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 371
... ducta DM parallela recta AN erit ocus cui æquatio propofita refpondebit . Nam PM = PN + NM = ( a × AP + AD ) ax + b . Quod fi equatio fit formæ yax - b vel yax + b , recta AD , vel PN , fumenda eft ad alteram partem abfciffæ AP ...
... ducta DM parallela recta AN erit ocus cui æquatio propofita refpondebit . Nam PM = PN + NM = ( a × AP + AD ) ax + b . Quod fi equatio fit formæ yax - b vel yax + b , recta AD , vel PN , fumenda eft ad alteram partem abfciffæ AP ...
Página 372
... omnes nonnunquam fiunt imagina- riæ , adeoque fieri poteft ut recta in plano lineæ paris ordinis ducta eidem nullibi occurrat . $ 3 . Æquatio fecundi aut fuperioris cujufcunque or- dinis $ 3 . 372 De LINEARUM GEOMETRICARUM.
... omnes nonnunquam fiunt imagina- riæ , adeoque fieri poteft ut recta in plano lineæ paris ordinis ducta eidem nullibi occurrat . $ 3 . Æquatio fecundi aut fuperioris cujufcunque or- dinis $ 3 . 372 De LINEARUM GEOMETRICARUM.
Página 378
... ducta linea geometrica cujufcunque ordinis in tot punctis quot ipfa eft dimenfionum ; reétæ figuram in his punctis contingentes abfcindant ab alia rectâ pofitione data per idem punctum datum ductâ segmenta totidem hoc puncto terminata ...
... ducta linea geometrica cujufcunque ordinis in tot punctis quot ipfa eft dimenfionum ; reétæ figuram in his punctis contingentes abfcindant ab alia rectâ pofitione data per idem punctum datum ductâ segmenta totidem hoc puncto terminata ...
Página 379
... ducta fegmenta PK , PL , PM , & c , et Pk , Pl , Pm , & c . dico fore ++ + & c . = + + T Pm PK I PM I Pk P / + & c . atque hanc fummam manere femper ean- dem manente puncto P & recta PE pofitione data . Supponamus enim rectas ABC , abc ...
... ducta fegmenta PK , PL , PM , & c , et Pk , Pl , Pm , & c . dico fore ++ + & c . = + + T Pm PK I PM I Pk P / + & c . atque hanc fummam manere femper ean- dem manente puncto P & recta PE pofitione data . Supponamus enim rectas ABC , abc ...
Página 386
... ducta curvæ in tot punctis D , A , B , & c . quot ipfa eft dimenfionum ; ducatur DT curvam contin- gens in D , quæ curvam fecet in punctis I , & c . binario paucioribus , & occurrat tangentibus AK , BL , & c . in K , L , & c . eritque ...
... ducta curvæ in tot punctis D , A , B , & c . quot ipfa eft dimenfionum ; ducatur DT curvam contin- gens in D , quæ curvam fecet in punctis I , & c . binario paucioribus , & occurrat tangentibus AK , BL , & c . in K , L , & c . eritque ...
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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.