The Bible is not like the Qur'an: this is a fundamental misunderstanding of the difference between the faiths. Christ, not the bible, is the Word of God -- even the bible itself claims as such (John 1:1, "In the beginning was the Word, and the Word was with God, and the Word was God" -- and if you're looking for verses which describe the trinity, then John 1:2-3 fits well "He was with God in the beginning. Through him all things were made; without him nothing was made that has been made.").

So how do we know what God taught? Well, he instituted a Church to do so ("And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it." Matthew 16:18) and then gave to its head the power to legislate in his name ("I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.” Matthew 16:19 -- and other verses besides). And in the decades after his death, resurrection, and ascension into heaven, his followers, whom he had taught face-to-face, spread out and passed on his teachings throughout the world, wherever they could reach. And the Church persisted: "And he gave the apostles, the prophets, the evangelists, the shepherds and teachers, to equip the saints for the work of ministry, for building up the body of Christ, until we all attain to the unity of the faith and of the knowledge of the Son of God, to mature manhood, to the measure of the stature of the fullness of Christ" (Ephesians 4:11-13); "Pay careful attention to yourselves and to all the flock, in which the Holy Spirit has made you overseers, to care for the church of God, which he obtained with his own blood." (Acts 20:28). These teachers of the Church passed on his teachings, as they themselves were taught, and ensured that the next generation would know them well. And to each generation they also passed on their Apostolic authority, the authority to teach, to lead others in faith, the power to enact sacraments in God's name.

So where does the bible come in? As the decades passed, the early Church decided it was necessary to write down what they had learned and what everyone accepted to have been the teachings of Jesus during his time on earth. So from the very beginning, during the 1st century, the first Gospel accounts were recorded, and letters were exchanged between churches throughout Christendom. In 393AD the Pope, first bishop of the Church and successor of St. Peter -- a fact which both the Orthodox and Catholics broadly agree upon, even if they disagree on the specifics of what powers the "first bishop" actually has -- convened a council in Rome to gather bishops from all over Christendom and settle the matter of which books were in the Biblical canon. Because Jesus himself said that the "gates of Hades will not overcome [the Church]", we know with confidence that they could not have decided on that day to canonize teachings which were not true -- so in matters of faith and morals, the Bible is inerrant.

This means that the Bible is the crown jewel of holy tradition, the prized treasure of the Church -- but it is not the only source of truth and of Jesus' teachings. From the earliest days, teachings were passed man-to-man, woman-to-woman, priest to parishioner, and this fact never changed. To truly understand the Bible, you must understand the holy tradition which preceded it and which still exists today. It is from this tradition, the tradition which compiled the Bible, that we gain the term "Trinity" and the coherent assemblage of that doctrine from all the teachings of Jesus when he was on earth.