[Note: This is the same question on MSE, but it has only five answers, one of which doesn't give an exact answer (it tells that a conjecture of Euler was wrong, but a conjecture isn't a mistake) and the question is unlikely to get answers since it was active 2 years ago.]
Euler was one of the greatest and smartest mathematician in the history. He contributed to many fields of mathematics. But no one is perfect, and this holds for Euler also. For example, this tells that Euler thought that
$$\sqrt{ab}=\sqrt{a}\sqrt{b}$$
whether or not $a$ and $b$ are positive or negative. So this is one of Euler's mistake. I want to see his some more mistakes. So my question is:
What are some of Euler's mistakes?
Like most big list questions, please give only one mistake per answer.