Many Definitions of 'Pious' in Euthyphro

Over the course of Euthryphro, Socrates and the title character have a long discussion about what is 'pious'.  Euthyphro begins by giving an ostensive definition, or definition by example.  Socrates rejects this and asks for an abstract conceptual definition.  Euthyphro then says that what is pious is what the gods love.  Socrates that since the gods disagree, some will hate something that others love--making that thing both god-loved and god-hated.  This is a contradiction, so we must reject this definition.  Euthyphro then modifies his definition to include only what ALL the gods love.  Socrates then asks if the gods love it because it is pious or if it is pious because the gods love it.  Euthyphro asserts that the gods love it because it is pious.  Here we have an example of circular reasoning.  To define piety in terms of gods' love and to claim that the gods love it because it is pious is a circular argument.  It is logically valid (If P, then Q.  If Q, then P.  Therefore, P if and only if Q).  Yet we have not actually learned anything about piety.  Socrates then tries to help out his interlocutor and offers up this distinction: piety is a part of justice.  Euthyphro then insists that it is the part of justice that is concerned with taking care of the gods.  Socrates clarifies that most examples of care mean that the thing that is cared for is made better in some way, but surely this cannot be the kind of care with which we provide the gods.  Euthyphro says that to be pious is to care for the gods like slaves care for their master.  Socrates asks what the purpose of our service is.  Euthyphro says that we are to make sacrifice and pray.  Socrates characterizes this as a sort of trade between gods and humans, according to which we sacrifice something and then ask for something in return in the form of prayer.  Socrates then asks if this trade somehow benefits the gods.  Euthyphro says no, there is no benefit, but agrees that the gods are pleased by this trade.  And here we end up back at a previously rejected definition.