An elementary treatise on curve tracing . ^ Fig 2 y Fig- 3 ^ Plate XV i IV / y. K K .^rx •m ^^^ ^. Y<--- •V I •.., .-/?? / 1 / %, ? ( ^A « <<:^ ?f I ^ m f k /? \ [ # « %, •y^ « < / /iv \ // / ^ \. METHOD BY THE TEIANGLE 193 METHOD BY THE TRIANGLE. 217. The arrangement of terms corresponding to infinitebranches and multiple points is made easy by consideringthe property proved in Art. 145, i., that all parallel linescontainingcircles which indicate terms of an equation give,when such are equated to zero, the same relation betweenX and y as far as degree is concerned; so that, if the
An elementary treatise on curve tracing . ^ Fig 2 y Fig- 3 ^ Plate XV i IV / y. K K .^rx •m ^^^ ^. Y<--- •V I •.., .-/?? / 1 / %, ? ( ^A « <<:^ ?f I ^ m f k /? \ [ # « %, •y^ « < / /iv \ // / ^ \. METHOD BY THE TEIANGLE 193 METHOD BY THE TRIANGLE. 217. The arrangement of terms corresponding to infinitebranches and multiple points is made easy by consideringthe property proved in Art. 145, i., that all parallel linescontainingcircles which indicate terms of an equation give,when such are equated to zero, the same relation betweenX and y as far as degree is concerned; so that, if there be,for example, a point of inflexion at the origin, the branchtouchingone of the axes, an equation giving such a formwould be y^ = Ax% where r and s are different odd numbers,and the same relation would be given for all parallel lines;the polygon must, therefore, have one of its lower sidesparallel to the line xlr-\-y/s = l. 218. If the form of the curve, whose equation is required,be represented in the neighbourhood of the origin by thetwo equations x^ccy^ and cc*oc y, in which r/s<^rls, letOx, Oy be the sides of the triangle, intersected by AB,AB, where OA=^r, OB = s, etc. Complete the paralle
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