The Elements of Algebra |
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... contain very nu- merous examples adapted to each , subject introduced into it . Yet although this intention of making the young algebraist skilful in what may be termed the mechani- cal part of his science has never been lost sight of ...
... contain very nu- merous examples adapted to each , subject introduced into it . Yet although this intention of making the young algebraist skilful in what may be termed the mechani- cal part of his science has never been lost sight of ...
Page 10
... contain no difficulty : had we however to subtract b - c from a , the result a - b + c , requires explanation . First , having to subtract b - c , if we only subtract b , the result ab , is obviously too little , for the quantity b ...
... contain no difficulty : had we however to subtract b - c from a , the result a - b + c , requires explanation . First , having to subtract b - c , if we only subtract b , the result ab , is obviously too little , for the quantity b ...
Page 21
... contained in the former : or since the dividend is equal to the pro- duct of the divisor and the quotient , we may define divi- sion to be , The having given one factor of a quantity to find the remaining factor . ' Thus 4abc ÷ by 2c or ...
... contained in the former : or since the dividend is equal to the pro- duct of the divisor and the quotient , we may define divi- sion to be , The having given one factor of a quantity to find the remaining factor . ' Thus 4abc ÷ by 2c or ...
Page 25
... contained exactly in the dividend , and the remainder is consequently nothing : we shall now give examples in which there is a remainder . x − a ) x3 + a3 ( x2 + a x + a2 x3- α x2 + a x2 a x2- a2x a2x + a3 a2x - a3 2 a3 the remainder ...
... contained exactly in the dividend , and the remainder is consequently nothing : we shall now give examples in which there is a remainder . x − a ) x3 + a3 ( x2 + a x + a2 x3- α x2 + a x2 a x2- a2x a2x + a3 a2x - a3 2 a3 the remainder ...
Page 36
... contains all the denominators . If then we multiply the nu- merator and denominator of the first fraction by 10 , of the second by 6 , and of the third by 3 , each will have the same denominator . 5x 10 50x 6 42x 3x 9x For X ; X 3 10 30 ...
... contains all the denominators . If then we multiply the nu- merator and denominator of the first fraction by 10 , of the second by 6 , and of the third by 3 , each will have the same denominator . 5x 10 50x 6 42x 3x 9x For X ; X 3 10 30 ...
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Common terms and phrases
2ab+b² a²+2ab+b² a²x² a³b ab² ab³ algebraical quantities arithmetic mean arithmetic series arithmetical progression ax² binomial coefficient common difference compound cube root decimal denominator digits divided dividend division divisor equal examples expressed Extract the square factor Find the greatest find the numbers Find the sum fraction geometrical progression greatest common divisor greatest common measure Hence last term least common multiple less letters logarithm multiplied negative number of terms numbers in arithmetical P₁ permutations QUADRATIC EQUATIONS quotient ratio remainder result rule shew square root subtract surd third unity unknown quantity whence write written xy³
Popular passages
Page 38 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 199 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 22 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 173 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.