Elements of Algebra for the Use of Students in Universities: To which is Added an AppendixWilliam Creech and sold, 1796 - 311 ページ |
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abfolute term affumed alfo algebra algebraical quantities alſo anſwer arifing cafe called Chap coefficient cofine common meaſure conftruction continued fraction correfponding cubic equation curve deduced denominator denote dimenfions divided dividend divifible divifion divifor diviſible eaſily equa equal example exponents expreffed expreffion faid fecond term feries fides fimple equations fince firft term firſt folution fome fraction ftraight line fubftitution fubtracted fuch fuppofed furds geometrical given equation greateſt hence impoffible inferted integer intereft interfection inveſtigation itſelf laft laſt lefs leſs logarithms moſt muft multiplied muſt neceffary negative notation number of terms obferved odd number phyfical poffible pofitive poſitive powers preceding Prob problem Prop propofition proportional equation quadratic quadratic equation quan queſtion quotient radical fign reaſon refolved refult remainder repreſented rule SCHOLIUM ſeries ſquare thefe theorem theſe thofe thoſe tion tities Tranfp unknown quantity uſed whofe
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64 ページ - A sets out from a certain place, and travels at the rate of 7 miles in 5 hours ; and 8 hours...
207 ページ - ... 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...
222 ページ - 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.
185 ページ - 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.
207 ページ - ... 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.
37 ページ - JJ/xJV; hence, The sum of the logarithms of any two numbers is equal to the logarithm of their product.
23 ページ - ... 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.
189 ページ - 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...
38 ページ - 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.
16 ページ - To multiply compound quantities. Rule. Multiply every term of the multiplicand by all the terms of the multiplier •, one after another, according to the preceding rule, and then collect all the products into one fum' that fum is the product required.