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 310
... parabola whose vertex is B , axis BE , and parameter equal to a . For fince BPbx , and PM y , if BF be equal to a ; then the rectangle BN ( ab ± ax ) will be equal to PMq ( = y ; ) which is the known property of the parabola . And it is ...
... parabola whose vertex is B , axis BE , and parameter equal to a . For fince BPbx , and PM y , if BF be equal to a ; then the rectangle BN ( ab ± ax ) will be equal to PMq ( = y ; ) which is the known property of the parabola . And it is ...
Página 311
... parabola whofe vertex is B , axis BE , and parameter equal to a . For fince BPbx , and PM = y , if BF be equal to a ; then the rectangle BN ( = abax ) will be equal to PMq ( = y ; ) which is the known property of the parabola . And it ...
... parabola whofe vertex is B , axis BE , and parameter equal to a . For fince BPbx , and PM = y , if BF be equal to a ; then the rectangle BN ( = abax ) will be equal to PMq ( = y ; ) which is the known property of the parabola . And it ...
Página 317
... parabola . A is the vertex , AE is the tan- M +4 M +4 E P Λ gent at the vertex ; and the two infinite arcs lie manifeftly on the fame fide of AE . But But the locus of the equation a1y = x3 , Chap . 1 . 317 ALGEBRA .
... parabola . A is the vertex , AE is the tan- M +4 M +4 E P Λ gent at the vertex ; and the two infinite arcs lie manifeftly on the fame fide of AE . But But the locus of the equation a1y = x3 , Chap . 1 . 317 ALGEBRA .
Página 318
... parabola , and is a line of the third order . The locus of the equation a3y = x4 is of a figure like the common parabola ; and " all thofe loci , in whofe equations y is of one di- menfion , x of an even number of dimenfions : But thofe ...
... parabola , and is a line of the third order . The locus of the equation a3y = x4 is of a figure like the common parabola ; and " all thofe loci , in whofe equations y is of one di- menfion , x of an even number of dimenfions : But thofe ...
Página 329
... parabola ; AE any line drawn in the fame plane ; and let it be re- quired to find the equation expreffing the re- lation betwixt the ordinate PM forming any given angle with AE , and the abfciffe AP begin- Y 4 beginning at A any given ...
... parabola ; AE any line drawn in the fame plane ; and let it be re- quired to find the equation expreffing the re- lation betwixt the ordinate PM forming any given angle with AE , and the abfciffe AP begin- Y 4 beginning at A any given ...
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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.