## A Treatise on Algebra |

### From inside the book

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Page xxxi

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**planes**, they are by no means con- fined to them , inasmuch as many other quantities are sus- ceptible of affections which correspond to general or par- ticular values of this sign : it enables us to consider , like- wise , the signs + ... Page 87

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**planes**parallel to three adjacent**planes**of the parallelopipedon were passed through the points of division , the solid would be divided into a number of equal cubes , constructed upon a linear unit , which would be equal to the ... Page 88

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**planes**, and have , therefore , two edge in common , such as ( 1 ) and ( 5 ) , ( 1 ) and ( 6 ) , ( 1 ) and ( 7 ) or ( 2 ) and ( 8 ) , ( 3 ) and ( 8 ) , ( 4 ) and ( 8 ) , will partak ( upon the principle mentioned in Art . 104 ) of the ... Page 111

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**plane**never meet , if produced ever so far ; " and they are therefore determined to be so by a test which is incapable of application , unless through the medium of another proposition : we are there- fore obliged , in order to complete ... Page 368

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**plane**is perpendi- cular to the**planes**of ABCD , ABcd or ADEb , and occupying the same position therefore , with respect to the rectangle represented by ab1 , that the rect- angle represented by -ab bears to the rectangle represented ...### 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...