I took A-Level Philosophy, during which we studied Descartes "Meditations" at length.
I remember our teacher explaining that, whilst "Cogito ergo sum" was the famous phrasing, Descartes original formulation of the concept was the "Non cogito" - presented in the opposite construction:
It would be absurd to claim "I do not think"! For if I make that claim ... what is it that is thinking that claim. This is absurd and therefore I must conclude that I both exist and think.
And that "Cogito ergo sum", came from a later writing (a letter to a friend summarising his position, I think?)
Briefly googling, however, hasn't shown me any reference to a "Non Cogito", or to an argument of this structure.
Is my recollection (and/or my teacher) wrong?