>I was reading the proofs of Morley's theorem by various
>people. A reference has been made to an geometrical proof by
>Narayaniengar circa 1907. The name has been spelt wrongly.

I hope you are right. I picked the spelling from Newman's note which was also repeated in D. Gale's book.

>Shri Narayaniengar had also proved the Steiner Lehmuus
>theorem by a direct method ( not by reductio ad absurdum).

Perhaps you can communicate to me one of his proofs. Search on the Web does not bring any result for either spelling.

Thank you,
Alex