This article is within the scope of the WikiProject Philosophy, which collaborates on articles related to philosophy. To participate, you can edit this article or visit the project page for more details.
I am not really sure that the Des Cartes example is an example of the consequentia. I could be wrong, but even if I'm not, it's still a confusing example. I say this because as someone with a lot of training in formal logic, I should be able to grasp that example without too much difficulty.