A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 - Algebra |
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Page 5
... numbers expressed 9. Let us now advance a step farther and suppose that the etters of the alphabet , such as a , b , c ... x , y , z , are used to denote umbers of any kind , whether known or unknown , whole or ractional ( Art . 3 ...
... numbers expressed 9. Let us now advance a step farther and suppose that the etters of the alphabet , such as a , b , c ... x , y , z , are used to denote umbers of any kind , whether known or unknown , whole or ractional ( Art . 3 ...
Page 104
... number divided by another , increased by the unknown quo- In the selection of the partial divisor , it is generally ... numbers , and there will be less danger of introducing erroneous digits into the quotient . tient which results , we ...
... number divided by another , increased by the unknown quo- In the selection of the partial divisor , it is generally ... numbers , and there will be less danger of introducing erroneous digits into the quotient . tient which results , we ...
Page 146
... number # may be considered as equivalent to the arithmetical solution equivalent of the equation traction of roots is to the solu- tion of an equation of the same the root . x2 = n , where x , or the square root of n , is an unknown ...
... number # may be considered as equivalent to the arithmetical solution equivalent of the equation traction of roots is to the solu- tion of an equation of the same the root . x2 = n , where x , or the square root of n , is an unknown ...
Page 186
... number of men , the number of days and the number of hours in each day . It ... unknown term of the proportion . The breadth varies as the number of men and ... numbers : but sarily lead in the ordinary form of solution which is followed ...
... number of men , the number of days and the number of hours in each day . It ... unknown term of the proportion . The breadth varies as the number of men and ... numbers : but sarily lead in the ordinary form of solution which is followed ...
Page 187
... numbers , and the arrangement which leads to the employment of them is a ... unknown term , will be precisely the same as if all the terms were placed in ... numbers , the nume- ratios rical value of the unknown term will be the same ...
... numbers , and the arrangement which leads to the employment of them is a ... unknown term , will be precisely the same as if all the terms were placed in ... numbers , the nume- ratios rical value of the unknown term will be the same ...
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.