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 72
... Suppose the distance between London and Edin- burgh to be 360 miles , and that a courier fets out from Edinburgh running at the rate of 10 miles an hour ; another fets out at the fame time from London , and runs 8 miles an hour . It is ...
... Suppose the distance between London and Edin- burgh to be 360 miles , and that a courier fets out from Edinburgh running at the rate of 10 miles an hour ; another fets out at the fame time from London , and runs 8 miles an hour . It is ...
Página 75
... Suppose them to be x and y , their fum s , and difference of their fquares d . x + y = s x2 - y2 = d x = S — y x2 = 52 25y + y2 x2 = d + y2 d + y2 = s2 — 25y + y2 ds2sy , whence = s2 * Then , 25y = s2 - d 52 - d y = 25 s2 + ď and x = 25 ...
... Suppose them to be x and y , their fum s , and difference of their fquares d . x + y = s x2 - y2 = d x = S — y x2 = 52 25y + y2 x2 = d + y2 d + y2 = s2 — 25y + y2 ds2sy , whence = s2 * Then , 25y = s2 - d 52 - d y = 25 s2 + ď and x = 25 ...
Página 76
... Suppose their pro- portion to be the fame as that of a to b , and let the fum of their fquares be c ; that is , let xy :: a : b 2x2 + y2 = c ay then x = a2y2 and x2 = but x2 = c 62 - y2 , whence cy2 = - y2 = 21 62 b2y2 + a2y2 = cb2 a2 + ...
... Suppose their pro- portion to be the fame as that of a to b , and let the fum of their fquares be c ; that is , let xy :: a : b 2x2 + y2 = c ay then x = a2y2 and x2 = but x2 = c 62 - y2 , whence cy2 = - y2 = 21 62 b2y2 + a2y2 = cb2 a2 + ...
Página 84
... Suppose , for example , that f and k are equal to nothing , then the term fz will vanish in the fecond equation , and kz in the aep — anh tdbmdbp + gbngem dhc - gec third , and z = gcn - y = dep dhc gec If If four equations are given ...
... Suppose , for example , that f and k are equal to nothing , then the term fz will vanish in the fecond equation , and kz in the aep — anh tdbmdbp + gbngem dhc - gec third , and z = gcn - y = dep dhc gec If If four equations are given ...
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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.