A Treatise On Conic Sections : Containing An Account of Some of the Most Important Modern Algebraic And Geometric Methods
A Treatise On Conic Sections : Containing An Account of Some of the Most Important Modern Algebraic And Geometric 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 And Geometric 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 And Geometric Methods
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To quickly assess the difficulty of the text, read a short excerpt:
Ex. 10. Two verticeB of a ffiven triangle move along fixed right lines; find th« locus of the third.
Digitized by LjOOQ IC EXAMPLES ON CONIC SECTIONS. 209 Ex. 11. A triangle ABC drcnmscribeB a given circle ; the angle at C is given, and B moves along a fixed line ; find the locna of A.
Let us nse polar coordinates, the centre O being the pole, and the angles being measured from the perpendicular on the fixed line ; let the coordinates of i4, J?, be />, B\p'j 6'. Then we have p' goaV —p. But it ...is easy to see that the angle AOB is given (= a). And since the perpendicular of the triangle AOB is given, we have _^ pp' sin a "'40>* + /t>''-2/B/B'COStf)* But 6 + O' = a ; therefore the polar equation of the locus ifl . jp V sin' a J ~ /)« COS* (o - 0) +i>» - 2pp cos o COS (a - 0) ' which represents a conic.
Ex. 12. Find the locus of the pole with respect to one conic A of any tangent to another conic B, Let afi be any point of the locus, and \x + fiy+ vita polar with respect to the conio A^ then (Art.
What to read after A Treatise On Conic Sections : Containing An Account of Some of the Most Important Modern Algebraic And Geometric 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:
Ex. 10. Two verticeB of a ffiven triangle move along fixed right lines; find th« locus of the third.
Digitized by LjOOQ IC EXAMPLES ON CONIC SECTIONS. 209 Ex. 11. A triangle ABC drcnmscribeB a given circle ; the angle at C is given, and B moves along a fixed line ; find the locna of A.
Let us nse polar coordinates, the centre O being the pole, and the angles being measured from the perpendicular on the fixed line ; let the coordinates of i4, J?, be />, B\p'j 6'. Then we have p' goaV —p. But it ...is easy to see that the angle AOB is given (= a). And since the perpendicular of the triangle AOB is given, we have _^ pp' sin a "'40>* + /t>''-2/B/B'COStf)* But 6 + O' = a ; therefore the polar equation of the locus ifl . jp V sin' a J ~ /)« COS* (o - 0) +i>» - 2pp cos o COS (a - 0) ' which represents a conic.
Ex. 12. Find the locus of the pole with respect to one conic A of any tangent to another conic B, Let afi be any point of the locus, and \x + fiy+ vita polar with respect to the conio A^ then (Art.
What to read after A Treatise On Conic Sections : Containing An Account of Some of the Most Important Modern Algebraic And Geometric 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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