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83 
and let EA, E'B' be the projections of any two circular 
sections not parallel to one another, and also their diameters. 
Bisect EA at right angles by IC, and let C be taken equidis 
tant from E and E'; therefore C is the center of a sphere 
intersecting the proposed surface in the circle EA and passing- 
through Eand therefore (Art. 78) intersecting the surface in 
a plane curve, that is, in a second circle passing through E'; 
this circle must be either E'B', or E'A! parallel to EA ; but 
it cannot be E'A', because two parallel circles on the same 
sphere have their centers in a diameter perpendicular to their 
planes, and here 101' being conjugate to the chords EA, E'A' 
cannot cut them at right angles unless the surface be one 
of revolution, in which case A'E' and B'E' become coincident; 
therefore the sphere will contain E'B'.