-I like a lot your humour for the first answer...
-You shouldn't open me the gate of geometry, because I'll destroy you...
Mind about your expression:
The first point induce a modality, a moderation, a partial admitting of something as being "true". And I blame you because of this: you apparently does not have understood, as I guessed.
The second point is irrelevant - due to the idea something cannot assert itself, except maybe the mind, if it is not only a formalism.
I despited Descartes for a long time before nowadays, for the reason I had only the french version (so not his own): "Je pense, donc je suis." absolutely equivalent to "If I think, so I am", what would be totally a nonsense, because to pose "I think", you shall pose "I", which itself is equivalent to "I am", what would be the inference.
The original quotation is:
Cogito ergo sum. Unfortunately, I have not studied ancient languages, but if I guess well, this expression has no common measure (with the previous), in being definitively better.
Effectively, I guess that ergo means I, Cogito means think, and sum means to be.
And here, it takes all its sense, and would rather be translated in: "en pensant je suis", or:
Thinking, I am.
-But let's go back to geometry (let me know if my translation is not good) - I will take only the first postulate:
- Trough 2 points goes one straight line.
-I disagree with this:
I obviously could consider that there are in a counterpart, an infinity of straight (totally merged) lines, which go through the 2 points, what could be, with a third dimension, the projections of an infinity of curves, going trough them.