Proceedings of the American Academy of Arts and Sciences Volume 53 download pdf
Proceedings of the American Academy of Arts and Sciences Volume 53 download pdf
Proceedings of the American Academy of Arts and Sciences Volume 53.cAmerican Academy of Sciences
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Author: American Academy of Sciences
Page Count: 252 pages
Published Date: 13 Sep 2013
Publisher: Rarebooksclub.com
Publication Country: United States
Language: English
ISBN: 9781230097572
Download Link: Proceedings of the American Academy of Arts and Sciences Volume 53
---------------------------------------------------------------
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1918 edition. Excerpt: ...The join of Pi and ri is a plane Pin. Permuting &, &, 3 we get three such planes. The three planes intersect in a point. By the above general discussion that point is on the plane into which Ap Bq transforms X. This is true for every set of three planes through X. 16. Double products with idemfactors. In particular the double product of a dyadic $ and an idemfactor is an invariant or covariant of $. This is a special case of the preceding general discussion. For example let Aa be the dyadic determining the identical point collineation and let = P/3 AB a/3 transforms any line L into a line or complex U = AB(a0.L) =-BA(a-BL). Since (a/3L) is a pure regressive product. Furthermore, this is equivalent to-B-AaBL =-B-PL = BL.8 since Aa is the idemfactor. This complex is determined as follows. Let X, Y be two points on L and X', Y' their transforms by $. Join X to Y' and Y to A'. Then by the general theorem of the preceding section V is a linear function of the two lines thus obtained. That is, these lines are polar lines with respect to V. This is true whatever pair of points A', Y are taken on L. This proves the following geometrical theorem. Let X, Y, Z be any three distinct points on L and X', Y' Z', three distinct points on any other line. A dyadic BB can be found which will transform X, Y, Z into X', Y', Z'. Therefore the three pairs of lines IF, YX'; XZ', ZX' YZ'.ZY' are pairs of polar lines with respect to a complex, namely, the complex into which AB a/3 transforms AT. This is the generalization of the theorem of Pappus for the hexagon inscribed in two lines in a plane. The dyadic AB a/3 will represent a collineation if and only if every line XY transforms into a line X'Y' cutting it. The collineation BB then gives a...
Read online Proceedings of the American Academy of Arts and Sciences Volume 53 Buy Proceedings of the American Academy of Arts and Sciences Volume 53 Download and read Proceedings of the American Academy of Arts and Sciences Volume 53 for pc, mac, kindle, readers Download to iPad/iPhone/iOS, B&N nook Proceedings of the American Academy of Arts and Sciences Volume 53 ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent
Osteopathie von A-Z download pdf
Proceedings of the American Academy of Arts and Sciences Volume 53.cAmerican Academy of Sciences
Author: American Academy of Sciences
Page Count: 252 pages
Published Date: 13 Sep 2013
Publisher: Rarebooksclub.com
Publication Country: United States
Language: English
ISBN: 9781230097572
Download Link: Proceedings of the American Academy of Arts and Sciences Volume 53
---------------------------------------------------------------
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1918 edition. Excerpt: ...The join of Pi and ri is a plane Pin. Permuting &, &, 3 we get three such planes. The three planes intersect in a point. By the above general discussion that point is on the plane into which Ap Bq transforms X. This is true for every set of three planes through X. 16. Double products with idemfactors. In particular the double product of a dyadic $ and an idemfactor is an invariant or covariant of $. This is a special case of the preceding general discussion. For example let Aa be the dyadic determining the identical point collineation and let = P/3 AB a/3 transforms any line L into a line or complex U = AB(a0.L) =-BA(a-BL). Since (a/3L) is a pure regressive product. Furthermore, this is equivalent to-B-AaBL =-B-PL = BL.8 since Aa is the idemfactor. This complex is determined as follows. Let X, Y be two points on L and X', Y' their transforms by $. Join X to Y' and Y to A'. Then by the general theorem of the preceding section V is a linear function of the two lines thus obtained. That is, these lines are polar lines with respect to V. This is true whatever pair of points A', Y are taken on L. This proves the following geometrical theorem. Let X, Y, Z be any three distinct points on L and X', Y' Z', three distinct points on any other line. A dyadic BB can be found which will transform X, Y, Z into X', Y', Z'. Therefore the three pairs of lines IF, YX'; XZ', ZX' YZ'.ZY' are pairs of polar lines with respect to a complex, namely, the complex into which AB a/3 transforms AT. This is the generalization of the theorem of Pappus for the hexagon inscribed in two lines in a plane. The dyadic AB a/3 will represent a collineation if and only if every line XY transforms into a line X'Y' cutting it. The collineation BB then gives a...
Read online Proceedings of the American Academy of Arts and Sciences Volume 53 Buy Proceedings of the American Academy of Arts and Sciences Volume 53 Download and read Proceedings of the American Academy of Arts and Sciences Volume 53 for pc, mac, kindle, readers Download to iPad/iPhone/iOS, B&N nook Proceedings of the American Academy of Arts and Sciences Volume 53 ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent
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