A Treatise on Algebra: For the Use of Schools and Colleges |
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algebraic arithmetical binomial column complete equation Completing the square continued fraction decimal denominator difference dividend division entire and positive entire numbers enunciation equa equal equation whose roots evident example exponent expression extract the root factors figure Find the roots find the square find the values formula given number gives greater greatest common divisor integral roots last term left hand member less logarithm manner monomial multiply negative roots nth root number of terms obtain operation perfect square performed polynomials positive roots preceding proportion proposed equation question radical sign ratio real roots reduced remainder Required the number resolve the equation result second degree second power second term shillings solution square root substitution subtract Synthetic Division third power third root tion transformed unity unknown quantity V₁ values of x whence yards
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Page 93 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 11 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...
Page 57 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans. A 14ff days, B 17ff, and C 23J y . 21.
Page 87 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 160 - Therefore, dx.—cy. 10. There are two numbers whose product is 135, and the difference of their squares, is to the square of their difference, as 4 to 1. What are the numbers ? Ans. 15 and 9.
Page 30 - 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 113 - CD, and on meeting, it appeared that A had travelled 18 miles more than B ; and that A could have gone B's journey in 15$ days, but B would have been 28 days in performing A's journey. What was the distance between C and D ? Ans.
Page 87 - To demonstrate that if both terms of a fraction be multiplied by the same number, the value of the fraction will not be changed.
Page 183 - ... number by the exponent of the power, to which it is to be raised; the number in the table corresponding to this product, will be the power sought.