Synopsis
Excerpt from The Axioms of Projective Geometry
In this tract only the outlines of the subject are dealt with. Accordingly I have endeavoured to avoid reasoning dependent upon the mere wording and on the exact forms of the axioms (which can be indefinitely varied), and have concentrated attention upon certain questions which demand consideration however the axioms are phrased.
Every group of the axioms is designed to secure the deduction of a certain group of properties. For the most part I have stated without proof the leading immediate consequences of the various groups. Also I have ignored most of the independence theorems, as being dependent upon mere questions of phrasing, and have only investigated those which appear to me to embody the essence of the subject; though, as far as I know, no formal line can be drawn between these two classes of theorems.
But there is one group of deductions which cannot be ignored in any consideration of the principles of Projective Geometry. I refer to the theorems, by which it is proved that numerical coordinates, with the usual properties, can be defined without the introduction of distance as a fundamental idea. The establishment of this result is one of the triumphs of modem mathematical thought. It has been achieved by the development of one of the many brilliant geometrical conceptions which we owe to the genius of von Staudt.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Autres éditions populaires du même titre
Résultats de recherche pour The Axioms of Projective Geometry (Classic Reprint)
Image fournie par le vendeur
The Axioms of Projective Geometry (Classic Reprint)
impression à la demandeVendeur : Forgotten Books, London, Royaume-Uni
Évaluation du vendeur 4 sur 5 étoiles
Paperback. Etat : New. Print on Demand. This book serves as an introduction to Projective Geometry and is an excellent supplement to school studies in advanced geometry. Projective Geometry has roots in the early 19th century and seeks to establish a mathematical system based on projection and perspective, rather than distance. The author includes numerous detailed examples to illustrate the central ideas Projective Geometry is built upon, examining concepts such as harmonic systems, the fundamental theorem, and order segments. These are described through careful theoretical explanations as well as graphical illustrations. The author does not limit investigation to theoretical Projective Geometry but explores practical applications such as the introduction of numerical coordinates in the field. Through accessible language and clear, logical illustration, this book provides a solid foundation from which readers can further explore Projective Geometry and its applications. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. N° de réf. du vendeur 9781330378854_0
Acheter neuf
EUR 16,08
Livraison gratuite
Expédition depuis Royaume-Uni vers Etats-Unis
Expédition depuis Royaume-Uni vers Etats-Unis
Quantité disponible : Plus de 20 disponibles
Image d'archives
The Axioms of Projective Geometry Classic Reprint
Vendeur : PBShop.store US, Wood Dale, IL, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781330378854
Acheter neuf
EUR 25,59
Livraison gratuite
Expédition nationale : Etats-Unis
Expédition nationale : Etats-Unis
Quantité disponible : 15 disponible(s)
Image d'archives
The Axioms of Projective Geometry Classic Reprint
Vendeur : PBShop.store UK, Fairford, GLOS, Royaume-Uni
Évaluation du vendeur 5 sur 5 étoiles
PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781330378854
Acheter neuf
EUR 24,72
Expédition à EUR 3,80
Expédition depuis Royaume-Uni vers Etats-Unis
Expédition depuis Royaume-Uni vers Etats-Unis
Quantité disponible : 15 disponible(s)