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What is a secant?

What is a secant? Here are some definitions.

Noun
  1. (geometry) A straight line that intersects a curve at two or more points.
  2. (trigonometry) In a right triangle, the reciprocal of the cosine of an angle. Symbol: sec
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Examples
Let P be a point outside a circle, let PA be a tangent line, and let PBC be a secant line.
There is no necessary connexion between a conical projection and any touching or secant cone.
A tangent line may be considered the limiting position of a secant line as the two points at which it crosses the curve approach one another.
The secant and cosecant were not used by the early astronomers or surveyors.
In this projection the meridians are vertical and parallels having increased spacing in proportion to the secant of the latitude.
The oblongs made of any secant from the same point, and of the outter segment of the secant are equall betweene themselves.

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