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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... general Theorems for the exterminating unknown quanti- ties in given equations XIII . Of Quadratic equations XIV . Of Surds Supplement to Chap . XIV . 17 24 34 42 54 61 68 81 85 94 127 PART PART II . 11 Of the Genefis and Refolution of.
... general Theorems for the exterminating unknown quanti- ties in given equations XIII . Of Quadratic equations XIV . Of Surds Supplement to Chap . XIV . 17 24 34 42 54 61 68 81 85 94 127 PART PART II . 11 Of the Genefis and Refolution of.
Página 31
... and denominator ; divide them by that common measure and place the quotients in their room , and you fhall have a fraction equivalent * See Chap . XIV . to Thus 25bc75abc = 3a + 36 to the given fraction Chap . 6 . 31 ALGEBRA .
... and denominator ; divide them by that common measure and place the quotients in their room , and you fhall have a fraction equivalent * See Chap . XIV . to Thus 25bc75abc = 3a + 36 to the given fraction Chap . 6 . 31 ALGEBRA .
Página 32
... given frac- tion to a fraction equal to it that fhall have a given denominator , you must multiply the nu- merator by the given denominator , and divide the product by the former denominater , the quotient fet over the given denominator ...
... given frac- tion to a fraction equal to it that fhall have a given denominator , you must multiply the nu- merator by the given denominator , and divide the product by the former denominater , the quotient fet over the given denominator ...
Página 42
... given , the root must be found by dividing the exponent of the given power by the number that denominates the kind of root that is re- quired . Fig . 38 . N P Ꭱ Fig . 40 1 $ 49 . 42 Part I. A TREATISE of Of Evolution.
... given , the root must be found by dividing the exponent of the given power by the number that denominates the kind of root that is re- quired . Fig . 38 . N P Ꭱ Fig . 40 1 $ 49 . 42 Part I. A TREATISE of Of Evolution.
Página 40
... given term , and to multiply the quotient by the exponent of a in the fame term , increased by unit . " Thus to find the coefficients of the terms of the 6th power of ab , you find the terms are ao , a3b , a113 , a3b3 , a2ba , ab3 , bo ...
... given term , and to multiply the quotient by the exponent of a in the fame term , increased by unit . " Thus to find the coefficients of the terms of the 6th power of ab , you find the terms are ao , a3b , a113 , a3b3 , a2ba , ab3 , bo ...
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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.