring deci- mal , whether integral or not , will not partake of the repetition : in this case , we must add the number or equivalent fraction which expresses this non - repeating portion , to the fraction which expresses the value ...
Page 104
... recurring decimal , for the partial divisor , no ambiguity could have occurred in the determination of the digits of the quotient . * 185. The same method is applicable to the solution of many other arithmetical problems of considerable ...
... recurring decimal , for the partial divisor , no ambiguity could have occurred in the determination of the digits of the quotient . * 185. The same method is applicable to the solution of many other arithmetical problems of considerable ...
Common terms and phrases
a₁ arith arithmetical algebra arithmetical series coefficient complete quotient consequently considered continued fraction continued product converging fractions corresponding cube denoted determined divided dividend division divisor equal equation expressed final digit finite number following are examples geometrical given greater greatest common measure identical inasmuch indeterminate equations involve known terms last Article last term least common multiple less magnitudes means metical minuend modulus multiplicand number of combinations number of days number of terms operation ordinary preceding primary unit primitive problem proposition quadratic quadratic equations quadratic surds quantities ratio recurring decimal reduced replace represent resolvend respectively result rule scale shewn similar manner square root subordinate units subtract subtrahend surds Symbolical Algebra third tion Transposing unknown numbers unknown symbols whole number zero
Popular passages
Page 266 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Page 272 - A and B can do a piece of work in 6 days ; A and C can do it in 9 days, and A, B, C can do 8 times the same work in 45 days.
Page 177 - When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third...
Page 166 - COMPOSITION ; that is, the sum of the first and second, will be to the second, as the sum of the third and fourth, is to the fourth.
Page 256 - 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?
Page 34 - The product of the sum and difference of two numbers is equal to the difference of their squares.
Page 34 - The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first and the second, plus the square of the second.
Page 269 - In wh.it time could each do it separately? Ans. A in 24, B in 48 days. 19. A and B drink from a cask of beer for 2 hours, after which A falls asleep, and B drinks the remainder in 2 hours and 48 minutes; but if B had fallen asleep and A had continued to drink. it would have taken him 4 hours and 40 minutes to finish the cask. In what time could each singly drink the whole? Ans. A in 10 hrs., B in 6 hrs.
Page 173 - If the first has to the second the same ratio which the third has to the fourth...
Page 167 - When four quantities are proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth, to their difference.