A Treatise On Conic Sections: Containing An Account of Some of the Most Important Modern Algebraic Andgeometric Methods
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In our eReader you can find the full English version of the book. Read A Treatise On Conic Sections: Containing An Account of Some of the Most Important Modern Algebraic Andgeometric Methods Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book 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.
What to read after A Treatise On Conic Sections: Containing An Account of Some of the Most Important Modern Algebraic Andgeometric Methods?
You can find similar books in the "Read Also" column, or choose other free books by George Salmon to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after A Treatise On Conic Sections: Containing An Account of Some of the Most Important Modern Algebraic Andgeometric Methods?
You can find similar books in the "Read Also" column, or choose other free books by George Salmon to read onlineMoreLess
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