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 13
... first term of the product being the latter term of the product muft bena , because the two together must destroy each other , or their amount be o , fince one of the factors ( viz . a — a ) is o . Therefore a multiplied by -n muft give ...
... first term of the product being the latter term of the product muft bena , because the two together must destroy each other , or their amount be o , fince one of the factors ( viz . a — a ) is o . Therefore a multiplied by -n muft give ...
Página 13
... first term of the product being → na , the latter term of the product must be + na , because the two together must destroy each other , or their amount be o , fince one of the factors ( viz . a a ) is o . Therefore a multiplied by -n ...
... first term of the product being → na , the latter term of the product must be + na , because the two together must destroy each other , or their amount be o , fince one of the factors ( viz . a a ) is o . Therefore a multiplied by -n ...
Página 18
... first , 2ab where it is of one dimenfion next , and b2 , where a is not at all , being placed laft . The divifor must be ranged ac- cording to the dimenfions of the fame letters ; then you are to divide the first term of the dividend by ...
... first , 2ab where it is of one dimenfion next , and b2 , where a is not at all , being placed laft . The divifor must be ranged ac- cording to the dimenfions of the fame letters ; then you are to divide the first term of the dividend by ...
Página 19
... first term of this new dividend by the firft term of the divifor and fet down the quotient , ( which in this example is b ) with its proper fign . Then multiply the whole divifor by this part of the quotient , and fubtract the product ...
... first term of this new dividend by the firft term of the divifor and fet down the quotient , ( which in this example is b ) with its proper fign . Then multiply the whole divifor by this part of the quotient , and fubtract the product ...
Página 23
... first two 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 ...
... first two 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 ...
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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.