There have been already given great answers to this question, but let me add something to it based on a Hadeeth:

There are many Ahadeeth in Shia books which narrates the arguments the holy prophet peace be upon him and his household, the infallible Imams, and some great Sahabas made with others, ranging from followers or even Imams of other sects, to the scholars of other religions or even isms, including those not believing in Allah. Among these narrations is one in which Imam Sadiq peace be upon argue with imam Shafei of Ahlul-Jamaa`a, and the whole thing is around Qiyas. Imam Sadiiq PBUH asked him if he approves Qiyas in Fiqh, and he answered "yes". Then Imam asked him which sin is greater and worse with also greater punishment even in Dunya, murdering or sexual intecourse? He answered back sexual intercourse, of course. Imam asked again: then why according to Quran, the former to be proved needs two witnesses, while the latter needs four?

The argument continues, but this much should suffice to make conclusion. Qiyas which is forbidden, is to make analogies to make new rules, it is something like extrapolation of the known rules to outside the domain of its application. Aql is usually like interpolation. Aql also testifies the validity of a rule by finding contradictions, as Imam Sadiq PBUH made use of Aql to exploit contradicting examples from Quran to prove why Qiyas is forbidden in Islam.