An Introductory Account of Certain Modern Ideas And Methods in Plane Analytical

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N n and the coordinates of the tangent are therefore that is, they are rational integral algebraic expressions in JUL, and the curve, qua envelope, is unicursal.
£x. Show that the degree to which [x occurs in the cooixlinate. S of the tangent cannot exceed 2(« — 1), and may fall short of this number; and that hence the class of a unicursal curve of order m is not greater than 2(m - 1 ), and the order of a unicursal curve of class n is not greater than 2(11-1).
141. Special examples of these pri
...nciples are familiar. The -point f\ + kf. , (Ji + hj. , li^ + hli. , lies on the line X y z [ = 0; /i r/i K j f-1 ih h I the \\\\Q f\-\-hf.^, . 7i + ^''^i- I'l + f^'f'-j, I'asses through the point ^ n ^ =0; /i Ui K I f-2 0-1 K I the line ii-\-hv = 0, that is passes through the point ?t = 0, v = 0.
Moreover, the coordinates of any point on the line joining l;34 UNICURSAL CURVES. TRACING OF CURVES.
*i' Uv ^1 ^o ''■>' . V-" ^■' ^^^ ^^ expressed in the form x^ + lcx.^, etc. , and similarfy for lines.


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