Quoted by Francis Bacon?

Most likely the sentences were written by Francis Bacon.

The way it is written, it is saying that Bacon is quoting someone else.

Which means that it is badly written, because i find it attributed to Bacon. What is your source? Is it from a native speaker of English?

I am reading Chicken Soup for the Soul.

In that case, the author wrote that badly. It should read "quoted from," not "quoted by."

By the way, the common style for rendering a quote is:

"Old wood best to burn, old wine to drink, old friends to trust, and old authors to read."

——Francis Bacon

This means that the author is quoting Bacon, and there is no question of it. I have no idea why the author of the book you're reading (which i have not read) delivered the quote in such a questionable manner.