NKJV - 33 And He took Peter, James, and John with Him, and He began to be troubled and deeply distressed.
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These three apostles were apparently especially close to Jesus. They are mentioned on multiple occasions as being the only ones who were present or whom Jesus took with Him when an extraordinary manifestation of His power or glory occurred, such as in the raising of Jairus' daughter (Mark 5:37; Luke 8:51) or the Transfiguration (Matthew 17:1; Mark 9:2; and Luke 9:28), or when He was very sorrowful and in special need of strength, such as in the Garden of Gethsemane prior to His arrest and crucifixion, as mentioned in the question. As far as I am aware, the Bible does not specifically discuss why those three were chosen in this way by Jesus. However, just before the Transfiguration, Peter (or Simon bar-Jonah, as he was still known at that time) had confessed (Matthew 16:16) his belief in Jesus as the Messiah and the Son of God, which the other apostles did not seem as certain or clear about. This caused Jesus to call Peter blessed, because Jesus said that this knowledge had not been revealed to Peter by human means, but by God the Father, and that it was upon this "rock" (which was why Jesus bestowed the name Peter (from the Greek word for rock (petros) on Simon) that Jesus said He would build His church. And, although Peter still subsequently showed himself capable of weakness (despite his self-proclaimed boldness (Matthew 26:35; Mark 14:31)) by denying Jesus (as Jesus had told him he would, and not just once, but three times), Peter nevertheless emerged as the most prominent and vocal of the apostles in evangelizing the people (Acts 2) following Jesus' ascension. As brothers, James and John were close to each other, and also to Jesus. Jesus gave them the nickname "Sons of Thunder" (or "Boanerges" in Greek), for they were both apparently of a brash, impetuous nature, such as on the occasion when they asked Jesus if He wanted them to call down fire from heaven to destroy a Samaritan town that had refused to receive Him because He was traveling to Jerusalem (Luke 9:51-56). They showed this same trait when they (along with their mother) came to Jesus asking that He would grant them the favored seats at His right and left sides in His kingdom, and quickly asserted that they were able to endure the same cup and baptism of suffering that Jesus was to experience. And yet, they both undoubtedly loved Jesus, to such a degree that James would be the first apostle martyred for his faith (Acts 12:2), and that John was the one to whom Jesus (as He was dying on the cross) entrusted the care His own mother, and who was kept alive (as the only apostle not martyred) to witness a vision of the events of the end times, as foretold in the book of Revelation). I believe that it was Jesus' knowledge of the faith and love of these three individuals, as well as His foreknowledge of the coming events in which they would be involved, and the roles that they would play in the early church, that led Him to select them to witness the prominent events at which only they were present.
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