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" ... geometry. My own view is that Euclid's twelfth axiom in Playfair's form of it does not need demonstration, but is part of our notion of space, of the physical space of our experience — the space, that is, which we become acquainted with by experience,... "
The Collected Mathematical Papers of Arthur Cayley - Page 435
by Arthur Cayley - 1896 - 664 pages
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English Mechanic and World of Science: With which are ..., Volume 38

Industrial arts - 1884 - 594 pages
...like system of non-Euclidian solid geometry. My own view is that Euclid's twelfth axiom in Playfair's form of it does not need demonstration, but is part...lying at the foundation of all external experience. Kiemauu's view before referred to may, I think, be eaid to be that, having in intellect и a more general...
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Proceedings of the Royal Society of London, Volume 37

Royal Society (Great Britain) - Electronic journals - 1884 - 572 pages
...need demonstration, but is part of our notion of space, of the physical space of our experience ; the space, that is, which we become acquainted with by...the representation lying at the foundation of all physical experience. 3. I propose in the present paper to further develope the geometry of the pseudosphere....
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Proceedings of the Royal Society of London, Volume 37

Royal Society (Great Britain) - Electronic journals - 1884 - 556 pages
...demonstration, but is part of our notion of •pace, of the physical apace of our experience ; the space, that is, which we become acquainted with by experience, but which is the representation lyiug at the foundation of all physical experience. 3. I propose in the present paper to further develope...
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Mysticism in Modern Mathematics

Hastings Berkeley - Mathematics - 1910 - 279 pages
...demonstration, but is part of our notion of space, of the physical space of our experience — the space, that is, which we become acquainted with by...referred to may, I think, be said to be that, having in intellects a more general notion of space (in fact a notion of non-Euclidean space), we learn by experience...
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Lectures on Ten British Physicists of the Nineteenth Century

Alexander Macfarlane - Physicists - 1916 - 162 pages
...demonstration, but is part of our notion of space, of the physical space of our experience — the space, that is, which we become acquainted with by...more general notion of space (in fact a notion of non-Euclidean space), we learn by experience that space (the physical space of our experience) is,...
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Lectures on Ten British Mathematicians of the Nineteenth Century

Alexander Macfarlane - Mathematicians - 1916 - 160 pages
...demonstration, but is part of our notion of space, of the physical space of our experience — the space, that is, which we become acquainted with by...more general notion of space (in fact a notion of non-Euclidean space), we learn by experience that space (the physical space of our experience) is,...
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Lectures on Ten British Mathematicians of the Nineteenth Century

Alexander Macfarlane - Mathematicians - 1916 - 164 pages
...demonstration, but is part of our notion of space, of the physical space of our experience — the space, that is, which we become acquainted with by...referred to may I think be said to be that, having in intelledu a more general notion of space (in fact a notion of non-Euclidean space), we learn by experience...
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Littell's Living Age, Volume 159

1883 - 1060 pages
...demonstration, but is part of our notion of space, of ihe physical space of our experience — the space, that is, which we become acquainted with by...lying at the foundation of all external experience. Kiemann's view before referred to may 1 think be said to be that, having in iiilellectii a more general...
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Mathematics: The Loss of Certainty

Morris Kline - Mathematics - 1982 - 380 pages
...demonstration, but is part of our notion of space, of the physical space of our experience — which one becomes acquainted with by experience, but which is the representation...lying at the foundation of all external experience. . . . Not that the propositions of geometry are only approximately true, but that they remain absolutely...
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Mathematics and the Search for Knowledge

Morris Kline - Mathematics - 1985 - 270 pages
...demonstration, but is part of our notion of space, of the physical space of our experience— which one becomes acquainted with by experience, but which is the representation...lying at the foundation of all external experience Not that Felix Klein (1849-1925), one of the truly great mathematicians of recent times, expressed...
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