An Introduction to Projective Geometry
An Introduction to Projective Geometry
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In our eReader you can find the full English version of the book. Read An Introduction to Projective Geometry 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 An Introduction to Projective Geometry
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Otherwise thus: the two ranges may be projected from any vertex and the self-corresponding rays of the concentric projective pencils so formed may be found by the construction given at the beginning of this article. They meet u at the self-corresponding points of the ranges.
115. Intersections of a straight line with a conic given by five points. Let C, 0', J, B, C be the five points on the conic, k any straight line.
The conic is the product of the two pencils defined by 0{ABC), a {A BO).
If O...A, OB, OC meet u at . 4, /i, , C\ and O'A, OB, O'G meet u SitA^BiC, the pencils O(ABC'), O'(^l^C') determine upon u two projective ranges of which A^B/Ji, A. B. C. Are corresponding triads.
Find the self-corresponding points of these ranges on u by either of the methods given in the last article. Let these be S, T. 'I'hen OS, O'S are corresponding rays of the pencils 0(ABC), 0'(ABa).
Therefore S is a point on the conic.
Similarly 7' is a point on the conic.
Hence S, 7' are the intersections of u with the conic.
What to read after An Introduction to Projective Geometry?
You can find similar books in the "Read Also" column, or choose other free books by L N G Louis Napoleon George Filon to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Otherwise thus: the two ranges may be projected from any vertex and the self-corresponding rays of the concentric projective pencils so formed may be found by the construction given at the beginning of this article. They meet u at the self-corresponding points of the ranges.
115. Intersections of a straight line with a conic given by five points. Let C, 0', J, B, C be the five points on the conic, k any straight line.
The conic is the product of the two pencils defined by 0{ABC), a {A BO).
If O...A, OB, OC meet u at . 4, /i, , C\ and O'A, OB, O'G meet u SitA^BiC, the pencils O(ABC'), O'(^l^C') determine upon u two projective ranges of which A^B/Ji, A. B. C. Are corresponding triads.
Find the self-corresponding points of these ranges on u by either of the methods given in the last article. Let these be S, T. 'I'hen OS, O'S are corresponding rays of the pencils 0(ABC), 0'(ABa).
Therefore S is a point on the conic.
Similarly 7' is a point on the conic.
Hence S, 7' are the intersections of u with the conic.
What to read after An Introduction to Projective Geometry?
You can find similar books in the "Read Also" column, or choose other free books by L N G Louis Napoleon George Filon to read onlineMoreLess
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