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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Página 150
... e = y there will arise an equation agreeing in all re- spects with the equation ( A ) , but that the se- cond and fourth terms will have contrary figns . And And by fuppofing x - 7 = y , there 150 Part II . A TREATISE of.
... e = y there will arise an equation agreeing in all re- spects with the equation ( A ) , but that the se- cond and fourth terms will have contrary figns . And And by fuppofing x - 7 = y , there 150 Part II . A TREATISE of.
Página 151
... arise an equation agreeing with ( B ) in all refpects , but that the fecond and fourth terms will have contrary figns to what they have in ( B ) . The first of these fuppofitions gives this equation , ( C ) y3 — 3ey2 + зe2y— e3 - + py2 ...
... arise an equation agreeing with ( B ) in all refpects , but that the fecond and fourth terms will have contrary figns to what they have in ( B ) . The first of these fuppofitions gives this equation , ( C ) y3 — 3ey2 + зe2y— e3 - + py2 ...
Página 157
... arise -ro , and multiplying all by Þy2 fr + 27 % 7 f y3 — fpy + ƒ2qy — fro , where the co- efficient of the fecond term of the propofed equa- tion multiplied into ƒ makes the coefficient of the Part II . the fecond term of the ...
... arise -ro , and multiplying all by Þy2 fr + 27 % 7 f y3 — fpy + ƒ2qy — fro , where the co- efficient of the fecond term of the propofed equa- tion multiplied into ƒ makes the coefficient of the Part II . the fecond term of the ...
Página 167
... arise will be = 0 , and will give an equation of a lower dimen- fion than the propofed , that fhall have one of its roots equal to one of the roots of the pro- pofed equation . " That the last two terms of the equation va- nifh when the ...
... arise will be = 0 , and will give an equation of a lower dimen- fion than the propofed , that fhall have one of its roots equal to one of the roots of the pro- pofed equation . " That the last two terms of the equation va- nifh when the ...
Página 240
... arise k + f " + pxk + fn − 1 + qxk + ƒn − z + rx k + ƒn − 3 , & c . + A = 0 , 12 by involution , difpofing the terms according to the dimenfions of ƒ . · kn + nka - x xf + n × * ——— I kn − 2ƒ2 + , & c . 2 rk " = 3 + r × n¬3k2¬4 × ƒ ...
... arise k + f " + pxk + fn − 1 + qxk + ƒn − z + rx k + ƒn − 3 , & c . + A = 0 , 12 by involution , difpofing the terms according to the dimenfions of ƒ . · kn + nka - x xf + n × * ——— I kn − 2ƒ2 + , & c . 2 rk " = 3 + r × n¬3k2¬4 × ƒ ...
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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.