## Elements of Algebra for the Use of Students in Universities: To which is Added an Appendix |

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Elements of Algebra. for the Use of Students in Universities. Third Edition ... William Trail No preview available - 2018 |

Elements of Algebra. for the Use of Students in Universities William Trail No preview available - 2018 |

### Common terms and phrases

abſolute term algebra alſo anſwer ariſe aſſumed baſe caſe Chap coefficient common meaſure conſidered conſtruction correſponding cubic equation curve deduced demonſtrated denominator denote deſcribed dimenſion diſcovered divided dividend diviſible diviſion diviſor E X A M P L E eaſily equa equal exponents expreſſed expreſſion figns fimple firſt term fraćtion geometrical given equation greateſt Hence impoſſible increaſed inſerted integer intereſt inveſtigation itſelf laſt leaſt leſs logarithms moſt multiplied muſt neceſſary negative obſerved odd number oppoſite phyſical poſitive poſſible powers preceding Prob problem produćt Prop proportional equation propoſition quadratic quadratic equation quan queſtion quotient reaſon repreſent reſolved reſult rule ſaid ſame ſcale ſecond term ſeries ſeveral ſhall ſides ſign ſimple equations ſin ſince ſolution ſome ſometimes ſought ſquare root ſtraight line ſubſtituted ſubtracted ſuch ſum ſuppoſed ſuppoſition ſurds theorem theſe thoſe tion tities Tranſp unknown quantity uſed whoſe

### Popular passages

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.

Page 16 - 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.