This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1910 Excerpt: ...x1 = 0; the point Jl by the fact that x2 = 0; and the point Jf by the fact that x1 = x3. Theorem 15. In homogeneous coordinates a projectivity on a line is represented by a linear homogeneous transformation in two variables, (1) K--+ fcq1, (ad-bc+0) px2 = cx1 + dx3, where p is an arbitrary factor of proportionality. (A ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1910 Excerpt: ...x1 = 0; the point Jl by the fact that x2 = 0; and the point Jf by the fact that x1 = x3. Theorem 15. In homogeneous coordinates a projectivity on a line is represented by a linear homogeneous transformation in two variables, (1) K--+ fcq1, (ad-bc+0) px2 = cx1 + dx3, where p is an arbitrary factor of proportionality. (A, E, P) Proof. By division, this clearly leads to the transformation (2) rf- - w cx + d provided x2 and x2 are both different from 0. If x3 = 0, the transformation (1) gives the point (x/, x2') = (a, c); i.e. the point H. = (1, 0) is transformed by (1) into the point whose nonhomogeneous coordinate is a/c. And if x2'=0, we have in (1) (xv x2) = (d, --c); i.e. (1) transforms the point whose nonhomogeneous coordinate is--d/c into the point R. By reference to Theorem 11 the validity of the theorem is therefore established. As before, the matrix (, J of the coefficients may conveniently be used to represent the projectivity. The double points of the projectivity, if existent, are obtained in homogeneous coordinates as follows: The coordinates of a double point (xv x3) must satisfy the equations px--ax1 + fo px3 = cx1 + dxr These equations are compatible only if the determinant of the system 3) (a-p)x1+bx2=0, K' cx1 + (d-p)x2=0, vanishes. This leads to the equation a--p b c d--p for the determination of the factor of proportionality p. This equation is called the characteristic equation of the matrix representing the projectivity. Every value of p satisfying this equation then leads to a double point when substituted in one of the equations (3); viz., if p1 be a solution of the characteristic equation, the point (xv x3) = (-b, a-P1) = (d-pv-c) is a double point. In homogeneous coordinates the cross ratio lb(AB, CD) of four points A = («.
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Add this copy of Projective Geometry; Volume 1 to cart. $21.42, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Projective Geometry; Volume 1 to cart. $31.73, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Projective Geometry Volume 1 1910 [Leather Bound] to cart. $72.00, new condition, Sold by Leather Book Shop rated 2.0 out of 5 stars, ships from Delhi, DELHI, INDIA, published 2018 by Facsimile Publisher.
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New in New jacket. {Size: 14.60 x 22.86 cms} Presenting an Exquisite Leather-Bound Edition, expertly crafted by the prestigious organization “Rare Biblio” with Original Natural Leather that gracefully adorns the spine and corners. The allure continues with Golden Leaf Printing that adds a touch of elegance, while Hand Embossing on the rounded spine lends an artistic flair. This masterpiece has been meticulously reprinted in 2018, utilizing the invaluable guidance of the original edition published many years ago in 1910. The contents of this book are presented in classic black and white. Its durability is ensured through a meticulous sewing binding technique, enhancing its longevity. Imprinted on top-tier quality paper. A team of professionals has expertly processed each page, delicately preserving its content without alteration. Due to the vintage nature of these books, every page has been manually restored for legibility. However, in certain instances, occasional blurriness, missing segments, or faint black spots might persist. We sincerely hope for your understanding of the challenges we faced with these books. Recognizing their significance for readers seeking insight into our historical treasure, we've diligently restored and reissued them. Our intention is to offer this valuable resource once again. We eagerly await your feedback, hoping that you'll find it appealing and will generously share your thoughts and recommendations. Lang: -English, Pages: -356. If it is a multi-volume set, then it is only a single volume. Product Disclaimer: Kindly be informed that, owing to the inherent nature of leather as a natural material, minor discolorations or textural variations may be perceptible. Explore the FOLIO EDITION (12x19 Inches): Available Upon Request.
