Here it is:
Note, this is not exactly modern. It’s from 1910. The first link goes to the Wikipedia page, which mentions that there are modern editions available, including a 1998 update by Martin Gardner with some preliminary chapters on functions, limits, and derivatives (what, Thompson didn’t talk about these in his original?), and an added chapter on recreational calculus problems. Allegedly, it doesn’t use the limit concept. In modern Calculus teaching, that would be a major omission, I think.
The modern Calculus textbook that I would recommend is the book by Larson, Hostetler (and maybe Edwards, depending on the edition). I learned from 2nd edition and later 5th edition. I found them very clear and readable. I think I liked the 2nd edition better, maybe just because that’s how I learned it first – they re-organize and re-explain various things with each edition.
They have a web site for their 6th edition. It appears to include the full text, and a interactive lessons, and a message board or chat room. It’s not free. You have to register and I think there’s some price for it. If I had my druthers, I’d just hit up a used book store and buy an earlier edition in the dead tree medium.