A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 - Algebra |
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Page 21
... continued product of a series of The multi- numbers such as 2 , 3 , 4 , 5 is written 2 × 3 × 4 × 5 , or more simply multiplier plicand and 2.3.4.5 , as there is no danger , when the dot is thus repeated , of are inter- confounding such ...
... continued product of a series of The multi- numbers such as 2 , 3 , 4 , 5 is written 2 × 3 × 4 × 5 , or more simply multiplier plicand and 2.3.4.5 , as there is no danger , when the dot is thus repeated , of are inter- confounding such ...
Page 24
... continued product of the symbol a repeated as often as unity is contained in the sum of the indices ( Art . 39. ) of all the factors which are multiplied together , and it will therefore be correctly represented by a single power of a ...
... continued product of the symbol a repeated as often as unity is contained in the sum of the indices ( Art . 39. ) of all the factors which are multiplied together , and it will therefore be correctly represented by a single power of a ...
Page 50
... quotient is therefore 2a1 since 2a1 x2 2 a * x as the nature of the process in this case leaves necessarily a new remainder after every operation , the quotient may evidently be continued without limit , and will consist of a series 50.
... quotient is therefore 2a1 since 2a1 x2 2 a * x as the nature of the process in this case leaves necessarily a new remainder after every operation , the quotient may evidently be continued without limit , and will consist of a series 50.
Page 51
... continued indefinitely , when the remainder never disappears , which must always be the case when the divisor is not a factor ( Art . 76. ) of the dividend : such quotients , therefore , may be considered as originating in the rule for ...
... continued indefinitely , when the remainder never disappears , which must always be the case when the divisor is not a factor ( Art . 76. ) of the dividend : such quotients , therefore , may be considered as originating in the rule for ...
Page 63
... continued product of the greatest common measure of two numbers and of the quotients which arise from dividing them by it . 117. Every other multiple of two numbers a and b , is a Every other multiple of their least common multiple m ...
... continued product of the greatest common measure of two numbers and of the quotients which arise from dividing them by it . 117. Every other multiple of two numbers a and b , is a Every other multiple of their least common multiple m ...
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.