A reader asked for a brief definiton of the Trinity. In fact, he spefically asked for a "terse, cogent" description of how the early Christians viewed the Trinity.
The early Christian view of the Trinity is complicated, but only to modern Christians because we have trouble making small adjustments to our thinking. That's just human nature.
In the beginning God was alone. He was not, however, really alone, because he had his Logos (his Word or Reason) inside of him. Before he created anything else, he gave birth to this Word in some manner that is beyond our understanding. The Word thus became the Son.
That was before all creation, and then the Word participated in the creation with God, the Father. All things were created through the Word.
The Word was actually the God who spoke and dealt with Israel, doing the will of his Father already. When the fullness of time came, he was born of a virgin, became man, lived, was crucified, rose from the dead, and has ascended into heaven, sending the Holy Spirit in his place. He will return to collect his saints and to judge the living and the dead.