The Mount of Olives is actually a small mountain chain, east of Jerusalem. The Garden of Gethsemane was at the foot of the mountain. Jesus and his followers retreated there a few times.
The story of the Agony in the Garden is told (differently) in three gospels: Matthew 26:36-56, Mark 14:32-52 and Luke 22:39-53. In John 18:1-12 only the episode of the arrest is told, which followed the prayer.
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