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From Pallas the giant and Styx [were born] : Scylla, Vis (Force) [Bia], Invidia (Jealousy) [Zelos], Potestas (Power) [Kratos], Victoria (Victory) [Nike].
Bia and her siblings were constant companions of Zeus. They achieved this honour after supporting him in the Titan War along with their mother. Bia is one of the characters named in the Greek tragedy Prometheus Bound, attributed to Aeschylus, where Hephaestus is compelled by the gods to bind Prometheus after he was caught stealing fire and offering the gift to mortals. Although she appears alongside her brother Kratos, she does not speak.
Along with their mother, Bia and her siblings helped Zeus in his war against the Titans. The war, which was referred to as the Titanomachy, lasted for ten years, with the Olympian gods emerging victorious. Due to their heroic actions during the war, the four siblings won Zeus's respect and became his constant companions. They were almost always by his side as he sat on his throne in Mount Olympus, and they were tasked with enforcing Zeus's orders whenever he required an act of strength.
And Styx the daughter of Okeanos (Oceanus) was joined to Pallas and bare Zelos (Zelus, Emulation) and trim-ankled Nike (Victory) in the house. Also she brought forth Kratos (Cratus, Strength) and Bia (Force), wonderful children. These have no house apart from Zeus, nor any dwelling nor path except that wherein God leads them, but they dwell always with Zeus the loud-thunderer. For so did Styx the deathless daughter of Okeanos plan on that day when the Olympian Lightener called all the deathless gods to great Olympos (Olympus), and said that whosoever of the gods would fight with him against the Titanes, he would not cast him out from his rights, but each should have the office which he had before amongst the deathless gods. And he declared that he who was without office and rights as is just. So deathless Styx came first to Olympos with her children through the wit of her dear father. And Zeus honoured her, and gave her very great gifts, for her he appointed to be the great oath of the gods, and her children to live with him always. And as he promised, so he performed fully unto them all.
Nike, Kratos (Cratus), Zelos (Zelus), and Bia were born to Pallas and Styx. Zeus instituted an oath to be sworn by the waters of Styx that flowed from a rock in Haides' realm, an honor granted in return for the help she and her children gave him against the Titanes (Titans).
Bia is not as well known as her siblings Kratos or Nike, and when she appears in myths, she's usually silent. However, she does play a pivotal role in the story of Prometheus. Prometheus was one of the Titans and was often in conflict with Zeus. Eventually, he angered Zeus so much that he decided to punish him for all of eternity. He ordered that Prometheus be chained to a rock in the Caucasus Mountains. Bia and her brother, Kratos, were sent to carry out this task, but Bia was the only one strong enough to actually bind Prometheus to the rock with the unbreakable chains. Each day, an eagle would pluck out Prometheus's liver and eat it in front of him. Each night his liver would regrow, and the cycle would begin again, leaving him in perpetual torment.
"[Enter Kratos (Power) and Bia (Force), bringing with them Prometheus captive; also Hephaistos (Hephaestus).]
Kratos (Cratus): To earth's remotest limit we come, to the Skythian (Scythian) land, an untrodden solitude. And now, Hephaistos, yours is the charge to observe the mandates laid upon you by the Father [Zeus]--to clamp this miscreant [the Titan Prometheus] upon the high craggy rocks in shackles of binding adamant that cannot be broken. For your own flower, flashing fire, source of all arts, he has purloined and bestowed upon mortal creatures. Such is his offence; for this he is bound to make requital to the gods, so that he may learn to bear with the sovereignty of Zeus and cease his man-loving ways.
Hephaistos: Kratos (Power) and Bia (Force), for you indeed the behest of Zeus is now fulfilled, and nothing remains to stop you [i.e. you are now released from the appointed task]. But for me--I do not have the nerve myself to bind with force a kindred god upon this rocky cleft assailed by cruel winter."
"Prometheus [who thought to steal fire from heaven for man] could not make so free as to enter the citadel which is the dwelling-place of Zeus, and moreover the guards of Zeus were terrible [i.e. Kratos (Cratus) and Bia]: but he entered unobserved the building shared by Athena and Hephaistos (Hephaestus) for the pursuit of their arts, and stealing Hephaistos's fiery art and all Athena's also he gave them to man."
"[On the Akropolis (Acropolis) of Korinthos (Corinth) there is] a sanctuary of Ananke (Necessity) and Bia (Force), into which it is not customary to enter."
"He [the Athenian statesman Themistokles (Themistocles)] made himself hateful to the allies also, by sailing round to the islands and trying to exact money from them. When, for instance, he demanded money of the Andrians, Herodotos says he made a speech to them and got reply as follows: he said he came escorting two gods, Peitho (Persuasion) and Bia (Compulsion); and they replied that they already had two great gods, Penia (Penury) and Aporia (Powerlessness), who hindered them from giving him money." [N.B. In the actual text of Herodotus Bia is replaced by Ananke (Necessity) and Aporia by Amekhania (Helplessness).]