A Treatise On Conic Sections Containing An Account of Some of the Most Importan
A Treatise On Conic Sections Containing An Account of Some of the Most Importan
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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 Importan 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 Importan
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To quickly assess the difficulty of the text, read a short excerpt:
+ &c. + h [a'aa! + &:g. ].
Hence, given four points on a conic^ the polar of any given point lyasses through a fixed point (Ex. 2, p. 148).
If Q and Q be the polars of another point with regard to S and /S", then the polar of this second point with regard to S-\-kS' 260 METHODS OF ABPIDOED NOTATION.
is Q-\-hQ', Thus, then, (see Art. 59) the polars of two points ■with regard to a system of conies through four points, form two homographie pencils of lines.
Given two homograj)1iic iiencils of line...Sj the locus of the inter- section of the corref^ponding lines of the pencils is a conic through the vertices of the jpe^xcils. For, if we eliminate h between F-^hP^ Q-{-hQ\ we get PQ' = P'Q. In the particular case tmder consideration, the intersection of P-\-kP\ Q + kQ' is the pole with respect to S + Jc8' of the line joining the two given points. And we see that, given four jwints on a conic^ the locus of the pole of a given line is a conic (Ex. 1, p. 243).
If an indeterminate enter in the second degree into the equation of a conic, it must also enter in the second degree into the equation of the polar of a given point, which will then envelope a conic.
What to read after A Treatise On Conic Sections Containing An Account of Some of the Most Importan?
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:
+ &c. + h [a'aa! + &:g. ].
Hence, given four points on a conic^ the polar of any given point lyasses through a fixed point (Ex. 2, p. 148).
If Q and Q be the polars of another point with regard to S and /S", then the polar of this second point with regard to S-\-kS' 260 METHODS OF ABPIDOED NOTATION.
is Q-\-hQ', Thus, then, (see Art. 59) the polars of two points ■with regard to a system of conies through four points, form two homographie pencils of lines.
Given two homograj)1iic iiencils of line...Sj the locus of the inter- section of the corref^ponding lines of the pencils is a conic through the vertices of the jpe^xcils. For, if we eliminate h between F-^hP^ Q-{-hQ\ we get PQ' = P'Q. In the particular case tmder consideration, the intersection of P-\-kP\ Q + kQ' is the pole with respect to S + Jc8' of the line joining the two given points. And we see that, given four jwints on a conic^ the locus of the pole of a given line is a conic (Ex. 1, p. 243).
If an indeterminate enter in the second degree into the equation of a conic, it must also enter in the second degree into the equation of the polar of a given point, which will then envelope a conic.
What to read after A Treatise On Conic Sections Containing An Account of Some of the Most Importan?
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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