A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 - Algebra |
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Page 3
... preceding examples , are obtained Explana- nd exhibited without the use of any sign of operation : but though of opera- tion of signs The use of signs of operation in arithmetical processes may generally tion . be dispensed with ...
... preceding examples , are obtained Explana- nd exhibited without the use of any sign of operation : but though of opera- tion of signs The use of signs of operation in arithmetical processes may generally tion . be dispensed with ...
Page 5
... preceding and similar results , with a view to the establishment of the fundamental rules of operation , when symbols are employed to represent numbers , which in common arithmetic are expressed by the nine digits and zero . I S Rule ...
... preceding and similar results , with a view to the establishment of the fundamental rules of operation , when symbols are employed to represent numbers , which in common arithmetic are expressed by the nine digits and zero . I S Rule ...
Page 9
... preceding Article , we have used brackets to denote Use of fromhat the whole number or quantity expressed by the symbols in- luded between them , connected with their proper sign or signs , is o be subjected to the operation which is ...
... preceding Article , we have used brackets to denote Use of fromhat the whole number or quantity expressed by the symbols in- luded between them , connected with their proper sign or signs , is o be subjected to the operation which is ...
Page 12
... preceding the terms of the minuend : change all the signs preceding the terms of the subtrahend , into , and into the final result will be found by writing in the same line all the terms preceded by the signs which thus result , in any ...
... preceding the terms of the minuend : change all the signs preceding the terms of the subtrahend , into , and into the final result will be found by writing in the same line all the terms preceded by the signs which thus result , in any ...
Page 14
... preceding the first term , the er istence of the sign + is assumed . ( Art . 23. ) Thus , a + b + ( c - d ) = a + b + c - d : and a + ( b - c ) + ( d - e ) = a + b - c + d - e . It follows , therefore , that quantities or expressions ...
... preceding the first term , the er istence of the sign + is assumed . ( Art . 23. ) Thus , a + b + ( c - d ) = a + b + c - d : and a + ( b - c ) + ( d - e ) = a + b - c + d - e . It follows , therefore , that quantities or expressions ...
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.