A Theory of Time And Space

Cover A Theory of Time And Space
A Theory of Time And Space
Alfred a Alfred Arthur Robb
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222 A THEORY OF TIME AND SPACE But, as in Theorem 144, OB is normal to a and thus OB is normal to the two intersecting general lines a and b which lie in P and there- fore it is normal to P. - Again if B' be any element in P which does not lie in 6, then BB' is a separation line and so as in Theorem 144 OB' cannot be normal to P.
Thus all general lines through normal to P which have an element in common with P intersect b.
Thus the first part of the theorem is proved.
Suppose next that is befor
...e some element, say E, in P.
Then through E one single generator of P passes which we may denote by /.
Since does not lie in / but is before an element of /, it follows that through there is an optical line which is a before-parallel of / and which we shall denote by c.
If f be any other generator of P it will be a neutral-parallel of / and so by Theorem 25 (a) c will be a before-parallel of /'.
Thus is before elements of every generator of P.
Similarly if be after any element of P it is after elements of every generator of P.


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