While I’m not sure that Article IX as such existed when Session V of the Council of Trent convened, nevertheless, the latter addresses the heretical notion of concupiscence which it contains:
[T]his holy council perceives and confesses that in the one baptized there remains concupiscence or an inclination to sin, which, since it is left for us to wrestle with, cannot injure those who do not acquiesce but resist manfully by the grace of Jesus Christ; indeed, he who shall have striven lawfully shall be crowned.
This concupiscence, which the Apostle sometimes calls sin, the holy council declares the Catholic Church has never understood to be called sin in the sense that it is truly and properly sin in those born again, but in the sense that it is of sin and inclines to sin.
But if anyone is of the contrary opinion, let him be anathema.
(See also Concupiscence, s.v. New Catholic Dictionary.)
Concerning Art. XXX (Communion under both kinds), see Trent, Sess. XXI. I won’t quote it here because it’s rather long for a post, but it shows from Scripture and Church teaching that receiving under one species is legitimate.