A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 - Algebra |
From inside the book
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Page 13
... dividend : a father extension of this analogy has led to the assumption of the terms radi- tand and logarithmand , to express the numbers whose roots are to be extracted or whose logarithms are to be taken : See Ohm's Versuch eines ...
... dividend : a father extension of this analogy has led to the assumption of the terms radi- tand and logarithmand , to express the numbers whose roots are to be extracted or whose logarithms are to be taken : See Ohm's Versuch eines ...
Page 38
... dividend be 96 and the divisor 8 , the quotient is 12 : for the dividend 96 is the product of the divisor 8 and of the quotient 12 or in other words , 8 is said to be contained in 96 , 12 times . If the dividend be ab and the divisor a ...
... dividend be 96 and the divisor 8 , the quotient is 12 : for the dividend 96 is the product of the divisor 8 and of the quotient 12 or in other words , 8 is said to be contained in 96 , 12 times . If the dividend be ab and the divisor a ...
Page 39
... dividend and divisor , may be struck out or exterminated without altering the dividend value of the quotient which results from their division : and con- may be versely , the dividend and divisor may be both of them multiplied by any ...
... dividend and divisor , may be struck out or exterminated without altering the dividend value of the quotient which results from their division : and con- may be versely , the dividend and divisor may be both of them multiplied by any ...
Page 40
... dividend D , will , when multiplied into ad , produce the dividend a D or A : and conversely , the same quantity or num- ber which multiplied into ad produces the dividend aD or A , will , when multiplied into d alone , produce the ...
... dividend D , will , when multiplied into ad , produce the dividend a D or A : and conversely , the same quantity or num- ber which multiplied into ad produces the dividend aD or A , will , when multiplied into d alone , produce the ...
Page 41
... dividend ; underneath what remains of the dividend write what remains of the divisor , and the resulting expression is the quotient required . If no part of the divisor remains except unity , the remaining part of the dividend is the ...
... dividend ; underneath what remains of the dividend write what remains of the divisor , and the resulting expression is the quotient required . If no part of the divisor remains except unity , the remaining part of the dividend is the ...
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.