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An essay on the foundations of geometry

Bertrand Russell

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Book Excerpt: 
. . .e of curvature of the surface at the point under consideration. To illustrate by a few simple examples: on a sphere, the curvatures of all such lines are equal to the reciprocal of the radius of the sphere, hence the measure of curvature everywhere is the square of the reciprocal of the radius of the sphere. On any surface, such as a cone or a cylinder, on which straight lines can be drawn, these have no curvature, so that the measure of curvature is everywhere zero—this is the case, in particular, with the plane. In general, however, the measure of curvature of a surface varies from point to point.

Gauss, the inventor of this conception[23], proved that, in order that two surfaces may be developable upon each other—i.e. may be such that one can be bent into the shape of the other without stretching or tearing—it is necessary that the two surfaces should have equal measures of curvature at corresponding points. When this is the case, every fig. . . Read More

Community Reviews

I think this is a really good work, really informative, even if wrong in some of its commitments and details. It also helped me to get a better grip on the real basis of Russell's later view of pluralism, as starts to develop more in his work on Leibniz and then in later works all the way up to and