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 LinesF. Wingrave; T. Longman; W. Richardson; G. G. and J. Robinson; F. and C. Rivington; W. Lowndes; and Cadell and Davies., 1796 - 504 páginas |
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... quantity 61 duce fimple equations 68 XI . Of the Solution of queftions that pro- XII . Containing fome general Theorems for the exterminating unknown quantities in given equations XIII . Of Quadratic equations XIV . Of Surds Supplement ...
... quantity 61 duce fimple equations 68 XI . Of the Solution of queftions that pro- XII . Containing fome general Theorems for the exterminating unknown quantities in given equations XIII . Of Quadratic equations XIV . Of Surds Supplement ...
Página 61
... UNKNOWN QUANTITY . § 69. AN equation is « a propofition alerting the equality of two quantities . " It is expreffed most commonly by fetting down the quantities , and placing the fign ( = ) between them . An equation gives the value of a ...
... UNKNOWN QUANTITY . § 69. AN equation is « a propofition alerting the equality of two quantities . " It is expreffed most commonly by fetting down the quantities , and placing the fign ( = ) between them . An equation gives the value of a ...
Página 62
... unknown quantity in a given equa- tion , and only one dimension of it , fuch a value may always be found by the following Rules . $ 70 . RULE I. " Any quantity may be tranfpofed from one fide of the equation to the other , if you change ...
... unknown quantity in a given equa- tion , and only one dimension of it , fuch a value may always be found by the following Rules . $ 70 . RULE I. " Any quantity may be tranfpofed from one fide of the equation to the other , if you change ...
Página 63
... quantity ; and when you divide equal quantities by the fame quantity , the quo- tients must be equal . Thus , $ 72 ... unknown quantity is divided by any quantity , that quantity may be taken away if you multiply all the other members of ...
... quantity ; and when you divide equal quantities by the fame quantity , the quo- tients must be equal . Thus , $ 72 ... unknown quantity is divided by any quantity , that quantity may be taken away if you multiply all the other members of ...
Página 64
... unknown quantity be a furd root , then the equation is to be reduced to another that fhall be free from any furd , by bringing that member first to stand alone upon one fide of the equation , and then taking away the radical fign from ...
... unknown quantity be a furd root , then the equation is to be reduced to another that fhall be free from any furd , by bringing that member first to stand alone upon one fide of the equation , and then taking away the radical fign from ...
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adeoque affumed afymptote alfo alſo arife arithmetical progreffion autem becauſe biquadratic cafe cafu coefficient common meaſure confequently conic fection contactus Corol cube cubic equation curvæ curvam curvature demonftrated dimenfions divided divifor drawn ducantur ducta enim equa equal erit expreffed fame manner fame right line fecond term feries fhall fide figns fimple equations fince firft firſt flexus fome fquare root fubftitute fubtract fuch fuppofe furd greateſt harmonical mean impoffible interfections laft term laſt leaft lefs lineæ locus meet the curve metical multiplied muſt negative occurrat parallel pofitive PROP propofed equation puncto punctum px² quadratic equation quæ quævis quotient recta rectæ refolved refult Rule ſhall ſuppoſe tangents tertii ordinis thefe theſe third order thofe tion touching the curve unknown quantity vaniſh whence whoſe
Pasajes populares
Página 88 - 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 431 - APM, cut a geometrical line of any order in as many points as it has dimensions, the product of the segments of the first terminated by P and the curve, will always be to the product of the segments of the latter, terminated by the same point and the curve, in an invariable ratio.
Página 426 - And by iimilar equations geometrical lines of fuperior orders are defined. § 2. A geometrical line may meet a right line in as many points as there are units in the number which denotes the order of the equation or line, and never in more. The number of times that any curve will meet its...
Página 43 - The general Theorem vhich we gave for the Involution of binomials will' ferve alfo for their Evolution ;" becaufe to extract any root of a given quantity is the fame thing as to raife that quantity to a power whofe exponent is a fraction that has...
Página 61 - 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.