## A Treatise on Algebra |

### From inside the book

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Page 18

... from the coefficient : the

... from the coefficient : the

**remainder**is 1 , and - 3 x 2 + 812 C. + ( 19 ) 172 2 a b - - a + b 112 913 -C 4 c + 3 3 8100 ( 20 ) a 12 - 5 x 1 2 За འ ེ ། 4 + 11x 2 a 3b + 1 4 3 5 a 12 - 59 36 Ꮳ 12 In the last example , from the sum of and 18. Page 46

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**remainder**Examples . after the last operation : as long as a**remainder**exists , the quotient is incomplete ; and in those cases in which the**remainder**can never disappear , however often the operation is repeated , the quotient is ... Page 47

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**remainder**after the first operation , and the quotient is complete in one term . ( 3 ) Divide a2 + 2ab + b2 by a + b . a + b ) a2 + 2 a b + b2 ( a + b Multiply a + b into a , a2 + ab ab + b2 Multiply a + b into b , ab + be By the first ... Page 49

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**remainders**: it is quite clear that by this process the**remainder**can never dis- appear , and consequently the quotient can never become complete . ( 4 ) Divide x2 + ( a + b ) x + ab by x + a . ( Art . 39. Ex . 8. ) x + a ) x2 + ( a ... Page 50

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**remainder**, as it would not be affected by the second operation : it is omitted there- fore to save superfluous ...**remainders**were brought down after each subtraction , the process would stand as follows : x - 7 ) x1 — 4x3 - 34x2 + 50.### Other editions - View all

### Common terms and phrases

a+b+c a₁ affected arith Arithmetical Algebra arithmetical values assumed b₁ binomial binomial theorem c₁ chance coefficients common connection consequently considered contravalent corresponding cosines cube cubic equation decimal deduced definition denoted determined digit divided dividend divisor equa equal equation equivalent form examples expression factors follows formula fraction geometrical greater identical inasmuch interpretation inverse involve least common multiple likewise logarithms magnitudes means metical multiplied necessary negative number of terms numerator and denominator operations P₁ partial fractions plane position powers primitive equation primitive line principle problem proportion proposition quadratic equation quotient ratio rectangle reduced remainder represent respect result right angles shew shewn sides signs similar manner sines solution square root Subtraction symbols tion triangle unknown quantities whole number zero

### Popular passages

Page 104 - Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent whatever those symbols denote.

Page 669 - But if the digits be inverted, and then divided by a number greater by unity than the sum of the digits, the quotient is greater by 2 than the preceding quotient ? Required the number.

Page 27 - The product is a2+2a6-}-62; from which it appears, that the square of the sum of two quantities, is equal to the square of the first plus twice the product of the first by the second, plus the square of the second.

Page 331 - ... of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Page 339 - If four quantities are in proportion, they will be in proportion by 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 332 - 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 340 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.

Page 674 - A person bought some sheep for £. 72 ; and found that if he had bought 6 more for the same money, he would have paid £. 1 less for each. How many did he buy...

Page 139 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.

Page 435 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...