## A Treatise on Algebra |

### From inside the book

Results 1-5 of 97

Page vii

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**definitions**of those operations in practice , though we have retained them in name : for the conse- quences of those operations , and of the assumptions con- nected with them , must be determined by the fundamental rules for performing ... Page ix

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**definitions**of alge- braical operations , to which symbols thus affected are sub- jected , we must necessarily omit every condition which is in any way connected with their specific value or repre- sentation : in other words , the ... Page x

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**define**the sym- bolical relation of pairs of those operations to each other , that we assume the operation denoted by + to be the inverse of that which is denoted by and conversely ; and the operation denoted by x to be the inverse of ... Page xii

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**defined**likewise to be respectively the inverse of each other . Having thus established the necessary identity of the results of arithmetical and symbolical Algebra , as far as this agreement can extend without violating the necessary ... Page xviii

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**defined**; but if n be a general symbol , we are unable to**define**the operation by which we pass from ( 1 + x ) " to its equivalent series , which exists therefore under such circumstances , only in virtue of the principle of the ...### 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...