A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 - Algebra |
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Page v
... the general rule of subtraction , which would give us fou for sut OCL 7a + 5b - a 3b - 3a + 2b − 3a - = 7 a · -- a - = 76-9b , - 3 a - - 76 3a + 5b - 3b + 2b − 7 b vi PREFACE . a result which indicates that the final.
... the general rule of subtraction , which would give us fou for sut OCL 7a + 5b - a 3b - 3a + 2b − 3a - = 7 a · -- a - = 76-9b , - 3 a - - 76 3a + 5b - 3b + 2b − 7 b vi PREFACE . a result which indicates that the final.
Page vi
George Peacock. vi PREFACE . a result which indicates that the final operation , to which the application of the rule conducts us , is impossible : w are perpetually encountering , in arithmetical algebra , a it were unconsciously and ...
George Peacock. vi PREFACE . a result which indicates that the final operation , to which the application of the rule conducts us , is impossible : w are perpetually encountering , in arithmetical algebra , a it were unconsciously and ...
Page vii
... final term , may be shewn , upon the same principle , to be the equivalent series for ( a + b ) " , when n is general both in form and value . for th numb for , i that numb there and letter 2 the e tables orde For , from orde subt form ...
... final term , may be shewn , upon the same principle , to be the equivalent series for ( a + b ) " , when n is general both in form and value . for th numb for , i that numb there and letter 2 the e tables orde For , from orde subt form ...
Page 2
... final result . ( 2 ) From 1695 subtract 763 . 1695 763 932 final result . ( 3 ) Multiply together 191 and 27 . 191 27 1337 382 5157 final result . adding together the numbers , or numerical quantities , denoted by the several in their ...
... final result . ( 2 ) From 1695 subtract 763 . 1695 763 932 final result . ( 3 ) Multiply together 191 and 27 . 191 27 1337 382 5157 final result . adding together the numbers , or numerical quantities , denoted by the several in their ...
Page 3
... final result . 224 728 672 560 560 ... ( 5 ) Extract the square root of 219961 . 219961 ( 469 16 86 ) 599 516 929 ) 8361 8361 final result . he ( 6 ) Extract the cube root of 474552 . ble rde For ron rd sub fort 474552 ( 78 final result ...
... final result . 224 728 672 560 560 ... ( 5 ) Extract the square root of 219961 . 219961 ( 469 16 86 ) 599 516 929 ) 8361 8361 final result . he ( 6 ) Extract the cube root of 474552 . ble rde For ron rd sub fort 474552 ( 78 final result ...
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.