...two-dimensional space, the plane, I have, in my Presidential Address (BA, Southport, 1883) expressed the opinion that Euclid's twelfth axiom in Playfair's form of...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....

...(BA, Southport, 1883) expressed the opinion that Euclid's twelfth axiom in Playfair's form of it docs not need demonstration, but is part of our notion...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....

...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...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...

...form of it does not need demonstration, but is part of our notion of •pace, of the physical apace of our experience ; the space, that is, which we become...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...

...himself gives of his standpoint is indeed not quite so clear as one could wish. * My own view/ he says, ' is that Euclid's twelfth axiom in Playfair's form...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...

...consistent theory, wherein this axiom was assumed not to hold good, or say a system of non-Euclidean plane geometry. My own view is that Euclid's twelfth axiom...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,...

...consistent theory, wherein this axiom was assumed not to hold good, or say a system of non-Euclidean plane geometry. My own view is that Euclid's twelfth axiom...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,...

...consistent theory, wherein this axiom was assumed not to hold good, or say a system of non-Euclidean plane geometry. My own view is that Euclid's twelfth axiom...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...

...axiom in Play fair's form of it does not need demonstration, but is part of our notion of space, of ihe physical space of our experience — the space, that...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...

...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...