This is an excerpt from Geerhardus Vos’ Reformed Dogmatics: Theology Proper, from the new English translation, edited by Dr. Richard Gaffin.
One will have to prove:
a) That there is one God.
b) That there are nevertheless three distinct persons named, respectively, Father, Son, and Holy Spirit, called God and considered as God.
c) That there is, therefore, unity in trinity and trinity in unity.
4. Which New Testament texts speak of the three persons alongside each other?
Luke 1:35; 3:21–22; Matt 28:19; 2 Cor 13:14; 1 Cor 12:3–4; 1 Pet 1:2. Also, above all, in chapters 14–16 of the Gospel of John the teaching of the Lord bears a Trinitarian character.
5. Which two matters are primarily of concern in argumentation for the Trinity?
The deity of the Son and the personality of the Holy Spirit. The personality of the Son and the deity of the Holy Spirit, in contrast, are so certain that argumentation is virtually superfluous.
6. Is there anywhere in the New Testament that provides us with a complete doctrine of the Trinity?
No, as in the case with other dogmas, here also it was left to the church, under the guidance of the Holy Spirit, to gather the givens spread abroad throughout Scriptures and then to formulate the dogma gradually and in contrast to all kinds of error.
7. Who used the name Trinity first?
In its Latin form the first to use the term was Tertullian, who speaks of a Trinitas Unius Divinitatis. Before him, however, related terms were already used in Greek. Theophilus, bishop of Antioch in Syria, spoke of ἡ τρίας τοῦ θεοῦ. This was in the last half of the second century after Christ.