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Projective Synthetic Geometry

Projective Synthetic Geometry PDF Author: George Bruce Halsted
Publisher: CreateSpace
ISBN: 9781495495922
Category : Mathematics
Languages : en
Pages : 62

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Book Description
AUTHOR'S PREFACE. MAN, imprisoned in a little body with short-arm hands instead of wings, created for his guidance a mole geometry, a tactile space, codified by Euclid in his immortal Elements, whose basal principle is congruence, measurement. Yet man is no mole. Infinite feelers radiate from the windows of his soul, whose wings touch the fixed stars. The angel of light in him created for the guidance of eye-life an independent system, a radiant geometry, a visual space, codified in 1847 by a new Euclid, by the Erlangen professor, Georg von Staudt, in his immortal Geometrie der Lage published in the quaint and ancient Nurnberg of Albrecht Durer. Born on the 24th of January, 1798, at Rothenburg ob der Tauber, von Staudt was an aristocrat, issue of the union of two of the few regierenden families of the then still free Reichsstadt, which four years later closed the 630 years of its renowned existence as an independent republic. This creation of a geometry of position disembarrassed of all quantity, wholly non-metric, neither positively nor negatively quantitative, resting exclusively on relations of situation, takes as point of departure the since-famous quadrilateral construction. To-day it must be reckoned with from the abstractest domains of philosophy to the bread-winning marts of applied science. Thus Darboux says of it: "It seems to us that under the form first given it by von Staudt, projective geometry must become the necessary companion of descriptive geometry, that it is called to renovate this geometry in its spirit, its procedures, its applications."

Projective Synthetic Geometry

Projective Synthetic Geometry PDF Author: George Bruce Halsted
Publisher: CreateSpace
ISBN: 9781495495922
Category : Mathematics
Languages : en
Pages : 62

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Book Description
AUTHOR'S PREFACE. MAN, imprisoned in a little body with short-arm hands instead of wings, created for his guidance a mole geometry, a tactile space, codified by Euclid in his immortal Elements, whose basal principle is congruence, measurement. Yet man is no mole. Infinite feelers radiate from the windows of his soul, whose wings touch the fixed stars. The angel of light in him created for the guidance of eye-life an independent system, a radiant geometry, a visual space, codified in 1847 by a new Euclid, by the Erlangen professor, Georg von Staudt, in his immortal Geometrie der Lage published in the quaint and ancient Nurnberg of Albrecht Durer. Born on the 24th of January, 1798, at Rothenburg ob der Tauber, von Staudt was an aristocrat, issue of the union of two of the few regierenden families of the then still free Reichsstadt, which four years later closed the 630 years of its renowned existence as an independent republic. This creation of a geometry of position disembarrassed of all quantity, wholly non-metric, neither positively nor negatively quantitative, resting exclusively on relations of situation, takes as point of departure the since-famous quadrilateral construction. To-day it must be reckoned with from the abstractest domains of philosophy to the bread-winning marts of applied science. Thus Darboux says of it: "It seems to us that under the form first given it by von Staudt, projective geometry must become the necessary companion of descriptive geometry, that it is called to renovate this geometry in its spirit, its procedures, its applications."

Synthetic Projective Geometry

Synthetic Projective Geometry PDF Author: George Bruce Halsted
Publisher:
ISBN:
Category : Geometry, Projective
Languages : en
Pages : 62

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Book Description


Synthetic Projective Geometry

Synthetic Projective Geometry PDF Author: Halsted George Bruce 1853-1922
Publisher: Hardpress Publishing
ISBN: 9781314470628
Category :
Languages : en
Pages : 96

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Book Description
Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Synthetic Projective Geometry

Synthetic Projective Geometry PDF Author: Ralph Grafton Sanger
Publisher:
ISBN:
Category : Geometry, Projective
Languages : en
Pages : 175

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Synthetic Projective Geometry

Synthetic Projective Geometry PDF Author: Allan Cecil Haskell
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages :

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Fundamental Concepts of Geometry

Fundamental Concepts of Geometry PDF Author: Bruce E. Meserve
Publisher: Courier Corporation
ISBN: 048615226X
Category : Mathematics
Languages : en
Pages : 336

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Book Description
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

An Elementary Course in Synthetic Projective Geometry

An Elementary Course in Synthetic Projective Geometry PDF Author: Derrick Norman Lehmer
Publisher: Forgotten Books
ISBN: 9781330376997
Category : Mathematics
Languages : en
Pages : 141

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Book Description
Excerpt from An Elementary Course in Synthetic Projective Geometry The following course is intended to give, in as simple a way as possible, the essentials of synthetic projective geometry. While, in the main, the theory is developed along the well-beaten track laid out by the great masters of the subject, it is believed that there has been a slight smoothing of the road in some places. Especially will this be observed in the chapter on Involution. The author has never felt satisfied with the usual treatment of that subject by means of circles and anharmonie ratios. A purely projective notion ought not to be based on metrical foundations. Metrical developments should be made there, as elsewhere in the theory, by the introduction of infinitely distant elements. The author has departed from the century-old custom of writing in parallel columns each theorem and its dual. He has not found that it conduces to sharpness of vision to try to focus his eyes 011 two things at once. Those who prefer the usual method of procedure can, of course, develop the two sets of theorems side by side; the author has not found this the better plan in actual teaching. As regards nomenclature, the author has followed the lead of the earlier writers in English, and has called the system of lines in a plane which all pass through a point a pencil of rays instead of a bundle of rays, as later writers seem inclined to do. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Synthetic Projective Geometry

Synthetic Projective Geometry PDF Author: George Bruce Halsted
Publisher:
ISBN:
Category : Geometry, Projective
Languages : en
Pages : 62

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Learning and Geometry: Computational Approaches

Learning and Geometry: Computational Approaches PDF Author: David Kueker
Publisher: Springer Science & Business Media
ISBN: 1461240883
Category : Computers
Languages : en
Pages : 212

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Book Description
The field of computational learning theory arose out of the desire to for mally understand the process of learning. As potential applications to artificial intelligence became apparent, the new field grew rapidly. The learning of geo metric objects became a natural area of study. The possibility of using learning techniques to compensate for unsolvability provided an attraction for individ uals with an immediate need to solve such difficult problems. Researchers at the Center for Night Vision were interested in solving the problem of interpreting data produced by a variety of sensors. Current vision techniques, which have a strong geometric component, can be used to extract features. However, these techniques fall short of useful recognition of the sensed objects. One potential solution is to incorporate learning techniques into the geometric manipulation of sensor data. As a first step toward realizing such a solution, the Systems Research Center at the University of Maryland, in conjunction with the Center for Night Vision, hosted a Workshop on Learning and Geometry in January of 1991. Scholars in both fields came together to learn about each others' field and to look for common ground, with the ultimate goal of providing a new model of learning from geometrical examples that would be useful in computer vision. The papers in the volume are a partial record of that meeting.

An Elementary Course in Synthetic Projective Geometry

An Elementary Course in Synthetic Projective Geometry PDF Author: Derrick Norman Lehmer
Publisher:
ISBN:
Category : Geometry, Projective
Languages : en
Pages : 123

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Book Description