A Treatise of Algebra, in Three Parts: Containing I. The Fundamental Rules and Operations; II. The Composition and Resolution of Equations of All Degrees, and the Different Affections of Their Roots; III. The Application of Algebra and Geometry to Each Other. To which is Added an Appendix Concerning the General Properties of Geometrical LinesA. Millar and J. Nourse, 1756 - 432 páginas |
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... involving two variable quantities , and of Geometrical Lines to each other ; the Doc- trine of the Loci ; and the Construction of Equations . Thefe make the Subject of the Third Part . * Vix . The finding of Divifers , and the evolution ...
... involving two variable quantities , and of Geometrical Lines to each other ; the Doc- trine of the Loci ; and the Construction of Equations . Thefe make the Subject of the Third Part . * Vix . The finding of Divifers , and the evolution ...
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... involve only one unknown quantity XI . Of the Solution of questions that pro- duce fimple equations XII . Containing fome general Theorems for the exterminating unknown quanti- ties in given equations XIII . Of Quadratic equations XIV ...
... involve only one unknown quantity XI . Of the Solution of questions that pro- duce fimple equations XII . Containing fome general Theorems for the exterminating unknown quanti- ties in given equations XIII . Of Quadratic equations XIV ...
Página 61
... involve only one unknown Quantity . $ 69 . A the equality of two quantities . " It N equation is " a propofition afferting is expreffed most commonly by fetting down the quantities , and placing the fign ( = ) between them . An equation ...
... involve only one unknown Quantity . $ 69 . A the equality of two quantities . " It N equation is " a propofition afferting is expreffed most commonly by fetting down the quantities , and placing the fign ( = ) between them . An equation ...
Página 70
... involving one un- known quantity ; which must be reduced by the Rules of the former Chapter . " EXAMPLE I. Let the fum of two quantities be s , and their difference d . Let s and d be given , and let it be required to find the ...
... involving one un- known quantity ; which must be reduced by the Rules of the former Chapter . " EXAMPLE I. Let the fum of two quantities be s , and their difference d . Let s and d be given , and let it be required to find the ...
Página 70
... involving one un- known quantity ; which must be reduced by the Rules of the former Chapter . " EXAMPLE I. Let the fum of two quantities be s , and their difference d . Let s and d be given , and let it be required to find the ...
... involving one un- known quantity ; which must be reduced by the Rules of the former Chapter . " EXAMPLE I. Let the fum of two quantities be s , and their difference d . Let s and d be given , and let it be required to find the ...
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adeoque affumed alfo arife arithmetical progreffion autem becauſe biquadratic cafe cafu coefficient common meaſure confequently contactus cube cube root cubic equation curvæ curvam curvaturæ curve demonftrated dimenfions diſcover divided divifor ducantur ducta enim equa equal erit ex puncto exponent expreffed expreffions fame manner fecond term feries fhall fide figns fimple equations fince firft firſt firſt term flexus fome fquare root fraction fubftitute fubtract fuch fuppofe furd give greateſt higheſt impoffible integer interfections itſelf laft term laſt leaft lefs lineæ locus metical muft multiplied muſt negative occurrat odd number parabola parallela pofed pofitive poſitive propofed equation puncto punctum quadratic equation quæ quævis quotient recta rectæ refolved refpectively refult repreſent Rule ſhall ſubſtituted ſuppoſe tangentes tertii ordinis thefe theſe thofe thoſe tion unknown quantity vaniſh whence whofe roots whoſe
Pasajes populares
Página 74 - AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C.
Página 55 - A privateer running at the rate of 10 miles an hour discovers a ship 18 miles off making way at the rate of 8 miles an hour : how many miles can the ship run before being overtaken ? Ans.
Página 107 - ... -{-24, equal to nothing, according to the propofed equation. And it is certain that there can be no other values of x...
Página 367 - This is a quarto volume, containing xxxii + 38 pages, and three plates of figures. The title points out that the work consists of two parts ; we are principally concerned with the first part : on...
Página 193 - The demonftration is deduced from the laft article, as the 7 8th is from the preceding. CHAP. IX. Of the Methods by which you may approximate to the roots of numeral Equations by their limits. §84. TT 7 HEN any equation is propofed W to be refolved, firft find the limits of the roots (by Chap. 5.) as for example...
Página 22 - Rule. Multiply the numerator of the dividend by the denominator of the divifor, their produit ¡hall give the numerator of the quotient. 'Then multiply t be denominator of the' dividend by the numerator of the divifor, and their predu£f jhall give the denominator.