A Treatise on Algebra: Containing the Latest Improvements. Adapted to the Use of Schools and Colleges
Harper & Brothers, 1846 - Algebra - 503 pages
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according affected algebraic becomes binomial calculations called cents changed coefficients column common consequently considered contain continued corresponding cube denominator derived determine difference divide divisible divisor elimination employed entire equal evident EXAMPLE exponent expression extract factors figures final formula four fourth fraction functions give given greater greatest Hence imaginary roots increased interest known least less letters limit logarithm manner means measure method modulus multiplied necessary negative obtain operation polynomial positive preceding present prime problem progression proposed equation prove quotient radical ratio reduce remainder represent resolved respect result rule second term simple solution square root substituting subtract successive suppose taken tens third tion transformed true units unity unknown quantity variations whence whole number write zero
Page 129 - ... two triangles are to each other as the products of their bases by their altitudes.
Page 172 - 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.
Page 107 - There will be as many figures in the root as there are periods in the given number.
Page 237 - B set out from two towns, which were distant 247 miles, and travelled the direct road till they met. A went 9 miles a day ; and the number of days, at the end of which they met, was greater by 3 than the number of miles which B went in a day. How many miles did each go ? 17.
Page 23 - 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 261 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 184 - It is required to divide the number 99 into five such parts, that the first may exceed the second by 3, be less than the third by 10, greater than the fourth by 9, and less than the fifth by 16.
Page 128 - When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c.
Page 48 - Multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.
Page 237 - There are two square buildings, that are paved with stones, a foot square each. The side of one building exceeds that of the other by 12 feet, and both their pavements taken together contain 2120 stones. What are the lengths of them separately ? Ans.