The word "Trinity" is not in the Bible. Many people, including very intelligent ones such as Isaac Newton and Joseph Priestly, could not accept this doctrine and instead became Arians (denying the deity of Christ) or unitarians, emphasizing the oneness of God's Person.
Arius (256-336) held that Jesus and God were not of the same substance. He argued that to equate Jesus to God would be tantamount to polytheism. However, the divinity of Christ seems clearly to be taught by the New Testament. "...and the Word was God." (John 1:3). "...Christ Jesus, Who, being in very nature God..." (Philippians 2:5-11).
Jesus himself claimed to be Lord: "The Son of Man is Lord of the Sabbath" (Mark 2:28). "Anyone who has seen me has seen the Father." (John 14:9). When the ruler of the Jews implored him to answer the question "Are you the Messiah, the Son of the Blessed One?", Jesus answered, "I am. And you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven." (Mark 14:62).
When Jesus made these outrageous claims, we either have to reject him as a lying fraud, or dismiss him as a lunatic; or believe him -- and bow down and worship him as who he said he was. If he were a liar, this is difficult to reconcile to the Jesus who was the teacher of the teachers of the Law, the source of the highest ethical standards the world has ever known. If he were a crazy man, again it is difficult to reconcile with the sanity that he exemplified in the New Testament. That leaves only the third option: to accept his claim: "Everyone on the side of truth listens to me." (John 19:37).
In the history of the early Church, some 18 councils were convened to consider the burning question of the divinity of Christ. The council of Nicaea in 325 repudiated Arius and finally, by the Council of Constantinople in 381 the orthodox doctrine was settled. Ever since then, the doctrine of the Trinity has been considered essential to all Christianity, whether Eastern Orthodox, Roman Catholic, or Protestant.
Establishing the divinity of the Holy Spirit was not as controversial. In the Old Testament, the expressions "God said" and "the Spirit said" are often used interchangeably. In the New Testament, this pattern continues. Consider the benediction that Paul offers at the end of II Corinthians: "The grace of the Lord Jesus Christ, and the love of God, and the communion of the Holy Spirit be with you all. Amen."
The doctrine of God's triune nature has to be carefully formulated to keep within the bounds of what Scripture tells us. Following are some representative creeds. Note their legal preciseness and qualifications:
"...we believe and teach that the same immense, one and indivisible God is in person inseparably and without confusion distinguished as Father, Son and Holy Spirit so, as the Father has begotten the Son from eternity, the Son is begotten by an ineffable generation, and the Holy Spirit truly proceeds from them both, and the same from eternity and is to be worshipped with both.
"Thus there are not three gods, but three persons, consubstantial, coeternal, and coequal; distinct with respect to hypostases, and with respect to order, the one preceding the other yet without any inequality."
Second Helvetic Confession, 1566.
"In the unity of the Godhead there be three Persons of one substance, power and eternity: God the Father, God the Son, and God the Holy Ghost. The Father is of none, neither begotten nor proceeding; the Son is eternally begotten of the Father; the Holy Ghost, eternally proceeding from the Father and the Son."
Westminster Confession of Faith, 1647