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| {\em Secant line} (or simply {\em secant}) of a curve is a straight line intersecting the curve in at least two distinct points. \,[The name is initially a participial form of the Latin verb {\em secare} `\PMlinkescapetext{to cut}'.] |
{\em Secant line} (or simply {\em secant}) of a curve is a straight line intersecting the curve in at least two distinct points. \,[The name is initially a participial form of the Latin verb {\em secare} `\PMlinkescapetext{to cut}'.] |
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| If one sets a secant e.g. to the ``cubic parabola'' \,$y = x^3$\, through its points $(0,\,0)$ and $(1,\,1)$, there is also a third common point $(-1,\,-1)$. |
If one sets a secant e.g. to the ``cubic parabola'' \,$y = x^3$\, through its points $(0,\,0)$ and $(1,\,1)$, there is also a third common point $(-1,\,-1)$. |
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| Notice that a secant line can also be tangent to the curve at some point, given that tangency is only a local property. In the following picture, $l$ is a secant line for the curve $C$ (since it intersects the curve at points $A,B$), yet it is also a tangent line at the point $A$. |
Notice that a secant line can also be tangent to the curve at some point, given that tangency is only a local property. In the following picture, $l$ is a secant line for the curve $C$ (since it intersects the curve at points $A,B$), yet it is also a tangent line at the point $A$. |
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\includegraphics{tangentsecant} |
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