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 23
... terms , and the letters are the pow- ers of x and a ; fo that the quotient may be continued as far as you please without any more divifion . But in Divifion , after you come to a remain- der of one term , as 2xx in the last example , it ...
... terms , and the letters are the pow- ers of x and a ; fo that the quotient may be continued as far as you please without any more divifion . But in Divifion , after you come to a remain- der of one term , as 2xx in the last example , it ...
Página 29
... terms , and the letters are the pow- ers of x and a ; fo that the quotient may be continued as far as you please without any more divifion . But in Divifion , after you come to a remain- der of one term , as 2xx in the last example , it ...
... terms , and the letters are the pow- ers of x and a ; fo that the quotient may be continued as far as you please without any more divifion . But in Divifion , after you come to a remain- der of one term , as 2xx in the last example , it ...
Página 56
... last terms is equal to the fum of any two terms equally diftant from the extremes . If the first terms are a , a + b , " 9 a + 2b , & c . and the laft term x , the laft term but one will be x - b , the last but two x - 2b , the last but ...
... last terms is equal to the fum of any two terms equally diftant from the extremes . If the first terms are a , a + b , " 9 a + 2b , & c . and the laft term x , the laft term but one will be x - b , the last but two x - 2b , the last but ...
Página 57
... term , then its fum fhall be equal to half the product of the last term multiplied by the number of terms . " For then , a For then , a beingo , the sum of the terms , which is in general a + xx 2 will in this case be TM . From which it ...
... term , then its fum fhall be equal to half the product of the last term multiplied by the number of terms . " For then , a For then , a beingo , the sum of the terms , which is in general a + xx 2 will in this case be TM . From which it ...
Página 59
... terms be in due or- der ; and you are to proceed according to the rule , multiplying the fecond by the third , and dividing their product by the ... last term , then then fhall the four laft terms of the feries be Chap . 9 . 59 ALGEBRA .
... terms be in due or- der ; and you are to proceed according to the rule , multiplying the fecond by the third , and dividing their product by the ... last term , then then fhall the four laft terms of the feries be Chap . 9 . 59 ALGEBRA .
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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.