Excerpt from A Geometrical Treatise on Conic Sections: With Numerous Examples

1. Def. The curve traced out by a point, which moves in such a manner that its distance from a given fixed point continually bears the same ratio to its distance from a given fixed line, is called a Conic Section.

The fixed point is called the Focus, and the fixed line the Directrix.

Thus if S be the focus, and KK' the directrix, and P a point from which PM is drawn at right angles to the directrix, the curve traced out by P will be a Conic Section, provided P move in such manner that SP always bears the same ratio to PM.

(1.) When the distance from the fixed point is equal to the distance from the fixed line, that is, when SP is equal to PM, the Conic Section is called a Parabola.

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