An Elementary Course in Synthetic Projective Geometry 0 1
An Elementary Course in Synthetic Projective Geometry 0 1
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In our eReader you can find the full English version of the book. Read An Elementary Course in Synthetic Projective Geometry 0 1 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 Elementary Course in Synthetic Projective Geometry 0 1
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Weexamine now the possibility of two forms related in this way, having anelement or elements that correspond to themselves. We have seen, indeed, that if _B_ and _D_ are harmonic conjugates with respect to _A_ and _C_, then the point-row described by _B_ is projective to the point-rowdescribed by _D_, and that _A_ and _C_ are self-corresponding points. Consider more generally the case of two pencils perspective to each otherwith axis of perspectivity _u’_ (Fig. 9). Cut across them by a line _u_.... We get thus two projective point-rows superposed on the same line _u_, anda moment’s reflection serves to show that the point _N_ of intersection_u_ and _u’_ corresponds to itself in the two point-rows. Also, the point_M_, where _u_ intersects the line joining the centers of the two pencils, is seen to correspond to itself. It is thus possible for two projectivepoint-rows, superposed upon the same line, to have two self-correspondingpoints. Clearly _M_ and _N_ may fall together if the line joining thecenters of the pencils happens to pass through the point of intersectionof the lines _u_ and _u’_.
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You can find similar books in the "Read Also" column, or choose other free books by Lehmer to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Weexamine now the possibility of two forms related in this way, having anelement or elements that correspond to themselves. We have seen, indeed, that if _B_ and _D_ are harmonic conjugates with respect to _A_ and _C_, then the point-row described by _B_ is projective to the point-rowdescribed by _D_, and that _A_ and _C_ are self-corresponding points. Consider more generally the case of two pencils perspective to each otherwith axis of perspectivity _u’_ (Fig. 9). Cut across them by a line _u_.... We get thus two projective point-rows superposed on the same line _u_, anda moment’s reflection serves to show that the point _N_ of intersection_u_ and _u’_ corresponds to itself in the two point-rows. Also, the point_M_, where _u_ intersects the line joining the centers of the two pencils, is seen to correspond to itself. It is thus possible for two projectivepoint-rows, superposed upon the same line, to have two self-correspondingpoints. Clearly _M_ and _N_ may fall together if the line joining thecenters of the pencils happens to pass through the point of intersectionof the lines _u_ and _u’_.
What to read after An Elementary Course in Synthetic Projective Geometry 0 1?
You can find similar books in the "Read Also" column, or choose other free books by Lehmer to read onlineMoreLess
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