 | Richard Anthony Proctor - Astronomy - 1884 - 422 pages
...lines cannot enclose a space, and the axiom' on which the theory of parallel lines is based. But ' a more extended experience and more accurate measurements...geometry, accurately representing the properties of the space ' in which they lived.' Be it noted, Professor Cayley here supposes the inhabitants of the spherical... | |
 | American periodicals - 1884 - 864 pages
...straight lines cannot enclose a space, and the axiom " on which the theory of parallel lines is based. But "a more extended experience and more accurate measurements...geometry, accurately representing the properties of the space "in which they lived." Be it noted, Professor Cayley here supposes the inhabitants of the spherical... | |
 | Frederick Newton Willson - Geometry, Descriptive - 1898 - 322 pages
...they had by experience established the axiom that two straight lines cannot enclose a space, and also the axiom as to parallel lines. A more extended experience...two-dimensional space of their experience. But their original Euclidean geometry would not the less be a true system : only it would apply to an ideal space, not... | |
 | Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - Education - 1893 - 554 pages
...extended experience and more accurate measurements would teach them that the axioms, each of them, are false, and that any two lines if produced far enough...two-dimensional space of their experience. But their original Euclidean geometry would not the less be a true system ; only it would apply to an ideal space, not... | |
 | Education - 1893 - 562 pages
...extended experience and more accurate measurements would teach them that the axioms, each of them, are false, and that any two lines if produced far enough...two-dimensional space of their experience. But their original Euclidean geometry would not the less be a true system ; only it would apply to an ideal space, not... | |
 | 1883 - 1060 pages
...experience and more accurate measurements would teach them that the axioms were each of them ialsc; and that any two lines if produced far enough each...the less be a true system; only it would apply to an Ądeal space, not the space of their experience. Secondly, consider an ordinary, indefinitely extended... | |
 | Pharmacy - 1884 - 1106 pages
...measurements would teach them that the axioms were each of them false ; and that any two lines if produced for enough each way, would meet in two points : they would...representing the properties of the two-dimensional cpace of their experience. But their original Euclidian geometry would not the less be a true system... | |
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A more extended experience and more accurate measurements would teach them that the axioms were each of them false ; and that any two lines if produced far enough each way, would meet in two points : they would in fact arrive at a spherical geometry,... 