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Simson’s lines of A, B’ and C’ concur in A, 
Simson’s lines of B, C’ and A’ concur in B, and 
Simson’s lines of C, A’ and B’ concur in C, 
Also, since the Simson’s line of Ha’, Hy’ and He’ must pass through Ha, 
Hy and He, respectively, we have the 
Simson’s lines of A, A’ and Ho’ concurring in Ha, 
Simson’s lines of B, B’ and Hy concurring in Hy and 
Simson’s lines of C, C’ and H-’ concurring in He. 
Since the point of concurrency of the Simson’s lines of the extremities of a 
chord | to BC is the point where tbis chord intersects BC, it follows that the 
Simson’s lines of the extremities of all chords | to BC are concurrent with Sim- 
son’s line of A’; the Simson’s lines of extremities of all chords | AC are concur- 
rent with Simson’s line of B’; and the Simson’s lines of the extremities of all 
