An Elementary Treatise on Algebra, Theoretical and Practical: With Attempts to Simplify Some of the More Difficult Parts of the Science, Particularly the Demonstration of the Binomial Theorem in Its Most General Form, [etc.]Hogan and Thompson, 1839 |
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Page 14
... difference between all the additive quantities , and all the subtractive quantities . EXAMPLES . Add together the following quantities : Ex . 1 . + 6ax Ex . 2 . Ex . 3 . 7xy 4bx2 - 2ax 16xy 10bx2 + 7ax -8xy - -7bx2 - ax 2xy 3bx2 Sum ...
... difference between all the additive quantities , and all the subtractive quantities . EXAMPLES . Add together the following quantities : Ex . 1 . + 6ax Ex . 2 . Ex . 3 . 7xy 4bx2 - 2ax 16xy 10bx2 + 7ax -8xy - -7bx2 - ax 2xy 3bx2 Sum ...
Page 19
... difference will be represented by ab , which is ob- viously the same as the addition of a and b ; but if b - c is to be subtracted from a , then , since b is greater than b · -c by C , if b be subtracted , too much will be taken away by ...
... difference will be represented by ab , which is ob- viously the same as the addition of a and b ; but if b - c is to be subtracted from a , then , since b is greater than b · -c by C , if b be subtracted , too much will be taken away by ...
Page 29
... difference , the sum will be twice the greater . 2. By the rule for subtraction , if the difference of any two quanti- ties be taken from their sum , the remainder will be twice the less . † 3. By multiplication , Article 21 , Example 2 ...
... difference , the sum will be twice the greater . 2. By the rule for subtraction , if the difference of any two quanti- ties be taken from their sum , the remainder will be twice the less . † 3. By multiplication , Article 21 , Example 2 ...
Page 32
... difference : For , let c divide a , and call the quotient m ; let it also divide b , and call the quotient n , then a = mc , and b = nc ; therefore a b * = mcnc ; now c evidently measures mc nc , consequently it measures its equal , ab ...
... difference : For , let c divide a , and call the quotient m ; let it also divide b , and call the quotient n , then a = mc , and b = nc ; therefore a b * = mcnc ; now c evidently measures mc nc , consequently it measures its equal , ab ...
Page 33
... difference a br c , would be divisible by it , as has been proved above ; that is , c would be divisible by a quantity greater than itself , which is absurd ; c , therefore , is the greatest common divisor of a and br , and ...
... difference a br c , would be divisible by it , as has been proved above ; that is , c would be divisible by a quantity greater than itself , which is absurd ; c , therefore , is the greatest common divisor of a and br , and ...
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Common terms and phrases
a²x² arithmetical progression ax² ax³ becomes bers BINOMIAL THEOREM bx² Clear the equation coefficients column common logarithms completing the square compound interest consequently cube root cubic equation cx² decimals difference Divide dividend division equal EXAMPLES expansion exponent extracting the root factors figure Find a number find the values Find two numbers fourth fraction gallons geometrical geometrical progression hence imaginary improper fraction integral last term logarithms method multiplied negative number of solutions number of terms numerator and denominator obtained positive preceding quadratic QUESTION quotient rational Reduce remainder represented Required the sum required to find result second term simple equation square root substituting subtracting surd third transposing transposition unknown quantity values of x whence whole number
Popular passages
Page 83 - В can perform a piece of work in 8 days, A and С together in 9 days, and В and С together in 10 days ; in how many days can each alone perform the same work ? Let...
Page 146 - PROBLEM I. To reduce a rational quantity to the form of a surd. RULE. Raise the quantity to a power...
Page 116 - The plate of a looking-glass is 18 inches by 12, and it is to be surrounded by a plain frame of uniform width/ having a surface equal to that of the glass.
Page 99 - The sum of the first and third of four numbers in geometrical progression is 148, and the sum of the second and fourth is 888.
Page 99 - 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 75 - There is a number consisting of two digits, which is equal to four times the sum of those digits; and if 18 be added to it, the digits will be inverted. What is the number?
Page 67 - Ans. 16 and 24. 42. It is required to find a number such, that if it be increased by 7, the square root of the sum shall be equal to the square root of the number itself, and 1 more. Ans. 9.
Page 52 - An equation of the third, fourth, &c. degree, is one in which the highest power of the unknown quantity is the third, fourth, &c.
Page 114 - It is required to find two numbers, such, that their sum, product, and difference of their squares, shall be all equal.
Page 145 - The fore-wheel of a carriage makes 6 revolutions more than the hind- wheel in going 120 yards; but if the circumference of each wheel be increased one yard, it will make only 4 revolutions more than the hind-wheel in the same distance.