Puisque je doute, je pense;
puisque je pense, j'existe.

   then later

je pense, donc je suis

   is what he wrote. (Discourse de la Methode; Project Gutenburg.

However, most of his works were written in Latin, which was the international language of scholarship at the time.

but it does exist - how do I know? ... well ... because "I"/my mind very clearly exists.

You possibly are wrong there. You could be mistaken. That's Zen, and much of current thinking, with some experimental evidence. The funny thing is, it doesn't deny that you exist in the sense of being an objective entity; what it says is that your sense of individuality is a construct. It's a difficult thought to take on board, but it identifies the error in "because I think, I exist", as the 'I'. Perhaps the thought can exist, because that's what happens in physical systems with a certain degree and type of organisation, and the feeling is what happens to the matter involved in that system?

Thought exists, therefore something exists?