Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 231
resent an interesting classof curves which serve to illustrate this theory. y=l+{x-ar. (1) Whence ^=m(a;—a)°-«. (2) ^=m(m-\){x-a)-K (3) 1st. If we assume that~=0, it follows that a;=a, and thisdx value put in (1) will give y=5. But to assume that —=0, is the same asdx to assume that the tangent… … THEORY OF CURVES. 223 give 2/and^—| positive, for suppose x=a±:h, then (x—a)=dzh,and substituting this in (3) we obtain g=m(m_l)(±;.)-^ Here as (m—2) is even, the power of k will be positive,whichever sign we give to h^ and as m is even, the whole productwill be positive, hence this curve is convex…
Geometry, Analytic · Calculus
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