I find no evidence that Shakespeare wrote this. I see no use of “ascertain” in his work, and only three unrelated uses of the word “resolutely.”
The question remains, however – who said it, if Shakespeare didn’t?
How about Aesop, the guy from all the fables?
This is the only reference I can find that suggests Aesop, and even then the context is a little weird – the quote in question stands out in the middle of the page, somewhat unrelated to the rest of the context.
Mmm, my guess is that part is a) quoted from somewhere else (?), or b) original to Rev. Geo. Fyler Townsend, who is named on the title page as author of the “new applications, morals, etc.”