A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 - Algebra |
From inside the book
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Page 8
... identical wit ceded both original number : thus if 7 be first added to 10 , makin by the signs and if the same number 7 be then subtracted from 17 result is 10 , which is the original number : or conversely , if first subtracted from 10 ...
... identical wit ceded both original number : thus if 7 be first added to 10 , makin by the signs and if the same number 7 be then subtracted from 17 result is 10 , which is the original number : or conversely , if first subtracted from 10 ...
Page 13
... identical with the rule for performing the operation of subtraction . the brackets are pre- When a quantity or number expressed by more terms than Rule when one is included between brackets , which are preceded by the sign + , no change ...
... identical with the rule for performing the operation of subtraction . the brackets are pre- When a quantity or number expressed by more terms than Rule when one is included between brackets , which are preceded by the sign + , no change ...
Page 16
... identical terms , will be reduced into one , and the results which involve them will be greatly simplified and abridged in form . The adop- 27. When a coefficient precedes a symbol , it means that the coefficients symbol is multiplied ...
... identical terms , will be reduced into one , and the results which involve them will be greatly simplified and abridged in form . The adop- 27. When a coefficient precedes a symbol , it means that the coefficients symbol is multiplied ...
Page 17
... identical in signification , and that the formal exhibition of where no 1 as a coefficient is unnecessary ( Art . 34. ) and therefore never made : efficient we are thus enabled to replace expressions such as a +2 a by 3a : appears . x + ...
... identical in signification , and that the formal exhibition of where no 1 as a coefficient is unnecessary ( Art . 34. ) and therefore never made : efficient we are thus enabled to replace expressions such as a +2 a by 3a : appears . x + ...
Page 22
... identical with ba , would prove indifference that abc is identical with acb , or bac , or bca , or cab , or cba . in which The same observation may clearly be extended to any number of they are written in of the order the pro- duct ...
... identical with ba , would prove indifference that abc is identical with acb , or bac , or bca , or cab , or cba . in which The same observation may clearly be extended to any number of they are written in of the order the pro- duct ...
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.