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 55
... Arithmetical proportionals ; as the numbers 3 , 7 , 12 , 16. And the quantities , a , a + b , e , e + b . But quantities form a feries in arithmetical proportion , when they " increase or decrease by the fame conftant difference . " As ...
... Arithmetical proportionals ; as the numbers 3 , 7 , 12 , 16. And the quantities , a , a + b , e , e + b . But quantities form a feries in arithmetical proportion , when they " increase or decrease by the fame conftant difference . " As ...
Página 56
... arithmetical proportionals " the fum of the first and 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 ...
... arithmetical proportionals " the fum of the first and 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 ...
Página 169
... arithmetical feries , as a + 3b , a + 2b , a + b , a , the product will beo . 3x2 For fince ax3 - apx2 + aqxar = 0 ; and 2px + q × bx = 0 , it follows that ax3 + 3bx3-- apx2 — 2bpx2 + aqx + bqx 2bpx2 + aqx + bqx — ar = 0 . Which is the ...
... arithmetical feries , as a + 3b , a + 2b , a + b , a , the product will beo . 3x2 For fince ax3 - apx2 + aqxar = 0 ; and 2px + q × bx = 0 , it follows that ax3 + 3bx3-- apx2 — 2bpx2 + aqx + bqx 2bpx2 + aqx + bqx — ar = 0 . Which is the ...
Página 181
... terms of the equation x -px2 + qx - r = 0 a + 3b , a + zb , a + b , a , ax3 - - apx2 + aqx — ar ( = 0 ) + 3bx3 - 2bpx2 + bqx ( = 3x2- 2px + qxbx ) . M 2 Any - Any arithmetical feries where a is the least term Chap . 5 . ALGEBRA . 181.
... terms of the equation x -px2 + qx - r = 0 a + 3b , a + zb , a + b , a , ax3 - - apx2 + aqx — ar ( = 0 ) + 3bx3 - 2bpx2 + bqx ( = 3x2- 2px + qxbx ) . M 2 Any - Any arithmetical feries where a is the least term Chap . 5 . ALGEBRA . 181.
Página 182
... arithmetical feries where a is the least term and the common difference , and the products ( if you fubftitute for x , fucceffively , a , b , c , the three roots of the proposed cubic ) shall be + Nxbx , Mxbx , + Lxbx . For the first ...
... arithmetical feries where a is the least term and the common difference , and the products ( if you fubftitute for x , fucceffively , a , b , c , the three roots of the proposed cubic ) shall be + Nxbx , Mxbx , + Lxbx . For the first ...
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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.