Axiom of metrical geometry: A)Axiom of distance:Axiom of distance correspondence to that of straight line of projective geometry.The possibility of spatial requirements involves a magnitude determined uniquely determined by two points. Since two points have some special relation it must excludes reference to external reference. There can only be one such relation. This must be measured by curve determined by two points.This curve must be determined by uniquely determined by two points. Spherical geometry contains an exception to this axiom. Which however is not equivalent to euclid.A relation between to point must be a line joing the two of them.Conversely,the existence of a unique line between two point can be deduced from the nature of the form of externality. and necessarily leads to distance when quatity is applied to it.Hence axiom of distance is also a priori in double sense.No metrical co-ordinate system can be made without the straight line.These three are necessary for the direct measurement of any continuum. C)Philosophical consequences:will be shown shortly. thanks
Posted on: Tue, 11 Mar 2014 04:14:54 +0000
Trending Topics
Recently Viewed Topics
© 2015