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Toohey as understudy for the hypotenuse

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LoBagola

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“There are so many variations upon the triangle, not necessarily unhappy. Like the three of us—with me serving as understudy for the hypotenuse, quite an appropriate substitution, since I’m replacing my antipode, don’t you think so, Dominique?”

 

 

P.445.
 
This is a scene where Toohey joins Dominique and Keating for dinner. Dominique has married Keating, and left Roark. I remember a quote like this "a love triangle with murder at the hypotenuse" and was wondering if there is any historic use of this "love triangle" symbol I'm unaware of.
 
Why is Toohey replacing Roark an appropriate substition? Is this sarcasm? Is there any meaning to Roark being the hypotenuse? 
 
I understand that a triangle can symbolise a 3-way love relationship, but here there is not 3 way love. 
 
 
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Toohey is telling Dominique the one thing she doesn't know:  that it's only him - and not some metaphysical shortcoming - that makes loving (and being exclusively with) Roark impossible.  Roark is the "hypotenuse" most of the time because most of the time Dominiuqe is only with Keating (or at least not with Roark) because she's convinced that being with Roark is pointless.  That such a relationship would be doomed from the start.  Because of who he is, in Dominique's mind, Roark leaves her with no choice but to be with a Keating (if she is to have any sort of relationship at all).  This is wrong, of course (a relationship with Roark is the only one that wouldn't be doomed - since it's based upon objective values instead of pretense) - but she doesn't know it.  Toohey does, however.  He knows that he (ie: the ideas he advocates and the influence he possesses) would be the only reason why a relationship between Dominique and Roark would fail, so since - at the time of that dinner - one doesn't exist, he sees himself as the hypotenuse that is binding the other two sides of the triangle (Dominique and Keating) together.

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