On The Hypotheses Which Lie At The Bases Of Geometry

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On The Hypotheses Which Lie At The Bases Of Geometry

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Author : Bernhard Riemann
language : en
Publisher: Birkhäuser
Release Date : 2016-04-19

On The Hypotheses Which Lie At The Bases Of Geometry written by Bernhard Riemann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.

This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.

Foundations Of Geometry And Induction

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Author : Jean Nicod
language : en
Publisher: Routledge
Release Date : 2014-06-17

Foundations Of Geometry And Induction written by Jean Nicod and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-17 with Philosophy categories.

This is Volume of IV eight on a series on the Philosophy of Logic and Mathematics. Originally published in 1930, this study contains sections on geometry in the sensible world and the logical problem of induction.

The Foundations Of Euclidian Geometry As Viewed From The Standpoint Of Kinematics

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Author : Israel Euclid Rabinovitch
language : en
Publisher:
Release Date : 1903

The Foundations Of Euclidian Geometry As Viewed From The Standpoint Of Kinematics written by Israel Euclid Rabinovitch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1903 with Geometry categories.

The Angular Ratio Transference Art Hypotheses

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Author : James Mulberry
language : en
Publisher:
Release Date : 2008-07-01

The Angular Ratio Transference Art Hypotheses written by James Mulberry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-01 with Mathematics categories.

On The Lie Riemann Helmholtz Hilbert Problem Of The Foundations Of Geometry

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Author : Robert Lee Moore
language : en
Publisher:
Release Date : 1919*

On The Lie Riemann Helmholtz Hilbert Problem Of The Foundations Of Geometry written by Robert Lee Moore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1919* with categories.

Space Number And Geometry From Helmholtz To Cassirer

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Author : Francesca Biagioli
language : en
Publisher: Springer
Release Date : 2016-08-22

Space Number And Geometry From Helmholtz To Cassirer written by Francesca Biagioli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-22 with Philosophy categories.

This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.

The Foundations Of Mathematics

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Author : Paul Carus
language : en
Publisher:
Release Date : 1908

The Foundations Of Mathematics written by Paul Carus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1908 with Geometry categories.

Foundations Of Projective Geometry

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Author : Robin Hartshorne
language : en
Publisher: Ishi Press
Release Date : 2009

Foundations Of Projective Geometry written by Robin Hartshorne and has been published by Ishi Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

The first geometrical properties of a projective nature were discovered in the third century by Pappus of Alexandria. Filippo Brunelleschi (1404-1472) started investigating the geometry of perspective in 1425. Johannes Kepler (1571-1630) and Gerard Desargues (1591-1661) independently developed the pivotal concept of the "point at infinity." Desargues developed an alternative way of constructing perspective drawings by generalizing the use of vanishing points to include the case when these are infinitely far away. He made Euclidean geometry, where parallel lines are truly parallel, into a special case of an all-encompassing geometric system. Desargues's study on conic sections drew the attention of 16-years old Blaise Pascal and helped him formulate Pascal's theorem. The works of Gaspard Monge at the end of 18th and beginning of 19th century were important for the subsequent development of projective geometry. The work of Desargues was ignored until Michel Chasles chanced upon a handwritten copy in 1845. Meanwhile, Jean-Victor Poncelet had published the foundational treatise on projective geometry in 1822. Poncelet separated the projective properties of objects in individual class and establishing a relationship between metric and projective properties. The non-Euclidean geometries discovered shortly thereafter were eventually demonstrated to have models, such as the Klein model of hyperbolic space, relating to projective geometry.

The Foundations Of Mathematics A Contribution To The Philosophy Of Geometry

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Author : Paul Carus
language : en
Publisher: Hardpress Publishing
Release Date : 2012-08

The Foundations Of Mathematics A Contribution To The Philosophy Of Geometry written by Paul Carus and has been published by Hardpress Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08 with History categories.

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.

The Foundations Of Geometry

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Author : David Hilbert
language : en
Publisher:
Release Date : 1947

The Foundations Of Geometry written by David Hilbert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1947 with categories.