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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... Impoffible roots of Equations , our Author had very fully confi- dered , as appears from his Manuscript papers : but as he had no where reduced any thing on that that Subject to a better form , than what was To the READER .
... Impoffible roots of Equations , our Author had very fully confi- dered , as appears from his Manuscript papers : but as he had no where reduced any thing on that that Subject to a better form , than what was To the READER .
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... Reduction of equations by furd divifors VIII . Of the Refolution of equations by Cardan's rule , and others of that kind IX . Of the Methods by which you may approximate to the roots of nu- 139 148 162 170 186 197 213 223 meral meral ...
... Reduction of equations by furd divifors VIII . Of the Refolution of equations by Cardan's rule , and others of that kind IX . Of the Methods by which you may approximate to the roots of nu- 139 148 162 170 186 197 213 223 meral meral ...
Página 25
... reduce a MIXT quantity to an IMPRO- PER FRACTION . Rule . Multiply the part that is an integer by the denominator of the fractional part ; and to the product add the numerator ; under their fum place the former denominator . Thus 23 reduced ...
... reduce a MIXT quantity to an IMPRO- PER FRACTION . Rule . Multiply the part that is an integer by the denominator of the fractional part ; and to the product add the numerator ; under their fum place the former denominator . Thus 23 reduced ...
Página 26
... reduce fractions of different denomina- tions to fractions of equal value that shall have the fame denominator . Rule . Multiply each numerator , Separately taken , into all the denominators but its own , and the products fhall give the ...
... reduce fractions of different denomina- tions to fractions of equal value that shall have the fame denominator . Rule . Multiply each numerator , Separately taken , into all the denominators but its own , and the products fhall give the ...
Página 27
... reduce it to the form of a fraction ( by Prob . 1. ) And if an integer is to be multiplied by a frac- tion , you may reduce it to the form of a frac tion by placing unit under it . EXAMPLES . 53 × = 3 51 X ; 9 × X l [ è 18 3 6 : 6+ bx X ...
... reduce it to the form of a fraction ( by Prob . 1. ) And if an integer is to be multiplied by a frac- tion , you may reduce it to the form of a frac tion by placing unit under it . EXAMPLES . 53 × = 3 51 X ; 9 × X l [ è 18 3 6 : 6+ bx X ...
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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.