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 18
... divided by fubtracting their exponents as they are multiplied by adding them . Thus if you divide as by a2 , the quotient is a5 - 2 or a3 . And b divided by b4 gives bo - 4 or b2 ; and abs divided by a2b3 gives ab for the quotient . -2 ...
... divided by fubtracting their exponents as they are multiplied by adding them . Thus if you divide as by a2 , the quotient is a5 - 2 or a3 . And b divided by b4 gives bo - 4 or b2 ; and abs divided by a2b3 gives ab for the quotient . -2 ...
Página 23
... divided by ba gives for the quotient b + 2ab Note , The fign ÷ placed between any two quantities , expreffes the quotient of the former divided by the latter . Thus a + b ÷ a -x is the quotient of a + b divided by a - x . C 3 CHAP . VI ...
... divided by ba gives for the quotient b + 2ab Note , The fign ÷ placed between any two quantities , expreffes the quotient of the former divided by the latter . Thus a + b ÷ a -x is the quotient of a + b divided by a - x . C 3 CHAP . VI ...
Página 24
... divided by bis expreffed by placing a above a small line and b under it , thus , Thefe quotients are also called Fractions ; and the dividend or quantity placed above the line is called the Numerator : of the fraction , and the divifor ...
... divided by bis expreffed by placing a above a small line and b under it , thus , Thefe quotients are also called Fractions ; and the dividend or quantity placed above the line is called the Numerator : of the fraction , and the divifor ...
Página 28
... divided by b ; and cbf divided by dbf gives the fame quotient as a divided by d ' ; and ebd divided by fbd the fame quotient as e di- vided by f . 2. Fractions reduced to the fame denomina- tor are added by adding their numerators and ...
... divided by b ; and cbf divided by dbf gives the fame quotient as a divided by d ' ; and ebd divided by fbd the fame quotient as e di- vided by f . 2. Fractions reduced to the fame denomina- tor are added by adding their numerators and ...
Página 29
... divided by , or , gives cb fór mba , and mbd = ad ; nd c , and nbd = cb ; therefore mbd nbd m ad 11 n cb ad cb ; that is , PROBLEM VII . § 31. To find the greatest common Measure of two numbers ; that is , the greatest number that can ...
... divided by , or , gives cb fór mba , and mbd = ad ; nd c , and nbd = cb ; therefore mbd nbd m ad 11 n cb ad cb ; that is , PROBLEM VII . § 31. To find the greatest common Measure of two numbers ; that is , the greatest number that can ...
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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.