A Treatise On Conic Sections: Containing An Account of Some of the Most Important Modern Algebraic Andgeometric Methods

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185 The double ordinate at the focus is called the parameter / its half is found, by making 6 = 90° in the equation just given, to be = — = a (I — e"^ The parameter is commonly denoted by the letter p. Hence the equation is often written = p 1_ P 2 ' 1+6COS0' The parameter is also called the Latus Eecturrt* Ex. 1. The harinonic mean between the segments of a focal Chord is constant^ and equal to the semi-parameter.
For, if the radius Vector FP, when produced backwards through the focus, meet P
...1 the curve again in P', then FP being ^ . . „^ e fl , .Pi 3 ', which answers to (8 + 189°), a x t c COS t/ # £ — j wil = f.
2 " l-eeos*" tt lit EenC * FP + W' = p' Ex. 2. The rectangle under the segments of a focal chord is proportional to the whole chord.
This is merely another way of stating trie result of the last Example ; but it may be proved directly by calculating the quantities FP. FP', and FP + FP', which are easily seen to be respectively i* 1 i25 2 1 at aud- it 2 l-e 2 cos 2 8' a l^e •n Ex.


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