Treatise on the elements of algebra |
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Page 42
... - x ) become , when a + b is substituted for x ? Ans . -2 ab - b2 . 94. What does ax - bx become , when a - b is substi- tuted for x ? Ans . a 2ab + b2 . SECTION IV.- DIVISION . PROPOSITIONS . ART . 39. PROP 42 MULTIPLICATION .
... - x ) become , when a + b is substituted for x ? Ans . -2 ab - b2 . 94. What does ax - bx become , when a - b is substi- tuted for x ? Ans . a 2ab + b2 . SECTION IV.- DIVISION . PROPOSITIONS . ART . 39. PROP 42 MULTIPLICATION .
Page 56
... substitution , the quo- tient of a5-65 by a — b . 108. From example 10 , find , by substitution , the quo- tient of a3 . b3 by a - b . - 109. From example 10 , find , by substitution , the quo- tient of a - b7 by a — b . 110. Find ...
... substitution , the quo- tient of a5-65 by a — b . 108. From example 10 , find , by substitution , the quo- tient of a3 . b3 by a - b . - 109. From example 10 , find , by substitution , the quo- tient of a - b7 by a — b . 110. Find ...
Page 92
... substitution in Ex . 11 . 21. Find the sum of ,,, by substitution in Ex . 11 . VI . To subtract fractions . RULE . 85. Reduce the fractions , if necessary , to equi- valent ones having a common denominator , and under the difference of ...
... substitution in Ex . 11 . 21. Find the sum of ,,, by substitution in Ex . 11 . VI . To subtract fractions . RULE . 85. Reduce the fractions , if necessary , to equi- valent ones having a common denominator , and under the difference of ...
Page 121
... substituted for n , in the general formu- la ; then the first and second terms are a12 , and 12a11b . The others are as follows : The third term 12 x 11 a10b266 a10b2 . 2 66 × 10 The fourth term al3 220 ab3 . 3 220 × 9 The fifth term ...
... substituted for n , in the general formu- la ; then the first and second terms are a12 , and 12a11b . The others are as follows : The third term 12 x 11 a10b266 a10b2 . 2 66 × 10 The fourth term al3 220 ab3 . 3 220 × 9 The fifth term ...
Page 178
... substitution . Multiply the terms of the first of the given equations by b ' , and those of the second by b ; we shall thus have the equations , ab'x + bb'y = b'c , a'bx + bb'y = bc ' . Taking the second from the first , the remainder ...
... substitution . Multiply the terms of the first of the given equations by b ' , and those of the second by b ; we shall thus have the equations , ab'x + bb'y = b'c , a'bx + bb'y = bc ' . Taking the second from the first , the remainder ...
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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...