## A Treatise on Algebra |

### From inside the book

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Page vii

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**Arith**- metic , and the close connection which it has been attempted to preserve between those sciences , which has led to the formation of the opinion , that one is really founded upon the other : there is one sense , which we PREFACE . Page xi

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**Arith**- metical Algebra as the science of suggestion : that is , as the science , whose operations and the general consequences of them should serve as the guides to the assumptions which become the foundation of symbolical Algebra ... Page xv

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**arith**- metic , where the incorporation of the digits leads to results which bear no visible or discoverable traces of their origin ; thus the number 24 may be the product of 12 x 2 , or 8 x 3 , or 6 x 4 , or 2 × 3 × 4 , and in passing ... Page xvi

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**Arith**- metic , to be denoted by multiplying the symbol affected with the sign by a number or coefficient which is equal to the number of repetitions of the symbol itself : in a similar manner , the repetition of the operation of ... Page xxiii

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**arith**- metical and symbolical Algebra : the processes in both these Chapters possess , in many cases , an analogy so very close and remarkable , as to have led to their being con- sidered as resting upon a common foundation , and as ...### 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...