The quote from Eusebius that you mention appears to be non-existent. I have previously read his History of the Church (Historia Ecclesiastica) in its entirety and there was no such mention anywhere in there. Eusebius was a defender of Christianity, and a rather rational one at that for his era. To make such a statement as what is quoted above would be 100% out of character for the book. I tried to find where this citation originates from and it appears to be a Nexus article. This is my first encounter with information from Nexus and already I am disappointed. I have read Eusebius previously and that quote is nowhere to be found in his work. I would have remembered it.
The other reference, Acta Concilii Nicaeni, from 1618, I could not find. Maybe you can help me find that work so we can see what it actually says. Since that citation comes from the same article I have serious doubts about it as well.