A Treatise on Algebra: For the Use of Schools and Colleges |
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algebraic algebraic quantities arithmetical binomial called coefficient continued fraction decimal divide the number dividend division entire number enunciation equa equal equation whose roots evident example exponent expression extract the root factors figure find the greatest find the square find the values formula given number gives greater greatest common divisor integral roots last term less logarithm manner monomial multiplied negative roots nth root number of terms obtain operation perfect square polynomials positive roots preceding progression by quotient proportion proposed equation proposed to find 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 third power third root tion transformed units unity unknown quantities V₁ values of x vulgar fraction whence
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Page 242 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 117 - 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 67 - 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 100 - ... 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 264 - A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished four times as many men as there were companies in the...
Page 98 - If both terms of a fraction be multiplied by the same number, the value of the fraction will not be changed.
Page 38 - 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 217 - Therefore, any term of the progression is equal to the first term multiplied by the ratio raised to a power 1 less than the number of the term.
Page 34 - QUANTITIES. 28. 1. The object of division in algebra is the same as that of division in arithmetic, viz. to find one of the factors of a given product, when the other is known. According to this definition the divisor multiplied by the quotient must produce anew the dividend ; the dividend, therefore, must contain all the factors both of the divisor and quotient ; whence the quotient is obtained by striking out of the dividend the factors of the divisor. Thus to divide...
Page 239 - The logarithm of a number, is, therefore, the exponent of the power, to which it is necessary to raise a given or invariable number, in order to produce the proposed number. Thus in the equation a...