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Euclid: Elementa

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Euclid: Elementa
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PROPOSITION 1. 
 
 
A part of a straight line cannot be in the plane of reference and a part in a plane more elevated. 
 
 
For, if possible, let a part AB of the straight line ABC be in the plane of reference, and a part BC in a plane more elevated. 
 
 
There will then be in the plane of reference some straight line continuous with AB in a straight line.  Let it be BD;  therefore AB is a common segment of the two straight lines ABC, ABD: which is impossible,  inasmuch as, if we describe a circle with centre B and distance AB, the diameters will cut off unequal circumferences of the circle. 
       
       
Therefore a part of a straight line cannot be in the plane of reference, and a part in a plane more elevated.  Q. E. D. 
   
   
 
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