A Course in Algebra: Being Course One in Mathematics in the University of Wisconsin, Part 1

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Capital city Publishing Company, printers, 1888 - Algebra - 216 pages
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Page 134 - If the coefficient of any term be multiplied by the exponent of a in that term, and the...
Page 201 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 8 - ... let him, for the present, reject the example in which it occurs, and defer the consideration of such equations until he has read the explanation of them to which we shall soon come. Above all, he must reject the definition still sometimes given of the quantity - a, that it is less than nothing. It is astonishing that the human intellect should ever have tolerated such an absurdity as the idea of a quantity less than nothing ; above all, that the notion should have outlived the belief in judicial...
Page 129 - There are n points in a plane, no three of which are in the same straight line with the exception of p, which are all in the same straight line; find the number of straight lines which result from joining them.
Page 61 - Щ miles down a river and back again in 1 hour and 40 minutes : supposing the river to have a current of 2 miles per hour, find the rate at which the crew would row in still water.
Page 130 - The coefficient of the first term is unity; the coefficient of the second term is the sum of the second terms of the binomial factors ; the coefficient of the third term is the sum of the...
Page 118 - To show that the number of combinations of n things taken i at a time is the same as the number taken n — r at a time.
Page 109 - The sum of three numbers in arithmetical progression is 15, and the sum of their squares is 83. Find the numbers. Let x — y, x, x + y represent the numbers.
Page 130 - ... taken two at a time; the coefficient of the fourth term is the sum of the products of the second terms of the binomial factors...
Page 25 - and — are equivalent expressions, also of and — — , we conclude that any factor may be transferred from the numerator to the denominator, or from the denominator to the numerator, by changing the sign of its exponent.

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