Recovered Proof by Euler on Irrational Numbers?

"By the time I return to experience, it is the world which seems great; (But I don't expect you to understand; It is a riddle about math)" ---Euler, from an unrecorded interview

"It meant so much to you that you've forgotten what it meant" ---The voice in Euler's head

I have been thinking that I lived a past life as a sick boy during World War I, and have hypothesized that I may have had a mathematical gift; Based on that, I have recently wondered if it's possible that I was Euler; Are these half-remembered fragments of a forgotten Euler equation or proof?

The memory centers around an interview while I was ill, during which I thought of five related equations or equation fragments, which supposedly constitute a proof about irrational numbers; But I warn you, my powers are not too sharp now;

Perhaps I was a madman who merely believed he was Euler; Maybe the equations are still interesting to some people::