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Elements of Algebra. for the Use of Students in Universities. Third Edition ...
No preview available - 2018
according added algebra alſo appears application ariſe arithmetical aſſumed becomes called caſe Chap coefficient common compound conſidered containing continued curve deduced definition denominator denote derived difference divided dividend diviſible diviſion diviſor eaſily equa equal equation example exponents expreſſed extracted firſt firſt term four fourth fraction geometrical give given greater greateſt hence integer intereſt known laſt leſs letters logarithms manner means meaſure method moſt multiplied muſt nature negative notation obſerved obtained obvious operation plain poſitive powers preceding principles Prob problem Prop proper properties proportionals quadratic quan queſtion quotient rational reaſon reduced relations remainder reſolved root rule ſame ſecond ſeries ſide ſign ſimple ſin ſolution ſome ſquare ſquare root ſubtracted ſuch ſum ſuppoſed ſurds taken theorem theſe third thoſe tion tities unknown quantity uſed whoſe
Page 64 - A sets out from a certain place, and travels at the rate of 7 miles in 5 hours ; and 8 hours...
Page 207 - ... cafe, it muft have been greater than each of an odd number of the pofitive roots. An odd number of the pofitive roots, therefore, muft lie between them when they give refults with oppofite figns. The fame obfervation is to be extended to the fubftitution of negative quantities and the negative roots. From this lemma, by means of trials, it will not be difficult to find the neareft integer to a root of a given numeral equation. This is the firft ftep towards the approximation ; and both the manner...
Page 222 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 185 - The coefficient of the fourth term is the fum of all the products which can be made by multiplying together any three of the roots with their figns changed ; and fo of others.
Page 207 - ... that of the given abfolute term, the figns of an odd number of the pofitive roots muft have been changed. In the firft cafe, then, the quantity fubftituted muft have been either greater than each of an even number of the pofitive roots of the given equation, or lefs than any of them ; in the fécond cafe, it muft have been greater than each of an odd number of the pofitive roots.
Page 37 - JJ/xJV; hence, The sum of the logarithms of any two numbers is equal to the logarithm of their product.
Page 23 - ... from the new dividend ; and thus the operation is to be continued till no remainder is left, or till it appear that there will always be a remainder.
Page 189 - From this transformation, the fecond, or any other intermediate term, may be taken away ; granting the refolution of equations. Since the coefficients of all the terms of the transformed equation, except the firft, involve the powers of e and known quantities only, by putting the coefficient of any term equal to o, and refolving that equation, a value of e may be determined; which being fubftituted, will make that term to...
Page 38 - Jhall give the numerator of the quotient. Then multiply the denominator of the dividend by the numerator of the divifor, and their produft Jhall give the denominator.