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 |
Dentro del libro
Resultados 1-5 de 5
Página 39
... same , and is equal to the exponent of the power required . " Thus in the 6th power of a + b , viz . ao + 6a3b + 15a + b2 + 20a3b3 + 15a2ba + 6ab3 + bo , D 3 the the exponents of a decrease in this order , 6 Chap . 7 . 39 ALGEBRA .
... same , and is equal to the exponent of the power required . " Thus in the 6th power of a + b , viz . ao + 6a3b + 15a + b2 + 20a3b3 + 15a2ba + 6ab3 + bo , D 3 the the exponents of a decrease in this order , 6 Chap . 7 . 39 ALGEBRA .
Página 64
... be found on both fides of the equation with the same sign prefixt , it may be taken away from both : " " Also , if all the quantities in the equation are multiplied or divided B Z D A S Fig.56 . b K Fig 66 Part I. A TREATISE of.
... be found on both fides of the equation with the same sign prefixt , it may be taken away from both : " " Also , if all the quantities in the equation are multiplied or divided B Z D A S Fig.56 . b K Fig 66 Part I. A TREATISE of.
Página 184
... same may be demonftrated of any number of roots what- ever . 2 Now if you add the fum of all the cubes taken affirmatively to their fum with their proper figns , they will give double the fum of the cubes of the affirmative roots . And ...
... same may be demonftrated of any number of roots what- ever . 2 Now if you add the fum of all the cubes taken affirmatively to their fum with their proper figns , they will give double the fum of the cubes of the affirmative roots . And ...
Página 253
... same straight line will be equal ; " but “ the di- mensions of y in the terms above that line will be greater than in thofe in that line ; " and " the dimenfions of y in the terms below the faid line will be less than its dimenfions in ...
... same straight line will be equal ; " but “ the di- mensions of y in the terms above that line will be greater than in thofe in that line ; " and " the dimenfions of y in the terms below the faid line will be less than its dimenfions in ...
Página 272
... same reasoning as we used , in § 113 , to demonftrate that , in the first order of terms x -Aynx P , the lowest dimenfions of y are m + ns + pr , we fhall find that , in the sub- fequent orders , the lowest dimenfions of y in the the ...
... same reasoning as we used , in § 113 , to demonftrate that , in the first order of terms x -Aynx P , the lowest dimenfions of y are m + ns + pr , we fhall find that , in the sub- fequent orders , the lowest dimenfions of y in the the ...
Otras ediciones - Ver todas
Términos y frases comunes
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.