Treatise on the elements of algebra |
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Page 9
... root of 64 ; 26 64 , therefore 2 is another root of 64 . = The different roots of a quantity are distinguished by ... square root , and the third the cube root ( Article 14 ) . 1 16. XII . The mark prefixed to a quantity indicates that a ...
... root of 64 ; 26 64 , therefore 2 is another root of 64 . = The different roots of a quantity are distinguished by ... square root , and the third the cube root ( Article 14 ) . 1 16. XII . The mark prefixed to a quantity indicates that a ...
Page 76
... square root of an integer number , which is not a complete square , can neither be expressed by an integer , nor by a fraction . Let a be the number ; then , from the nature of square numbers , it is plain that a cannot have an integral ...
... square root of an integer number , which is not a complete square , can neither be expressed by an integer , nor by a fraction . Let a be the number ; then , from the nature of square numbers , it is plain that a cannot have an integral ...
Page 115
... square root may be expressed as a power , by using an index which , when added to itself , will give this index must be : = a : hence a = a . xa a a1 , and 1 2 ; then axaa } + = a1 In the same manner , since a × Va 1 1 1 3 + + = 1 , we ...
... square root may be expressed as a power , by using an index which , when added to itself , will give this index must be : = a : hence a = a . xa a a1 , and 1 2 ; then axaa } + = a1 In the same manner , since a × Va 1 1 1 3 + + = 1 , we ...
Page 127
... root of 64 a6 b12 . Here it is required to find of what quantity 64 ab12 is the third power : the quantity is plainly 4 ab * , because ( 4 a2b1 ) 3 = 64 a6b12 ( Art . 98 ) ; therefore ( 64 a6 b12 ) = 4 a2b1 . 2. Find the square root of ...
... root of 64 a6 b12 . Here it is required to find of what quantity 64 ab12 is the third power : the quantity is plainly 4 ab * , because ( 4 a2b1 ) 3 = 64 a6b12 ( Art . 98 ) ; therefore ( 64 a6 b12 ) = 4 a2b1 . 2. Find the square root of ...
Page 130
... square root of a compound quantity . RULE . 108. 1o Arrange the terms of the compound quantity according to the dimensions of some one letter , placing the highest power first , the next highest second , and so on ; 2o . find ( Art ...
... square root of a compound quantity . RULE . 108. 1o Arrange the terms of the compound quantity according to the dimensions of some one letter , placing the highest power first , the next highest second , and so on ; 2o . find ( Art ...
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Common terms and phrases
4th power added Algebra algebraic quantities ANSWERS arithmetical ax² Belfast Academy binomial binomial theorem called coefficient common denominator common divisor compound quantity contained cube root cubic equation denote difference Divide dividend divisor equal equidifferent EXAMPLES FOR PRACTICE expressed Extract the square factors Find the sum find the value Given Equations gives greatest common measure Hence hypotenuse indicates infinite series least common multiple letters linear units logarithms means multiplied negative quantities nth root number of terms odd number plain positive prime proportion quadratic quadratic equation quan quotient ratio Reduce remainder Required the number RULE second term sides solved square root substitution subtracted surds symbol tion tity transposing transposition unknown quantities whence Art whole number
Popular passages
Page 249 - London, in order to distinguish his own from any he might meet on the road, pulled three feathers out of the tail of each turkey, and one out of the tail of each goose ; and, upon counting them, found that the number of turkey's feathers exceeded twice those of the geese by 15.
Page 271 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 242 - A vintner sold 7 dozen of sherry and 12 dozen of claret for £50, and finds that he has sold 3 dozen more of sherry for £10 than he has of claret for £6. Required the price of each.
Page 256 - In any proportion, the product of the means is equal to the product of the extremes.
Page 256 - In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them; as in the latter of the above series 6 + 1=4+3, and =5+2.
Page 294 - To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment.
Page 249 - ... feathers exceeded twice those of the geese by 15. Having bought 10 geese and sold 15 turkeys by the way, he was surprised to find, as he drove them into the poulterer's yard, that the number of geese exceeded the number of turkeys in the proportion of 7 to 3.
Page 246 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days ; how many days would the man alone be in drinking it ? Ans.
Page 250 - There are two square buildings, that are paved with stones, a foot square each. The side of one building exceeds that of the other by 12 feet, and both their pavements taken together contain 2120 stones. What are the lengths of them separately 1 Ans.
Page 249 - A man and his wife could drink a barrel of beer in 15 days. After drinking together 6 days, the woman alone drank the remainder in 30 days. In what time would either alone drink a barrel...