Elements of Algebra for the Use of Students in Universities: To which is Added an Appendix |
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Page 1
... easily derived from the established me- thod of notation , and the moît fimple rea- fonings concerning the relations of magni- tude . A Invef Investigations by the common arithmetic are greatly limited , from INTRODUCTION Page.
... easily derived from the established me- thod of notation , and the moît fimple rea- fonings concerning the relations of magni- tude . A Invef Investigations by the common arithmetic are greatly limited , from INTRODUCTION Page.
Page 20
... following diftinction of the Cafes . CASE I. When the divifor is fimple , and is a factor of all the terms of the Dividend . This is easily discovered by inspection ; for then N then the coefficient of the divifor measures that of ( 20 )
... following diftinction of the Cafes . CASE I. When the divifor is fimple , and is a factor of all the terms of the Dividend . This is easily discovered by inspection ; for then N then the coefficient of the divifor measures that of ( 20 )
Page 58
... easily expreffed : Many others oc- cur , which are lefs obvious ; but , as they cannot be described in particular rules , the algebraical expreffion of them is beft ex- plained by examples , and must be acquired by experience . A ...
... easily expreffed : Many others oc- cur , which are lefs obvious ; but , as they cannot be described in particular rules , the algebraical expreffion of them is beft ex- plained by examples , and must be acquired by experience . A ...
Page 69
... , but fome other quantities con- nected with them , as their fum , difference , & c . from which they may be easily derived . ( See Ex . 1. of Chap . 5. ) . 3. In the operation alfo , circumftances will fuggeft a 3. In ( 69 )
... , but fome other quantities con- nected with them , as their fum , difference , & c . from which they may be easily derived . ( See Ex . 1. of Chap . 5. ) . 3. In the operation alfo , circumftances will fuggeft a 3. In ( 69 )
Page 106
... easily shewn to arife from an impoffible fuppofition in the original equation . 4. If the equation , however , exprefs the relation of magnitudes abstractly confider- ed , where a contrariety cannot be fuppofed to take place ; the ...
... easily shewn to arife from an impoffible fuppofition in the original equation . 4. If the equation , however , exprefs the relation of magnitudes abstractly confider- ed , where a contrariety cannot be fuppofed to take place ; the ...
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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
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
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.