A Treatise On Conic Sections: Containing An Account of Some of the Most Important Modern Algebraic Andgeometric Methods
The book A Treatise On Conic Sections: Containing An Account of Some of the Most Important Modern Algebraic Andgeometric Methods was written by author George Salmon Here you can read free online of A Treatise On Conic Sections: Containing An Account of Some of the Most Important Modern Algebraic Andgeometric Methods book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is A Treatise On Conic Sections: Containing An Account of Some of the Most Important Modern Algebraic Andgeometric Methods a good or bad book?
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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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