Abarim Publications' online Biblical Greek Dictionary

κρεμαω

• Together with the preposition εκ (ek), meaning out, from or of: the verb εκκρεμαμαι (ekkremamai), meaning to hang out. In the classics this rare verb is used in the same sense as the parent verb: to hang out on obvious display. Plato uses our word to describe how all creatures are suspended from and dependent on pains, pleasures and desires (Laws.732e). Plutarch makes a similar use of this word, as he describes how in 104 BC king Jugurtha clung to the desire for life (while starving in a Roman cell, waiting to be executed). In the New Testament our verb is used in Luke 19:48 only, where it describes listeners "clinging" (i.e. being invested with a vital dependency) to Jesus' words.
• The noun κρημνος (kremnos) means overhang: a geographical feature common to Homer's Iliad, usually a river bank or edge of a trench. In the New Testament our noun occurs in Matthew 8:32, Mark 5:13 and Luke 8:33 only, solely in the story of the man named Legion, whose demonic infestation transferred to a herd of pigs, who subsequently transferred themselves off an overhang and into the water below. This story makes a great number of allusions, but perhaps most clearly to the Battle of Beth-horon of 66 AD, which marked the beginning of the Jewish war that would result in the destruction of the Temple of YHWH in Jerusalem and the beginning of the Flavian dynasty in Rome. From this noun in turn comes:
  • Together with the preposition κατα (kata), meaning down from, down upon: the verb κατακρημνιζω (katakremnizo), meaning to fall or throw down off an overhang (or the side of a ship: Xen Hel.2.1.31). Plutarch uses this verb twice in combination with references to the Tarpeian Rock (Sul.1, Mar.45), which is a still existing steep cliff on the south side of the Capitoline Hill in Rome, from which particularly traitors (starting with a girl named Tarpeia, who, in the 8th century BC had opened Rome's doors to the Sabines) were thrown down to the Forum below by means of execution. This particular means of execution was also common in Greece, although in Greece not the rock but the trench at the bottom was named: Kaeadas in Sparta, Varathron in Athens and Korakes in Thessaly. In 2 Chronicles 25:12, the death of 10,000 men of Seir is accomplished by driving them off a cliff (which is where the Septuagint uses our verb), but that appears to be a spontaneous act of warfare rather than a planned form of execution.
    Much more spectacular is the scene in which the men of Nazareth attempt to throw Jesus off a local cliff (which is where in the New Testament our verb occurs: Luke 4:29 only). Much of the intranational friction in Jesus' time existed between the traditional Mosaic Jews and the liberal Hellenized Jews, and Jesus obviously favors the latter — which he makes clear with his salty references to other foreign heroes, like Naaman the Syrian and the proverbial widow of Phoenician Zarephath, and of course Homer, the blind bard of the Greeks (see Luke 4:18). The Jews of Nazareth favor the former, but in their zeal and anger can't help to blatantly reenact the familiar story of Sisyphus, who was condemned to roll a huge rock (see 1 Corinthians 10:4, and of course the names Cephas and Peter) up a hill only to see it roll right back down again.
    Most significantly, possibly the last to be executed on Tarpeian Rock was Simon bar Giora, who in 66 CE had lead the rebels at Beth-horon (see above) and stood his last in Jerusalem, until he was arrested in late 70, transported to Rome and tossed off the Tarpeian Rock. The gospel of Luke was written in the years after the fall of Jerusalem in 70, while Luke was possibly in Rome (2 Timothy 4:11), and had witnessed the execution of Simon.
    Another name of note is the 5th century BC senator Gnaeus Marcius Coriolanus, who, according to Plutarch, came very close to being hurled off the Tarpeian Rock by a seething mob, but was rescued by the same spin-doctoring tribune-of-the-plebs who had whipped the crowd into a frenzy in the first place.