One need not plumb the depth of the ancient Hebrew and Aramaic scriptures to find the time of Christ's crucifixion because saint Luke gives a reasonable set of historic events with which to approximate the year of the crucifixion. Consider this passage:
In the fifteenth year of the reign of Tiberius Caesar, when Pontius Pilate was governor of Judea, and Herod was tetrarch of Galilee, and his brother Philip tetrarch of the region of Ituraea and Trachonitis, and Lysanias was tetrarch of Abilene, during the high priesthood of Annas and Caiaphas, the word of God came to John the son of Zechariah in the desert. He went throughout (the) whole region of the Jordan, proclaiming a baptism of repentance for the forgiveness of sins, as it is written in the book of the words of the prophet Isaiah: A voice of one crying out in the desert: 'Prepare the way of the Lord, make straight his paths. Every valley shall be filled and every mountain and hill shall be made low. The winding roads shall be made straight, and the rough ways made smooth, and all flesh shall see the salvation of God.' ... Now Herod the tetrarch, who had been censured by him because of Herodias, his brother's wife, and because of all the evil deeds Herod had committed, added still another to these by (also) putting John in prison. After all the people had been baptised and Jesus also had been baptised and was praying, heaven was opened and the holy Spirit descended upon him in bodily form like a dove. And a voice came from heaven, You are my beloved Son; with you I am well pleased. Luke 3:1-22
I truncated the passage for brevity but please read it and the rest of the chapter. It is not too hard to fix a date for the reign of Tiberius and adding 14 to that will tell you when the prophet John's preaching began and if one takes the information from Luke chapter one about Mary visiting Elizabeth when Elizabeth was already six months into her pregnancy it is rather likely that John had been preaching at least six months when Jesus came to be baptised. Add to that around 2 or 3 years to account for the Lord Jesus Christ's public preaching and you can derive the approximate date for the crucifixion.
Tiberius became emperor in 14 AD, add 14 and you get 28 or 29 AD as the year of Christ's baptism (allowing for the six months), add another 2 or 3 for Christ's public preaching and you arrive at 30 to 32 AD. It's possible that 33 AD is correct because John may have been preaching for more than six months when Jesus was about thirty years old. Do these dates fit the theory of Sir Robert Anderson? No? Then he is likely wrong.
You are of course correct about using the text as the primary proof.
However, most do not know that Tiberius became co-precept with his father Augustus in AD 12. Ancient coins from Antioch have been discovered with the face of Augustus on one side and that of Tiberius on the other.
His father did die in 14 AD. However, Tiberius actually began ruling 2 years before.
Another piece of evidence is from John 2:13-20 when the Jews said it had taken forty-six years to build the temple. We know now that Herod began construction in 20 BC. 20 BC plus 46 comes to AD 27. This discussion was near the beginning of Christ's ministry.
We also know Christ was born before 4 BC which was the year Herod died.
At His baptism we know He was about 30 years old.
When taken as a whole, all of this evidence shows the date to be earlier than previously known.
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